Find counter arguments by entering NameVs… or …VsName.
The author or concept searched is found in the following 47 entries.
| Disputed term/author/ism | Author |
Entry |
Reference |
|---|---|---|---|
| Abstraction | Field | I 158 Introduction/Abstract Objects/Abstraction/Wright: Thesis: Sets as well as directions and numbers are to be introduced by abstraction. >Introduction. I 157 Field: E.g.simple abstraction: it is suitable for us saying that our talk of directions refers to parallelism. - But that does not quite work accordingly for numbers as it does for non-numeric talk (and "non-set theory"). >Definitions, >Everyday language, >Reference, >Definitions/Frege. III 24 Homomorphism/Field: (structure-preserving representation) is the bridge to find abstract counterparts to concrete statements ((s) observation statements). >Observation sentence. Semantic Ascent/Abstract Counterparts: we would always obtain the results without them. Field: we save a lot of time with this. >Semantic ascent. |
Field I H. Field Realism, Mathematics and Modality Oxford New York 1989 Field II H. Field Truth and the Absence of Fact Oxford New York 2001 Field III H. Field Science without numbers Princeton New Jersey 1980 Field IV Hartry Field "Realism and Relativism", The Journal of Philosophy, 76 (1982), pp. 553-67 In Theories of Truth, Paul Horwich Aldershot 1994 |
| Abstraction | Frege | Stuhlmann-Laeisz II 49 Definition abstraction/Frege/St: abstraction is a process to identify each other in the various elements of a region, e.g. same color, same size, same shape. New objects are gained by abstraction of the partial identity. ((s) Such objects which are only about numerical equality or color identity are individuated.) If A is such an abstraction, then there is by definition a (base) object a, so that the following is true: A is the F of a. --- Thiel I 131 Abstraction/Mathematics/Frege/Thiel: abstraction is a purely logical process, an operation with statements, the logical character of which is revealed by the change from the structure of the complicated initial statement to the structure of the new statement. Frege understood this first. Tere are statements not only about numbers, but also about sets, functions, concepts, situations, meaning and truth value of a statement, about structures. I 133 Numbers/digits/number names/names/mathematics/Thiel: the philosophical punch line of the transition from general statements via digits to arithmetic statements is that although we have introduced the speech about numbers in addition to the speech about digits, it is still a form of speech, a facon de parler, whose possibility does not depend on the fact that there are still abstract objects beyond the concrete digits, which we call "numbers". >Numerals. I 134 We also had no reason to conceive the digits as "names" of numbers, so that 4, IV, and |||| would denote the same number four, as it was assumed in the traditional philosophy of numbers. >Numbers. |
F I G. Frege Die Grundlagen der Arithmetik Stuttgart 1987 F II G. Frege Funktion, Begriff, Bedeutung Göttingen 1994 F IV G. Frege Logische Untersuchungen Göttingen 1993 SL I R. Stuhlmann Laeisz Philosophische Logik Paderborn 2002 Stuhlmann II R. Stuhlmann-Laeisz Freges Logische Untersuchungen Darmstadt 1995 T I Chr. Thiel Philosophie und Mathematik Darmstadt 1995 |
| Abstractness | Boer | I 13 Definition abstract/terminology/Boer: be a thing for which it is not possible that it exists/is actual. --- I 14 Abstract/Boer: then an abstract entity is necessarily non-existent and has no individual essence. A fortiori they have no haecceitas. --- I 14 Abstract/identity/identifiability/identification/individuation/Boer: but also for abstract objects the principle "no entity without identity" applies. That is, their identities must be articulated in such a way that they are not presumed to be identifiable by the characteristics which they exemplify. ((s) For abstract objects). --- I 14 Actual/Identification/Individuation/Boer: trivially, actual objects are, of course, identifiable by their properties. The principle of indistinguishability of identity applies to them. This also applies to normal individuals in general. Abstract: but it is not certain that it applies to abstract individuals. Here it may be, since numerically different individuals exemplify exactly the same characteristics. --- I 37 Note Abstract/Abstract Objects/Zalta: Thesis: an abstract individual may encode every possible property of first order, even contradictory ones, even if that cannot be a concrete object. Such objects can be used in the analysis. --- I 14 Abstract characteristics/abstract relation/Boer: we need them, even more urgent. For example, the ability to run faster than a flying pistol bullet (Superman). They do not need to be exemplified. Fiction: sometimes attributes such qualities to fictional characters as necessary. |
Boer I Steven E. Boer Thought-Contents: On the Ontology of Belief and the Semantics of Belief Attribution (Philosophical Studies Series) New York 2010 Boer II Steven E. Boer Knowing Who Cambridge 1986 |
| Abstractness | Dennett | I 497 f Abstraction/Explanation/Dennett: Dan Sperber(1): You must not proceed too abstract intentionally. Abstract objects do not enter directly into the causal relationships. E.g. the excitement of a child is not caused by the abstract story of Little Peter's Journey to the Moon, but by the fact that he understands his mother's words. Dennett: this is no obstacle for science, on the contrary: it can cut the Gordian knot of tangled causal relationships by using an abstract formulation and ignoring all those complications. (>Intentional stance), >Propositional attitudes. I 498 E.g. the excitement of the child does not result from the abstract story, but from the understanding of the words of its mother. 1. Sperber, Dan 1985."Anthropology and Psychology: Towards an Epidemiology of Representations." Man, vol. 20, pp. 73-99. |
Dennett I D. Dennett Darwin’s Dangerous Idea, New York 1995 German Edition: Darwins gefährliches Erbe Hamburg 1997 Dennett II D. Dennett Kinds of Minds, New York 1996 German Edition: Spielarten des Geistes Gütersloh 1999 Dennett III Daniel Dennett "COG: Steps towards consciousness in robots" In Bewusstein, Thomas Metzinger Paderborn/München/Wien/Zürich 1996 Dennett IV Daniel Dennett "Animal Consciousness. What Matters and Why?", in: D. C. Dennett, Brainchildren. Essays on Designing Minds, Cambridge/MA 1998, pp. 337-350 In Der Geist der Tiere, D Perler/M. Wild Frankfurt/M. 2005 |
| Abstractness | Lewis | V 20 Abstract entities/possible world/Lewis: abstract entities do not live in certain possible worlds. They exist simultaneously in all of them. Properties/Lewis: (2004, 4): at least abstract geometric objects can simply be round, so "round" is not generally a relation to times. --- Schwarz I 42 Def Surrogate Four-Dimensionalism/Schwarz: this position in the philosophy of time interprets other times as abstract entities of a different kind from the present. LewisVs: other times are just as real. Lewis doesn't care if you call his worlds concrete or abstract. This has no clear meaning (1986e(1), §1,7). Schwarz I 43 Ontology/Lewis: Lewis compares his position with the platonism of mathematics: beyond ordinary things there are abstract objects. For these, however, we do not need supernatural cognitive powers. >Possible Worlds/Plantinga. 1. David Lewis [1986e]: On the Plurality of Worlds. Malden (Mass.): Blackwell. |
Lewis I David K. Lewis Die Identität von Körper und Geist Frankfurt 1989 Lewis I (a) David K. Lewis An Argument for the Identity Theory, in: Journal of Philosophy 63 (1966) In Die Identität von Körper und Geist, Frankfurt/M. 1989 Lewis I (b) David K. Lewis Psychophysical and Theoretical Identifications, in: Australasian Journal of Philosophy 50 (1972) In Die Identität von Körper und Geist, Frankfurt/M. 1989 Lewis I (c) David K. Lewis Mad Pain and Martian Pain, Readings in Philosophy of Psychology, Vol. 1, Ned Block (ed.) Harvard University Press, 1980 In Die Identität von Körper und Geist, Frankfurt/M. 1989 Lewis II David K. Lewis "Languages and Language", in: K. Gunderson (Ed.), Minnesota Studies in the Philosophy of Science, Vol. VII, Language, Mind, and Knowledge, Minneapolis 1975, pp. 3-35 In Handlung, Kommunikation, Bedeutung, Georg Meggle Frankfurt/M. 1979 Lewis IV David K. Lewis Philosophical Papers Bd I New York Oxford 1983 Lewis V David K. Lewis Philosophical Papers Bd II New York Oxford 1986 Lewis VI David K. Lewis Convention. A Philosophical Study, Cambridge/MA 1969 German Edition: Konventionen Berlin 1975 LewisCl Clarence Irving Lewis Collected Papers of Clarence Irving Lewis Stanford 1970 LewisCl I Clarence Irving Lewis Mind and the World Order: Outline of a Theory of Knowledge (Dover Books on Western Philosophy) 1991 Schw I W. Schwarz David Lewis Bielefeld 2005 |
| Abstractness | Prior | I 5 Abstract/Prior: objects are sometimes abstract, but what we think about them is always abstract. >Abstract objects, >Thinking, >World/thinking. I 31 Abstracts/abstract/Prior: "3 is greater than 4" even if not true. - It is not eliminable. >Elimination. Adverbs and connections can be eliminated if we introduce nominators. >Adverbs. E.g. "that" in "that P comes implies that Q stays away". - E.g. "that P is wrong"- e.g. instead of "everything moves": "Movement is universal". Problem: there are still links (abstractions) needed. These links must be meaningful because they can be true or false. >Truth, >Truth values, >Connectives, >Logical constants. |
Pri I A. Prior Objects of thought Oxford 1971 Pri II Arthur N. Prior Papers on Time and Tense 2nd Edition Oxford 2003 |
| Abstractness | Quine | I 102 Abstract/Concrete/Quine: abstract and concrete are independent from stimulus meaning. I 212 ff Abstract terms: abstract terms are alleged names of properties. "Roundness": "F"/"round":"a" in "Fa" - should not be used unhesitatingly without metaphysical definition because this would be too non-binding. Every abstract singular term provides an abstract general term. I 219 Not all abstract objects are properties: numbers, classes, functions, geometrical figures, ideas, possibilities - some of these categories can be abandoned or reduced. - One can faithfully distinguish them from concrete ones by use of "-ness". I 238 Plural: the plural is an abstract singular term: "lions are dying out". The disposition is "eats mice" (31). I 286 Intensional abstraction: intensional abstraction is "the act of being a dog", "the act of baking a cake", "the act of erring". I 289 Class abstraction is attributed to singular descriptions: (iy)(x)(x from y iff ..x..) instead of: x^(..x..). This is not possible for intensional abstraction. Difference classes/Properties: classes with the same elements are identical. Properties are not quite identical if they are attributed to the same things. I 361f Abstraction of relations, propositions and properties are opaque (>Planets-example/Quine). I 295 Class abstraction is transparent, whereas intensional abstraction is opaque. V 167 Abstract general term: is a relative clause: "Y is a class X such that FX". New is that these are classes of classes. A normal relative clause equals a general term: "y is a thing x such that Fx". VII (d) 75 Concrete/abstract/Quine: by pointing to a square we do not assume identity with others. "Squareness" is shared by other objects, but we do not need to insinuate entities like "attributes". We do not point to the "attributes" (as an entity) nor do we need it in reference to the word "square". VII (d) 77 Abstract Singular Term/Quine: the abstract singular term functions like names. Philosophically revolutionary is setting abstract entities (unlike general term). VII (f) 113 Abstract Entities/Quine: classes and truth values may be accepted as abstract entities. Only statements and predicates should not be regarded as names of these and other entities, i.e. "p", "q"p,"F" etc. These should not be bindable (quantifiable) variables (>2nd order logic) - (E.g.)(x is a dog. x is white.) does not commit X to "dogness" or to the class of white things as universals. The solution is using the explicit form: belonging to two classes: (Ex)(xεy.xεz). Of course, there are names for abstract entities like the singular term "dogness", "class of white things" (as names ((s) it does not imply existence)). |
Quine I W.V.O. Quine Word and Object, Cambridge/MA 1960 German Edition: Wort und Gegenstand Stuttgart 1980 Quine II W.V.O. Quine Theories and Things, Cambridge/MA 1986 German Edition: Theorien und Dinge Frankfurt 1985 Quine III W.V.O. Quine Methods of Logic, 4th edition Cambridge/MA 1982 German Edition: Grundzüge der Logik Frankfurt 1978 Quine V W.V.O. Quine The Roots of Reference, La Salle/Illinois 1974 German Edition: Die Wurzeln der Referenz Frankfurt 1989 Quine VI W.V.O. Quine Pursuit of Truth, Cambridge/MA 1992 German Edition: Unterwegs zur Wahrheit Paderborn 1995 Quine VII W.V.O. Quine From a logical point of view Cambridge, Mass. 1953 Quine VII (a) W. V. A. Quine On what there is In From a Logical Point of View, Cambridge, MA 1953 Quine VII (b) W. V. A. Quine Two dogmas of empiricism In From a Logical Point of View, Cambridge, MA 1953 Quine VII (c) W. V. A. Quine The problem of meaning in linguistics In From a Logical Point of View, Cambridge, MA 1953 Quine VII (d) W. V. A. Quine Identity, ostension and hypostasis In From a Logical Point of View, Cambridge, MA 1953 Quine VII (e) W. V. A. Quine New foundations for mathematical logic In From a Logical Point of View, Cambridge, MA 1953 Quine VII (f) W. V. A. Quine Logic and the reification of universals In From a Logical Point of View, Cambridge, MA 1953 Quine VII (g) W. V. A. Quine Notes on the theory of reference In From a Logical Point of View, Cambridge, MA 1953 Quine VII (h) W. V. A. Quine Reference and modality In From a Logical Point of View, Cambridge, MA 1953 Quine VII (i) W. V. A. Quine Meaning and existential inference In From a Logical Point of View, Cambridge, MA 1953 Quine VIII W.V.O. Quine Designation and Existence, in: The Journal of Philosophy 36 (1939) German Edition: Bezeichnung und Referenz In Zur Philosophie der idealen Sprache, J. Sinnreich (Hg) München 1982 Quine IX W.V.O. Quine Set Theory and its Logic, Cambridge/MA 1963 German Edition: Mengenlehre und ihre Logik Wiesbaden 1967 Quine X W.V.O. Quine The Philosophy of Logic, Cambridge/MA 1970, 1986 German Edition: Philosophie der Logik Bamberg 2005 Quine XII W.V.O. Quine Ontological Relativity and Other Essays, New York 1969 German Edition: Ontologische Relativität Frankfurt 2003 Quine XIII Willard Van Orman Quine Quiddities Cambridge/London 1987 |
| Abstractness | Tugendhat | I 499 Abstract singular terms/Tugendhat: cannot be identified in space and time. - They are a collective terms, which break up into different subject areas with different identity criteria. >Singular terms, >Identity criteria, >Identity, >cf >General terms. I 500 Example 1. attributes 2. states of affairs 3. types 4. institutions and their parts 5. classes 6. numbers >Attributes, >States of affairs, >Type/Token, >Institutions, >Classes. II 97 Abstract terms/Tugendhat: events occur in space and time, but not abstract objects. >Events, >Space, >Time. |
Tu I E. Tugendhat Vorlesungen zur Einführung in die Sprachanalytische Philosophie Frankfurt 1976 Tu II E. Tugendhat Philosophische Aufsätze Frankfurt 1992 |
| Abstractness | Wright | I 226 f Abstract/Purely Abstract Objects/Dummett: (Frege:" logical objects "): Dummett: nothing more than reflections of certain linguistic expressions, analogous to the proper names of objects whose meaning, however, cannot be presented as being our ability to identify objects as their carriers. >Identification. Wright: could be read as nominalism (i.e. that there are no abstract objects). >Nominalism. But that is not Dummett's view. Dummett precisely does not deny that there are singular terms that ostensibly refer to abstract objects, but have reference indeed. They even play a semantic role! >Singular terms, >Reference, >Conceptual role, >Inferential role. Example "largest prime number": empty singular term, but the mere meaning ensures that it plays a semantic role! >Meaning, >Semantics, >Non-existence. Dummett: seems to think here that there is no question about whether Platonism or Nominalism provides the better approach according to which the question is decided whether abstract objects exist. >Numbers, >Platonism. I 227f Abstract/Morality/Ethics/Wright: that matches our approach to discourse of morality well: the cause of moral realism is not really confined to the question whether moral discourse is evaluable in relation to truth, or not. >Truth-evaluableness, >Morals, Discourse. If the "capacity for truth" (truth evaluability) is affirmed, there are still a number of realism-relevant questions. >Realism. I 223 ff It is also not in dispute that we use abstract singular terms in an intelligent manner. Wright: There is no linguistically unmediated cognitive contact with abstract objects. Frege (Platonist) asserts quite correctly, that doubts about the reality of the reference to abstract objects do not contain any rational sense. (Wright: This is minimalism regarding reference). >Minimalism. I 242 Abstract Singular Terms/Wright: it is impossible that they influence the thinking of someone who does not know what they are. >Objects of thought. |
WrightCr I Crispin Wright Truth and Objectivity, Cambridge 1992 German Edition: Wahrheit und Objektivität Frankfurt 2001 WrightCr II Crispin Wright "Language-Mastery and Sorites Paradox" In Truth and Meaning, G. Evans/J. McDowell Oxford 1976 WrightGH I Georg Henrik von Wright Explanation and Understanding, New York 1971 German Edition: Erklären und Verstehen Hamburg 2008 |
| Beliefs | Prior | Cresswell II 146 Belief/Prior/Cresswell: Thesis: Belief should not be considered a predicate of that-sentence - but instead believes-that should be seen as a syntactic unit that is applied directly to a sentence. Cf. >That-sentences, >Predicates, >Beliefs, >Objects of thought, >Objects of belief. Prior I 6f Belief/Prior: no adequate approach without distinction between mind state of belief and that which is believed (state/content). >Belief state/Perry, >Mind state. Prior: in case of false beliefs: instead of non-existing object: attribution: E.g. Othello attributes infidelity to Desdemona. >`Attribution, >Predication, >Non-existence. PriorVsRussell: Problem: above it is abstract loyalty. >Abstract objects, >Abstractness. In case of falsity, the belief relation would then need to have an additional position (to the true fact). >Relation theory. I 11 False Belief/Russell: false facts fail in truth-making. >Truthmakers, >Facts. Montague: points in the wrong direction. >R. Montague. PriorVs: not for a neutral observer. >Intentionality, >Thinking. I 27 Belief/Prior: belief is no relation - E.g. ...that nothing is perfect: there is no object. >Generality, >Generalization. I 53 Belief Function/Prior: E.g. X believes that ... is not identical in identical propositions: e.g. ...is a bachelor/...is an unmarried man. although one may feel that the propositions are self-identical. I 81 Belief/Prior: you do not have to believe rightly that you believe something. >about/Prior) You can also simultaneously believe p and not-p. You can believe something contradictory. E.g. the fear that God will punish you for your disbelief. >Thinking, >Logic. You can find out that you did not believe what was thought you believed. - If someone believes what he says when he says that he mistakenly believes that it is raining, then this belief is not necessarily mistaken. >Error, >Deception, >Falsehood, >Levels/order, >Description levels. No epistemic logic ist necessary, propositional calculus is sufficient. >Epistemic logic, >Propositional calculus. |
Pri I A. Prior Objects of thought Oxford 1971 Pri II Arthur N. Prior Papers on Time and Tense 2nd Edition Oxford 2003 Cr I M. J. Cresswell Semantical Essays (Possible worlds and their rivals) Dordrecht Boston 1988 Cr II M. J. Cresswell Structured Meanings Cambridge Mass. 1984 |
| Conservativity | Quine | X 86 Definition Conservativity/substitution/variables/Harman/Quine: substitutions must be conservative. The grammatical structure and logical truth shall be preserved: i.e. the variable or lexicon word used in the object language must not already occur elsewhere in the context. >Variables/Quine, >Substitution/Quine. V 189 Theory/Ontology/Quine: how should a scientific theory look best? We want as many and good predictions as possible. Guiding principles: Simplicity and conservativity. V 190 A great simplification can justify a relatively great deviation. We need a compromise between the two. Conservativity/Quine: conservativity is among other things due to our lack of imagination. But also wise caution against hypotheses. Simplicity/Conservativity: both are already at work in language learning. Language learning/Quine: does jumps and is always oriented towards similarities and analogies. >Language Acquisition/Quine. V 191 Short steps are conservative. They are guided by relative empiricism. Def relative empiricism/Quine: do not venture further away from the sense data than necessary. Quine pro: this keeps the theoretical changes low. QuineVsRadical Empiricism: we gave it up when we gave up hope of reducing the speech of the body to the speech of sense data. N.B.: this requires sticking to the substitutional quantification of abstract objects. That appeals to the nominalistic mind. It is expressed in relative empiricism, because both are the same. Nominalism: must not, however, overestimate the ontological harmlessness of the variables of substitutional quantification. In general, one can say that the values of variables make up the whole ontology if we only have object variables, truth functions and predicates. |
Quine I W.V.O. Quine Word and Object, Cambridge/MA 1960 German Edition: Wort und Gegenstand Stuttgart 1980 Quine II W.V.O. Quine Theories and Things, Cambridge/MA 1986 German Edition: Theorien und Dinge Frankfurt 1985 Quine III W.V.O. Quine Methods of Logic, 4th edition Cambridge/MA 1982 German Edition: Grundzüge der Logik Frankfurt 1978 Quine V W.V.O. Quine The Roots of Reference, La Salle/Illinois 1974 German Edition: Die Wurzeln der Referenz Frankfurt 1989 Quine VI W.V.O. Quine Pursuit of Truth, Cambridge/MA 1992 German Edition: Unterwegs zur Wahrheit Paderborn 1995 Quine VII W.V.O. Quine From a logical point of view Cambridge, Mass. 1953 Quine VII (a) W. V. A. Quine On what there is In From a Logical Point of View, Cambridge, MA 1953 Quine VII (b) W. V. A. Quine Two dogmas of empiricism In From a Logical Point of View, Cambridge, MA 1953 Quine VII (c) W. V. A. Quine The problem of meaning in linguistics In From a Logical Point of View, Cambridge, MA 1953 Quine VII (d) W. V. A. Quine Identity, ostension and hypostasis In From a Logical Point of View, Cambridge, MA 1953 Quine VII (e) W. V. A. Quine New foundations for mathematical logic In From a Logical Point of View, Cambridge, MA 1953 Quine VII (f) W. V. A. Quine Logic and the reification of universals In From a Logical Point of View, Cambridge, MA 1953 Quine VII (g) W. V. A. Quine Notes on the theory of reference In From a Logical Point of View, Cambridge, MA 1953 Quine VII (h) W. V. A. Quine Reference and modality In From a Logical Point of View, Cambridge, MA 1953 Quine VII (i) W. V. A. Quine Meaning and existential inference In From a Logical Point of View, Cambridge, MA 1953 Quine VIII W.V.O. Quine Designation and Existence, in: The Journal of Philosophy 36 (1939) German Edition: Bezeichnung und Referenz In Zur Philosophie der idealen Sprache, J. Sinnreich (Hg) München 1982 Quine IX W.V.O. Quine Set Theory and its Logic, Cambridge/MA 1963 German Edition: Mengenlehre und ihre Logik Wiesbaden 1967 Quine X W.V.O. Quine The Philosophy of Logic, Cambridge/MA 1970, 1986 German Edition: Philosophie der Logik Bamberg 2005 Quine XII W.V.O. Quine Ontological Relativity and Other Essays, New York 1969 German Edition: Ontologische Relativität Frankfurt 2003 Quine XIII Willard Van Orman Quine Quiddities Cambridge/London 1987 |
| Constructivism | Quine | XIII 33 Constructivism/Mathematics/Quine: (VsUniversals). Thesis: theorems that can be shown constructively should be preferred. Def Constructivism/Mathematics/Quine: Thesis: any abstract object is specifiable. Against: Predicative Set Theory: is too weak to prove that there must be unspecifiable classes and unspecifiable real numbers. Quantification/Variables/Quine: the quantification is different if it is certain that every object in the domain is specifiable. For example, the natural numbers are such a domain. This is because there is an Arabic number for each of them. Def Substitutional Quantification/sQ/Quine: (Universal Quantification (x)): the formula preceding the quantifier becomes true under any grammatically permissible substitution for the letter "x". Referential Quantification/refQ/Substitutional Quantification: For example, natural numbers: here both are the same. >Substitutional Quantification/Quine. On the other hand: If not all objects can be specified: If not all objects in a domain can be specified by singular terms of the language used, then the two types of quantification diverge. For example, if the universal quantifier is fulfilled by all specifiable objects, but not by the non-specifiable ones, then the substitutional quantification is true and the referential quantification is false. Existential Quantification/EQu/Substitutional Quantification/refQ/Quine: behaves accordingly. XIII 35 Substitutional Quantification/Referential Quantification: diverge in the case of existential quantification if the formula is satisfied by some unspecifiable, but not by any specifiable one. Substitutional Quantification/Quine: is unrealistic for concrete objects. Specifiability/Name/Namability/namable/Quine: Question: is each concrete object individually specifiable? For example every past or future bee, every atom and every electron? Yes, by numerical coordinates with rational numbers. But unlimited referential quantification is simply more natural here. Predicative set theory: here substitutional quantification is more attractive and manageable because abstract objects are parasitic in relation to language, in a way that concrete objects are not. Abstract/Charles Parsons/Quine: abstract objects are parasitic in relation to language, concrete objects are less parasitic. Substitutional Quantification/Quine: does not simply eliminate abstract objects from ontology, but grants them a "thinner" kind of existence. Abstract/Quine: expressions themselves are abstract, but not as wild as the inhabitants of higher set theory. Substitutional Quantification/Quine: is a compromise with militant nominalism. Abstract Objects/Quine: are then classes, like those of predicative set theory (RussellVs). >Abstractness/Quine. Substitutional Quantification/Referential Quantification/Parsons: has shown how both go together (Lit). By using two kinds of variables. Then you can also link them together (intertwine). Problem/Russell: predicative set theory is inadequate for the classical mathematics of real numbers. XIII 36 Real Numbers/Russell/Quine: their theory leads to unspecifiable real numbers and other unspecifiable classes. Substitutional Quantification/Quine: this problem did not lead to the substitutional quantification by itself. Constructive Mathematics/Constructivism/QuineVsBrouwer: heated minds developed and still develop constructive mathematics that are suitable for all sciences. Problem: this leads to unattractive deviations from standard logic. Standard Logic/Constructivism/Quine: Experiments with standard logic: Weyl, Paul Lorenzen, Erret Bishop. Hao Wang, Sol Feferman. These are solutions with predicative set theory together with artistic circles. Problem: you do not know exactly how much mathematics scientists need. Nominalism/Quine: we probably do not need nominalism through and through, but an attractive approach to it. |
Quine I W.V.O. Quine Word and Object, Cambridge/MA 1960 German Edition: Wort und Gegenstand Stuttgart 1980 Quine II W.V.O. Quine Theories and Things, Cambridge/MA 1986 German Edition: Theorien und Dinge Frankfurt 1985 Quine III W.V.O. Quine Methods of Logic, 4th edition Cambridge/MA 1982 German Edition: Grundzüge der Logik Frankfurt 1978 Quine V W.V.O. Quine The Roots of Reference, La Salle/Illinois 1974 German Edition: Die Wurzeln der Referenz Frankfurt 1989 Quine VI W.V.O. Quine Pursuit of Truth, Cambridge/MA 1992 German Edition: Unterwegs zur Wahrheit Paderborn 1995 Quine VII W.V.O. Quine From a logical point of view Cambridge, Mass. 1953 Quine VII (a) W. V. A. Quine On what there is In From a Logical Point of View, Cambridge, MA 1953 Quine VII (b) W. V. A. Quine Two dogmas of empiricism In From a Logical Point of View, Cambridge, MA 1953 Quine VII (c) W. V. A. Quine The problem of meaning in linguistics In From a Logical Point of View, Cambridge, MA 1953 Quine VII (d) W. V. A. Quine Identity, ostension and hypostasis In From a Logical Point of View, Cambridge, MA 1953 Quine VII (e) W. V. A. Quine New foundations for mathematical logic In From a Logical Point of View, Cambridge, MA 1953 Quine VII (f) W. V. A. Quine Logic and the reification of universals In From a Logical Point of View, Cambridge, MA 1953 Quine VII (g) W. V. A. Quine Notes on the theory of reference In From a Logical Point of View, Cambridge, MA 1953 Quine VII (h) W. V. A. Quine Reference and modality In From a Logical Point of View, Cambridge, MA 1953 Quine VII (i) W. V. A. Quine Meaning and existential inference In From a Logical Point of View, Cambridge, MA 1953 Quine VIII W.V.O. Quine Designation and Existence, in: The Journal of Philosophy 36 (1939) German Edition: Bezeichnung und Referenz In Zur Philosophie der idealen Sprache, J. Sinnreich (Hg) München 1982 Quine IX W.V.O. Quine Set Theory and its Logic, Cambridge/MA 1963 German Edition: Mengenlehre und ihre Logik Wiesbaden 1967 Quine X W.V.O. Quine The Philosophy of Logic, Cambridge/MA 1970, 1986 German Edition: Philosophie der Logik Bamberg 2005 Quine XII W.V.O. Quine Ontological Relativity and Other Essays, New York 1969 German Edition: Ontologische Relativität Frankfurt 2003 Quine XIII Willard Van Orman Quine Quiddities Cambridge/London 1987 |
| Content | Boer | I XIII Definition Thought/Boer: can be common to different states of mind. Proposition/Boer: I do not call it thought content, because this expression brings too much ballast with it. --- Note I XVIII Intensional transitive verbs: have three conditions, each of which is sufficient for itself: (i) failure of the principle of the substitutability of identity (ii) quantification permits a specific "narrow range" (iii) there is no existential (ontological) commitment. --- I XIV Direct objects/direct object/propositional settings/Boer: it is controversial whether the relation to direct thought objects can be analyzed as propositional attitudes. E.g. "search": here it is certainly the case, e.g. "worship": seems to contradict this analysis. Fulfillment conditions/EB/proopositional attitudes/individuation/Boer: N.B.: The fulfillment conditions do not appear to be sufficient to individuate a propositional attitude. On the other hand: Thought content/GI: seems to be sufficient for the individuation of a propositional attitude. Truth conditions: (and hence also the fulfillment conditions) can be the same for two beliefs, while the subject is not sure whether it is the same object. E.g. woodchucks/groundhogs. Propositional attitudes/Individuation/Lewis: (1969)(1): the mere existence of a convention of this kind presupposes that speakers from a community have certain propositional attitudes with certain fulfillment conditions. Abstract objects/propositional attitudes/Boer: in order to believe that patience is a virtue, one must think of patience. Definition mental reference/Terminology/Boer: Thinking of: be a mental analogue to speaker reference. Speaker reference/some authors: thesis: never exists in isolation, but is only a partial aspect of a speech act (utterance). --- I XV Mental reference: should then only be a partial aspect of thinking-of-something. Probably, there is also predication. Definition mental reference/Boer: be in a state of thought with a content of thought which defines a fulfillment condition of which the object is a constituent. Problem: non-existent objects. --- I XV Thought content/GI/Boer: must be carefully distinguished from any objects that it might contain. Definition object of thought/object/GO/Boer: "object of the propositional attitudes ψ" is clearly only the item/s to which a subject by the power of having ψ refers to. (s) So not the propositional attitudes themselves. Individuation/identification/Boer: should be identified by a that-sentence (in a canonical attribution of ψ). That-sentence/Boer: is the content (thought content). Content/thought content/Boer: is the that-sentence. Thinking about/Boer: what you think of something is the object itself. 1. David Lewis 1969. Convention: A Philosophical Study, Cambridge, MA: Harvard University Press. |
Boer I Steven E. Boer Thought-Contents: On the Ontology of Belief and the Semantics of Belief Attribution (Philosophical Studies Series) New York 2010 Boer II Steven E. Boer Knowing Who Cambridge 1986 |
| Description Levels | Tugendhat | I 372 Levels/abstract/Tugendhat: for predicates of a higher level (that classify abstract objects) there are no analogues at the level of quasi-predicates. >Terminology/Tugendhat, >Predicates/Tugendhat. But there are also singular terms of a higher level. One will probably be able to say that the reference to abstract objects presupposes the reference to concrete objects - at least equiprimordial. >Abstractness, >Abstraction, >Reality, >Reference, >World/thinking, >Levels, >World. |
Tu I E. Tugendhat Vorlesungen zur Einführung in die Sprachanalytische Philosophie Frankfurt 1976 Tu II E. Tugendhat Philosophische Aufsätze Frankfurt 1992 |
| Empty Set | Prior | I 63 ~ Empty set/Prior: creates only the logical construction identity between unicorns and Pegasi. - A logical structure is not any sort of entity. ((s) There is only one empty set, so it is unlike anything. - And it makes unicorns and Pegasi not comparable because it has no elements). >Relations, >Objects, >Abstract objects, >Abstractness, >Comparisons, >Comparability. I 63ff Empty set/Prior: solution: to say that there is exactly one null class, is simply: for a φ: nothing φ-s and for each φ and ψ, nothing φ-s and nothing ψ-s. Then whatever ψ-s,φ-s and whatever ψ-s, φ-s - related: relation-in-extension. Relation in Extension/Prior: two digit predicates can be associated in the same way with Relation in Extension. E.g. both: being father and mother of is not the same as both: being greater than and less than. But the corresponding "relations-in-extension" are the same. Because you can say that for an x and a y, if x is both father and mother of y then x is also bigger and smaller than y and vice versa, because both implications are just empty. >Implication. |
Pri I A. Prior Objects of thought Oxford 1971 Pri II Arthur N. Prior Papers on Time and Tense 2nd Edition Oxford 2003 |
| Existence Statements | Quine | VIII 24ff Existence Statement/Quine: special: "There is one thing that is so and so" (mentions the name) - general: "There is a thing that is so" (specifies a variable instead of names) - E.g. Pegasus: is a sense equivalent to description. >Descriptions, >Pegasus example, >Non-existence, >Unicorn example. XII 27 Object/Translation/Indefiniteness/Expression Conditions/Language Learning/Radical Interpretation/Quine: the expression conditions are not sufficient to be able to say with certainty what a speaker of a foreign language regards as objects. Problem: how can assertions of existence (theorems of existence) ever be empirically invalidated? Solution: the knowledge of the conditions of utterance does not ensure the reference to the subject, but it does help to clarify what serves as empirical confirmation of the truth of the whole sentence. XII 28 We then project our own acceptance of objects onto the indigenous language. We can be sure that the assumed object is an observed object in the sense that the amplified stimuli emanate quite directly from it. XII 33 Abstract/abstract object/existence/coherence/Quine: Existence assertions about abstract objects can only be judged by their coherence or by simplicity considerations. Example: to avoid paradoxes with classes. Property/Quine: the law of education for properties states that every statement that speaks about a thing ascribes a property to it (predication). This is a cultural heritage. VII (i) 167 Existence/Logic/Quine: we can dispense with such confusing notations as "a exists" because we know how to translate singular sentences of existence into more basic expressions if the singular term is contained in a description. Observation sentence: is meaningless in the past, since it is assumed that it was learned by direct conditioning. Theorem of Existence/Russell: For this reason, Russell declares singular theorems of existence pointless if their subject is a real proper name. ((s) Real proper name: "this". No, not only!"Nine" too: are names whose reference is saved. So from acquaintance, which corresponds to a descriptions. For fake names, the description corresponds to what a fiction says about it: e.g. Pegasus. "winged horse". Name/identification(s): each name corresponds to a description because no thing in the world can only be referenced by a name and for each description a name can be invented but not every description is fulfilled by an object. ((s) Precisely because of the necessary acquaintance the question whether the theorem of existence is true is pointless.) Quine: the reason is the same here. ((s) Theorem of existence (s): Example "There is Napoleon": can only refer to one learning situation. Circular, so to speak, from the very beginning. Exactly the same: e.g. "There are daisies". Davidson/(s): One could also not say meaningfully: Example: "It has turned out that this and that does not exist": because then one says only that one has learned a word wrongly. >Reference, >Learning. |
Quine I W.V.O. Quine Word and Object, Cambridge/MA 1960 German Edition: Wort und Gegenstand Stuttgart 1980 Quine II W.V.O. Quine Theories and Things, Cambridge/MA 1986 German Edition: Theorien und Dinge Frankfurt 1985 Quine III W.V.O. Quine Methods of Logic, 4th edition Cambridge/MA 1982 German Edition: Grundzüge der Logik Frankfurt 1978 Quine V W.V.O. Quine The Roots of Reference, La Salle/Illinois 1974 German Edition: Die Wurzeln der Referenz Frankfurt 1989 Quine VI W.V.O. Quine Pursuit of Truth, Cambridge/MA 1992 German Edition: Unterwegs zur Wahrheit Paderborn 1995 Quine VII W.V.O. Quine From a logical point of view Cambridge, Mass. 1953 Quine VII (a) W. V. A. Quine On what there is In From a Logical Point of View, Cambridge, MA 1953 Quine VII (b) W. V. A. Quine Two dogmas of empiricism In From a Logical Point of View, Cambridge, MA 1953 Quine VII (c) W. V. A. Quine The problem of meaning in linguistics In From a Logical Point of View, Cambridge, MA 1953 Quine VII (d) W. V. A. Quine Identity, ostension and hypostasis In From a Logical Point of View, Cambridge, MA 1953 Quine VII (e) W. V. A. Quine New foundations for mathematical logic In From a Logical Point of View, Cambridge, MA 1953 Quine VII (f) W. V. A. Quine Logic and the reification of universals In From a Logical Point of View, Cambridge, MA 1953 Quine VII (g) W. V. A. Quine Notes on the theory of reference In From a Logical Point of View, Cambridge, MA 1953 Quine VII (h) W. V. A. Quine Reference and modality In From a Logical Point of View, Cambridge, MA 1953 Quine VII (i) W. V. A. Quine Meaning and existential inference In From a Logical Point of View, Cambridge, MA 1953 Quine VIII W.V.O. Quine Designation and Existence, in: The Journal of Philosophy 36 (1939) German Edition: Bezeichnung und Referenz In Zur Philosophie der idealen Sprache, J. Sinnreich (Hg) München 1982 Quine IX W.V.O. Quine Set Theory and its Logic, Cambridge/MA 1963 German Edition: Mengenlehre und ihre Logik Wiesbaden 1967 Quine X W.V.O. Quine The Philosophy of Logic, Cambridge/MA 1970, 1986 German Edition: Philosophie der Logik Bamberg 2005 Quine XII W.V.O. Quine Ontological Relativity and Other Essays, New York 1969 German Edition: Ontologische Relativität Frankfurt 2003 Quine XIII Willard Van Orman Quine Quiddities Cambridge/London 1987 |
| Facts | Strawson | Horwich I 189 Facts/StrawsonVsAustin: Incorrect alignment of facts and things. Horwich I 190 Fact/StrawsonVsAustin: should go beyond the "beyond" of the statement. - But there is nothing. - This comes from Austin's need for a "truth maker". >Truthmakers. Horwich I 191 The fact that the cat is sick, is not made true by the cat, but at most by the fact that is expressed by the sentence. - Reference/Strawson: a statement: is the material corollary, not its fact. - I can possibly measure the corollary with the clock, issue etc. - Fact: pseudo-material correlate of the entire statement. Fact/Strawson: not a thing, not even a composite object. cf. >Situation. Horwich I 192 It is what the statement notes, not what it is. - Facts are not "about". >"About", >Intentionality. Horwich I 193 Facts and statements are in accordance with each other, they are made for each other, if one eliminates one, then also the other. But the world will not be poorer through that.(1) 1. Peter F. Strawson, "Truth", Proceedings of the Aristotelian Society, Suppl. Vol XXIV, 1950, in: Paul Horwich (ed.) Theories of Truth, Aldershot 1994 --- Seel III 104f Fact/Strawson/Seel: if we call something a fact, we think it is real like the sentence says it. - A fact is nothing more than the contents of a true belief - the alleged facts are not even from this the world. III 104/105 In contrast to actual processes facts are abstract objects - they relate to a real state, without being themselves an occurrence in the world. - E.g. the fact that Napoleon won the battle, is not the same as the battle - the images do not correspond with beings in the world. --- Strawson II 20 Facts cannot burn, they do not wither - (timeless). II 250 Fact/StrawsonVsAustin: equating fact and thing leads to equating of saying-something and relate-to-something. - Statement and sentence must not be equated. >Reference/Strawson, >Statement/Strawson, >Sentence/Strawson. II 253 Fact/thing/StrawsonVsAustin/StrawsonVsSpeech Act Theory: completely different types. - Fact: what is said. Thing: about what something is said. VsAustin: believes, a statement would be something in the world. - This is a confusion with the event of utterance (speech act). >Speech act. II 254 Of course facts and statements correspond, they are made for each other - Facts, fact and situations are not seen but rather recorded or summarized. >State of affairs, >Knowledge, >Recognition. II 255 E.g. being worried by facts, is not the same as being worried by a shadow. - He is worried because... II 259 Fact: already implies a discourse context - but we do not talk about this framework, also not with terms such as statement and true. >Reference system, >Discourse. --- IV 150/51 Fact/Strawson: something to determine, nothing to be described. - There are always different descriptions possible. >Descriptions. |
Strawson I Peter F. Strawson Individuals: An Essay in Descriptive Metaphysics. London 1959 German Edition: Einzelding und logisches Subjekt Stuttgart 1972 Strawson II Peter F. Strawson "Truth", Proceedings of the Aristotelian Society, Suppl. Vol XXIV, 1950 - dt. P. F. Strawson, "Wahrheit", In Wahrheitstheorien, Gunnar Skirbekk Frankfurt/M. 1977 Strawson III Peter F. Strawson "On Understanding the Structure of One’s Language" In Truth and Meaning, G. Evans/J. McDowell Oxford 1976 Strawson IV Peter F. Strawson Analysis and Metaphysics. An Introduction to Philosophy, Oxford 1992 German Edition: Analyse und Metaphysik München 1994 Strawson V P.F. Strawson The Bounds of Sense: An Essay on Kant’s Critique of Pure Reason. London 1966 German Edition: Die Grenzen des Sinns Frankfurt 1981 Strawson VI Peter F Strawson Grammar and Philosophy in: Proceedings of the Aristotelian Society, Vol 70, 1969/70 pp. 1-20 In Linguistik und Philosophie, G. Grewendorf/G. Meggle Frankfurt/M. 1974/1995 Strawson VII Peter F Strawson "On Referring", in: Mind 59 (1950) In Eigennamen, Ursula Wolf Frankfurt/M. 1993 Horwich I P. Horwich (Ed.) Theories of Truth Aldershot 1994 Seel I M. Seel Die Kunst der Entzweiung Frankfurt 1997 Seel II M. Seel Ästhetik des Erscheinens München 2000 Seel III M. Seel Vom Handwerk der Philosophie München 2001 |
| Facts | Wright | I 243 Fact/state of affairs/Wright: There are situations where it is simply inappropriate to say "he is not aware ..." Such situations and facts point to a certain inertia that corresponds exactly to the inertia of pure abstract objects. >Situations, >Subjects, >Consciousness, >Abstractness, >Object. We can not use something as a content for which we have no words. >Content, >Concepts. I 261 Fact/Wright: evaluating any fact requires a point of view. >Perspective, >Aspects, >Objectivity. |
WrightCr I Crispin Wright Truth and Objectivity, Cambridge 1992 German Edition: Wahrheit und Objektivität Frankfurt 2001 WrightCr II Crispin Wright "Language-Mastery and Sorites Paradox" In Truth and Meaning, G. Evans/J. McDowell Oxford 1976 WrightGH I Georg Henrik von Wright Explanation and Understanding, New York 1971 German Edition: Erklären und Verstehen Hamburg 2008 |
| Forms | Quine | V 107 Form/similarity/Quine: E.g. ovate: is something that is more similar in shape to each of two eggs than these are to one another. It is always between two things. (s) Idealization: applies to two arbitrarily chosen things. It cannot differ independently in one direction from both eggs - pomegranate-colored: in the middle between two concrete colors. V 165 Form/analytic geometry/Quine: are class of classes of pairs of real numbers. ((s) Two-dimensional). V 184 Form: a variety can only be recognized as a square if it is marked - against this: Colour: Scarlet red, for example, does not need to be marked. Form/Colour/Quine: Difference: the union of squares is usually not a square, while the union of several scarlet areas is scarlet red. Form/Colour/Ontology/Quine: classic solution: comes down to a double ontology: matter and space. Spatial diversity: is an aggregate of points, physical objects, particles. Certain particular at a time. Squares: are spatial manifolds. For example, a certain cross-section of a physical object will occupy almost exactly a certain square, and it will occupy an infinite number of squares that almost coincide with it almost exactly. Spatiotemporal Identity/Quine: is then no longer a problem. A square, a certain aggregate of points retains its identity for all times. V 186 Manifold/Quine: these were merely individual squares, circles, etc. These were not abstract objects like squares. Forms: would be classes of such, i.e. objects of higher abstraction - Forms/(s) i.e. are classes of classes of points. Letter forms: are classes of inscriptions. >Similarity. |
Quine I W.V.O. Quine Word and Object, Cambridge/MA 1960 German Edition: Wort und Gegenstand Stuttgart 1980 Quine II W.V.O. Quine Theories and Things, Cambridge/MA 1986 German Edition: Theorien und Dinge Frankfurt 1985 Quine III W.V.O. Quine Methods of Logic, 4th edition Cambridge/MA 1982 German Edition: Grundzüge der Logik Frankfurt 1978 Quine V W.V.O. Quine The Roots of Reference, La Salle/Illinois 1974 German Edition: Die Wurzeln der Referenz Frankfurt 1989 Quine VI W.V.O. Quine Pursuit of Truth, Cambridge/MA 1992 German Edition: Unterwegs zur Wahrheit Paderborn 1995 Quine VII W.V.O. Quine From a logical point of view Cambridge, Mass. 1953 Quine VII (a) W. V. A. Quine On what there is In From a Logical Point of View, Cambridge, MA 1953 Quine VII (b) W. V. A. Quine Two dogmas of empiricism In From a Logical Point of View, Cambridge, MA 1953 Quine VII (c) W. V. A. Quine The problem of meaning in linguistics In From a Logical Point of View, Cambridge, MA 1953 Quine VII (d) W. V. A. Quine Identity, ostension and hypostasis In From a Logical Point of View, Cambridge, MA 1953 Quine VII (e) W. V. A. Quine New foundations for mathematical logic In From a Logical Point of View, Cambridge, MA 1953 Quine VII (f) W. V. A. Quine Logic and the reification of universals In From a Logical Point of View, Cambridge, MA 1953 Quine VII (g) W. V. A. Quine Notes on the theory of reference In From a Logical Point of View, Cambridge, MA 1953 Quine VII (h) W. V. A. Quine Reference and modality In From a Logical Point of View, Cambridge, MA 1953 Quine VII (i) W. V. A. Quine Meaning and existential inference In From a Logical Point of View, Cambridge, MA 1953 Quine VIII W.V.O. Quine Designation and Existence, in: The Journal of Philosophy 36 (1939) German Edition: Bezeichnung und Referenz In Zur Philosophie der idealen Sprache, J. Sinnreich (Hg) München 1982 Quine IX W.V.O. Quine Set Theory and its Logic, Cambridge/MA 1963 German Edition: Mengenlehre und ihre Logik Wiesbaden 1967 Quine X W.V.O. Quine The Philosophy of Logic, Cambridge/MA 1970, 1986 German Edition: Philosophie der Logik Bamberg 2005 Quine XII W.V.O. Quine Ontological Relativity and Other Essays, New York 1969 German Edition: Ontologische Relativität Frankfurt 2003 Quine XIII Willard Van Orman Quine Quiddities Cambridge/London 1987 |
| Four-Dimensionalism | Quine | X 54 Four Dimensionalism/Quine: E.g. a shrinking body tapers into the future, a growing one tapers sharply into the past. That makes tense formation superfluous. It always has to be in the present tense - so you can quantify over objects that never exist simultaneously. ((s) Time slice/(s): is not flat like a slice of a sausage, but a complete body at a point of time.) XIII 75 Four Dimensionalism/Possibilities/possible objects/Possibilia/Quine: four dimensionalism creates a place in the sun for all future actualities, however unpredictable, but it does not give comfort or help for mere possibilities. XIII 197 Four Dimensionalism/Change/Quine: it is wrong, as some have claimed, that in four dimensionalism (not Quine's expression) there is no change and instead there is only an eternally static reality. Change: still exists, it is merely embodied (incorporated). It is now simply said that the earlier stages of a body differ from the later ones, just as its upper stages differ from the lower ones. The later stages are just as inaccessible from the earlier ones as the lower ones from the upper ones! ((s) >Facts are not necessary). Time/Time Use/Tense/Logic/Quine: Time is not present in pure mathematics and logic. If it is brought in, then by predicates like "later than". Four-Dimensionalism: corresponds to this extension of logical notation by predicates like "later than". Time/Logic/Time Logic: alternatively one could take time into logic, but this would be very cumbersome and would only be appropriate if one wanted to investigate everyday language. Time/Time Use/Tense/Logic/Quine: Time is not present in pure mathematics and logic. If it is brought in, then by predicates like "later than". Four-dimensionalism: corresponds to this extension of logical notation by predicates like "later than". Time/logic/time logic: alternatively one could take time into logic, but this would be very cumbersome and would only be appropriate if one wanted to investigate everyday language. Time/Spatialization/Space Time/Quine Dimensionism/Quine: shouldn't one be surprised about relations between things that no longer exist? For example Mark Anton and Cleopatra are both dead, the relation between them existed earlier, even if it no longer exists today. Question: what about the great-great-grandfather relation? ((s) here always only a part exists). For example the class of the great generals in history: the elements hardly exist at the same time. XIII 198 Simplest Solution: to see them all as inhabitants of space-time. As timelessly coexistent. Time/Translation/Quine: we translate by moving into the 4th dimension. Time/Dimension/Quine: time as the 4th dimension is treated on the same level as the spatial dimensions, but in an important sense it is independent of them: Space/Quine: here we also distinguish directions between the axes, unlike in time. N.B.: we can amalgamate time with space by saying e.g. so and so many miles correspond to one hour; we haven't used that yet, but we need it in relativity theory. Relativity Theory/Space-time/Relativity/third/Quine: For example two piles at a distance of 5 meters: can be described differently by different observers. Theory of Relativity: here we have spatiotemporal diagonals. It does not allow any measure, XIII 199 not even over all four dimensions simultaneously, which is analogous to the distance and independent of the velocity of the observer. Interval/Solution/Quine: instead of the distance there can be an interval, but it is different: it can be 0, even if the events are spatially far apart. Four Dimensionalism/Quine: we maintain it completely independent of relativity. XIII 221 Square Measure to the Square/Quine: square measure should have four spatial dimensions! Unlike liters per hour: ((s) because now we have to calculate m² x 2!). Fourdimensionality/Quine: For example, if we take time as the fourth dimension, the square of a surface is then XIII 222 the spatiotemporal size of a cube over time, the temporal equivalent of the edge length, whatever that is. Squares of surfaces/Relativity Theory/Relativity/Einstein/Quine: Example E = mc²: c: is distance by time c²: is the square of the distance divided by the square of the time, or surface by square hour. E = mc² thus equates energy with area tons per square hour. V 182 Object/Ontology/Quine: great progress: four dimensionalism, four dimensional spatio-temporal objects. We are so body-oriented that we do not take the Evening Star and the Morning Star as phases of Venus either, they are simply Venus and can be referred to with one or the other term depending on the time of day. Similarly: Example Carnap: Rumber and Titisee: is the same lake, depending on the weather. Example Dr. Jekyll and Mr. Hyde. N.B.: they would not be seen as complementary temporal parts of an entire nameless person, but as an identical person with two names. Four Dimensionalism/Quine: for example, one can identify a battle with the physical object, which consists of the union of the corresponding time segments of all participants. Or one can make substance terms (mass terms) into singular terms, each naming a diffuse physical object. ((s) Example Putnam: Water: all H2O in the universe). V 184 Four Dimensionalism/Ontology/Quine: ((s) here still in the classical separation matter/space) the points are replaced by the point moments. For example, purely spatial squares, i.e. squares perpendicular to the time axis, are then identified only instantaneously and not over time. Probably there is still the above time-consuming square, but now oriented as a three-dimensional square parallelepiped of infinite length, parallel to the time axis of space time or someone's time axis. Vs: 1. inelegance of the double ontology of matter and space. 2. (more severe): invalidity of a theory of absolute position. Without it, an ontology of purely spatial or spatiotemporal manifolds seems inconsistent. V 185 Solution/Quine: we try to construct the manifolds somehow according to physical objects. Maybe with the help of numbers and measurements, a Point: is then a number triple of real numbers, a space-time point is a quadruple. Squares etc. are identified as classes of such triples or quadruples according to analytical geometry. Until then there is no talk of physical objects or physical space. Next step: Measurement/Measuring: Connection with objects by using pure numbers by measurement. For example, if you say that four villages are located so that they form the points of a square, you only say something about the relationships between the distances: that four of the six are equal and the other two are also equal. >Measurements/Quine. Manifoldness: with this we got rid of the ontology of manifolds, but we are now dealing with much more than physical objects: with numbers, pairs of numbers, triples, quadruples, and classes of such. Thus we have abstract objects. So we still have a double ontology. Abstract/Quine: but we would have needed the ontology of abstract objects for many purposes anyway: V 186 E.g. to talk about squares etc. Manifoldness/Quine: these were only single squares, circles, etc. Form: Forms would be classes of such. Thus objects of higher abstraction. |
Quine I W.V.O. Quine Word and Object, Cambridge/MA 1960 German Edition: Wort und Gegenstand Stuttgart 1980 Quine II W.V.O. Quine Theories and Things, Cambridge/MA 1986 German Edition: Theorien und Dinge Frankfurt 1985 Quine III W.V.O. Quine Methods of Logic, 4th edition Cambridge/MA 1982 German Edition: Grundzüge der Logik Frankfurt 1978 Quine V W.V.O. Quine The Roots of Reference, La Salle/Illinois 1974 German Edition: Die Wurzeln der Referenz Frankfurt 1989 Quine VI W.V.O. Quine Pursuit of Truth, Cambridge/MA 1992 German Edition: Unterwegs zur Wahrheit Paderborn 1995 Quine VII W.V.O. Quine From a logical point of view Cambridge, Mass. 1953 Quine VII (a) W. V. A. Quine On what there is In From a Logical Point of View, Cambridge, MA 1953 Quine VII (b) W. V. A. Quine Two dogmas of empiricism In From a Logical Point of View, Cambridge, MA 1953 Quine VII (c) W. V. A. Quine The problem of meaning in linguistics In From a Logical Point of View, Cambridge, MA 1953 Quine VII (d) W. V. A. Quine Identity, ostension and hypostasis In From a Logical Point of View, Cambridge, MA 1953 Quine VII (e) W. V. A. Quine New foundations for mathematical logic In From a Logical Point of View, Cambridge, MA 1953 Quine VII (f) W. V. A. Quine Logic and the reification of universals In From a Logical Point of View, Cambridge, MA 1953 Quine VII (g) W. V. A. Quine Notes on the theory of reference In From a Logical Point of View, Cambridge, MA 1953 Quine VII (h) W. V. A. Quine Reference and modality In From a Logical Point of View, Cambridge, MA 1953 Quine VII (i) W. V. A. Quine Meaning and existential inference In From a Logical Point of View, Cambridge, MA 1953 Quine VIII W.V.O. Quine Designation and Existence, in: The Journal of Philosophy 36 (1939) German Edition: Bezeichnung und Referenz In Zur Philosophie der idealen Sprache, J. Sinnreich (Hg) München 1982 Quine IX W.V.O. Quine Set Theory and its Logic, Cambridge/MA 1963 German Edition: Mengenlehre und ihre Logik Wiesbaden 1967 Quine X W.V.O. Quine The Philosophy of Logic, Cambridge/MA 1970, 1986 German Edition: Philosophie der Logik Bamberg 2005 Quine XII W.V.O. Quine Ontological Relativity and Other Essays, New York 1969 German Edition: Ontologische Relativität Frankfurt 2003 Quine XIII Willard Van Orman Quine Quiddities Cambridge/London 1987 |
| Intensional Objects | Boer | I XIV Direct objects/direct object/propositional attitudes/Boer: it is controversial whether the relation to direct thought objects can be analyzed as propositional attitudes. E.g. "search": here it is certainly the case, e.g. "worship": seems to contradict this analysis. Fulfillment conditions/EB/propositional attitudes/Individuation/Boer: N.B.: The conditions of fulfillment do not seem to be sufficient to individuate a propositional attitude. On the other hand: Thought content/GI: seems to be sufficient for the individuation of a propositional attitude. Truth conditions: (and hence also the fulfillment conditions) can be the same for two beliefs, while the subject is not sure whether it is the same object. E.g. woodchucks/groundhogs. Abstract objects/propositional attitudes/Boer: In order to believe that patience is a virtue, one must think of patience. Definition reference/terminology/Boer: Thinking of: be a mental analogue to speaker reference. Speaker reference/some authors: thesis: never exists in isolation, but is only partial aspect of a speech act (utterance). --- I XV Mental reference: should then be only a partial aspect of thinking-of-something. Probably, there is also predication. Definition mental reference/Boer: be in a state of thought with a content of thought which defines a fulfillment condition of which the object is a constituent. Problem: non-existent objects. Thought object/Tradition/Boer: Thought objects are often understood in the tradition as the thought content of a propositional attitude with all involved objects: BoerVs: confusion of thinking-that with thinking-about. --- I XV Thought content/GI/Boer: must be carefully distinguished from any objects that it might contain. Definition object of thought/object/GO/Boer: "object of the propositional attitudes ψ" is clearly only that/these item/s to which a subject refers to by the power of ψ. (s) So not the propositional attitudes themselves! Individuation/identification/Boer: should be identified by a that-sentence (in a canonical attribution of ψ). That-sentence/Boer: is the content (thought content). Content/Thought content/Boer: is the that-Satz. Thinking about/Boer: what you think of something is the object itself. |
Boer I Steven E. Boer Thought-Contents: On the Ontology of Belief and the Semantics of Belief Attribution (Philosophical Studies Series) New York 2010 Boer II Steven E. Boer Knowing Who Cambridge 1986 |
| Introduction | Field | I 158 Introduction/Abstract Objects/Abstraction/Crispin Wright: Thesis: volumes as well as directions and numbers are to be introduced by abstraction. >Abstraction. I 157 Field: E.g. simple abstraction: is suitable for saying that our speech of directions is related to parallelism. Cf. >Definitions/Frege. But this does not quite correspond appropriately for numbers as related to non-numerical speech (and "non-quantification"). >Numbers, >Ontology, >Mathematical entities, >Abstract objects, >Platonism. --- II 166 Introduction/Field/(s): the use of expressions must follow according to the rules of their introduction. >Language use, cf. >Use theory, >Word meaning. |
Field I H. Field Realism, Mathematics and Modality Oxford New York 1989 Field II H. Field Truth and the Absence of Fact Oxford New York 2001 Field III H. Field Science without numbers Princeton New Jersey 1980 Field IV Hartry Field "Realism and Relativism", The Journal of Philosophy, 76 (1982), pp. 553-67 In Theories of Truth, Paul Horwich Aldershot 1994 |
| Lambda Calculus | Prior | I 45 Lamda-operator/abstraction operator/Prior: the lamda-operator is not equivalent with abstract nouns. It does not refer to properties, for it cannot replace the name variable. - ((s) Adjunction of characteristics.) No problem: "something φ-s or ψ-s" but not "the property of φ-ing-or-ψ-ing" as an abstract entity. >Abstractness, >Abstract objects, >Properties. Solution: "A v C "(either A-ing or C-ing" - is not an abstract noun, but acomplex verb that forms a sentence. The lamda-operator is necessary if one wants to formulate laws on propositions. >Operators, >Lambda notation. |
Pri I A. Prior Objects of thought Oxford 1971 Pri II Arthur N. Prior Papers on Time and Tense 2nd Edition Oxford 2003 |
| Mathematics | Chihara | Field III 44 f Mathematics / Chihara: Thesis: numbers are only linguistic entities - not abstract entities. >Numbers, >Mathematical entities, >Abstract objects. FieldVsChihara: 1st then there may only be predicative predicates (i.e. no bound variables of a higher order than ^ x). >Predicativeness, >Levels/order, >Second Order Logic. 2nd Chihara must also take account of never expressed tokens 3rd Chihara does not show the use of extrinsic, causally irrelevant entities. >Causality, >Extrinsic, >Use, >Relevance, Cf. >Electron example. |
Field I H. Field Realism, Mathematics and Modality Oxford New York 1989 Field II H. Field Truth and the Absence of Fact Oxford New York 2001 Field III H. Field Science without numbers Princeton New Jersey 1980 Field IV Hartry Field "Realism and Relativism", The Journal of Philosophy, 76 (1982), pp. 553-67 In Theories of Truth, Paul Horwich Aldershot 1994 |
| Meaning | Stalnaker | I 204 Meaning/Stalnaker (like Putnam): meanings are not in the head. Reason: the reason that meanings are not in the head is because they are abstract objects. Abstract objects: abstract objects are associated with things, some of which are actually in the head - namely things that have meanings or content. ((s) e.g. phrases, signs, symbols). >Meanings are not in the head, >Objects, >Content, >Abstract objects, >Abstract concepts. |
Stalnaker I R. Stalnaker Ways a World may be Oxford New York 2003 |
| Motion | Langacker | Gärdenfors I 9 Motion/Image/Langacker/Gärdenfors: (Langacker, 1987(1), Reprint 1999 p. 311): how can motion be shown in a picture? In Langacker's example by two lines: a) for a figure that points at an obstacle - this obstacle is mapped three times. b) the three adjacent images of the obstacle are connected by a second line for the time sequence. I 10 If this image stands for "rise", it can be easily reinterpreted into a picture for "mountaineer" without changing anything in the image. This transformation can be seen as a change in the focus. >Representation, >Image, >Interpretation, >Unambiguity, >Objects, >Abstract objects. 1. R. W. Langacker (1987). Foundations of cognitive grammar (Vol I). Stanford, CA: Stanford Universtity Press. |
Langa I Ronald W. Langacker Foundations of Cognitive Grammar Stanford, CA 1999 Gä I P. Gärdenfors The Geometry of Meaning Cambridge 2014 |
| Necessity | Simons | I 269 Necessity of origin/organism/Kripke: (1972(1), 312ff, 1980(2), 110ff): thesis: an organism could not have descended from another cell of origin as it actually did (Simons pro). But the zygote is still no permanent essential part because it dies early. Phase-sortal/McGinn: e.g. "child" and "adult" are accordingly also zygotes. >Sortals. I 270 Solution/Simons: it is essential for the organism, that it follows from sexual reproduction and that it has its zygote as an initial spurious part. However, it is unclear whether the brain is an essential part (> Brain Transplant, see also Identity/Parfit, >Body/B. Williams). I 295 Necessary Existence/Simons: necessary existence is only possible with abstract objects: e.g. universals, numbers, etc. Problem: if something exists necessarily, everything else depends on it. >Existence. 1. Kripke, S. A. (1972). Naming and Necessity, in: Davidson/Harmann (eds.) (1972), 253-355 2. Kripke, S. A. (1980). Naming and Necessity. Oxford: Blackwell |
Simons I P. Simons Parts. A Study in Ontology Oxford New York 1987 |
| Numbers | Bigelow | I 352 Real Numbers/Bigelow/Pargetter: Thesis: Real numbers are universals of higher level. >Universals, >Real numbers, >Levels/order, >Description levels I 353 They are relations between relations (or between properties). They are precisely the relations of higher levels or proportions with which we had compared quantities (see above 2.5). >Relations. Proportions/Bigelow/Pargetter: should be identified with real numbers. Real numbers/Bigelow/Pargetter: are then themselves physical! Like other proportions and relations. They are instantiated by physical quantities such as length. >Proportions. Instantiation/Bigelow/Pargetter: Quantities such as length, mass, speed are in turn instantiated by individuals such as photons, electrons, macroscopic objects. >Instantiation. Instantiation/Bigelow/Pargetter: being instantiated makes a causal difference. They are then abstract as universals, but not abstract in the sense that they would be causally inactive. >Abstraction, >Abstractness. Abstraction/Bigelow/Pargetter: is only a process of drawing attention to one or the other universal that are instantiated around us. But this does not create a new thing. I 354 Numbers/Bigelow/Pargetter: there is a strong tendency to assume that they are objects that instantiate relations and properties, but are not themselves properties or relations. They seem to be "abstract objects". >Numbers/Frege. Bigelow/Pargetter: pro: they can be that without ceasing to be universals. Numbers/Frege/Bigelow/Pargetter: the theory we are discussing here is about relations of relations. This probably also applies to relations between properties. For example: length comparisons etc. >Properties, >Measurements. Properties/Bigelow/Pargetter: if we want to avoid them, we can also compare the endpoints instead of the lengths of two objects. Relation/Bigelow/Pargetter: we can generally come from properties to relations by saying that there is a relation between objects by virtue of a shared property (e.g. length). For example "smaller than" etc. that is a derived relation. >Definitions/Frege. Derived relation/Bigelow/Pargetter: will then exist between the properties that generate these relations. Frege/Bigelow/Pargetter: his theory is now based on relations between relations. For example, parent relation and grandparent relation. (Lit. Quine 1941(1), 1961(2)). >Relations/Frege. I 355 Parents/Grandparents/Bigelow/Pargetter: the relations are different, but closely related, if two things are connected by the grandparent relation, the same two things will be connected by a chain involving two instances of the parent relation. If a is grandparent of b, there is a c so that a is a parent of c and c is a parent of b. Notation (see above 2.6): Rn: n-fold relation: e.g. (s) Grandparents-R = (parents-R)². X Rn y Means that we get from x to y through n applications of the relation R x R x1 x1 R x2 xn-1 R y. Grandparents/formal/spelling/Bigelow/Pargetter: if x is grandparent of y then x is parent² of y. Ancestor/Ancestor Relation/Bigelow/Pargetter: is just a generalization of it. Descent/predecessors/predecessor relation/ancestor/nominalism/Bigelow/Pargetter: the predecessor relation or ancestor relation was one of the biggest problems for nominalism. Problem: you have to have a realistic attitude towards relations, there must be relations here. Frege/Whitehead/Bigelow/Pargetter: get much more out of the parent relation than one could have predicted. I 356 Def grandparents/Frege/Quine/Bigelow/Pargetter: x GE y iff x E² y Def great-grandparents: x UGE y iff x E³ y etc. N.b.: because grandparent relation and great-grandparent relation are connected in different ways with the same basic relation (parents), there is now automatically a relation between these: If x UGE² y then x GE³ y. In general: given are two relations R and S, we can have a relation between them, by virtue of the x Rn y iff x Sm y. Ratio/Proportion/logical form/Bigelow/Pargetter: these relations of relations are called ratios or proportions. For example, in the above case, R to S is m:n. Negative ratios/Bigelow/Pargetter: we obtain by changing the variables x and y: x Rn y iff y Sm x. For example, grandchild-relation: has the ratio -2:1 ((s) inverse relation of the grandparents-relation) x grandchild y iff y E² x. Recursive rule/relationship/ratio/Bigelow/Pargetter: if R and S have a proportion (ratio) with respect to another relation Q: If there's a relationship between R and Q,... I 357 ...and one between S and Q, then there is a derived relation between R and S. Wiener: (1912)(3) varies the approach of Whitehead: when The ratio of R to Q is n:1 If the ratio of S to Q is m:1 Then we conclude the ratio of R to S is n:m. N.b.: this allows us to set up the ratio n:m between R and S, even if it is not possible to iterate R or S. For example, your relation to Eva and your mother's relation to Eva. The ratio of these two relations will then be n:(n+1) N.b.: We cannot simply get such relationships through iteration! For example, because no one stands in relation to them as you stand to Eve (you do not have so many successors). Solution/Wiener/Bigelow/Pargetter: no iteration of the relation to Eva, but iteration of the basic unit: here the parent relation. Rational numbers/Bigelow/Pargetter: in order to receive them in their full complexity, we must assume that the given relation has the correct patterns of instances. Problem: the parent relation may not have enough instances to generate an infinite number of rational numbers. ((s) Parent relation: is linear). Ratio/ratios/proportions/rational numbers/solution/Bigelow/Pargetter: set theory. >Sets, >Set theory. 1. Quine, W.V.O. (1941). Whitehead and the rise of modern logic. In: The philosophy of Alfred North Whitehead (ed. P.A. Schilpp). pp.125-63. La Salle, Ill. Open Court. 2. Quine, W.V.O. (1961). From a logical point of view. Logico-philosophical essays 2d ed. New York, Harper & Row. 3. Wiener, N. (1912). A simplification of the logic of relations. Proceedings of the Cambridge Philosophical Society 17 (1912-14), pp.387-90. |
Big I J. Bigelow, R. Pargetter Science and Necessity Cambridge 1990 |
| Numbers | Quine | I 219 Not all abstract objects are properties: numbers, classes, functions, geometric shapes, ideas, possibilities - give up or re-trace abstract objects - can be distinguished by the faithful use of "-ness" from concrete objects. II 26 Numbers: quantification is objectification, numeric name - diagonals: are irrational, scope: is transcendental. Measure: measuring scale: is a multidigit general term, puts physical objects in relation to pure numbers - counting: measuring a class. >Measuring/Quine. II 28 Numbers/Ontology: Numbers are merely a "facon de parler". - Higher classes needed to replace numbers - otherwise there would only be physical objects. IX 54 Numbers/Frege/Quine: like predecessors (ancestor): Definition Predecessor/Frege: the common elements of all classes for which the initial condition was fulfilled: "y ε z" and the seclusion condition: which resulted in "a" "z 0 ε z]}. - Problem: the successor relation could also lead to things that are not numbers. Numbers/Quine: we will mainly use them as a measure of multiplicities (that is how Frege had defined them). - a has x elements"- the scheme goes back to Frege: a has 0 elements ↔ a = Λ. - s has S°x elements ↔ Ey(y ε a n _{y} has x elements. IX 59 Numbers/Zermelo: (1908)(1) takes Λ as 0, then {x} as S°x for each x. (i.e. "{x}" always one more than x! - {x} successor of x! - As numbers we then receive Λ, {Λ}, {{Λ}}.. etc. IX 59ff Numbers/Von Neumann (1923)(2) regards every natural number as the class of the previous numbers: 0 becomes Λ again, - but successor S°x does not become {x}, but x U {x}. (Combined with) - 1: as in Zermelo: equal {Λ} - but 2: {0,1} or {∧,{∧}}. - 3: {0,1,2} or {Λ,{Λ},{Λ,{Λ,{Λ}}}. For von Neuman this says that a has x elements, that a ~ x. (number, equipotent) - that’s just the "a ~ {y: y < x}" from chapter 11, because for von Neumann is x = {y: y ‹ x}. Decimal numbers/dimidial numbers/decimal system/Quine: Example en gros: comes from "large quantities" = 1 dozen times 1 dozen. Score: = 20. Decimal system: Example 365 = 3 x 10² + 6 x 101 + 5 x 100. 1. Zermelo, E. (1908). Untersuchungen über die Grundlagen der Mengenlehre I. Mathematische Annalen, 65, 261-281. http://dx.doi.org/10.1007/BF01449999 2. Neumann, John von. (1923) Zur Einführung der transfiniten Zahlen; in: Acta Scientiarum Mathematicarum (Szeged); Band: 1; Nummer: 4; Seite(n): 199-208; XIII 41 Exponent/high numbers/high zero/high 0: why is n0 = 1 and not 0? Because we want that n m + n is always nm x n. Example m = 0: then n1 is = n0, or n = n0 x n; therefore n0 must be = 1. Decimal system: the positions correspond to a built-in abacus. Comma/Decimal Point: was inspired by negative exponents: Example 3.65 = 3 x 100 + 6 10-1 + 5 x 10-2. Counting/Division: had little to do with each other before this breakthrough. Because division happened on the basis of division by 2, while at the same time already in the decimal system was counted. Real numbers: some are finite, e.g. ½ = 0.5. Decimal Numbers: their correspondence with real numbers is not perfect: each finite decimal number is equivalent to an infinite: Example 5 to .4999... Solution: the correspondence can simply be made perfect by forgetting the ".5" and sticking to the ",4.999". Infinite/infinite extension/decimal number/Quine: Example a six-digit decimal number like 4.237251 is the fraction (ratio) 4,237,251 1 million Infinite decimal number: is then approximated as a limit value by the series of fractions, which of ever longer fractions, is represented by sections of this decimal number. Limit value: can be here again a fraction Example .333..., or .1428428... or irrational e.g. in the case of 3,14159 ((s) N.B.: here for the first time a number before the decimal point, because the concrete number is π). XIII 42 Infinite decimal numbers/Quine: we must not regard them as expressions! This is because real numbers that exceed any means of expression are ((s) temporarily) written as infinite decimal numbers. ((s) So one (necessarily finitely written decimal number) can correspond to several real numbers). Decimal system/Quine: each number >= 2 could function instead of the 10 as basis of a number system. The larger the base, the more compact the notation of the multiplication table. Dual System/binary/"dimidial"/binary numbers/binary system/Quine: from "0" and "1", i.e. numbers are divided by halves (partes dimidiae): Example 365 = 28 + 22 + 25 + 23 + 22 + 20. N.B.: Law: every positive integer is a sum of distinct multiples of 2. This is only possible with 2 as a base, no other number! I.e. at 365 the 10² does not occur once, but three times. Decimal Comma/binary: in binary notation: the places on the right are then negative powers of 2. Example ,0001 is a 16th. Real numbers/binary notation: nice consequence: if we consider the series of real numbers between 0 and 1 (without the 0), we have a 1:1 correspondence between these real numbers and the infinite classes of positive integers. Solution: each binary represented real number is identified with a binary extension which is infinite in the sense that there is no last "1". XIII 43 Integers: the corresponding class of integers is then that of the integers that count the places where the "1" occurs. For example, suppose the binary representation of the real number in question begins with "001011001": the corresponding class of integers will then begin with 3,5,6 and 9. Because "1" occurs at the third, fifth, sixth and ninth digit of the binary expansion. N.B.: the class thus determined is therefore infinite! Because there is no last occurrence of "1" in the binary expansion. And vice versa: Real numbers: every infinite class of positive integers defines a real number by specifying all places where "1" occurs instead of "0". |
Quine I W.V.O. Quine Word and Object, Cambridge/MA 1960 German Edition: Wort und Gegenstand Stuttgart 1980 Quine II W.V.O. Quine Theories and Things, Cambridge/MA 1986 German Edition: Theorien und Dinge Frankfurt 1985 Quine III W.V.O. Quine Methods of Logic, 4th edition Cambridge/MA 1982 German Edition: Grundzüge der Logik Frankfurt 1978 Quine V W.V.O. Quine The Roots of Reference, La Salle/Illinois 1974 German Edition: Die Wurzeln der Referenz Frankfurt 1989 Quine VI W.V.O. Quine Pursuit of Truth, Cambridge/MA 1992 German Edition: Unterwegs zur Wahrheit Paderborn 1995 Quine VII W.V.O. Quine From a logical point of view Cambridge, Mass. 1953 Quine VII (a) W. V. A. Quine On what there is In From a Logical Point of View, Cambridge, MA 1953 Quine VII (b) W. V. A. Quine Two dogmas of empiricism In From a Logical Point of View, Cambridge, MA 1953 Quine VII (c) W. V. A. Quine The problem of meaning in linguistics In From a Logical Point of View, Cambridge, MA 1953 Quine VII (d) W. V. A. Quine Identity, ostension and hypostasis In From a Logical Point of View, Cambridge, MA 1953 Quine VII (e) W. V. A. Quine New foundations for mathematical logic In From a Logical Point of View, Cambridge, MA 1953 Quine VII (f) W. V. A. Quine Logic and the reification of universals In From a Logical Point of View, Cambridge, MA 1953 Quine VII (g) W. V. A. Quine Notes on the theory of reference In From a Logical Point of View, Cambridge, MA 1953 Quine VII (h) W. V. A. Quine Reference and modality In From a Logical Point of View, Cambridge, MA 1953 Quine VII (i) W. V. A. Quine Meaning and existential inference In From a Logical Point of View, Cambridge, MA 1953 Quine VIII W.V.O. Quine Designation and Existence, in: The Journal of Philosophy 36 (1939) German Edition: Bezeichnung und Referenz In Zur Philosophie der idealen Sprache, J. Sinnreich (Hg) München 1982 Quine IX W.V.O. Quine Set Theory and its Logic, Cambridge/MA 1963 German Edition: Mengenlehre und ihre Logik Wiesbaden 1967 Quine X W.V.O. Quine The Philosophy of Logic, Cambridge/MA 1970, 1986 German Edition: Philosophie der Logik Bamberg 2005 Quine XII W.V.O. Quine Ontological Relativity and Other Essays, New York 1969 German Edition: Ontologische Relativität Frankfurt 2003 Quine XIII Willard Van Orman Quine Quiddities Cambridge/London 1987 |
| Numerals | Thiel | I 131 Abstraction/Mathematics/Frege/Thiel: Abstraction is a purely logical process, an operating with statements whose logical character is revealed by the change from the structure of the complicated initial statement to the structure of the new statement. >Abstraction, >Structures. Frege was the first to understand this. Statements not only about numbers, but also about quantities, functions, concepts, state of affairs, meaning and truth value of a statement, about structures. I 133 Numbers/Numerals/Number Names/Names/Mathematics/Thiel: The philosophical point of the transition from general statements about numerals to arithmetical statements lies in the fact that, although we have introduced speech about numerals in addition to speech about numbers, we have introduced speech about numbers as a way of speaking, as a facon de parler, the possibility of which does not depend on there being abstract objects beyond the concrete numerals, which we call "numbers". >Numbers, >Mathematical entities. I 134 We also had no reason to regard the numerals as "names" of numbers, so that about 4, IV, and |||| would denote the same number Four, as probably assumed in the traditional philosophy of numbers. |
T I Chr. Thiel Philosophie und Mathematik Darmstadt 1995 |
| Object | Quine | I 102 Goodman: "Rabbitness": is a discontinuous space-time segment, which consists of rabbits. --- I 372f Objects of propositional attitude eliminated: "Thomas believes (Cicero has): no longer the form" Fab" a = Thomas, b = () - but: "Fa" where "F" is a complex expression - no longer "believes" term, but operator. I 402 Existence: does not arise from dichotomy "single thing" - "universal" - it does not matter whether they do exist. "Equator", "North Pole" - linking with stimuli is weak argument for primacy of physical objects, but makes terms accessible for all positions. >Existence/Quine. I 412 Object: name which is denoted by singular terms, accepts it as values - (but the singular term is eliminated!) - E.g. "glimmer", but not "glimmeriness". I 438 Ideal objects are not permitted - geometric objects are permitted (no identity without localization). I 435 Relativity: additional dimension: space-time: point moments are absolutely different, independent of relative movement of the viewpoint. II 30 Object/Quine: space-time piece can also be distributed or scattered. (Nominalism, Goodman). II 23 Physical object is deceptive - better space-time pieces - "space" and "places as such" untenable, otherwise there would be absolute standstill and absolute movement - 4-digit coordinates suffice - ontology of pure set theory - no more physical object. II 156 ff Object (physical)/Quine: arbitrarily scattered and arbitrarily singled out - pocket contents, single coin at various points in time, combination with the Eiffel Tower, space-time points, anything - are not so strongly body-oriented - identification like from one possible world to another: without content as long as no instructions are given - value of a variable. VI 32 Object/Ontology/Quine: bodies constitute themselves as ideal nodes in the centers of overlapping observation sentences - problem: observation sentences are not permanent - therefore the objectification (reification) is always already a theory. VI 34 Question: what should be considered real objectification and not just a theoretically useful one (like classes). VI 35 Abstract objects: it is pointless to speak of permanent stimulus phases - solution: pronouns and bound variables - Vs singular term: are often not referring - there must be unspecifiable irrational numbers - Solution: bound variable instead of singular term. VI 38f Objectification/Reification/Quine: for the first time in predicative connection of observation sentences - instead of their mere conjunction - "This is a blue pebble": calls for embedding pebble into the blue. VI 41 Abstract objects/Modal/Putnam/Parsons: modal operators can save abstract objects - QuineVsModal logic: instead quantification (postulation of objects) - so we can take the slack out of the truth function. >Modal Logic/Quine. VII (d) 69 Object/Quine: may be unconnected: E.g. USA Alaska. XII 36 Properties/Identity/Quine: Problem: (unlike objects) they are ultimately based on synonymy within a language - more language-specific identity. >Properties/Quine. V 39 Ultimately we do without rigorous individuation of properties and propositions. (different term scheme) - Frege dito: (Basic Laws): do not extend identity to terms. XII 68 Object/Theory/Quine: what is an object, ultimately, cannot be stated - only in terms of a theory - (ultimately overall theory, i.e. language use) - but wrong: to say that talk about things would only make sense within a wider range - that would correspond to the false thesis that no predicate applied to all things - there are universal predicates. >Mention, >use, >word, >object. |
Quine I W.V.O. Quine Word and Object, Cambridge/MA 1960 German Edition: Wort und Gegenstand Stuttgart 1980 Quine II W.V.O. Quine Theories and Things, Cambridge/MA 1986 German Edition: Theorien und Dinge Frankfurt 1985 Quine III W.V.O. Quine Methods of Logic, 4th edition Cambridge/MA 1982 German Edition: Grundzüge der Logik Frankfurt 1978 Quine V W.V.O. Quine The Roots of Reference, La Salle/Illinois 1974 German Edition: Die Wurzeln der Referenz Frankfurt 1989 Quine VI W.V.O. Quine Pursuit of Truth, Cambridge/MA 1992 German Edition: Unterwegs zur Wahrheit Paderborn 1995 Quine VII W.V.O. Quine From a logical point of view Cambridge, Mass. 1953 Quine VII (a) W. V. A. Quine On what there is In From a Logical Point of View, Cambridge, MA 1953 Quine VII (b) W. V. A. Quine Two dogmas of empiricism In From a Logical Point of View, Cambridge, MA 1953 Quine VII (c) W. V. A. Quine The problem of meaning in linguistics In From a Logical Point of View, Cambridge, MA 1953 Quine VII (d) W. V. A. Quine Identity, ostension and hypostasis In From a Logical Point of View, Cambridge, MA 1953 Quine VII (e) W. V. A. Quine New foundations for mathematical logic In From a Logical Point of View, Cambridge, MA 1953 Quine VII (f) W. V. A. Quine Logic and the reification of universals In From a Logical Point of View, Cambridge, MA 1953 Quine VII (g) W. V. A. Quine Notes on the theory of reference In From a Logical Point of View, Cambridge, MA 1953 Quine VII (h) W. V. A. Quine Reference and modality In From a Logical Point of View, Cambridge, MA 1953 Quine VII (i) W. V. A. Quine Meaning and existential inference In From a Logical Point of View, Cambridge, MA 1953 Quine VIII W.V.O. Quine Designation and Existence, in: The Journal of Philosophy 36 (1939) German Edition: Bezeichnung und Referenz In Zur Philosophie der idealen Sprache, J. Sinnreich (Hg) München 1982 Quine IX W.V.O. Quine Set Theory and its Logic, Cambridge/MA 1963 German Edition: Mengenlehre und ihre Logik Wiesbaden 1967 Quine X W.V.O. Quine The Philosophy of Logic, Cambridge/MA 1970, 1986 German Edition: Philosophie der Logik Bamberg 2005 Quine XII W.V.O. Quine Ontological Relativity and Other Essays, New York 1969 German Edition: Ontologische Relativität Frankfurt 2003 Quine XIII Willard Van Orman Quine Quiddities Cambridge/London 1987 |
| Ontological Commitment | Prior | I 43 Ontological commitment/Quine: quantification over non-nominal variables (higher quantification, over properties) nominalised them and thus forces us to believe in corresponding abstract objects. >Abstract objects, >Quantification over properties, cf. >Mentalism, >Objects of thought, >Objects of belief. |
Pri I A. Prior Objects of thought Oxford 1971 Pri II Arthur N. Prior Papers on Time and Tense 2nd Edition Oxford 2003 |
| Platonism | Field | I 8 Platonism/Field: his only argument is the applicability of mathematics. >Mathematics/Field, >Mathematical entities. I 14 FieldVsPlatonism: Platonism has to answer the fictionalist in his language - it cannot rely on it's "initial plausibility". I 152 Def Priority Thesis/PT/Crispin Wright: Thesis: the priority of the syntactic over the ontological categories. Platonism/Wright: that allows Frege to be a Platonist. >Numbers/Frege, >Gottlob Frege. Def Gödelian Platonism/Crispin Wright: in addition: the thesis that mathematical knowledge must be explained by a quasi-perceptual relation. FregeVsGödel. WrightVsGödel: we do not need that. I 153 Def weak Priority Thesis/PT: that each syntactic singular term also works automatically in a semantical way as a singular term. l 159 Equivalence/Platonism/Nominalism/Field: Question: In which sense is a Platonist statement (e.g. "direction 1 = direction 2") and a nominalistic statement equivalent (c1 is parallel to c2)? Problem: if there are no directions, the second cannot be a sequence of the first. >Nominalism. I 186 Def Moderate Platonism/mP/Field: the thesis that there are abstract objects like numbers. - Then there are probably also relations between numbers and objects. - Moderate Platonism: these relations are conventions, derived from physical relations. Def Heavy Duty Platonism/HDP/Field: takes relations between objects and numbers as a bare fact. l 189 Strong moderation condition/(Field (pro): it is possible to formulate physical laws without relation between objects and numbers. I 192 Heavy Duty Platonism/Field: assumes size relationships between objects and numbers. FieldVs: instead only between objects. --- II 332 Platonism/Mathematics/VsStructuralism/Field: isomorphic mathematical fields do not need to be indistinguishable. >Field theory. II 334 Quinish Platonism/Field: as a basic concept a certain concept of quantity, from which all other mathematical objects are constructed. So natural numbers and real numbers would actually be sets. III 31 Number/Points/Field: no Platonist will identify real numbers with points on a physical line. - That would be too arbitrary ( "What line?") - What should be zero point - What should be 1? III 90 Platonistic/Field: are terms such as e.g. gradient, Laplace Equation, etc. III 96 1st order Platonism/Field: accepts abstract entities, but no 2nd order logic - Problem: but he needs these (because of the power quantifiers). |
Field I H. Field Realism, Mathematics and Modality Oxford New York 1989 Field II H. Field Truth and the Absence of Fact Oxford New York 2001 Field III H. Field Science without numbers Princeton New Jersey 1980 Field IV Hartry Field "Realism and Relativism", The Journal of Philosophy, 76 (1982), pp. 553-67 In Theories of Truth, Paul Horwich Aldershot 1994 |
| Platonism | Prior | I 32 Platonism/Prior: eliminates parts of speech by multiplied entities. - Natural language is mostly anti-Platonic because abstract nouns are usually bound to their verbs. >Everyday language, >Ontology, >Existence, >Abstract objects, >Verbs, >Predication. |
Pri I A. Prior Objects of thought Oxford 1971 Pri II Arthur N. Prior Papers on Time and Tense 2nd Edition Oxford 2003 |
| Possible Worlds | Adams | Stalnaker I 32 Possible worlds/Robert Adams: if there are true propositions that speak of the existence of nonactual possible worlds, they must be able to be reduced to sentences in which only things from the actual world are mentioned which are not identical with non-actual possibilities. >Possible worlds, >Actuality, >Actual world, >Possibility, >Counterfactuals. StalnakerVsAdams: I do not see why this should be necessary. Possible worlds/Stalnaker: Two questions: 1. Are they really so obscure? I 33 2. Does the belief in possible worlds and the indexical analysis of actuality oblige us to extreme realism? Certainly not. >Centered worlds. World stories/world-story/Possible worlds/Robert Adams: Thesis: a world-story is a maximally consistent set of propositions. The concept of a possible world can be given in a contextual analysis in terms of world stories. Proposition/Truth/Adams/Stalnaker: a proposition is true in some or all possible worlds if it is an element of some or all of the world-stories. StalnakerVsAdams: in his approach, there are three undefined terms: Proposition, consistent, and contradictory. >Propositions, >Consistency, >Contradiction. Proposals/Adams/Stalnaker: proposals can be presented as language-independent, abstract objects. They have truth values. >Truth value, >Abstract objects. Consistency/Adams/Stalnaker: consistency is a property of sets of propositions. >Consistency. One can define them in terms of possible worlds in which all propositions are true. I 34 Two conditions for consistency: (W1) The set of all true propositions is consistent (W2) Each subset of a consistent set is consistent. Contradiction/Adams/Stalnaker: contradiction could be defined in terms of consistency: A and B are contradictory, iff. {A, B} is not consistent And for each consistent set of propositions Γ is either Γ U {A} or Γ U {B} consistent. The theory presupposes: (W3) Each proposition has a contradiction. Proposition/Adams/Stalnaker: this is a minimal theory of propositions. It does not impose any structure on propositions, except for what is needed for compatibility, implication, and equivalence. And to ensure that e.g. the right kind of implication is present. E.g. implication: Definition Implication/Proposition/Stalnaker: (here): A implies B iff. a set consisting of A and a contradiction of B is not consistent. (W1) and (W2) ensure that our implication has the right properties. Stalnaker I 36 Proposition/Possible World/Stalnaker: an analysis of propositions as worlds provides definitions of consistency, etc., in concepts of set-theoretical relations between sets of worlds. World Story Theory/Adams/Stalnaker: the theory of world stories is weaker because it leaves open questions that clarify the analysis of propositions as worlds. >Stronger/weaker, >Strength of theories. The following two theses are consequences of the possible-worlds-theory but not of the world-story theory: (W5) Seclusion condition: For any set of propositions G there is a proposition A such that G implies A and A implies every element of G. Stalnaker: i.e. that for any set of propositions there is a proposition which says that every proposition in the set is true. Proposition/Seclusion/Stalnaker: whatever propositions are, if there are any, there are also sets of them. And for any set of propositions, it is definitely true or false that all their elements are true. And of course this is a proposition. So I assume that the world-story theorist wants to add (W5) to his theory. (W6) Equivalent propositions are identical. Problem: the problems of (W6) are known. ((s)> hyperintensionalism/hyperintentionality: sentences that are true in the same worlds are indistinguishable, equivalence of "snow is white" to "grass is green", etc.). >Hyperintensionality, >Semantics of Possible Worlds. |
Stalnaker I R. Stalnaker Ways a World may be Oxford New York 2003 |
| Possible Worlds | Plantinga | Schwarz I 68 Def Possible worlds/Plantinga: Plantinga defines possible worlds as maximum possible facts ("magic ersatzism"). >Ersatz worlds. Schwarz I 69 Facts as abstract entities about whose structure not much can be said. >States of affairs, >Abstract objects. At any case, they are no real universes or constructions of real things. Existence/"existence"/Plantinga: existence is a fundamental property that cannot be further analyzed. Other facts do not exist, but could exist. >"there is", >Existence. Def maximum/state of aafairs/Plantinga: a fact is maximum if its existence implies either its existence or non-existence for any other fact. Cf. >Maximum, >Dependence, >Conceptual dependence, >Counterfactual dependence, >Logical dependence. Possible worlds/Plantinga: possible worlds are maximum possible facts. For example, that "in" a world donkeys can speak means that donkeys could speak if the facts had the property of existence. VsPlantinga: this connection between a primitive property of abstract entities and the existence of talking donkeys must be accepted as inexplicable. In particular, it has nothing to do with the internal structure or composition of the abstract entity: it contains neither a talking donkey nor a picture or model of a donkey, nor a sentence or sign that somehow represents talking donkeys. LewisVsPlantinga: 1. Why can't this abstract entity have that primitive quality even though there are no talking donkeys? Why this necessary relationship between distinct entities? Plantinga's facts make it impossible to reduce modal truths to truth about what things with what qualities exist. Plantinga thus presupposes modality in the characterization of worlds. ((Lewis 1986e(1),§3,4) 2. Plantingas states of affairs make it impossible to reduce modal truths to truth about what things with what properties exist. Plantinga thus already assumes modality in the characterization of worlds. 3. We also want to talk not only about worlds, but also about their inhabitants. Plantinga must accept Sherlock Holmes as an irreducible abstract entity. (Plantinga 1976(2),262, 272). >Fictions. This is a non-qualitative (haecceitistic) property that is necessarily instantiated by an object x exactly when x is Holmes. >Haecceitism. So if in modal realism we have countless merely possible things, then in Plantinga we have countless entities of merely possible things. >Modal realism, >Realism, >Possibilism, >Possibilia, cf. >Actualism. 1. David Lewis [1986e]: On the Plurality of Worlds. Malden (Mass.): Blackwell 2. Alvin Plantinga 1976]: “Actualism and Possible Worlds”. Theoria, 42: 139–160. In [Loux 1979] |
Plant I A. Plantinga The Nature of Necessity (Clarendon Library of Logic and Philosophy) Revised ed. Edition 1979 Schw I W. Schwarz David Lewis Bielefeld 2005 |
| Predicates | Danto | I 110 Predicates "good", "yellow": simple, indefinable (> axioms) - Horse: composed, therefore definable. >Definitions, >Definability, >Simplicity, >Basic concepts. In contrast: "Horse" is composite, definable. Cf. >Good/The Good. Strawson: Strawson devises an image of a world with two main components: people and things. The corresponding M-predicates and P-predicates. I 260 M-predicates: e.g. "weighs 150 pounds," P-predicates: e.g. »dreams of glory." Mere things are writable with M-predicates, however, is not alone describable with P-predicates, though, if there were really disembodied spirits, they could also be described quite well by this. A person, however, is described by both, by M-and P-predicates. >P.F. Strawson, >Individuals, >Individuation, >Description, >Abstract Objects. |
Danto I A. C. Danto Connections to the World - The Basic Concepts of Philosophy, New York 1989 German Edition: Wege zur Welt München 1999 Danto III Arthur C. Danto Nietzsche as Philosopher: An Original Study, New York 1965 German Edition: Nietzsche als Philosoph München 1998 Danto VII A. C. Danto The Philosophical Disenfranchisement of Art (Columbia Classics in Philosophy) New York 2005 |
| Proofs | Deutsch | I 211 Experiment/proof/tradition: A proof does not refer to the physical world. (DeutschVsTradition: this is wrong.) We can perform a proof in our head, or even when we are stuck in a reality simulator in which virtual reality false physics applies. >Simulation, >Reality, >Provability. I 212 Traditional idea: Certain abstract sizes are not only part of the reality, but even more real than the things of the physical world. >Mathematical entities, >Abstract objects, >Theoretical terms, >Reality. I 237f Proof/David Deutsch: A proof is a physical process. - In contrast to this: size and knowledge of this size. >Description levels, >Levels/order, >Knowledge. Theory: the aim of a theory: not certainty but explanation. Physics is totally understandable. >Physics, >Explanation. Mathematical intuition is incompatible with classical physics. >Quantum Theory. |
Deutsch I D. Deutsch Fabric of Reality, Harmondsworth 1997 German Edition: Die Physik der Welterkenntnis München 2000 |
| Properties | Quine | Rorty VI 151 Major Property/holism/Quine/Rorty: at best: "property, which is necessary for the use of a certain description" - but not: "property, which is necessary for the identity of an object with itself." Quine I 43 Features: independent existence is pointless. >Existence/Quine I 218 Mass Term/Quine: is archaic(> (> E. Cassirer, Philosophie der symbolischen Formen, Berlin 1923-1929))) - Properties: a) Is commonality decisive? b) Is it about cattered clumps? I 217 Features: are usually merely convenient abbreviations for long cross-references - Quine/Cassirer: features of archaic remains. I 219 Not all abstract objects are properties: numbers, classes, functions, geometric figures, ideas, possibilities - give up or trace back to abstract objects - one can faithfully distinguished concrete objects by use of "-ness". >Object/Quine I 322 Property abstraction (elimination) instead of "a = x(..x..)" - new: irreducible two-digit operator "0": "a0x(..x..)" - variables remain as the only ones - primacy of the pronoun. >Variables/Quine I 344/45 Properties/Quine: there are no necessary or contingent properties (VsModal Logic) - there are only more or less important properties. I 344 Properties/relations: meaning of timeless open sentences - is unidentifiable (How-propositions). I 361 Elimination of relations and properties in favor of classes of ordered pairs, open sentences, general terms - even scattered objects (in the case of color) (46). I 412 QuineVsProperties: fallacy of subtraction: to derive existence from "about" and "deals with" - "round" and "dog" are terms for physical objects - but no additional features. "Round" and "dog" are general terms for objects not singular terms for properties or classes. The same argument would be for classes instead of properties: general term symbolizes its extension as well as its intension. >General Term/Quine I 412 Properties: not every general term is necessarily about properties or classes - properties and classes are acceptable as values of variables. I 464 QuineVsRussell/Whitehead: theory of incomplete symbols: eliminated classes only in favor of properties. II 129f Properties: are hard to individuate - not to define like classes by the same elements - various properties can get to the same things. Properties: "Zettsky" (like Russell): properties are identical when they were members of the same classes - QuineVs - solution: property is identical if two sentences ↔ (follow seperately) - unsatisfactory, less analyticity and necessity-operator. Properties/Quine: identical when coextensive-classes: are not specified by elements, but by condition of containment (open sentence). Property is not the same as predicate - property: open sentences - propositions: completed sentences. Properties are not the same as classes: since no individuation principle for properties - solution "last classes" (do not belong to any other class, only have elements themselves) - like Russell: statement function only comes through their values - properties = last classes or properties = statement function. >Classes/Quine Properties as last classes are every element of the zero class, therefore all identical? - Vs: this identity definition only applies to theories that allow no objects who belong to no class (Unicorn). Properties/identity: (here) are interchangeability in all contexts - Prerequisite: exhaustion of a finite lexicon by interchangeability of atomic contexts - RyleVs: Category confusion. Properties: QuineVsCarnap/Russell: minimize grammatical categories, expand scope - if all can be attributed to "has", then all properties are extensional - rest could be listed by list. Properties: contexts with "has" unproblematic - "contained in" prohibited (less classes) - "is" leads to circular definition of properties - properties do not count. "Nap had all properties but one": is prohibited. - however: "all properties" allowed. II 144 f De re: E.g. spy should be an essential property (wrong) - no belief is de re (essential property). Modal Logic/Quine: the entire modal logic is context-dependent - what role does someone or something play? - Same level as essential properties. Necessity/Quine: the whole concept is only meaningful in context. Property Einstein/Quine: are preserved. - But not de re. >de re/Quine X 95 Properties/Quine: do not exist for lack of distinctness (only amounts) - "synonymy unclear" - open sentences that apply to the same objects never determine different amounts, but differnt properties could underlie. |
Quine I W.V.O. Quine Word and Object, Cambridge/MA 1960 German Edition: Wort und Gegenstand Stuttgart 1980 Quine II W.V.O. Quine Theories and Things, Cambridge/MA 1986 German Edition: Theorien und Dinge Frankfurt 1985 Quine III W.V.O. Quine Methods of Logic, 4th edition Cambridge/MA 1982 German Edition: Grundzüge der Logik Frankfurt 1978 Quine V W.V.O. Quine The Roots of Reference, La Salle/Illinois 1974 German Edition: Die Wurzeln der Referenz Frankfurt 1989 Quine VI W.V.O. Quine Pursuit of Truth, Cambridge/MA 1992 German Edition: Unterwegs zur Wahrheit Paderborn 1995 Quine VII W.V.O. Quine From a logical point of view Cambridge, Mass. 1953 Quine VII (a) W. V. A. Quine On what there is In From a Logical Point of View, Cambridge, MA 1953 Quine VII (b) W. V. A. Quine Two dogmas of empiricism In From a Logical Point of View, Cambridge, MA 1953 Quine VII (c) W. V. A. Quine The problem of meaning in linguistics In From a Logical Point of View, Cambridge, MA 1953 Quine VII (d) W. V. A. Quine Identity, ostension and hypostasis In From a Logical Point of View, Cambridge, MA 1953 Quine VII (e) W. V. A. Quine New foundations for mathematical logic In From a Logical Point of View, Cambridge, MA 1953 Quine VII (f) W. V. A. Quine Logic and the reification of universals In From a Logical Point of View, Cambridge, MA 1953 Quine VII (g) W. V. A. Quine Notes on the theory of reference In From a Logical Point of View, Cambridge, MA 1953 Quine VII (h) W. V. A. Quine Reference and modality In From a Logical Point of View, Cambridge, MA 1953 Quine VII (i) W. V. A. Quine Meaning and existential inference In From a Logical Point of View, Cambridge, MA 1953 Quine VIII W.V.O. Quine Designation and Existence, in: The Journal of Philosophy 36 (1939) German Edition: Bezeichnung und Referenz In Zur Philosophie der idealen Sprache, J. Sinnreich (Hg) München 1982 Quine IX W.V.O. Quine Set Theory and its Logic, Cambridge/MA 1963 German Edition: Mengenlehre und ihre Logik Wiesbaden 1967 Quine X W.V.O. Quine The Philosophy of Logic, Cambridge/MA 1970, 1986 German Edition: Philosophie der Logik Bamberg 2005 Quine XII W.V.O. Quine Ontological Relativity and Other Essays, New York 1969 German Edition: Ontologische Relativität Frankfurt 2003 Quine XIII Willard Van Orman Quine Quiddities Cambridge/London 1987 Rorty I Richard Rorty Philosophy and the Mirror of Nature, Princeton/NJ 1979 German Edition: Der Spiegel der Natur Frankfurt 1997 Rorty II Richard Rorty Philosophie & die Zukunft Frankfurt 2000 Rorty II (b) Richard Rorty "Habermas, Derrida and the Functions of Philosophy", in: R. Rorty, Truth and Progress. Philosophical Papers III, Cambridge/MA 1998 In Philosophie & die Zukunft, Frankfurt/M. 2000 Rorty II (c) Richard Rorty Analytic and Conversational Philosophy Conference fee "Philosophy and the other hgumanities", Stanford Humanities Center 1998 In Philosophie & die Zukunft, Frankfurt/M. 2000 Rorty II (d) Richard Rorty Justice as a Larger Loyalty, in: Ronald Bontekoe/Marietta Stepanians (eds.) Justice and Democracy. Cross-cultural Perspectives, University of Hawaii 1997 In Philosophie & die Zukunft, Frankfurt/M. 2000 Rorty II (e) Richard Rorty Spinoza, Pragmatismus und die Liebe zur Weisheit, Revised Spinoza Lecture April 1997, University of Amsterdam In Philosophie & die Zukunft, Frankfurt/M. 2000 Rorty II (f) Richard Rorty "Sein, das verstanden werden kann, ist Sprache", keynote lecture for Gadamer’ s 100th birthday, University of Heidelberg In Philosophie & die Zukunft, Frankfurt/M. 2000 Rorty II (g) Richard Rorty "Wild Orchids and Trotzky", in: Wild Orchids and Trotzky: Messages form American Universities ed. Mark Edmundson, New York 1993 In Philosophie & die Zukunft, Frankfurt/M. 2000 Rorty III Richard Rorty Contingency, Irony, and solidarity, Chambridge/MA 1989 German Edition: Kontingenz, Ironie und Solidarität Frankfurt 1992 Rorty IV (a) Richard Rorty "is Philosophy a Natural Kind?", in: R. Rorty, Objectivity, Relativism, and Truth. Philosophical Papers Vol. I, Cambridge/Ma 1991, pp. 46-62 In Eine Kultur ohne Zentrum, Stuttgart 1993 Rorty IV (b) Richard Rorty "Non-Reductive Physicalism" in: R. Rorty, Objectivity, Relativism, and Truth. Philosophical Papers Vol. I, Cambridge/Ma 1991, pp. 113-125 In Eine Kultur ohne Zentrum, Stuttgart 1993 Rorty IV (c) Richard Rorty "Heidegger, Kundera and Dickens" in: R. Rorty, Essays on Heidegger and Others. Philosophical Papers Vol. 2, Cambridge/MA 1991, pp. 66-82 In Eine Kultur ohne Zentrum, Stuttgart 1993 Rorty IV (d) Richard Rorty "Deconstruction and Circumvention" in: R. Rorty, Essays on Heidegger and Others. Philosophical Papers Vol. 2, Cambridge/MA 1991, pp. 85-106 In Eine Kultur ohne Zentrum, Stuttgart 1993 Rorty V (a) R. Rorty "Solidarity of Objectivity", Howison Lecture, University of California, Berkeley, January 1983 In Solidarität oder Objektivität?, Stuttgart 1998 Rorty V (b) Richard Rorty "Freud and Moral Reflection", Edith Weigert Lecture, Forum on Psychiatry and the Humanities, Washington School of Psychiatry, Oct. 19th 1984 In Solidarität oder Objektivität?, Stuttgart 1988 Rorty V (c) Richard Rorty The Priority of Democracy to Philosophy, in: John P. Reeder & Gene Outka (eds.), Prospects for a Common Morality. Princeton University Press. pp. 254-278 (1992) In Solidarität oder Objektivität?, Stuttgart 1988 Rorty VI Richard Rorty Truth and Progress, Cambridge/MA 1998 German Edition: Wahrheit und Fortschritt Frankfurt 2000 |
| Real Numbers | Dedekind | Thiel I 192 Definition Dedekind's cuts/real numbers/Dedekind(1): I find (...) the essence in the continuity in the reversal, namely in the following principle: if all points of the line disintegrate into two classes in such a way that each point of the first class is to the left of every point of the second class, so one and only one point exists, which brings this division of all points into two classes. ConstructivismVsDedekind: since the mathematical means used in this provision are not explicitly mentioned, the requirement of constructivist basic critics remains unfulfilled to regard an abstract entity as "given" when a concrete expression representing it is given, so that abstract objects can ultimately be traced back to corresponding properties of the expressions expressing it. >Constructivism, >Dedekind cuts. VsConstructivism: Representatives of the "classical" point of view reject this as "too narrow," because the explicit statement of the means of expression used to define the Dedekind's cuts limits the range of definable real numbers. "New" real figures can only be introduced by the extension of the means permitted at a certain stage and only to be justified. I 192/193 This applies if we abandon the mixing of the arithmetic and the geometrical point of view in the speech of the "number line" (also used in the explanation of the Dedekind method) in favor of a clear separation. To speak of the totality of "all" real numbers and also of the totality of "all" points on a line or straight line. Infinite/infinity/constructive: an infinite set is present if it can be enumerated by a generation process. Weaker sense: a set of principles must be known. Stronger meaning: The totality of the real numbers is not available. It is not a definite set. Classical analysis on real numbers presupposes a stronger view. Already in every statement about "all" real numbers, the totality is interpreted as being actual. Cf. >Intuitionism. 1. Dedekind, R. (1872). Stetigkeit und irrationale Zahlen. Nachdruck 1965: Braunschweig: Vieweg. |
T I Chr. Thiel Philosophie und Mathematik Darmstadt 1995 |
| Realism | Stalnaker | I 41 Modal Realism/Stalnaker: thesis: there are possible worlds. VsModal Realism: objection: it is not possible, to know any metaphysical facts about modal realism (whether a possible world exist). >Metaphysics. Thesis: there is no strategy to counter this objection that would be analog to VsBenacerraf. Benacerraf: there is a tension between the need for a plausible representation of mathematical statements and the representation of our respective knowledge about their truth. >Paul Benacerraf. I 42 Platonism: the platonism gives plausible semantics but no epistemology. Reference/Benacerraf: thesis: a reference needs a causal link. LewisVsBenacerraf: this does not apply to abstract objects such as numbers and so on. >Mathematical entities. I 47 Conclusion: we cannot distinguish platonism in terms of mathematical objects from that in terms of possible worlds. >Platonism. I 49 Modal Realism/VsMR/possible world/Stalnaker: problem: the modal realism cannot say on the one hand that possible worlds are things of the same kind as the real world (contingent physical objects) and on the other hand, that possible worlds are things of which we know in the same way as of numbers, etc. Modal Realism: modal realism will insist on the fact that even the reference to ordinary objects (actual or merely possible) needs no causal connection. |
Stalnaker I R. Stalnaker Ways a World may be Oxford New York 2003 |
| Simplicity | Quine | VII (a) 17 Simplicity/Quine: is itself ambiguous and unclear. It is a double or multiple standard depending on the terminology. Immediate experiences can be presented more easily in a physical conceptual scheme. VII (d) 70 Simplicity/Ontology/Quine: we simplify our discussion, in that we make the objects as big and as few as possible - e.g. river instead of temporal river states. >Ontology. XI 135 Ontology/Existence/Theory/Quine/Lauener: decisive are simplicity considerations, but not so much about the set of objects, but rather about theory. Good chances as items are those that already play a role in language learning. While the objects, which correspond to the theoretical terms of modern physics, could fall victim to a later revision. XII 33 Abstract/abstract object/existence/coherence/Quine: Existence assertions about abstract objects can only be judged by their coherence or by simplicity considerations. Example: to avoid paradoxes with classes. >Paradoxes, >Classes. |
Quine I W.V.O. Quine Word and Object, Cambridge/MA 1960 German Edition: Wort und Gegenstand Stuttgart 1980 Quine II W.V.O. Quine Theories and Things, Cambridge/MA 1986 German Edition: Theorien und Dinge Frankfurt 1985 Quine III W.V.O. Quine Methods of Logic, 4th edition Cambridge/MA 1982 German Edition: Grundzüge der Logik Frankfurt 1978 Quine V W.V.O. Quine The Roots of Reference, La Salle/Illinois 1974 German Edition: Die Wurzeln der Referenz Frankfurt 1989 Quine VI W.V.O. Quine Pursuit of Truth, Cambridge/MA 1992 German Edition: Unterwegs zur Wahrheit Paderborn 1995 Quine VII W.V.O. Quine From a logical point of view Cambridge, Mass. 1953 Quine VII (a) W. V. A. Quine On what there is In From a Logical Point of View, Cambridge, MA 1953 Quine VII (b) W. V. A. Quine Two dogmas of empiricism In From a Logical Point of View, Cambridge, MA 1953 Quine VII (c) W. V. A. Quine The problem of meaning in linguistics In From a Logical Point of View, Cambridge, MA 1953 Quine VII (d) W. V. A. Quine Identity, ostension and hypostasis In From a Logical Point of View, Cambridge, MA 1953 Quine VII (e) W. V. A. Quine New foundations for mathematical logic In From a Logical Point of View, Cambridge, MA 1953 Quine VII (f) W. V. A. Quine Logic and the reification of universals In From a Logical Point of View, Cambridge, MA 1953 Quine VII (g) W. V. A. Quine Notes on the theory of reference In From a Logical Point of View, Cambridge, MA 1953 Quine VII (h) W. V. A. Quine Reference and modality In From a Logical Point of View, Cambridge, MA 1953 Quine VII (i) W. V. A. Quine Meaning and existential inference In From a Logical Point of View, Cambridge, MA 1953 Quine VIII W.V.O. Quine Designation and Existence, in: The Journal of Philosophy 36 (1939) German Edition: Bezeichnung und Referenz In Zur Philosophie der idealen Sprache, J. Sinnreich (Hg) München 1982 Quine IX W.V.O. Quine Set Theory and its Logic, Cambridge/MA 1963 German Edition: Mengenlehre und ihre Logik Wiesbaden 1967 Quine X W.V.O. Quine The Philosophy of Logic, Cambridge/MA 1970, 1986 German Edition: Philosophie der Logik Bamberg 2005 Quine XII W.V.O. Quine Ontological Relativity and Other Essays, New York 1969 German Edition: Ontologische Relativität Frankfurt 2003 Quine XIII Willard Van Orman Quine Quiddities Cambridge/London 1987 |
| Singular Terms | Strawson | Substitutions/Strawson/(s): of singular terms: reversible of predicates: not reversible. ((s) For this asymmetry cf. >Singular terms/Brandom, >Predicates/Brandom.) I 198 Singular Term/QuineVsGeach/QuineVsFrege/QuineVsRamsey: a singular term can occur at the places of quantifiable variables, general expressions not. Singular term: is quantifiable, General Term: is not quantifiable. >Singular terms/Quine, >General terms/Quine. StrawsonVsQuine: this distinction ist not so important. I 198 Singular Term/Quine: abstract singular terms: E.g. "piety", "wisdom": names of abstract objects - no general terms. Names of concrete objects: e.g. "Earth". On the other hand general term: E.g "philosopher". >Abstraction/Quine. StrawsonVsQuine: no good explanation: we would not like to say that this would be true of many things. Solution/Quine: in reality we make the distinction between singular term and predicates. General term/Quine: the location which is taken by them, has no own status. Decisive: predicates cannot be quantified. >Quantification/Quine, >Schematic letters/Quine. I 203 "a philosopher"/Quine: no singular term. --- IV 63 QuineVs singular Term: eliminable. StrawsonVsQuine. |
Strawson I Peter F. Strawson Individuals: An Essay in Descriptive Metaphysics. London 1959 German Edition: Einzelding und logisches Subjekt Stuttgart 1972 Strawson II Peter F. Strawson "Truth", Proceedings of the Aristotelian Society, Suppl. Vol XXIV, 1950 - dt. P. F. Strawson, "Wahrheit", In Wahrheitstheorien, Gunnar Skirbekk Frankfurt/M. 1977 Strawson III Peter F. Strawson "On Understanding the Structure of One’s Language" In Truth and Meaning, G. Evans/J. McDowell Oxford 1976 Strawson IV Peter F. Strawson Analysis and Metaphysics. An Introduction to Philosophy, Oxford 1992 German Edition: Analyse und Metaphysik München 1994 Strawson V P.F. Strawson The Bounds of Sense: An Essay on Kant’s Critique of Pure Reason. London 1966 German Edition: Die Grenzen des Sinns Frankfurt 1981 Strawson VI Peter F Strawson Grammar and Philosophy in: Proceedings of the Aristotelian Society, Vol 70, 1969/70 pp. 1-20 In Linguistik und Philosophie, G. Grewendorf/G. Meggle Frankfurt/M. 1974/1995 Strawson VII Peter F Strawson "On Referring", in: Mind 59 (1950) In Eigennamen, Ursula Wolf Frankfurt/M. 1993 |
| States of Affairs | Tugendhat | I 141 State of Affairs/TugendhatVsHusserl/TugendhatVsObject Theory (= Thesis State of Affairs = object) not every sentence corresponds to state of affairs - false "theory of objects". >Attributes, >Abstract objects, >Abstractness. I 161 State of Affairs- not composed like an object - State of Affairs: like attributes: "abstract objects". I 164f State of Affairs/fact/Husserl/Tugendhat: imperceptible - composition of state of affairs different than of objects - linguistically composed (thinking) - (VsObject theory; >object theory). Def "categorical Synthesis"/Husserl: task: of the real composition of an object of components is a special, not real composition which would be constitutive for the state of affairs to distinguish. >Edmund Husserl, >Experience/Husserl. I 167 TugendhatVsHusserl, Vs categorical synthesis: Heidelberg castle is castle and red - even "red" represents object. >Predicates, >Predication, >Properties. I 176 TugendhatVsObject theory: it fails at the question, how the meaning of the whole sentence is given by the meanings of the phrases. There are no combinations of objects in the sentence. >Compositionality. I 280ff State of Affairs/fact/Tugendhat: state of affairs as that what the sentence says: this does not work, due to potential lie. Identification of the states of affairs requires understanding the usage rules. - The same sentence can stand for different situations, and vice versa (like Austin). The states of affairs in deictic expressions: Classifications principle of incidents - the state of affairs also lacks the contention mode, which is part of the assertion of "p" - VsObject theory. >Assertions, >Meaning. |
Tu I E. Tugendhat Vorlesungen zur Einführung in die Sprachanalytische Philosophie Frankfurt 1976 Tu II E. Tugendhat Philosophische Aufsätze Frankfurt 1992 |
| Terminology | Boer | I XI TI/Boer: Thesis: Believe as a 2-digit relation to a special kind of property ("thought content"). Spelling: German writing (fracture). --- I XI Stock: Relation theory: Boer pro: belief as a relation to thought content (certain property) STI/Boer: Semantics for belief attribution, which considers substitutional opacity in belief reports as a genuine semantic feature. Thesis: these two together solve many known puzzles. Object-dependent senses/Frege/Boer: these are to be defended here (Boer pro Frege). --- I 6 Participating/Participation/Boer: a thing that does not participate in the world is either e.g. a non-existent thing or a non-space-time individual, a non-existent or false proposition, a non-existent or non-persisting state, a non-existent or unexplained property or relation, or a non-existent or non-occurring event. So more precisely: (D2) R is a participation-independent relation = it is possible for an existing thing to have a relation R to a thing that does not participate in the world. E.g. mental reference: would then be intentional simply because one can think of abstract as well as of concrete individuals (also unexemplified properties, etc.). Relation/Participation/Boer: although a tolerant actualist who acknowledges the existence of relations at all, accepts that some relations are participation-independent, the relation of such relations is not limited to existing things. (D2) only requires that an existing thing has such a relation to a non-participating thing. Relation R: from the fact that someone has R to something does not follow that this something participates in the world ((s) one can think of abstract objects). Non-existence: if there are non-existent things, there is nothing in (D2) that forbids one to have a participation-independent relation like mental reference to them. ((s One can think of something non-existent) That at most will be rejected by a very strict nominalism. --- I 12 Notation/Boer: N: be an entity of a given type (E: spelling in the book: black letter) EN: be the essential property of things of this type N iff --- I 13 i) EN can be exemplified (i.e., that there may be such a thing) ii) necessary: a thing exemplifies EN iff it is identical to N. Haecceitas: of N. the property to be N. This would be trivially the essence of N. --- I 13 Definition normal/terminology/Boer: if we wanted to name things for which it is possible that they exist/that they are actual. Definition abstract/terminology/Boer: be a thing for which it is not possible that it exists/is actual. Fiction/fictitious/Boer: a) in the first sense: (mere Possibilia): normal, if non-existent. b) as essentially fictional: abstract. |
Boer I Steven E. Boer Thought-Contents: On the Ontology of Belief and the Semantics of Belief Attribution (Philosophical Studies Series) New York 2010 Boer II Steven E. Boer Knowing Who Cambridge 1986 |
| Terminology | Field | I 18 Explanation/Field: a) Def intrinsic explanation/Field: does not contain causally irrelevant entities (namely: mathematical entities) b) Def extrinsic explanation/Field: also contains causally irrelevant entities. For example, the attribution of finite sentences for the behavior of animals. II 159 Linguistic view/Field: assumes no meanings as mind-independent entities, but assigns words of a speaker to words of an interpreter. - The relations are based on different characteristics. - I.e. to inferences that contain this word - that's what I call "meaning-characteristic". - E.g. II 226 Definiteness/determined/definition/definite/vagueness/precision/(s)"definite"/Field: we cannot define "definitively true" ("determined", "determinately") by truth - we must conceive it as a reinforcement. Solution : Operator: "Definiteness-Operator"/dft-operator: this one is independent of truth-theoretical terms - but there is no physical information which decides. II 201 Signification/Terminology/Field: here: Relations are signed - objects are denoted. - predicates signify their extension. II 211 Def Basis/Field: here: E.g. the basis for predicates whose extension depends on other predicates: - E.g. "rabbit", "dinosaur": depend on the basis: predicate "identical". - The functional dependency of the other predicates from the basic predicate "identical" allows the partial extensions of the predicate to be correlated with the partial extension of the others. Def dependent: is a predicate, if it has a basis. - Now we can define relevance. Def Relevance/Structure/Language/Gavagai/Field: a structure partially agrees with the semantics of O, iff a) each independent term t of L denoted or signified partially m(t) b) each dependent term t of L denoted or signified m(t) with b(t) relative to the correlation of m(b(t)). ((s) in b) not partial). Still unsolved: how do we know which terms have a basis and which that is? - Problem: the words should also have a physical sense. II 287 Def "weak true"/truew/Field: "It is true that p" as equivalent to "p". Def "strongly true"/trues/Field: "It is true that p" as equivalent to "There is a certain fact that p". Det-Operator/D/Field: "It is a certain fact that". - This cannot be explained with "true". III 12 Def Principle C/Conservativity/Field: Let A be a nominalistic formulated claim. N: a corpus of such nominalistic assertions. - S a mathematical theory. A* is then not a consequence of N* + S if A is not itself a consequence of N* alone. ((s) "A* only if A", that is, if A * is not determined yet, that any nominalistic formulation is sufficient). III 60 Nominalization/Field: ... this suggests that laws about T (i.e., T obeying a particular differential equation) can be reformulated as laws over the relation between f and y. That is, ultimately the predicates Scal-Cong, St-Bet, Simul, S-Cong and perhaps Scal-Less. II 230 Def strongly true: is a sentence with a vague predicate then iff it is true relative to each of the candidates of an extension. Then it is a borderline case without definition-operator (dft-operator): "Jones is bald in some, but not in all extensions". I 152 Def Priority Thesis/PT/Crispin Wright: Thesis: the priority of the syntactic over the ontological categories. Platonism/Wright: that allows Frege to be a Platonist. I 153 Def weak Priority Thesis/PT: that each syntactic singular term also works automatically in a semantical way as a singular term. I 186 Def Moderate Platonism/mP/Field: the thesis that there are abstract objects like numbers. - Then there are probably also relations between numbers and objects. - Moderate Platonism: these relations are conventions, derived from physical relations. Def Heavy Duty Platonism/HDP/Field: takes relations between objects and numbers as a bare fact. l 189 Strong moderation condition/(Field (pro): it is possible to formulate physical laws without relation between objects and numbers. I 192 Heavy Duty Platonism/Field: assumes size relationships between objects and numbers. - FieldVs: instead only between objects. III 96 1st order Platonism/Field: accepts abstract entities, but no 2nd order logic. Problem: anyway he needs these (because of the power quantifiers). II 228 Def Weakly true/vagueness/truth/truth-predicate/Field: to be able to say general things about borderline cases. Not only that somebody represents a certain limiting case. Not weakly true/deflationism: e.g. "Either bald or not-bald is true". Then the Truth-predicate itself inherits the vagueness. It is not definitely true whether or not. Def Strongly true/Field: assuming, Jones is a limiting case: then neither "bald" nor its negation (strongly) plus classical logic: then the disjunction "bald or not bald" should be true even in strong interpretation. Law of the excluded middle: if we give it up: a) weakly true: then the disjunction is not true b) strongly true: then the disjunction is without truth value. Strongly true: is less vague, does not inherit the vagueness. II 230 Def strongly true: is a sentence with a vague predicate then iff it is true relative to each of the candidates of an extension. - Then the limiting case without definite-operator: "Jones is bald in some extensions but not in all". |
Field I H. Field Realism, Mathematics and Modality Oxford New York 1989 Field II H. Field Truth and the Absence of Fact Oxford New York 2001 Field III H. Field Science without numbers Princeton New Jersey 1980 Field IV Hartry Field "Realism and Relativism", The Journal of Philosophy, 76 (1982), pp. 553-67 In Theories of Truth, Paul Horwich Aldershot 1994 |
| Universals | Meixner | Ad I 42 Universals/(s): can apply gradually. Facts: cannot apply gradually. Facts are mutually exclusive, universals are not. >States of affairs, >Facts. I 85 Exemplification: Ability to be at different places at the same time - applies to universals. >Exemplification. I 85 Non-predicative universals/Meixner: non-predicative: no property, no function: type objects/TO: objects! The letter that "looks like A", the logo of the Railroad Company, the Lion, the High C, the book Anna Karenina (not the figure), homo sapiens, carmine red (not crimson). Type objects are differently perceived mentally than predicative universals: differences between individual specimens do not stand out. - This does not apply to the corresponding properties. >Type/Token, >Properties, >Predicates, >Predication. I 86/87 Universals problem: narrow sense: Question whether some entities are abstract - not identical with the question of whether or not some entities are properties, relations, types or not? >Abstractness, >Abstract objects, >Relations. I 149 Def Normal Universal/NU/Meixner: is a finite-digit predicative universal. The results of a complete saturation of NU with entities are facts. >States of affairs, >Facts. Conversely: the results of the extraction of these entities from these facts are those normal universals - just like we differentiate facts as gross we also differentiate normal universals as gross. Coarse: e.g. the property of being an equiangular triangle is identical to the property of being a equilateral triangle. >Coarse-grained/fine-grained. Normal universals are identical if they have the same number of digits and can be saturated by the same entities. I 153 Universal Name: means the property. >Names, >Names of expressions, >Levels/order, >Meaning. |
Mei I U. Meixner Einführung in die Ontologie Darmstadt 2004 |
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| Disputed term/author/ism | Author Vs Author |
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Reference |
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| Adams, R. | Stalnaker Vs Adams, R. | I 32 Possible Worlds/Poss.W./Robert Adams: if there are true sentences in which the existence of non-actual possible worlds is mentioned, it must be possible to reduce them to sentences in which only things from the actual world are mentioned that are not identical with non-actual possibilities. StalnakerVsAdams: I do not see why that should be necessary. World Stories/Possible Worlds/Robert Adams: Thesis: a world story is a maximum consistent quantity of propositions. The concept of a possible world can be given in a contextual analysis in terms of world stories. Proposition/Truth/Adams/Stalnaker: a proposition is true in some or all possible worlds if it is an element of some or all of the world stories. StalnakerVsAdams: in his approach, there are three undefined terms: Proposition, consistent and contradictory. Propositions/Adams/Stalnaker: can be language-independent, abstract objects. They have truth values. Consistency/Adams/Stalnaker: is a property of sets of propositions. They can be defined in terms of possible worlds in which all propositions are true. I 34 Two conditions for consistency: (W1) The set of all true propositions is consistent (W2) Every subset of a consistent set is consistent. Contradiction/Adams/Stalnaker: could be defined in terms of consistency: A and B are contradictory, iff {A,B} is not consistent and for each set of consistent propositions Γ either Γ U {A} or Γ U {B} is consistent. The theory assumes: (W3) Every proposition has a contradiction. Proposition/Adams/Stalnaker: this is a minimal theory of propositions. It does not impose any structure on the propositions except what is needed for the sake of compatibility, implication and equivalence. And to ensure, for example, that the right kind of implication exists. E.g. implication: Def Implication/Proposition/Stalnaker: (here): A implies B iff a set consisting of A and a contradiction of B is not consistent. (W1) and (W2) ensure that our implication has the right properties. This minimal theory is suited to support the view of Adams: Possibility/Robert Adams: Thesis: possibility is rather holistic than atomistic, in the sense that what is possible only exists as part of a possible completely determinate world. ((s) there are no isolated possibilities). Stalnaker: so far, our considerations do not imply that every consistent set of propositions is a subset of a world story. For the following (W4) does not follow from them, but must be added as an addition: (W4) Every consistent set is a subset of a maximum consistent set. I 36 Proposition/Possible World/Stalnaker: in contrast, an analysis of propositions as possible worlds provides definitions of consistency and so on in terms of set-theoretic relations between sets of possible worlds. World Stories Theory/Possible World/Adams/Stalnaker: the theory of the world stories is weaker, because it leaves open questions that are clarified by the analysis of propositions as possible worlds. The following two theses are consequences of the possible world theory, but not of the world stories theory: (W5) Closure Condition: For each set of propositions Γ there is a proposition A such that G implies A and A implies every element of G. Stalnaker: i.e. for each set of propositions, there is a proposition that says that every proposition in the set is true. |
Stalnaker I R. Stalnaker Ways a World may be Oxford New York 2003 |
| Dummett, M. | Wright Vs Dummett, M. | Rorty VI 45 WrightVsDummett/Rorty: it is necessary to say more about the pragmatic use of the terms "realism", "representation" and "agreement" than Dummett. For example, judgments may coincidentally converge for historical reasons. Representation (and thus realism) must be explained by means of a concept that is neither merely logical nor merely sociological. (Rorty pro). Wright I 225/226 Abstract/"pure abstract objects"/Dummett: (Frege: "logical objects"): Dummett: nothing more than reflections of certain linguistic expressions, analogous to the proper names of objects, whose meaning, however, cannot be represented as consisting in our ability to identify objects as their carriers. Wright: could be read as Nominalism. (i.e. that there are no abstract objects). But this is not Dummett's view. Dummett does not deny that there are singular terms that ostensibly refer to abstract objects, but in fact have reference. I 227 They even play a semantic role! Example the "largest prime number": is an empty singular term, but the mere meaning ensures that it plays a semantic role! Dummett: seems to think here that there is no question whether Platonism or Nominalism provides the better approach after the question is decided whether abstract objects exist. (> Numbers). Abstract/Moral/Ethics/Wright: this fits well with our attitude to the discourse of morality: the matter of moral realism is not really exhausted in the question of whether the moral discourse is truthful or not. If the truth ability is affirmed, there are still a number of questions relevant to realism. I 228 Identification/WrightVsDummett: it is simply unclear what the "identification" of an object should mean, if the recognition of the truth of an identity statement, which contains a term for the object, is not sufficient! It is also not controversial that we use abstract singular terms in a reasonable way. Wright: there is no linguistically unmediated cognitive contact with abstract objects. (> Abstractness). Abstract objects can only affect us in this way! Frege (Platonist) quite rightly claims that doubts about the reality of the reference to abstract objects do not contain any reasonable sense. (Wright: this is minimalism regarding reference). Realism/Wright: but then there still remain the considerations that force us to assign concrete things an independent role in an independent world. I 229 Def Minimalism/Wright: is a better name for Dummett's >"Anti-Realism" or >"Nominalism". |
WrightCr I Crispin Wright Truth and Objectivity, Cambridge 1992 German Edition: Wahrheit und Objektivität Frankfurt 2001 WrightCr II Crispin Wright "Language-Mastery and Sorites Paradox" In Truth and Meaning, G. Evans/J. McDowell Oxford 1976 WrightGH I Georg Henrik von Wright Explanation and Understanding, New York 1971 German Edition: Erklären und Verstehen Hamburg 2008 Rorty I Richard Rorty Philosophy and the Mirror of Nature, Princeton/NJ 1979 German Edition: Der Spiegel der Natur Frankfurt 1997 Rorty II Richard Rorty Philosophie & die Zukunft Frankfurt 2000 Rorty II (b) Richard Rorty "Habermas, Derrida and the Functions of Philosophy", in: R. Rorty, Truth and Progress. Philosophical Papers III, Cambridge/MA 1998 In Philosophie & die Zukunft, Frankfurt/M. 2000 Rorty II (c) Richard Rorty Analytic and Conversational Philosophy Conference fee "Philosophy and the other hgumanities", Stanford Humanities Center 1998 In Philosophie & die Zukunft, Frankfurt/M. 2000 Rorty II (d) Richard Rorty Justice as a Larger Loyalty, in: Ronald Bontekoe/Marietta Stepanians (eds.) Justice and Democracy. Cross-cultural Perspectives, University of Hawaii 1997 In Philosophie & die Zukunft, Frankfurt/M. 2000 Rorty II (e) Richard Rorty Spinoza, Pragmatismus und die Liebe zur Weisheit, Revised Spinoza Lecture April 1997, University of Amsterdam In Philosophie & die Zukunft, Frankfurt/M. 2000 Rorty II (f) Richard Rorty "Sein, das verstanden werden kann, ist Sprache", keynote lecture for Gadamer’ s 100th birthday, University of Heidelberg In Philosophie & die Zukunft, Frankfurt/M. 2000 Rorty II (g) Richard Rorty "Wild Orchids and Trotzky", in: Wild Orchids and Trotzky: Messages form American Universities ed. Mark Edmundson, New York 1993 In Philosophie & die Zukunft, Frankfurt/M. 2000 Rorty III Richard Rorty Contingency, Irony, and solidarity, Chambridge/MA 1989 German Edition: Kontingenz, Ironie und Solidarität Frankfurt 1992 Rorty IV (a) Richard Rorty "is Philosophy a Natural Kind?", in: R. Rorty, Objectivity, Relativism, and Truth. Philosophical Papers Vol. I, Cambridge/Ma 1991, pp. 46-62 In Eine Kultur ohne Zentrum, Stuttgart 1993 Rorty IV (b) Richard Rorty "Non-Reductive Physicalism" in: R. Rorty, Objectivity, Relativism, and Truth. Philosophical Papers Vol. I, Cambridge/Ma 1991, pp. 113-125 In Eine Kultur ohne Zentrum, Stuttgart 1993 Rorty IV (c) Richard Rorty "Heidegger, Kundera and Dickens" in: R. Rorty, Essays on Heidegger and Others. Philosophical Papers Vol. 2, Cambridge/MA 1991, pp. 66-82 In Eine Kultur ohne Zentrum, Stuttgart 1993 Rorty IV (d) Richard Rorty "Deconstruction and Circumvention" in: R. Rorty, Essays on Heidegger and Others. Philosophical Papers Vol. 2, Cambridge/MA 1991, pp. 85-106 In Eine Kultur ohne Zentrum, Stuttgart 1993 Rorty V (a) R. Rorty "Solidarity of Objectivity", Howison Lecture, University of California, Berkeley, January 1983 In Solidarität oder Objektivität?, Stuttgart 1998 Rorty V (b) Richard Rorty "Freud and Moral Reflection", Edith Weigert Lecture, Forum on Psychiatry and the Humanities, Washington School of Psychiatry, Oct. 19th 1984 In Solidarität oder Objektivität?, Stuttgart 1988 Rorty V (c) Richard Rorty The Priority of Democracy to Philosophy, in: John P. Reeder & Gene Outka (eds.), Prospects for a Common Morality. Princeton University Press. pp. 254-278 (1992) In Solidarität oder Objektivität?, Stuttgart 1988 Rorty VI Richard Rorty Truth and Progress, Cambridge/MA 1998 German Edition: Wahrheit und Fortschritt Frankfurt 2000 |
| Empiricism | Quine Vs Empiricism | IV 397 British Empiricism: based on ideas in the mind. These are of course not intersubjectively observable. That means the foundation is private, not public. QuineVsBritish Empiricism: VsMentalistic approach: in the Quine's eyes not consistent. One should stick to what openly observed is true to anyone. Language is nothing private, but something social. IV 398 The language: a social skill that is acquired through the observation of the social use. The externalization of empiricism leads to behavioral access to meaning. (Behaviorism). IV 402 QuineVsBritish Empiricism: Is based on the assumption of ideas (derived from Locke). Uncritical mentalism. Too simple picture of the experiential reference of languages and theories. VI 11 "Linguistic Turn"/Quine: that was good, but not good enough: the distinction between observation sentences and theoretical propositions was only made derivatively, no theoretical terms should appear. Therefore Reichenbach used "bridge sentences" to connect the two sentence types. (VsBritish Empiricism). Observation/Quine: we do not start with objects (we eliminate them), but with sentences! This allows us to define the observation sentence, without bothering about whether it is theory-free or not! We also no longer need to decide which objects the words should designate! (Without reification). Instead of objects stimulus meaning: the willingness to agree to a sentence. VI 11/12 Singular Term/Singular Terms/Ontology/Existence/Quine: if we had assumed terms instead of sentences, we would have skipped the whole issue of objectification and always conceded object-relation from the hollow gut. Meaning Theory/M.Th./Quine: must be empirical. QuineVsLogical Empiricism: neither the analytical truths nor the observation base resists the skeptical attack. V 189 Theory/Ontology/Quine: how should a scientific theory look like at best? We want as many as possible and good predictions. Guiding principles: simplicity and conservatism. V 190 Both are in a dialectical relation! (To use an expression by my students). An strong oversimplification can justify a relatively large deviation. Between the two, we need a compromise. Conservatism/Quine: among other things, caused by our lack of imagination. But also prudence when it comes to hypotheses. Simplicity/Conservativeness: both are already at work in language learning. Language Learning/Quine: occurs in leaps and bounds. Is always based on similarities and analogies. V 191 Short steps are conservative. They are guided by relative empiricism. Def Relative Empiricism/Quine: do not stray further from sense data than necessary. Quine pro: That keeps theory changes low. QuineVsRadical Empiricism: we gave it up when we gave up hope to reduce talk of objects to talk of sense data. Important argument: that requires us to stick with the substitutional quantification over abstract objects. This speaks to the nominalistic mind. It manifests itself in relative empiricism, for both are the same. Nominalism: must not overestimate the ontological harmlessness of the variables of sQ. In general, we can say the values of variables determine the whole ontology if we only have object variables, truth functions and predicates. Stalnaker I 3 QuineVsEmpiricism/Two Dogmas/Stalnaker: when it comes to accepting or not accepting a whole language, along with a theory that is formulated in this language, then it is not certain that there is a base for a distinction which are the language rules (rules), and what are the judgments about the world. There is no theory-neutral way to separate factual questions from semantic ones. |
Quine I W.V.O. Quine Word and Object, Cambridge/MA 1960 German Edition: Wort und Gegenstand Stuttgart 1980 Quine II W.V.O. Quine Theories and Things, Cambridge/MA 1986 German Edition: Theorien und Dinge Frankfurt 1985 Quine III W.V.O. Quine Methods of Logic, 4th edition Cambridge/MA 1982 German Edition: Grundzüge der Logik Frankfurt 1978 Quine V W.V.O. Quine The Roots of Reference, La Salle/Illinois 1974 German Edition: Die Wurzeln der Referenz Frankfurt 1989 Quine VI W.V.O. Quine Pursuit of Truth, Cambridge/MA 1992 German Edition: Unterwegs zur Wahrheit Paderborn 1995 Quine VII W.V.O. Quine From a logical point of view Cambridge, Mass. 1953 Quine VII (a) W. V. A. Quine On what there is In From a Logical Point of View, Cambridge, MA 1953 Quine VII (b) W. V. A. Quine Two dogmas of empiricism In From a Logical Point of View, Cambridge, MA 1953 Quine VII (c) W. V. A. Quine The problem of meaning in linguistics In From a Logical Point of View, Cambridge, MA 1953 Quine VII (d) W. V. A. Quine Identity, ostension and hypostasis In From a Logical Point of View, Cambridge, MA 1953 Quine VII (e) W. V. A. Quine New foundations for mathematical logic In From a Logical Point of View, Cambridge, MA 1953 Quine VII (f) W. V. A. Quine Logic and the reification of universals In From a Logical Point of View, Cambridge, MA 1953 Quine VII (g) W. V. A. Quine Notes on the theory of reference In From a Logical Point of View, Cambridge, MA 1953 Quine VII (h) W. V. A. Quine Reference and modality In From a Logical Point of View, Cambridge, MA 1953 Quine VII (i) W. V. A. Quine Meaning and existential inference In From a Logical Point of View, Cambridge, MA 1953 Quine VIII W.V.O. Quine Designation and Existence, in: The Journal of Philosophy 36 (1939) German Edition: Bezeichnung und Referenz In Zur Philosophie der idealen Sprache, J. Sinnreich (Hg) München 1982 Quine IX W.V.O. Quine Set Theory and its Logic, Cambridge/MA 1963 German Edition: Mengenlehre und ihre Logik Wiesbaden 1967 Quine X W.V.O. Quine The Philosophy of Logic, Cambridge/MA 1970, 1986 German Edition: Philosophie der Logik Bamberg 2005 Quine XII W.V.O. Quine Ontological Relativity and Other Essays, New York 1969 German Edition: Ontologische Relativität Frankfurt 2003 Quine XIII Willard Van Orman Quine Quiddities Cambridge/London 1987 Stalnaker I R. Stalnaker Ways a World may be Oxford New York 2003 |
| Field, H. | Verschiedene Vs Field, H. | Field I 51 Infinity/Physics/Essay 4: even without "part of" relation we do not really need the finity operator for physics. VsField: many have accused me of needing every extension of 1st level logic. But this is not the case. I 52 I rather assume that the nominalization program has not yet been advanced far enough to be able to say what the best logical basis is. Ultimately, we are going to choose only a few natural means that go beyond the 1st level logic, preferably those that the Platonist would also need. But we can only experience this by trial and error. I 73 Indispensability Argument/Logic/VsField: if mE may be dispensable in science, they are not in logic! And we need logic in science. Logical Sequence Relation/Consequence/Field: is normally defined in terms of model theory: (Models are mE, semantic: a model is true or not true.) Even if one formulates them in a proven theoretical way ("there is a derivation", syntactically, or provable in a system) one needs mE or abstract objects: arbitrary sign sequences of symbol tokens and their arbitrary sequences. I 77 VsField: some have objected that only if we accept a Tarski Theory of truth do we need mE in mathematics. FieldVsVs: this led to the misunderstanding that without Tarskian truth mathematics would have no epistemic problems. Mathematics/Field: indeed implies mE itself, (only, we do not always need mathematics) without the help of the concept of truth, e.g. that there are prime numbers > 1000. I 138 Logic of Part-of-Relation/Field: has no complete evidence procedure. VsField: how can subsequent relations be useful then? Field: sure, the means by which we can know that something follows from something else are codifiable in an evidentiary procedure, and that seems to imply that no appeal to anything stronger than a proof can be of practical use. FieldVsVs: but you do not need to take any epistemic approach to more than a countable part of it. I 182 Field Theory/FT/Relationalism/Substantivalism/Some AuthorsVsField: justify the relevance of field theories for the dispute between S/R just the other way round: for them, FT make it easy to justify a relationalist view: (Putnam, 1981, Malament 1982): they postulate as a field with a single huge (because of the infinity of physical forces) and a corresponding part of it for each region. Variant: the field does not exist in all places! But all points in the field are not zero. FieldVsPutnam: I do not think you can do without regions. Field II 351 Indeterminacy/Undecidability/Set Theory/Number Theory/Field: Thesis: not only in the set theory but also in the number theory many undecidable sets do not have a certain truth value. Many VsField: 1. truth and reference are basically disquotational. Disquotational View/Field: is sometimes seen as eliminating indeterminacy for our present language. FieldVsVs: that is not the case :>Chapter 10 showed that. VsField: Even if there is indeterminacy in our current language also for disquotationalism, the arguments for it are less convincing from this perspective. For example, the question of the power of the continuum ((s)) is undecidable for us, but the answer could (from an objectivist point of view (FieldVs)) have a certain truth value. Uncertainty/Set Theory/Number Theory/Field: Recently some well-known philosophers have produced arguments for the impossibility of any kind of uncertainty in set theory and number theory that have nothing to do with disquotationalism: two variants: 1. Assuming that set theory and number theory are in full logic of the 2nd level (i.e. 2nd level logic, which is understood model theoretically, with the requirement that any legitimate interpretation) Def "full" in the sense that the 2nd level quantifiers go over all subsets of the 1st level quantifier range. 2. Let us assume that number theory and the set theory are formulated in a variant of the full logic of the 2nd level, which we could call "full schematic logic of level 1". II 354 Full schematic logic 1st Level/LavineVsField: denies that it is a partial theory of (non-schematic!) logic of the 2nd level. Field: we now better forget the 2nd level logic in favour of full schematic theories. We stay in the number theory to avoid complications. We assume that the certainty of the number theory is not in question, except for the use of full schemata. |
Field I H. Field Realism, Mathematics and Modality Oxford New York 1989 Field II H. Field Truth and the Absence of Fact Oxford New York 2001 Field III H. Field Science without numbers Princeton New Jersey 1980 Field IV Hartry Field "Realism and Relativism", The Journal of Philosophy, 76 (1982), pp. 553-67 In Theories of Truth, Paul Horwich Aldershot 1994 |
| Field, H. | Soames Vs Field, H. | I 467 Truth Theory/WT/Tarski/Soames: two statuses: a) as a mathematical theory with many rich results b) philosophically significant for the concept of truth. Truth Theory/Soames: there is controversy about what a truth theory should be; in general it should do one of the following three things: (i) give the meaning of the truth predicate for natural languages. (ii) replace these truth predicates reductionistically (iii) use a previously understood truth concept to explain meaning or for other metaphysical purposes. Proposition/Soames: for the following purposes you need propositions rather than sentences or utterances: Example (1) a. the proposition that the earth is moving is true. b. Church's theorem is true c. Everything he said is true. I 468 SoamesVsPropositions. Truth Predicate/Generalization/Quine/Soames: e.g. to characterize realism: (5) There is a doppelgänger of the sun in a distant region of space, but we will never find sufficient evidence that he exists. Soames: of course you can be a realist without believing (5). ((s) (5) is too special, it is only an example). Anti-Realism/Soames: what then distinguishes it from realism? One is tempted to say: (6) Either there is a doppelgänger of our sun.... or no doppelgänger.... and we will have no evidence at all.... I 470 SoamesVs: this leads to an infinite list that we should avoid. Solution: semantic rise: (7) There is at least one sentence S, so that S is true (in German) but we will never find (sufficient) evidence for S. I 472 Truth Definition/Field: consists of two parts: 1. "primitive denotation": e.g. (s) "Caesar" refers to Caesar. 2. the truth definition in terms of primitive denotation. The result is a sentence of the metalanguage: (8) For all sentences S of L, S is true iff T(S). FieldVsTarski/Soames: (Field: "Tarski's Truth Theory" (this journal, I XIX, 1972): this assumption (that truth, truth and reference are physically acceptable in Tarski) is wrong! Field: the proposed substitutions for the notions of primitive denotation are not physically acceptable reductions I 474 of our pre-theoretical concepts of reference and truth. Soames: this is only true if Field assumes that Tarski has reduced truth to primitive denotation. Truth-Def/Correctness/Tarski/Field/Soames: Field does not deny that the truth definition is extensionally correct. FieldVsTarski: but extensional correctness is not sufficient. "Cb" is a sentence and the semantic n facts about it are given in (9): (9) a. "b" refers (in L) to Boston b. "C" applies (in L) to cities (and cities only) c. "Cb" is true (in L) iff Boston is a city. (speaker dependent) Problem: you cannot just identify the facts from (10) with the facts from (9) now. Semantic Property/Field: expressions of a language have only force through the way they are used by speakers (usage). Problem: the facts from (9) would not have existed at all if the language behaviour (in the broadest sense) had been different! N.B.: the facts from (10) are not dependent on speakers. Therefore they are not semantic facts. Therefore Tarski cannot reduce them to physical facts. Truth Predicate/FieldVsTarski: it is both physicalistic and coextensive with "true in L", but it is still not a physicalistic truth concept. Problem: the inadequacy inherits the characterization of the truth from the pseudo reductions that constitute the "base clauses" ((s) recursive definitions?) ((s) among other things for and, or etc. base clauses). I 475 Solution/Field: we need to find real reductions for the concepts of primitive denotation or something like a model of the causal theory of reference. Field/Soames: these are again two stages: 1. Tarski's reduction from truth to primitive denotation ((s) as above) 2. an imagined reduction of the concepts of the reference of names and of the accuracy of predicates, similar to a causal theory. Language independence/Field/Soames: if the physical facts that determine the denotation in a language do so for all languages, then the denotation applies to all languages. If logical constants and syntax are kept constant, we get a truth concept that is language independent. Problem: 1. Reference to abstract objects ((s) for these there are no semantic facts). 2. Ontological relativity and undeterminedness of the reference. SoamesVsField: he even understated his criticism of Tarski (FieldVsTarski)! Tarski/Soames: because if Tarski did not reduce primitive denotation to physical facts, then he did not reduce truth to primitive denotation at all ((s) so he missed point 1). Example two languages L1 and L2 which are identical except: L1: here "R" applies to round things L2: here on red things. Truth conditional: are then different for some sentences in both languages: (11) a. "Re" is true in L1 iff the earth is round b. "Re" is true in L2 iff the earth is red. Tarski/Soames: in its truth definition, this difference will be traceable back to the base clauses of the two truth definitions for each language, because here the applications of the predicates are presented in a list. FieldVsTarski: its truth definition correctly reports that "R" applies to different things in the two languages, but it does not explain how the difference came about from the use of language by speakers. SoamesVsField/SoamesVsTarski: Field does not say that the same accusation can be made against VsTarski I 476 in relation to logical vocabulary and syntax in the recursive part of its definition. Example L1: could treat [(A v B)] as true if A or B is true, L2: ...if A and B are true. FieldVsTarski: then it is not sufficient for the characterization of truth to simply "communicate" that the truth conditions are different. It would have to be explained by the language behavior in the two different languages ((s) > speaker meaning). FieldVsTarski: because he says nothing about language behavior (speaker meaning in a community), he does not meet the demands of physicalism ((s) to explain physical facts of behavior). Soames: this means that Field's strategy of obtaining a real reduction of truth by supplementing Tarski with non-trivial definitions of primitive denotation cannot work. For according to Field, Tarski did not reduce truth to primitive denotation. He has reduced them at best to lists of semantic basic concepts: (13) the term of a name referring to an object The term of a predicate that applies to an object. The concept of a formula which is the application of an n digit predicate to an n tuple of terms ... I 477 Soames: but this requires a reformulation of each clause in Tarski's recursive definition. E.g. old: 14 a, new: 14.b: (14) a. if A = [~B] , then A is true in L (with respect to a sequence s) iff B is not true in L (with respect to s). b. If A is a negation of a formula B, then A is .... Soames: the resulting abstraction extends the generality of truth definition to classes of 1. Level languages: these languages differ arbitrarily in syntax, plus logical and non-logical vocabulary. SoamesVsField: Problem: this generality has its price. Old: the original definition simply stipulated that [~A) is a negation ((s) >symbol, definition). New: the new definition gives no indication which formulas fall into these categories. SoamesVsField: its physicist must now reduce each of the semantic terms. Logical Linkage/Constants/Logical Terms/Soames: we can either a) define about truth, or b) specify that certain symbols should be instances of these logical terms. SoamesVsField: neither of these two paths is open to him now! a) he cannot characterize negation as a symbol that is appended to a formula to form a new formula that is true if the original formula was false because that would be circular. b) he cannot simply take negation as a basic concept (primitive) and determine that [~s] is the negation of s. For then there would be no facts about speakers, ((s) Language behavior, physicalistic), that would explain the semantic properties of [~s]. Soames: there are alternatives, but none is convincing. Truth functional operator/Quine: (roots of the reference) are characterized as dispositions in a community for semantic ascent and descent. Problem/Quine: uncertainty between classical and intuitionist constructions of linkages are inevitable. SoamesVsField: Reduction from primitive denotation to physical facts is difficult enough. I 478 It becomes much more difficult for logical terms. SoamesVsField: this is because semantic facts on physical facts must supervene over speakers. ((s) >speaker meaning, language behavior). Problem: this limits adequate definitions to those that legitimize the use of semantic terms in contexts such as (15) and (16). ((s) (15) and (16) are fine, the later ones no longer). (15) If L speakers had behaved differently, "b" (in L) would not have referred to Boston and "C" to cities and .....((s) Counterfactual Conditionals). (16) The fact that L speakers behave the way they do explains why "b" (in L) refers to Boston, etc. ((s) Both times reference) Soames: FieldVsTarski is convinced that there is a way to decipher (15) and (16) that they become true when the semantic terms are replaced by physical ones and the initial clauses are constructed in such a way that they contain contingents to express physical possibilities. This is not the character of Tarski's truth definition. I 481 Primitive Reference/language independent/SoamesVsField: For example a name n refers to an object o in a language L iff FL(n) = o. FL: is a purely mathematical object: a set of pairs perhaps. I.e. it contains no undefined semantic terms. Truth Predicate/Truth/Theory/Soames: the resulting truth predicate is exactly what we need to metatheoretically study the nature, structure, and scope of a multiple number of theories. Truth Definition/Language/Soames: what the truth definition does not tell us is something about the speakers of the languages to which it is applied. According to this view, languages are abstract objects. ((s) All the time you have to distinguish between language independence and speaker independence). Language/primitive denotation/language independent/truth/SoamesVsField: according to this view languages are abstract objects, i.e. they can be understood in such a way that they essentially have their semantic properties ((s) not dependent on language behaviour or speakers, (speaker meaning), not physical. I.e. with other properties it would be another language). I.e. it could not have turned out that expressions of a language could have denoted something other than what they actually denote. Or that sentences of one language could have had other truth conditions. I 483 SoamesVsField: this too will hardly be able to avoid this division. Index Words/Ambiguity/Field: (p. 351ff) Solution: Contextually disambiguated statements are made unambiguous by the context. Semantic terms: should be applied to unambiguous entities. I.e. all clauses in a truth definition must be formulated so that they are applied to tokens. Example Negation/Field (21) A token of [~e] is true (with respect to a sequence) iff the token of e it includes is not true (with respect to that sequence). SoamesVsField: that does not work. Because Field cannot accept a truth definition in which any syntactic form is simply defined as a negation. ((s) Symbol, stipulates, then independent of physical facts). Soames: because this would not explain facts about speakers by virtue of whom negative constructions have the semantic properties they have. Semantic property(s): not negation itself, but that the negation of a certain expression is true or applies in a situation. Example "Caesar" refers to Caesar: Would be completely independent from circumstances, speakers, even if not from the language, the latter, however, actually only concerns the metalanguage. Solution/Soames: (22) A token of a formula A, which is a negation of a formula B, is true (with respect to a sequence) iff a designated token of B is not true (with respect to this sequence). "Designated"/(s): means here: explicitly provided with a truth value. |
Soames I Scott Soames "What is a Theory of Truth?", The Journal of Philosophy 81 (1984), pp. 411-29 In Theories of Truth, Paul Horwich Aldershot 1994 Soames II S. Soames Understanding Truth Oxford 1999 |
| Hegel, G.W.F. | Wessel Vs Hegel, G.W.F. | I 221 Identity/Hegel: rejected the sentence "a = a". "No object remains the same to itself". WesselVsHegel: Error: confusion of word and object. I 222 ...+... Z. Numbers/Wessel: In mathematics numbers are objects which are introduced by definition. They exist only if one introduces signs for them. A distinction is made between digits and numbers, but without designations (digits) numbers do not exist as abstract objects either. As a result, numbers and number terms are often indistinguishable. Identity/Hegel: for example "The tree is the tree" expresses "not the view of it", because it "does not represent it as something reflected in itself". (WesselVs). Identity/WesselVsHegel: 3. Error by Hegel: to not regard identity and difference as two-digit predicates (relation) but on the one hand as a subject term and on the other as a one-digit predicate. Diversity is simply the negation of identity! WesselVsHegel: is also wrong in limiting himself to the trivial identity a = a in his discussion. This identity would be the only one really superfluous. We cannot draw any conclusions from it or describe any change. I 365 Being/Nothing/Hegel: tries to define the concept of "becoming" through the words "being" and "nothing". WesselVsHegel: that is doomed to failure: without any recourse to the empirically given, terms of change cannot be introduced. (>Change/Hegel). I 365/366 Similar to the existential predicate, change terms cannot be introduced purely logically. Empirical conception of change is already assumed to be known in logic. For example, concepts of time are defined by change. I 366 Change/Wessel: can be introduced in two ways, 1. using time terms - 2. without using time terms. I 367 Problem: two possibilities: properties on an object can modify themselves, disappear completely or emerge anew. Accordingly, one can also distinguish between transition states or static states. s(s~E(a) => sE(a)) an emergence of a s(sE(a) => s~E(a)) a vanishing of a s(S~A => sA) an emergence of sA s(sP(a) => s -i P(a) a loss of the property P. Paradox of change/Wessel: "a changing body possesses a property p and does not possess it at the same time". Dialectical Identity/Hegel/Wessel: logical form: there is a property P such that P(a1) u P(a2) applies, and there is a property Q such that Q(a1) u -i Q(a2) or -i Q(a1) u Q(a2) applies. ((s) Something remains and something changes). Change/Predicate/Wessel: so far we have considered the two-digit predicate =>: something becomes something else. But there is also the one-digit predicate llv (arrow down) "something changes", "something becomes true" or untrue. Example: "The water is moved". WesselVsHegel: this makes it clear how unfounded the opposition of being and becoming terms is. Change/event/predicate/Wessel: with the change predicate sA => sB subject terms can now be formed: s(SA => sB). This is what events are called! (s) Event: singular term, which is formed from a predicate for change. Wessel: for such predicates, however, it must be proved in each case whether they may link with subject terms of this type. |
Wessel I H. Wessel Logik Berlin 1999 |
| Lesniewski, St. | Prior Vs Lesniewski, St. | I 43 Abstracts/Prior: Ontological Commitment/Quine: quantification of non-nominal variables nominalises them and thus forces us to believe in the corresponding abstract objects. Here is a more technical argument which seems to point into Quine's direction at first: Properties/Abstraction Operator/Lambda Notation/Church/Prior: logicians who believe in the real existence of properties sometimes introduce names for them. Abstraction Operator: should form names from corresponding predicates. Or from open sentences. Lambda: λ followed by a variable, followed by the open sentence in question. E.g. if φx is read as "x is red", I 44 then the property of redness is: λxφx. E.g. if Aφxψx: "x is red or x is green" (A: Here adjunction) "Property of being red or green": λx∀φxψx. To say that such a property characterizes an object, we just put the name of the property in front of the name of the object. Lambda Calculus/Prior: usually has a rule that says that an object y has the property of φ-ness iff. y φt. I.e. we can equate: (λy∀φxψx)y = ∀φyψy. ((s) y/x: because "for y applies: something (x) is...") One might think that someone who does not believe in the real existence of properties does not need such a notation. But perhaps we do need it if we want to be free for all types of quantification. E.g. all-quantification of higher order: a) C∏φCφy∑φyCAψyXy∑xAψxXx, i.e. If (1) for all φ, if y φt, then φt is something then (2) if y is either ψt or Xt, then something results in either ψ or X. That's alright. Problem: if we want to formulate the more general principle of which a) is a special case: first: b) C∏φΘφΘ() Where we want to insert in the brackets that which symbolizes the alternation of a pair of verbs "ψ" and "X". AψX does not work, because A must not be followed by two verbs, but only by two sentences. We could introduce a new symbol A', which allows: (A’ φψ)x = Aψxψx this turns the whole thing into: c) C∏φΘφΘA’ψX From this we obtain by instantiation: of Θ d) C∏φCφy∑xφxCA’ψXy∑xA’ψXx. And this, Lesniewski's definition of "A", results in a). This is also Lesniewski's solution to the problem. I 45 PriorVsLesniewski: nevertheless, this is somewhat ad hoc. Lambda Notation: gives us a procedure that can be generalized: For c) gives us e) C∏φΘφΘ(λzAψzXz) which can be instatiated to: f) C∏φCφy∑xφx(λzAψzXz)y∑x(λzAψzXz)y. From this, λ-conversion takes us back to a). Point: λ-conversion does not take us back from e) to a), because in e) the λ-abstraction is not bound to an individual variable. So of some contexts, "abstractions" cannot be eliminated. I 161 Principia Mathematica(1)/PM/Russell/Prior: Theorem 24.52: the universe is not empty The universal class is not empty, the all-class is not empty. Russell himself found this problematic. LesniewskiVsRussell: (Introduction to Principia Mathematica): violation of logical purity: that the universal class is believed to be not empty. Ontology/Model Theory/LesniewskiVsRussell: for him, ontology is compatible with an empty universe. PriorVsLesniewski: his explanation for this is mysterious: Lesniewski: types at the lowest level stand for name (as in Russell). But for him not only for singular names, but equally for general names and empty names! Existence/LesniewskiVsRussell: is then something that can be significantly predicted with an ontological "name" as the subject. E.g. "a exists" is then always a well-formed expression (Russell: pointless!), albeit not always true. Epsilon/LesniewskiVsRussell: does not only connect types of different levels for him, but also the same level! (Same logical types) E.g. "a ε a" is well-formed in Lesniewski, but not in Russell. I 162 Set Theory/Classes/Lesniewski/Prior: what are we to make of it? I suggest that we conceive this ontology generally as Russell's set theory that simply has no variables for the lowest logical types. Names: so-called "names" of ontology are then not individual names like in Russell, but class names. This solves the first of our two problems: while it is pointless to split individual names, it is not so with class names. So we split them into those that are applied to exactly one individual, to several, or to none at all. Ontology/Lesniewski/Russell/Prior: the fact that there should be no empty class still requires an explanation. Names/Lesniewski/Prior: Lesniewski's names may therefore be logically complex! I.e. we can, for example, use to form their logical sum or their logical product! And we can construct a name that is logically empty. E.g. the composite name "a and not-a". Variables/Russell: for him, on the other hand, individual variables are logically structureless. Set Theory/Lesniewski/Prior: the development of Russell's set theory but without variables at the lowest level (individuals) causes problems, because these are not simply dispensable for Russell. On the contrary; for Russell, classes are constructed of individuals. Thus he has, as it were, a primary (for individuals, functors) and a secondary language (for higher-order functors, etc.) Basic sentences are something like "x ε a". I 163 Def Logical Product/Russell: e.g. of the αs and βs: the class of xs is such that x is an α, and x is a β. 1. Whitehead, A.N. and Russel, B. (1910). Principia Mathematica. Cambridge: Cambridge University Press. |
Pri I A. Prior Objects of thought Oxford 1971 Pri II Arthur N. Prior Papers on Time and Tense 2nd Edition Oxford 2003 |
| Modal Logic | Quine Vs Modal Logic | Chisholm II 185 QuineVsModal Logic: instead space time points as quadruples. Reason: permanent objects (continuants) seem to threaten the extensionality. SimonsVsQuine: the Achilles heel is that we must have doubts whether anyone could learn a language that refers not to permanent objects (continuants). --- Lewis IV 32 QuineVsModal Logic: which properties are necessary or accidental, is then dependent on the description. Definition essentialism/Aristotle: essential qualities are not dependent on description. QuineVs: that is as congenial as the whole modal logic. LewisVsQuine: that really is congenial. --- I 338 But modal logic has nothing to do with it. Here, totally impersonal. The modal logic, as we know it, begins with Clarence Lewis "A survey of Symbolic Logic" in 1918. His interpretation of the necessity that Carnap formulates even more sharply later is: Definition necessity/Carnap: A sentence that starts with "it is necessary that", is true if and only if the remaining sentence is analytic. Quine provisionally useful, despite our reservations about analyticity. --- I 339 (1) It is necessary that 9 > 4 it is then explained as follows: (2) "9 > 4" is analytically. It is questionable whether Lewis would ever have engaged in this matter, if not Russell and Whitehead (Frege following) had made the mistake, the philonic construction: "If p then q" as "~ (p and ~ q)" if they so designate this construction as a material implication instead of as a material conditional. C.I.Lewis: protested and said that such a defined material implication must not only be true, but must also be analytical, if you wanted to consider it rightly as an "implication". This led to his concept of "strict implication". Quine: It is best to view one "implies" and "is analytical" as general terms which are predicated by sentences by adding them predicatively to names (i.e. quotations) of sentences. Unlike "and", "not", "if so" which are not terms but operators. Whitehead and Russell, who took the distinction between use and mention lightly, wrote "p implies q" (in the material sense) as it was with "If p, then q" (in the material sense) interchangeable. --- I 339 Material implication "p implies q" not equal to "p > q" (>mention/>use) "implies" and "analytical" better most general terms than operators. Lewis did the same, he wrote "p strictly implies q" and explained it as "It is necessary that not (p and not q)". Hence it is that he developed a modal logic, in which "necessary" is sentence-related operator. If we explain (1) in the form of (2), then the question is why we need modal logic at all. --- I 340 An apparent advantage is the ability to quantify in modal positions. Because we know that we cannot quantify into quotes, and in (2) a quotation is used. This was also certainly Lewis' intention. But is it legitimate? --- I 341 It is safe that (1) is true at any plausible interpretation and the following is false: (3) It is necessary that the number of planets > 4 Since 9 = the number of planets, we can conclude that the position of "9" in (1) is not purely indicative and the necessity operator is therefore opaque. The recalcitrance of 9 is based on the fact that it can be specified in various ways, who lack the necessary equivalence. (E.g. as a number of planets, and the successor to the 8) so that at a specification various features follow necessarily (something "greater than 4 ") and not in the other. Postulate: Whenever any of two sentences determines the object x clearly, the two sentences in question are necessary equivalent. (4) If Fx and only x and Gx and exclusively x, it is necessary that (w)(Fw if and only if when Gw). --- I 342 (This makes any sentence p to a necessary sentence) However, this postulate nullifies modal distinctions: because we can derive the validity of "It is necessary that p" that it plays no role which true sentence we use for "p". Argument: "p" stands for any true sentence, y is any object, and x = y. Then what applies clearly is: (5) (p and x = y) and exclusively x as (6) x = y and x exclusively then we can conclude on the basis of (4) from (5) and (6): (7) It is necessary that (w) (p and w = y) if and only if w = y) However, the quantification in (7) implies in particular "(p and y = y) if and only if y = y" which in turn implies "p"; and so we conclude from (7) that it is necessary that p. --- I 343 The modal logic systems by Barcan and Fitch allow absolute quantification in modal contexts. How such a theory can be interpreted without the disastrous assumption (4), is far from clear. --- I 343 Modal Logic: Church/Frege: modal sentence = Proposition Church's system is structured differently: He restricts the quantification indirectly by reinterpreting variables and other symbols into modal positions. For him (as for Frege) a sentence designated then, to which a modal operator is superior, a proposition. The operator is a predicate that is applied to the proposition. If we treat the modalities like the propositional attitude before, then we could first (1) reinterpret (8) [9 > 4] is necessary (Brackets for class) and attach the opacity of intensional abstraction. One would therefore interpret propositions as that what is necessary and possible. --- I 344 Then we could pursue the model from § 35 and try to reproduce the modality selectively transparent, by passing selectively from propositions to properties: (9) x (x > 4) is necessary in terms 9. This is so far opposed to (8) as "9" here receives a purely designated position in one can quantify and in one can replace "9" by "the number of planets". This seemed to be worth in the case of en, as we e.g. wanted to be able to say (§ 31), there would be someone, of whom is believed, he was a spy (> II). But in the case of modal expressions something very amazing comes out. The manner of speaking of a difference of necessary and contingent properties of an object. E.g. One could say that mathematicians are necessarily rational and not necessarily two-legged, while cyclist are necessarily two-legged but not necessarily rational. But how can a bicycling mathematician be classified? Insofar as we are talking purely indicatively of the object, it is not even suggestively useful to speak of some of its properties as a contingent and of others as necessary. --- I 344 Properties/Quine: no necessary or contingent properties (VsModal Logic) only more or less important properties Of course, some of its properties are considered essential and others unimportant, some permanently and others temporary, but there are none which are necessary or contingent. Curiously, exactly this distinction has philosophical tradition. It lives on in the terms "nature" and "accident". One attributes this distinction to Aristotle. (Probably some scholars are going to protest, but that is the penalty for attributing something to Aristotle.) --- I 345 But however venerable this distinction may be, it certainly cannot be justified. And thus the construction (9) which carries out this distinction so elegantly, also fails. We cannot blame the analyticity the diverse infirmities of modality. There is no alternative yet for (1) and (2) that at least sets us a little on something like modal logic. We can define "P is necessary" as "P = ((x) (x = x))". Whether (8) thereby becomes true, or whether it is at all in accordance with the equation of (1) and (2), will depend on how closely we construct the propositions in terms of their identity. They cannot be constructed so tightly that they are appropriate to the propositional properties. But how particularly the definition may be, something will be the result that a modal logic without quantifiers is isomorphic. --- VI 41 Abstract objects/modal logic/Putnam/Parsons: modal operators can save abstract objects. QuineVsModal Logic: instead quantification (postulating of objects) thus we streamline the truth functions. Modal logic/Putnam/Parsons/Quine: Putnam and Charles Parsons have shown how abstract objects can be saved in the recourse to possibility operators. Quine: without modal operators: E.g. "Everything is such that unless it is a cat and eats spoiled fish, and it gets sick, will avoid fish in the future." ((s) logical form/(s): (x) ((Fx u Gx u Hx)> Vx). Thus, the postulation of objects can streamline our only loosely binding truth functions, without us having to resort to modal operators. --- VI 102 Necessity/opportunity/Quine: are insofar intensional, as they do not fit the substitutivity of identity. Again, vary between de re and de dicto. --- VI 103 Counterfactual conditionals, unreal conditionals/Quine: are true, if their consequent follows logically from the antecedent in conjunction with background assumptions. Necessity/Quine: by sentence constellations, which are accepted by groups. (Goes beyond the individual sentence). --- VI 104 QuineVsModal logic: its friends want to give the necessity an objective sense. --- XI 52 QuineVsModal Logic/Lauener: it is not clear here on what objects we are referring to. --- XI 53 Necessesity/Quine/Lauener: ("Three Grades of Modal Involvement"): 3 progressive usages: 1. as a predicate for names of sentences: E.g. "N "p"": "p is necessarily true". (N: = square, box). This is harmless, simply equate it with analyticity. 2. as an operator which extends to close sentence: E.g. "N p": "it is necessarily true that p" 3. as an operator, too, for open sentences: E.g. "N Fx": through existence generalization: "(Ex) N Fx". |
Quine I W.V.O. Quine Word and Object, Cambridge/MA 1960 German Edition: Wort und Gegenstand Stuttgart 1980 Quine XIII Willard Van Orman Quine Quiddities Cambridge/London 1987 Chisholm I R. Chisholm The First Person. Theory of Reference and Intentionality, Minneapolis 1981 German Edition: Die erste Person Frankfurt 1992 Chisholm II Roderick Chisholm In Philosophische Aufsäze zu Ehren von Roderick M. Ch, Marian David/Leopold Stubenberg Amsterdam 1986 Chisholm III Roderick M. Chisholm Theory of knowledge, Englewood Cliffs 1989 German Edition: Erkenntnistheorie Graz 2004 Lewis I David K. Lewis Die Identität von Körper und Geist Frankfurt 1989 Lewis I (a) David K. Lewis An Argument for the Identity Theory, in: Journal of Philosophy 63 (1966) In Die Identität von Körper und Geist, Frankfurt/M. 1989 Lewis I (b) David K. Lewis Psychophysical and Theoretical Identifications, in: Australasian Journal of Philosophy 50 (1972) In Die Identität von Körper und Geist, Frankfurt/M. 1989 Lewis I (c) David K. Lewis Mad Pain and Martian Pain, Readings in Philosophy of Psychology, Vol. 1, Ned Block (ed.) Harvard University Press, 1980 In Die Identität von Körper und Geist, Frankfurt/M. 1989 Lewis II David K. Lewis "Languages and Language", in: K. Gunderson (Ed.), Minnesota Studies in the Philosophy of Science, Vol. VII, Language, Mind, and Knowledge, Minneapolis 1975, pp. 3-35 In Handlung, Kommunikation, Bedeutung, Georg Meggle Frankfurt/M. 1979 Lewis IV David K. Lewis Philosophical Papers Bd I New York Oxford 1983 Lewis V David K. Lewis Philosophical Papers Bd II New York Oxford 1986 Lewis VI David K. Lewis Convention. A Philosophical Study, Cambridge/MA 1969 German Edition: Konventionen Berlin 1975 LewisCl Clarence Irving Lewis Collected Papers of Clarence Irving Lewis Stanford 1970 LewisCl I Clarence Irving Lewis Mind and the World Order: Outline of a Theory of Knowledge (Dover Books on Western Philosophy) 1991 |
| Quine, W.V.O. | Strawson Vs Quine, W.V.O. | NS I 149 Strawson/Newen/Schrenk: pro descriptive metaphysicsVsRevisionist metaphysics. Definition descriptive metaphysics/Strawson: detects which ontology suggests our every day doing and speaking. Definition revisionists Metaphysics/StrawsonVsQuine: a physicalist ontology. This stands in contrast to the everyday's way of thinking. StrawsonVsQuine: for Strawson it is just about the everyday language, not about the ontology of any language. Ontology/language/Strawson: Thesis: pro-thing-property-ontology. This is necessarily the most elementary. Because of the similarity to the subject-predicate form. --- NS I 150 Space/Time/Strawson: are tools to differentiate different cases. Transcendental/Kant: are arguments that relate to the conditions of possibility. Strawson/Newen/Schrenk: his arguments are transcendental. --- Strawson I 198 QuineVsGeach/QuineVsFrege: singular expressions (singular term) can occur at the points of quantifiable variables, general expressions cannot. Singular Term: can be quantified, general term: not quantifiable. StrawsonVsQuine: on closer inspection, these differences of approach seem far less significant. Quine strongly distinguishes between types of non-linguistic objects on one side and the distinction between singular and general terms, on the other side. (Word/object). In Quine "piety" and "wisdom" are singular expressions, namely names of abstract objects like the nouns "Socrates" and "earth" are the names of concrete objects. Abstract Singular Term/Quine: E.g. "piety" (Universal). The distinction between singular and general term is more important for Quine from the logical point of view. The singular term gives the impression, and to name only one object, while the general term does not claimed at all, to name something, although it "may be true of many things." StrawsonVsQuine: this is an unsatisfactory way of explaining that the word "philosopher" should be a general and not a singular term. We would not like to say that this expression is true of many things or people. --- Strawson I 252 Circle/StrawsonVsQuine: regardless of their captivating simplicity of this analysis, I believe that it will be unacceptable by the form in which it is created. The language terms, in which the analysis is drawn up, presuppose the existence of subject expressions of linguistic singular terms. Other consequence: we are invited, to see the expressions that replace the "Fs" and "Gs" in the quantified sentences as ordinary predicate expressions. That is allright. --- I 253 Circle/StrawsonVsQuine: but again these forms have only their place in normal language because singular terms, subject expressions occupy the place they have there. Circularity: because we cannot simultaneously regard Fs and Gs as predicate expressions and accept that they all resolve subject expressions totally in the form of quantified sentences. Circle/StrawsonVsQuine: the argument is based on the linguistic forms that require in turn the use of these expressions. StrawsonVsGadamer/StrawsonVsQuine: one could argue against that this is too narrow, one must proceed inventively. In the case one would have to say what a teaching really should say, which is, taken literally, unacceptable. --- Strawson IV 69 StrawsonVsQuine: Suppose we want to manage without quantification over properties. Does it follow that the belief in objects would be justified, but not the belief in properties? --- IV 70 Strawson: we can accept a different kind of existence. A secondary, although a usual sense of existence, which applies to properties and relations. --- IV 71 Vs: E.g. a) "There is at least one property that has no machine, namely perfect efficiency". b) "no machine is completely efficient." In a) I quantify, in b) I do not. |
Strawson I Peter F. Strawson Individuals: An Essay in Descriptive Metaphysics. London 1959 German Edition: Einzelding und logisches Subjekt Stuttgart 1972 Strawson II Peter F. Strawson "Truth", Proceedings of the Aristotelian Society, Suppl. Vol XXIV, 1950 - dt. P. F. Strawson, "Wahrheit", In Wahrheitstheorien, Gunnar Skirbekk Frankfurt/M. 1977 Strawson III Peter F. Strawson "On Understanding the Structure of One’s Language" In Truth and Meaning, G. Evans/J. McDowell Oxford 1976 Strawson IV Peter F. Strawson Analysis and Metaphysics. An Introduction to Philosophy, Oxford 1992 German Edition: Analyse und Metaphysik München 1994 Strawson V P.F. Strawson The Bounds of Sense: An Essay on Kant’s Critique of Pure Reason. London 1966 German Edition: Die Grenzen des Sinns Frankfurt 1981 Strawson VI Peter F Strawson Grammar and Philosophy in: Proceedings of the Aristotelian Society, Vol 70, 1969/70 pp. 1-20 In Linguistik und Philosophie, G. Grewendorf/G. Meggle Frankfurt/M. 1974/1995 Strawson VII Peter F Strawson "On Referring", in: Mind 59 (1950) In Eigennamen, Ursula Wolf Frankfurt/M. 1993 |
| Russell, B. | Prior Vs Russell, B. | PriorVsRussell I 7 Belief/Theory of Multiple Relation/Meinong/Russell/Prior: (also realistic): Proposition/Meinong: he calls "objects" and facts a subclass: the true propositions. Thus, only two instead of three types of abstract objects remain. But for some this is still too much. Russell/Moore: they eliminated "falsity", but kept facts as abstract objects. Russell: represented two variants: a) major difference: between belief and knowledge. (Theory of multiple relations) b) between true and false beliefs. ad a): Knowledge is always of facts and is a double-digit relation between two real objects, the knower and the known fact. Belief, however, is not a double-digit relation, I 8 but a multi-digit one between the believer and various elements, which (if they existed) would be the believed proposition. E.g. Othello believes that Desdemona loves Cassio, or believes in Desdemona's infidelity. Problem: There is no object that is Desdemona's infidelity. Solution: Attribution! He attributed infidelity! I.e. the story is about two real objects, Desdemona and infidelity, and Othello is in the complex relation of attribution. I 9 Russell: in this sense, propositions are logical constructions. PriorVsRussell: propositions are logical constructions, but not for this reason. 1) Although Russell's theory does not require us to believe that there is an object such as Desdemona's infidelity, it nevertheless requires us to believe that about Desdemona herself there is an object as her fidelity! 2) Russell's construction is a four-term relation instead of a three-term relation. Russell: revised (1) (following Wittgenstein), but not (2). Belief/Russell: (late): sentences that describe beliefs have two verbs and none is swallowed by an abstract noun. (?). Prior: neverthelss, precisely in the attribution of infidelity, this abstract object infidelity requires an explanation. And also a kind of "universal infidelity". I 31 PriorVsRussell: multiple relations: With his solution, Russell burdens himself with new abstract entities. And the same might be said about Ramsey's solution. Abstract Entities/Verb/Predicate/Prior: but we cannot get rid of all of them, anyway! Verb: I can dissolve it: instead of "Jones smokes" I can say "I predict the smoking of Jones". But then I have another verb again: "I predict"! Verbs and nouns are always needed. |
Pri I A. Prior Objects of thought Oxford 1971 Pri II Arthur N. Prior Papers on Time and Tense 2nd Edition Oxford 2003 |
| Russell, B. | Quine Vs Russell, B. | Chisholm II 75 Predicates/Denote/Russell: denoting expressions: proper names stand for individual things and general expressions for universals. (Probleme d. Phil. p. 82f). In every sentence, at least one word refers to a universal. QuineVsRussell: confusion! II 108 Theory of Descriptions/VsRussell/Brandl: thus the whole theory is suspected of neglecting the fact that material objects can never be part of propositions. QuineVsRussell: confusion of mention and use. Quine II 97 Pricipia mathematica, 1903: Here, Russell's ontology is rampant: every word refers to something. If a word is a proper name, then its object is a thing, otherwise it is a concept. He limits the term "existence" to things, but has a liberal conception of things which even includes times and points in empty space! Then there are, beyond the existent things, other entities: "numbers, the gods of Homer, relationships, fantasies, and four-dimensional space". The word "concept", used by Russell in this manner, has the connotation of "merely a concept". Caution: Gods and fantasies are as real as numbers for Russell! QuineVsRussell: this is an intolerably indiscriminate ontology. Example: Take impossible numbers, e.g. prime numbers that are divisible by 6. It must be wrong in a certain sense that they exist, and that is in a sense in which it is right that there are prime numbers! Do fantasies exist in this sense? II 101 Russell has a preference for the term "propositional function" against "class concept". In P.M. both expressions appear. Here: Def "Propositional Function": especially based on forms of notation, e.g. open sentences, while concepts are decidedly independent of notation. However, according to Meinong Russell's confidence is in concepts was diminished, and he prefers the more nominalistic sound of the expression "propositional function" which is now carries twice the load (later than Principia Mathematica.) Use/Mention/Quine: if we now tried to deal with the difference between use and mention as carelessly as Russell has managed to do sixty years ago, we can see how he might have felt that his theory of propositional functions was notation based, while a theory of types of real classes would be ontological. Quine: we who pay attention to use and mention can specify when Russell's so-called propositional functions as terms (more specific than properties and relations) must be construed as concepts, and when they may be construed as a mere open sentences or predicates: a) when he quantifies about them, he (unknowingly) reifies them as concepts. For this reason, nothing more be presumed for his elimination of classes than I have stated above: a derivation of the classes from properties or concepts by means of a context definition that is formulated such that it provides the missing extensionality. QuineVsRussell: thinks wrongly that his theory has eliminated classes more thoroughly from the world than in terms of a reduction to properties. II 102 RussellVsFrege: "~ the entire distinction between meaning and designating is wrong. The relationship between "C" and C remains completely mysterious, and where are we to find the designating complex which supposedly designates C?" QuineVsRussell: Russell's position sometimes seems to stem from a confusion of the expression with its meaning, sometimes from the confusion of the expression with its mention. II 103/104 In other papers Russel used meaning usually in the sense of "referencing" (would correspond to Frege): "Napoleon" particular individual, "human" whole class of such individual things that have proper names. Russell rarely seems to look for an existing entity under any heading that would be such that we could call it the meaning that goes beyond the existing referent. Russell tends to let this entity melt into the expression itself, a tendency he has in general when it comes to existing entities. QuineVsRussell: for my taste, Russell is too wasteful with existing entities. Precisely because he does not differentiate enough, he lets insignificance and missed reference commingle. Theory of Descriptions: He cannot get rid of the "King of France" without first inventing the description theory: being meaningful would mean: have a meaning and the meaning is the reference. I.e. "King of France" without meaning, and "The King of France is bald" only had a meaning, because it is the short form of a sentence that does not contain the expression "King of France". Quine: actually unnecessary, but enlightening. Russell tends commingle existing entities and expressions. Also on the occasion of his remarks on Propositions: (P.M.): propositions are always expressions, but then he speaks in a manner that does not match this attitude of the "unity of the propositions" (p.50) and of the impossibility of infinite propositions (p.145) II 105 Russell: The proposition is nothing more than a symbol, even later, instead: Apparently, propositions are nothing..." the assumption that there are a huge number of false propositions running around in the real, natural world is outrageous." Quine: this revocation is astounding. What is now being offered to us instead of existence is nothingness. Basically Russell has ceased to speak of existence. What had once been regarded as existing is now accommodated in one of three ways a) equated with the expression, b) utterly rejected c) elevated to the status of proper existence. II 107 Russell/later: "All there is in the world I call a fact." QuineVsRussell: Russell's preference for an ontology of facts depends on his confusion of meaning with reference. Otherwise he would probably have finished the facts off quickly. What the reader of "Philosophy of logical atomism" notices would have deterred Russell himself, namely how much the analysis of facts is based on the analysis of language. Russell does not recognize the facts as fundamental in any case. Atomic facts are as atomic as facts can be. Atomic Facts/Quine: but they are composite objects! Russell's atoms are not atomic facts, but sense data! II 183 ff Russell: Pure mathematics is the class of all sentences of the form "p implies q" where p and q are sentences with one or more variables, and in both sets the same. "We never know what is being discussed, nor if what we say is true." II 184 This misinterpretation of mathematics was a response to non-Euclidean geometry. Numbers: how about elementary arithmetic? Pure numbers, etc. should be regarded as uninterpreted. Then the application to apples is an accumulation. Numbers/QuineVsRussell: I find this attitude completely wrong. The words "five" and "twelve" are nowhere uninterpreted, they are as much essential components of our interpreted language as apples. >Numbers. They denote two intangible objects, numbers that are the sizes of quantities of apples and the like. The "plus" in addition is also interpreted from start to finish, but it has nothing to do with the accumulation of things. Five plus twelve is: how many apples there are in two separate piles. However, without pouring them together. The numbers "five" and "twelve" differ from apples in that they do not denote a body, that has nothing to do with misinterpretation. The same could be said of "nation" or "species". The ordinary interpreted scientific speech is determined to abstract objects as it is determined to apples and bodies. All these things appear in our world system as values of variables. II 185 It even has nothing to do with purity (e.g. of the set theory). Purity is something other than uninterpretedness. XII 60 Expression/Numbers/Knowledge/Explication/Explanation/Quine: our knowledge of expressions is alone in their laws of interlinking. Therefore, every structure that fulfills these laws can be an explication. XII 61 Knowledge of numbers: consists alone in the laws of arithmetic. Then any lawful construction is an explication of the numbers. RussellVs: (early): Thesis: arithmetic laws are not sufficient for understanding numbers. We also need to know applications (use) or their embedding in the talk about other things. Number/Russell: is the key concept here: "there are n such and suches". Number/Definition/QuineVsRussell: we can define "there are n such and suches" without ever deciding what numbers are beyond their fulfillment of arithmetic addition. Application/Use/QuineVsRussell: wherever there is structure, the applications set in. E.g. expressions and Gödel numbers: even the mention of an inscription was no definitive proof that we are talking about expressions and not about Gödel numbers. We can always say that our ostension was shifted. VII (e) 80 Principia Mathematica(1)/PM/Russell/Whitehead/Quine: shows that the whole of mathematics can be translated into logic. Only three concepts need to be clarified: Mathematics, translation and logic. VII (e) 81 QuineVsRussell: the concept of the propositional function is unclear and obscures the entire PM. VII (e) 93 QuineVsRussell: PM must be complemented by the axiom of infinity if certain mathematical principles are to be derived. VII (e) 93/94 Axiom of infinity: ensures the existence of a class with infinitely many elements. Quine: New Foundations instead makes do with the universal class: θ or x^ (x = x). 1. Whitehead, A.N. and Russel, B. (1910). Principia Mathematica. Cambridge: Cambridge University Press. VII (f) 122 Propositional Functions/QuineVsRussell: ambiguous: a) open sentences b) properties. Russell no classes theory uses propositional functions as properties as value-bound variables. IX 15 QuineVsRussell: inexact terminology. "Propositional function", he used this expression both when referring to attributes (real properties) and when referring to statements or predicates. In truth, he only reduced the theory of classes to an unreduced theory of attributes. IX 93 Rational Numbers/QuineVsRussell: I differ in one point: for me, rational numbers are themselves real numbers, not so for Russell and Whitehead. Russell: rational numbers are pairwise disjoint for them like those of Peano. (See Chapter 17), while their real numbers are nested. ((s) pairwise disjoint, contrast: nested) Natural Numbers/Quine: for me as for most authors: no rational integers. Rational Numbers/Russell: accordingly, no rational real numbers. They are only "imitated" by the rational real numbers. Rational Numbers/QuineVsRussell: for me, however, the rational numbers are real numbers. This is because I have constructed the real numbers according to Russell's version b) without using the name and the designation of rational numbers. Therefore, I was able to retain name and designation for the rational real numbers IX 181 Type Theory/TT/QuineVsRussell: in the present form our theory is too weak to prove some sentences of classical mathematics. E.g. proof that every limited class of real numbers has a least upper boundary (LUB). IX 182 Suppose the real numbers were developed in Russell's theory similar to Section VI, however, attributes were now to take the place of classes and the alocation to attributes replaces the element relation to classes. LUB: (Capters 18, 19) of a limited class of real numbers: the class Uz or {x:Ey(x ε y ε z)}. Attribute: in parallel, we might thus expect that the LUB of a limited attribute φ of real numbers in Russell's system is equal to the Attribute Eψ(φψ u ψ^x). Problem: under Russell's order doctrine is this LUB ψ is of a higher order than that of the real numbers ψ which fall under the attribute φ whose LUB is sought. Boundary/LUB/QuineVsRussell: You need LUB for the entire classic technique of calculus, which is based on continuity. However, LUB have no value for these purposes if they are not available as values of the same variables whose value range already includes those numbers whose upper boundary is wanted. An upper boundary (i.e. LUB) of higher order cannot be the value of such variables, and thus misses its purpose. Solution/Russell: Axiom of Reducibility: Def Axiom of Reducibility/RA/Russell/Quine: every propositional function has the same extension as a certain predicative one. I.e. Ey∀x(ψ!x φx), Eψ∀x∀y[ψ!(x,y) φ(x,y)], etc. IX 184 VsConstruktivism/Construction/QuineVsRussell: we have seen Russell's constructivist approach to the real numbers fail (LUB, see above). He gave up on constructivism and took refuge in the RA. IX 184/185 The way he gave it up had something perverse to it: Axiom of Reducibility/QuineVsRussell: the RA implies that all the distinctions that gave rise to its creation are superfluous! (... + ...) IX 185 Propositional Function/PF/Attribute/Predicate/TT/QuineVsRussell: overlooked the following difference and its analogs: a) "propositional functions": as attributes (or intentional relations) and b) proposition functions: as expressions, i.e. predicates (and open statements: e.g. "x is mortal") Accordingly: a) attributes b) open statements As expressions they differ visibly in the order if the order is to be assessed on the basis of the indices of bound variables within the expression. For Russell everything is "AF". Since Russell failed to distinguish between formula and object (word/object, mention/use), he did not remember the trick of allowing that an expression of higher order refers straight to an attribute or a relation of lower order. X 95 Context Definition/Properties/Stage 2 Logic/Quine: if you prefer properties as sets, you can introduce quantification over properties, and then introduce quantification over sets through a schematic context definition. Russell: has taken this path. Quine: but the definition has to ensure that the principle of extensionality applies to sets, but not to properties. That is precisely the difference. Russell/QuineVsRussell: why did he want properties? X 96 He did not notice at which point the unproblematic talk of predicates capsized to speaking about properties. ((s) object language/meta language/mention/use). Propositional Function/PF: Russell took it over from Frege. QuineVsRussell: he sometimes used PF to refer to predicates, sometimes to properties. |
Quine I W.V.O. Quine Word and Object, Cambridge/MA 1960 German Edition: Wort und Gegenstand Stuttgart 1980 Quine XIII Willard Van Orman Quine Quiddities Cambridge/London 1987 Chisholm I R. Chisholm The First Person. Theory of Reference and Intentionality, Minneapolis 1981 German Edition: Die erste Person Frankfurt 1992 Chisholm III Roderick M. Chisholm Theory of knowledge, Englewood Cliffs 1989 German Edition: Erkenntnistheorie Graz 2004 |
| substit. Quantific. | Quine Vs substit. Quantific. | V 158 VsSubstitutional Quantification/SQ/Quine: the SQ has been deemed unusable for the classic ML for a false reason: because of uncountability. The SQ does not accept nameless classes as values of variables. ((s) E.g. irrational numbers, real numbers, etc. do not have names, i.e. they cannot be Gödel numbered). I.e. SQ allows only a countable number of classes. Problem: Even the class of natural numbers has uncountably many sub-classes. And at some point we need numbers! KripkeVs: in reality there is no clear contradiction between SQ and hyper-countability! No function f lists all classes of natural numbers. Cantor shows this based on the class {n:~ (n e f(n))} which is not covered by the enumeration f. refQ: demands it in contrast to a function f enumerating all classes of natural numbers? It seems so at first glance: it seems you could indicate f by numbering all abstract terms for classes lexicographically. Vs: but the function that numbers the expressions is not quite the desired f. It is another function g. Its values are abstract terms, while the f, which would contradict the Cantor theorem, would have classes as values... V 159 Insertion character: does ultimately not mean that the classes are abstract terms! ((s) I.e. does not make the assumption of classes necessary). The cases of insertion are not names of abstract terms, but the abstract terms themselves! I.e. the alleged or simulated class names. Function f: that would contradict Cantor's theorem is rather the function with the property that f(n) is the class which is denoted by the n-th abstract term g(n). Problem: we cannot specify this function in the notation of the system. Otherwise we end up with Grelling's antinomy or that of Richard. That's just the feared conflict with Cantor's theorem. This can be refute more easily: by the finding that there is a class that is not denoted by any abstract term: namely the class (1) {x.x is an abstract term and is not a member of the class it denotes}. That leaves numbers and uncountability aside and relates directly to expressions and classes of expressions. (1) is obviously an abstract expression itself. The antinomy is trivial, because it clearly relies on the name relation. ((s) x is "a member of the class of abstract expressions and not a member of this class"). V 191 Substitutional Quantification/SQ/Nominalism/Quine: the nominalist might reply: alright, let us admit that the SQ does not clean the air ontologically, but still we win something with it: E.g. SQ about numbers is explained based on expressions and their insertion instead of abstract objects and reference. QuineVsSubstitutional Quantification: the expressions to be inserted are just as abstract entities as the numbers themselves. V 192 NominalismVsVs: the ontology of real numbers or set theory could be reduced to that of elementary number theory by establishing truth conditions for the sQ based on Gödel numbers. QuineVs: this is not nominalistic, but Pythagorean. This is not about the extrapolation of the concrete and abhorrence of the abstract, but about the acceptance of natural numbers and the refutal of the most transcendent nnumbers. As Kronecker says: "The natural numbers were created by God, the others are the work of man." QuineVs: but even that does not work, we have seen above that the SQ about classes is, as a matter of principle, incompatible with the object quantification over objects. V 193 VsVs: the quantification over objects could be seen like that as well. QuineVs: that was not possible because there are not enough names. Zar could be taught RZ coordination, but that does not explain language learning. Ontology: but now that we are doing ontology, could the coordinates help us? QuineVs: the motivation is, however, to re-interpret the SQ about objects to eliminate the obstacle of SQ about classes. And why do we want to have classes? The reason was quasi nominalistic, in the sense of relative empiricism. Problem: if the relative empiricism SQ talks about classes, it also speaks for refQ about objects. This is because both views are closest to the genetic origins. Coordinates: this trick will be a poor basis for SQ about objects, just like (see above) SQ about numbers. Substitutional/Referential Quantification/Charles Parsons/Quine: Parsons has proposed a compromise between the two: according to this, for the truth of an existential quantification it is no longer necessary to have a true insertion, there only needs to be an insertion that contains free object variables and is fulfilled by any values of the same. Universal quantification: Does accordingly no longer require only the truth of all insertions that do not contain free variables. V 194 It further requires that all insertions that contain free object variables are fulfilled by all values. This restores the law of the single sub-classes and the interchangeability of quantifiers. Problem: this still suffers from impredicative abstract terms. Pro: But it has the nominalistic aura that the refQ completely lacks, and will satisfy the needs of set theory. XI 48 SQ/Ontology/Quine/Lauener: the SQ does not make any ontological commitment in so far as the inserted names do not need to designate anything. I.e. we are not forced to assume values of the variables. XI 49 QuineVsSubstitutional Quantification: we precisely obscure the ontology by that fact that we cannot get out of the linguistic. XI 51 SQ/Abstract Entities/Quine/Lauener: precisely because the exchange of quantifiers is prohibited if one of the quantifiers referential, but the other one is substitutional, we end up with refQ and just with that we have to admit the assumption of abstract entities. XI 130 Existence/Ontology/Quine/Lauener: with the saying "to be means to be the value of a bound variable" no language dependency of existence is presumed. The criterion of canonical notation does not suppose an arbitrary restriction, because differing languages - e.g. Schönfinkel's combinator logic containing no variables - are translatable into them. Ontological Relativity/Lauener: then has to do with the indeterminacy of translation. VsSubstitutional Quantification/Quine/Lauener: with it we remain on a purely linguistic level, and thus repeal the ontological dimension. But for the variables not singular terms are used, but the object designated by the singular term. ((s) referential quantification). Singular Term/Quine/Lauener: even after eliminating the singular terms the objects remain as the values of variables. XI 140 QuineVsSubstitutional Quantification: is ontologically disingenuous. |
Quine I W.V.O. Quine Word and Object, Cambridge/MA 1960 German Edition: Wort und Gegenstand Stuttgart 1980 Quine XIII Willard Van Orman Quine Quiddities Cambridge/London 1987 |
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| Disputed term/author/ism | Pro/Versus |
Entry |
Reference |
|---|---|---|---|
| Causal theory of knowledge | Versus | Stalnaker I 42 Knowledge/causality/causal theory of knowledge: Benacerraf: Thesis: knowledge / reference requires causal connection. - LewisVsBenacerraf: abstract objects such as numbers, etc. do not require a causal connection - Stalnaker ditto. |
Stalnaker I R. Stalnaker Ways a World may be Oxford New York 2003 |
| Causal theory of knowledge | Pro | Stalnaker I 42 Knowledge/causality/causal theory of knowledge: Benacerraf: Thesis: knowledge/reference requires causal connection - LewisVsBenacerraf: abstract objects such as numbers, etc. do not require a causal connection - Stalnaker ditto. |
Stalnaker I R. Stalnaker Ways a World may be Oxford New York 2003 |
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The author or concept searched is found in the following 4 theses of the more related field of specialization.
| Disputed term/author/ism | Author |
Entry |
Reference |
|---|---|---|---|
| Ontology | Chisholm, R. | I 18 Thesis: my ontology is platonic: I accept eternal and abstract objects: namely: properties, relations, and circumstances. |
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| Platonism | Field, Hartry | I 44 To succeed in VsPlatonism, we must also show, thesis: that mathematics is dispensable in science and metalogic. Then we have reason not to literally have to believe in mathematics. (>Indispensability argument). I 45 If that succeeds, we can get behind the agnosticism. I 186 Def moderate platonism/mP/Field: the thesis that there are abstract objects like numbers. Then one probably also believes that there are relations of physical size between objects and numbers. (But only derived): Example "mass in kilogram" is then relation between a given physical object and the real number 15,2. Example "distance in meters" is a relation between two objects ((s) on one side) and the real number 7,4. The difference to high-performance platonism (HPP) lies in the attitude to these relations: Moderate Platonism: Thesis: These are conventional relations derived from more fundamental relations existing between physical objects alone. Def High Performance Platonism/Field: denies that and takes the relations between objects and numbers as a bare fact that cannot be explained in other terms. Inflated one could explain this as "platonistic participation". II 332 Standard Platonism: Thesis: Mathematical theories such as set theory or the theory of real numbers are about different mathematical domains, or at least about certain structures, because there is no need to assume that isomorphic domains (i.e. domains with the same structure) would be mathematically indistinguishable. Thus, "regions" should not be assumed as sets. II 333 Def "Platonism of perfection": (plenitude): postulates a set of mathematical objects. Thesis: Whenever we have a consistent purely mathematical theory, there are mathematical objects that fulfill the theory under a standard-fulfillment relation. Platonism of perfection: but also suggests that we can consider all quantifiers about mathematical entities in this way, I 334 that they are implicitly limited by a predicate to which all other predicates of mathematical entities are subordinated: The "overarching" predicate: is then different between the different mathematical theories. These theories then no longer conflict. II 335 Universe/Standard Platonism/Field: (Thesis: "Only one universe exists"). Problem/PutnamVsPlatonism: how do we even manage to pick out the "full" (comprehensive) universe and confront it with a sub-universe, and accordingly the standard element relationship as opposed to a non-standard element relationship? (Putnam 1980). (Here placed from the perspective of "Universe"). Putnam: Thesis: We simply cannot do that. |
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| Abstraction | Wright, Cr. | Field I 158 Introduction/Abstract Objects/Abstraction/Wright: Thesis: sets as well as directions and numbers are to be introduced by abstraction. I 157 Field: Example: simple abstraction: is suitable for saying that our speech of directions is related to parallelism - but that does not quite work for numbers as related to non-numeric speech (and "non-set theory"). I 161 Thesis: even then it is harmless to pretend as if one accepts the directional theory in order to make inferences between such assertions. Because any inference between directional statements licensed by directional theory is licensed by parallelism theory. |
Field I H. Field Realism, Mathematics and Modality Oxford New York 1989 Field IV Hartry Field "Realism and Relativism", The Journal of Philosophy, 76 (1982), pp. 553-67 In Theories of Truth, Paul Horwich Aldershot 1994 |
| Ontology | Wright, Cr. | Field I 163 ... ontological inflationism: thesis: the surface grammar of sentences like "line c1 is parallel to line c2": Ontological Inflationism/Field: the obvious explanation is that Wright represents the ontological inflationism and assumes that all facts contain abstract objects so that (a) is made true by facts that are as concrete as possible. I 165 Def extended ontological reductionism/eoR: thesis: not only apparent singular term for directions but also existential quantification about directions are semantically misleading. WrightVseoR. |
Field I H. Field Realism, Mathematics and Modality Oxford New York 1989 |
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