Find counter arguments by entering NameVs… or …VsName.
The author or concept searched is found in the following 19 entries.
| Disputed term/author/ism | Author |
Entry |
Reference |
|---|---|---|---|
| Attitude-Semantics | Cresswell | I 64 Attitude Semantics/VsPossible World Semantics/Semantics of Possible Worlds/BarwiseVsCresswell: there are often two propositions, one of which is believed by the person, yet the other one is not, but still both are true in the same possible world. >Pierre eyample. Cresswell: E.g. all logical and mathematical truths. But they are not all known, otherwise there could be no progress. >Logical omniscience. I 65 CresswellVsSituation Semantics: the situations are to play roles that cannot be played simultaneously. Solution: possible world semantics: the roles are played by entities of various kinds. >Semantics of possible worlds. Solution: context with space-time indication - incorrect sentences: describe non-actual situations. >Situations, >Situation Semantics. I 66 Sentences describe situations in a context. - The context is itself a situation that provides the listener with time, place, etc. >Context. Interpretation/Barwise: meaning of sentences in context. >Intepretation, >Barwise/Perry. |
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 |
| Beliefs | Benacerraf | Field II 373 Belief/empiricism/rules/irrefutability/Benacerraf(1973)(1): if our system of rules were independent of any evidence for a particular physical theory, this would make our belief causally and counterfactually independent of the facts. This would, however, thwart the epistemic value of considerations based on this belief. >Evidence, >Rules, >Knowledge, >Certainty, >Theories, cf. >Empiricism, >Causal explanation, >Causality. Logic/Apriority/Field: it looks at first as if one could also use the argument for a priori belief in logic. >a priori, >Logic. FieldVs: but it is pointless to ask whether logical beliefs depend on logical facts. >Beliefs, >Facts, >Dependence. 1. Benacerraf, P. Mathematical Truth, The Journal of Philosophy 70, 1973, S. 661–679. |
Bena I P. Benacerraf Philosophy of Mathematics 2ed: Selected Readings Cambridge 1984 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 |
| Correctness | Mates | I 16 Correctness Criterion/Correct/Mates: the criterion needs "true" and "possible": "impossible to reach false conclusion from true premises. >Conditional, >Premises, >Truth, cf. >Validity. I 18 Correctness does not provide any information about the truth value of the conclusion. >Truth values, >Conclusion. I 19 Def correct: is a conclusion if the associated subjunction is analytical. >Subjunction, >Analyticity/Syntheticity. Def analytical: is a statement that cannot be wrong - or if it cannot be the conclusion of an incorrect conclusion. >Conclusion. I.e. a conclusion with mathematical truth as a conclusion cannot be incorrect - Point: this demonstrates that you cannot equate concepts like "correct conclusion" and "proof" - proof requires more. >Proofs, >Provability. I 128 Def correct derivation/Mates: carried out according to rules (to be specified). >Derivation, >Derivability. |
Mate I B. Mates Elementare Logik Göttingen 1969 Mate II B. Mates Skeptical Essays Chicago 1981 |
| Goedel | Mates | I 289 Goedel/Mates: main result: Goedel showed by the incompleteness theorem that one can not identify mathematical truth with derivability from a particular system of axioms. >K. Gödel, >Incompleteness/Gödel, >Mathematical truth, >Validity, >Derivation, >Derivability, >Axioms, >Axiom systems. |
Mate I B. Mates Elementare Logik Göttingen 1969 Mate II B. Mates Skeptical Essays Chicago 1981 |
| Interpretation | Benacerraf | Field I 22 Interpretation/Benacerraf: (1965)(1) Thesis: Identification of mathematical objects with others is arbitrary - E.g. numbers with quantities. - E.g. real numbers with Dedekind cuts, Cauchy sequences, etc. - There is no fact that decides which is the right one. >Equations, >Equality, >Identification, >Real numbers, >Numbers, >Mathematics, >Mathematical entities. Field ditto. I 22 Indeterminacy of reference/Field: is not a problem, but commonplace. >Reference, >Indeterminacy. I 25 For Benacerraf it is about identity, not about reference - otherwise he might falsely be refuted with primitive reference: "Numbers" refers to numbers but not to quantities - But that is irrelevant. Cf. >Reference/Field. I 25 BenacerraffVsPlatonism: locus classicus - VsBenacerraf: based on an outdated causal theory of knowledge. >Platonism, >Causal theory of knowledge. Field I 25 BenacerrafVsPlatonism: (1973)(2): if without localization and interaction we cannot know whether they exist. VsBenacerraf: indispensability argument. 1. Benacerraf, P. What Numbers Could Not Be, The Philosophical Review 74, 1965, S. 47–73. 2. Benacerraf, P. Mathematical Truth, The Journal of Philosophy 70, 1973, S. 661–679. |
Bena I P. Benacerraf Philosophy of Mathematics 2ed: Selected Readings Cambridge 1984 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 |
| Intuitionism | Heyting | I 59ff Intuitionism/Heyting: Brouwer studied the conceptual mathematical construction as such, without questioning the nature of things, for example, whether these things exist independently of our knowledge of them. >L. Brouwer. I 60 Sentence of the excluded middle: e.g. the invalidity of the sentence of the excluded middle: if we compare the definitions of two natural numbers, k and l then: (A) k is the largest prime number such that k 1 is also a prime number, if there is no such number, k = 1. (B) l is the largest prime number such that l 2 is also a prime number, if there is no such number, l = 1. Intuitionists reject (B) as a definition of an integer. K can be really calculated (k = 3), while we have no method of determining l, since it is not known whether the sequence of the prime number twins is infinite or not. The intuitionists regard something as well-defined only when a method of determination is given. >Law of the Excluded Middle, >Numbers. Classical mathematics: one can argue that the extent of our knowledge about the existence of the last twin is purely coincidental. And completely irrelevant in questions of mathematical truth. Existence/intuitionism/Heyting: the argument of the representative of classical mathematics is of a metaphysical kind. If existing does not mean "constructible", it must have a metaphysical meaning. Cf. >Constructivism. I 61 Classical mathematics/VsIntuitionism/Heyting: assuming that on January 1st, 1970, it is proved that there are infinitely many twins, l is equal to 1. Was that not already the case before the date (Menger, 1930)? Intuitionism/Heyting: a mathematical assertion states that a certain construction is possible. Before the construction exists, the construction is not there. Even the intuitionists are convinced that mathematics is based on eternal truths in some sense, but when one attempts to define this meaning one gets entangled in metaphysics. >Metaphysics. I 62 Formalism/Carnap/Heyting: there always remains the doubt, which conclusions are correct, and which are not (Carnap, 1934(1), S. 44; 1937(2), S. 51). >Correctness. I 63 Intuitionism: we are not interested in the formal side, but precisely in the nature of inferences in meta-mathematics. There is a fundamental ambiguity in the language. Classical mathematics: the semanticists are even worse relativists than the formalists and intuitionists. Cf. >Semantic truth, >Truth conditions. I 65 Intuitionism: there is an intuitionist logic, e.g. transitivity. Conclusion: logic is a part of mathematics and therefore cannot be taken as its basis. >Blackening of the paper, >Formalism, >Evidence, >Proofs, >Provability, >VsFormalism, cf. >Foundation. 1. R. Carnap, Logische Syntax der Sprache, Wien 1934, p. 44. 2. R. Carnap, Testability and Meaning, in: Philosophy of Science 4, 1937, p. 51. 3. Karl Menger. Der Intuitionismus. Blätter Für Deutsche Philosophie 4:311--325 (1930) |
Heyting I Arend Heyting "Disputation", in: Intuitionism, Amsterdam 1956 German Edition: Streitgespräch In Kursbuch 8/1967, H. M. Enzensberger Frankfurt/M. 1967 Heyting II Arend Heyting Intuitionism: An Introduction (Study in Logic & Mathematics) 1971 |
| Mathematical Entities | Benacerraf | Stalnaker I 41 Mathematics/Benacerraf/Stalnaker: (Benacerraf, 1973)(1): Benacerraf sees a tension between the need for a plausible representation of what mathematical statements say and a representation of the way we know that such statements are true. Suppose we demand a causal connection to things that we claim to know. Then it is not clear how this is supposed to work in the case of numbers that are acasual. >Causality, >Knowledge, >Causal theory of knowledge, cf. >Theoretical terms, >Theoretical entities, >Reference. 1. Benacerraf, P. Mathematical Truth, The Journal of Philosophy 70, 1973, S. 661–679. |
Bena I P. Benacerraf Philosophy of Mathematics 2ed: Selected Readings Cambridge 1984 Stalnaker I R. Stalnaker Ways a World may be Oxford New York 2003 |
| Necessity | Quine | I 344/45 Properties/Quine: are no necessary or contingent properties (VsModal Logic) - are only more or less important properties. >Properties/Quine. II 143 ff "Nec." is predicate in laws, extensional, no quote, but unclear - "Q" (functor) modal logic, intensional de re: is out of range: x = planets, x = 9, 9 odd - predicate applies to value of the variable, not to the name. - De Re: referencing position. De dicto: the term that is meant is in the sentence: "nec." planets odd: is wrong. De re: E.g. spy should be an essential property (wrong) - not a belief de re (essential property). Modal Logic/Quine: the entire metalanguage is context-dependent - what role does someone or something play? - Same level as essential properties. Necessity/(Quine: the whole concept only makes sense in the context! propositional attitude/Quine: is preserved! - But not de re. >de re/Quine, >de dicto/Quine. VII (h) 152 Necesity/Quine: works only for intensional objects, they should necessarily be like this or like that (s) conceptually. X 133 Necessity/principle/Quine: the principle of minimum mutilation is what underlies the logical necessity: it can explain the nature of the necessity which is connected to the logical and mathematical truth. - ((s) > Simplicity). Rorty IV 60 Necessary/contingent/Quine: there is no distinction between necessary and contingent truths. |
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 |
| Number Theory | Quine | IX 81 Elementary Number Theory/Quine: this is the theory that can only be expressed with the terms "zero, successor, sum, power, product, identity" and with the help of connections from propositional logic and quantification using natural numbers. One can omit the first four of these points or the first two and the fifth. But the more detailed list is convenient, because the classical axiom system fits directly to it. Quine: our quantifiable variables allow other objects than numbers. However, we will now tacitly introduce a limitation to "x ε N". Elementary Number Theory/Quine: less than/equal to: superfluous here. "Ez(x + z = y)" - x ε N > Λ + x = x. - x,y ε N >{x} + y = {x+y}. IX 239 Relative Strength/Proof Theory/Theory/Provability/Quine: Goedel, incompleteness theorem (1931)(1). Since number theory can be developed in set theory, this means that the class of all theorems IX 239 (in reality, all the Goedel numbers of theorems) of an existing set theory can be defined in that same set theory, and different things can be proved about it in it. >Set Theory/Quine. Incompleteness Theorem: as a consequence, however, Goedel showed that set theory (if it is free of contradiction) cannot prove one thing through the class of its own theorems, namely that it is consistent, i.e., for example, that "0 = 1" does not lie within it. If the consistency of one set theory can be proved in another, then the latter is the stronger (unless both are contradictory). Zermelo's system is stronger than type theory. >Type theory, >Strength of theories, >Set theory, >Provability. 1.Kurt Gödel: Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I. In: Monatshefte für Mathematik und Physik. 38, 1931, S. 173–198, doi:10.1007/BF01700692 II 178 Elementary number theory is the modest part of mathematics that deals with the addition and multiplication of integers. It does not matter if some true statements will remain unprovable. This is the core of Goedel's theorem. He has shown how one can form a sentence with any given proof procedure purely in the poor notation of elementary number theory, which can be proved then and only then if it is wrong. But wait! The sentence cannot be proved and still be wrong. So it is true, but not provable. Quine: we used to believe that mathematical truth consists in provability. Now we see that this view is untenable to mathematics as a whole. II 179 Goedel's incompleteness theorem (the techniques applied there) has proved useful in other fields: Recursive number theory, or recursion theory for short. Or hierarchy theory. >Goedel/Quine. III 311 Elementary Number Theory/Quine: does not even have a complete proof procedure. Proof: reductio ad absurdum: suppose we had it with which to prove every true sentence in the spelling of the elementary number theory, III 312 then there would also be a complete refutation procedure: to refute a sentence one would prove its negation. But then we could combine the proof and refutation procedure of page III 247 to a decision procedure. V 165 Substitutional Quantification/Referential Quantification/Numbers/Quine: Dilemma: the substitutional quantification does not help elementary number theory to any ontological thrift, for either the numbers run out or there are infinitely many number signs. If the explanatory speech of an infinite number sign itself is to be understood again in the sense of insertion, we face a problem at least as serious as that of numbers - if it is to be understood in the sense of referential quantification, then one could also be satisfied from the outset uncritically with object quantification via numbers. >Quantification/Quine. V 166 Truth conditions: if one now assumes substitutional quantification, one can actually explain the truth conditions for them by numbers by speaking only of number signs and their insertion. Problem: if numerals are to serve their purpose, they must be as abstract as numbers. Expressions, of which there should be an infinite number, could be identified by their Goedel numbers. No other approach leads to a noticeable reduction in abstraction. Substitutional quantification: forces to renounce the law that every number has a successor. A number would be the last, but the substitutional quantification theorist would not know which one. It would depend on actual inscriptions in the present and future. (Quine/Goodman 1947). This would be similar to Esenin Volpin's theory of producible numbers: one would have an unknown finite bound. V 191 QuineVsSubstitutional Quantification: the expressions to be used are abstract entities as are the numbers themselves. V 192 NominalismVsVs: one could reduce the ontology of real numbers or set theory to that of elementary number theory by establishing truth conditions for substitutional quantification on the basis of Goedel numbers. >Goedel Numbers/Quine. QuineVs: this is not nominalistic, but Pythagorean. It is not about the high estimation of the concrete and disgust for the abstract, but about the acceptance of natural numbers and the rejection of most transcendent numbers. As Kronecker says: "The natural numbers were created by God, the others are human work". QuineVs: but even that is not possible, we saw above that the subsitutional quantification over classes is basically not compatible with the object quantification over objects. V 193 VsVs: one could also understand the quantification of objects in this way. QuineVs: that wasn't possible because there aren't enough names. You could teach space-time coordination, but that doesn't explain language learning. X 79 Validity/Sentence/Quantity/Schema/Quine: if quantities and sentences fall apart in this way, there should be a difference between these two definitions of validity about schema (with sentences) and models (with sentences). But it follows from the Löwenheim theorem that the two definitions of validity (using sentences or sets) do not fall apart as long as the object language is not too weak in expression. Condition: the object language must be able to express (contain) the elementary number theory. Object Language: In such a language, a scheme that remains true in all insertions of propositions is also fulfilled by all models and vice versa. >Object Language/Quine The requirement of elementary number theory is rather weak. Def Elementary Number Theory/Quine: speaks about positive integers by means of addition, multiplication, identity, truth functions and quantification. Standard Grammar/Quine: the standard grammar would express the functors of addition, multiplication, like identity, by suitable predicates. X 83 Elementary Number Theory/Quine: is similar to the theory of finite n-tuples and effectively equivalent to a certain part of set theory, but only to the theory of finite sets. XI 94 Translation Indeterminacy/Quine/Harman/Lauener: ("Words and Objections"): e.g. translation of number theory into the language of set theory by Zermelo or von Neumann: both versions translate true or false sentences of number theory into true or false sentences of set theory. Only the truth values of sentences like e.g. "The number two has exactly one element", which had no sense before translation, differ from each other in both systems. (XI 179: it is true in von Neumann's and false in Zermelo's system, in number theory it is meaningless). XI 94 Since they both serve all purposes of number theory in the same way, it is not possible to mark one of them as a correct translation. |
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 |
| Numbers | Field | I 153 Numbers/Frege/Crispin Wright: Frege suggests that the fact that our arithmetical language has these qualities is sufficient to establish natural numbers as a sortal concept whose instances, if they have some, are the objects. WrightVsFrege: but the objects do not have to exist. Problem: Frege thus demands that empirical concerns are irrelevant. - Then there is also no possibility of an error. >Numbers/Frege, >Existence/Frege. II 214 Numbers/BenacerrafVsReduction/Benacerraf/Field: there may be several correlations so that one cannot speak of "the" referent of number words. >Paul Benacerraf. Solution/Field: we have to extend "partially denoted" also to sequences of terms. >Denotation, >Partial denotation, >Generalization/Field. Then "straight", "prim", etc. become base-dependent predicates whose basis is the sequence of the numbers. - Then one can get mathematical truth (> truth preservation, truth transfer). - E.g. "The number two is Caesar" is neither true nor false. (without truth value). >Senseless. II 326 Def Natural numbers/Zermelo/Benacerraf/Field: 0 is the empty set and every natural number > 0 is the set that is the only element which includes the set which is n-1. Def Natural numbers/von Neumann/Benacerraf/Field: Every natural number n is the set that has the sets as elements which are the predecessors of n as elements. Fact/Nonfactualism/Field: it is clear that there is no fact about whether Zermelos or von Neumann's approach "presents" the things "correctly" - there is no fact which decides whether numbers are sets. That is what I call the Definition Structural Insight: it makes no difference what the objects of a mathematical theory are, if they are only in a right relationship with each other. |
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 |
| Objectivity | Quine | I 29 Objectivity: people of normal vision as well as red-green-blind are trained in the same way. I 24 The company's method: to reward "Ouch" if the speaker shows further signs of discomfort. Trained in a way that the speaker says this even on stimuli that are not visible to her what she deems appropriate. When the man visibly looks at something red, the utterance "red" is rewarded. With regard to "red" there is a symmetry of verifiability, which is missing in the sense of "Ouch". "Ouch" is to a greater degree subjective. "Ouch" is not independent of social training. II 85 It is a bitter irony that such a vital distinction as that between good and evil should have no comparable claim to objectivity. Everyone who deals with moral problems refers to causal relationships. The number of ethical axioms can be reduced to a minimum by causal feedback. Utilitarianism is a remarkable example of such systematization. For example, for the settlement of conflicts: Problem of white lie: if we agree that truthfulness is not an end in itself, but only a means to higher morality, the problem becomes a question of science or technology. On the one hand, the usefulness of language requires an overweight of truthfulness, on the other hand, truth can hurt. >Truth/Quine. II 113 Austin's introspection contrasts with linguistics. He gains objectivity through "group introspection" (Urmson). For example, an exotic linguist would probably first find out what we designate with "male dog". But he could never find out what "bachelors" are. He must question all test subjects individually and later apply a society-related summation. II 180 Mathematical objectivity: For example, the continuum hypothesis but also its negation can be added to the axioms of set theory. Do these results cast doubt on the objectivity of mathematical truth? VI 48 Theory/Existence/Ontology/Quine: when a theory is about the radical question of what exists at all, quantification can only play the role of the arbitrator over questions of existence within the framework of a standardized and regulated form of language; a language that goes beyond truth functions (not, or, and). >Existence/Quine. VI 49 The objectivity of our knowledge remains rooted in our causal contact with external reality. |
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 |
| Omniscience | Lewis | Schwarz I 178 Omniscience/Lewis/Schwarz: Problem: you have to know all the logical and mathematical truths that follow from what you know already. Solution: genuine ignorance of contingent truths instead of seeming ignorance of necessary truths. >Contingency, >Necessity. Numeracy/mathematical solutions: one learns nothing new - previously only cognitive limitation. The brain cannot always retrieve all information. --- Schwarz I 180 Logical omniscience/Schwarz: the most common objection VsPossible Worlds as an analysis of mental content. Solution: rather cognitive limitation: usually no contingent information. >Possible world/Lewis. |
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 |
| Principles | Quine | VII (f) 107f Principles/Quine: are given in the following form, ex: (1) [(x)(Fx > Gx) . (Ex)Fx] > (Ex)Gx - "Fx" could be: "x swims" or "x is a whale" (general term) - the form (1) and the like can easily be regarded as schemes that take the form of different true statements -E.g. x has mass > x is extended... - it is not necessary to assume that "has mass" etc. is the name of classes or anything else - just as "F" and "G" from (1) must not be considered to be something else than values for the classes or anything else. >Classes/Quine. IX 119 Substitution Principle/Quine: guarantees the existence of all classes that are equal to an ordinal number. X 90 Principle/Quine: E.g. utilisation of all possibilities. X 133 Necessity/Principle/Quine: the principle of minimum mutilation is what underlies the logical necessity: it can explain the type of necessity which is connected to the logical and mathematical truth. - ’((s)> Simplicity). >Necessity/Quine |
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 |
| Reality | Deutsch | I 105 Criterion for reality: something that can hit back exists. But also Dr. Johnson did not directly hit the stone. He just hit some nerves, and so on. Cf. >Reality/Hacking. I 107 Def Reality/Deutsch: if a quantity is complex and autonomous according to the simplest explanation, then it is real. >Simplicity, >Complexity, >Explanation. I 111 Theory: the more fundamental a theory is, the more comprehensive are the observations that play a role in it. Physical reality is therefore self-similar in several ways. >Theory, >Theory/Deutsch, >Self-similarity. After all, not everything that is real must be easy to identify. I 119 Simulation: A reality simulator indirectly conveys both internal and external experiences to the recipient, but it cannot be programmed to simulate a particular internal experience. Roulette example and tennis example: the framework conditions are defined here, the course of the game must be open, which means that the abstract laws themselves and not only their predictive power can be simulated in virtual reality. >Laws, >Laws of nature, >Simulation, >Prediction. I 190 Life = simulation: both are embodiments of theories about the environment; Something that only exists in the laws of classical physics does not exist in reality. Real hurricanes and butterflies obey the laws of quantum theory, not those of classical mechanics! I 225/26 Plato's apparent refutation that the methods of natural science could lead to mathematical truth: we cannot know anything about perfect circles because we only have access to imperfect circles. DeutschVsPlato: then we can also only build inaccurate tool machines, because the first ones are built with inaccurate tools. So there would be no possibility of self-correction. Cf. >Ideas/Plato. |
Deutsch I D. Deutsch Fabric of Reality, Harmondsworth 1997 German Edition: Die Physik der Welterkenntnis München 2000 |
| Sensory Impressions | Descartes | Stroud I 8 Senses/Descartes: Even if we know that we can be deceived, it is not wiser to assume that we are always being deceived than to think we would never be. Stroud: we should not assume all our senses to be fundamentally unreliable. >Deceptions. Stroud I 16 Senses/Knowledge/Descartes: E.g. If he knows that he is sitting at the fireplace, he thinks that he knows it due to the senses. But he also knows that it is compatible with the fact that he is only dreaming. VsDescartes: if we allow a dreaming person to know something (e.g. mathematics, mathematical truths), does this not show that Descartes is wrong with his skepticism? VsVs: this is not shown by that. >Certainty, >Skepticism, >Knowledge, >Perception. |
Stroud I B. Stroud The Significance of philosophical scepticism Oxford 1984 |
| Situation Semantics | Barwise | Cresswell II 169 Situation semantics/Barwise/Perry/Cresswell: (Barwise/Perry, 1983)(1): here it is explicitly denied that logically equivalent sentences in contexts with propositional attitudes are interchangeable. (1983(1), 175, 1981b(4), 676f) - e.g. double negation in the attribution of propositional attitudes. >Equivalence, >Double negation. Solution: partial character of situations. - Not everything has to be given - or the speaker may have to suspend judgment. ("do not ..."). >Situations. Def sentence meaning/Barwise/Perry: a relation between situations. Cresswell I 63 Situation SemanticsVsPossible World Semantics/knowledge/meaning/Barwise/Perry/BarweiseVsCresswell/ PerryVsCresswell/Cresswell: the possible worlds are too big to explain what the speaker knows when he/she utters a meaningful sentence. Possible worlds: are complete possible situations. >Possible worlds, >Possible World Semantics. Situation semantics: we need a more partial type of entity. ((s) partial, not complete). CresswellVsSituation Semantics: (Cresswell 1985a(2), 168 ff, 1985b(3), Chapter 7) Solution/Cresswell: Thesis: The situations only have to be partial in the sense that they are small worlds. Def Abstract Situation/Barwise/Perry: (1983(1), 57 ff): abstract situations are theoretical constructs used for an adequate semantic modeling of reality consisting of real situations. Cresswell: I ignore this distinction here. The semantics of possible worlds is better here, even if one differentiates between reality and theoretical representation. >Possible World Semantics. What we need to compare are abstract situations and worlds. I 64 Situation-SemanticsVsPossible World Semantics/BarwiseVsCresswell: there are often two propositions, one of which is believed by the person, but the other is not, but both are still true in the same worlds - for example, all logical and mathematical truths - but they are not all known, otherwise there could be no progress. I 65 CresswellVs: the situations should play roles that cannot be played at the same time. Solution: Semantics of possible worlds: the roles are played by entities of different kinds. Solution: Context with space-time specification. >Context. False sentences: describe non-actual situations. I 66 Sentences describe situations in a context - context is itself a situation that provides the listener with time, place, etc. Interpretation/Barwise: Meaning of sentences in a context. >Interpretation, >Sentence meaning. Meaning/CresswellVsSituation Semantics/CresswellVsBarwise/CresswellVsPerry: Meaning: = set of worlds in which they are true. Problem: Meanings are often equated with proposition, and then there are problems in playing roles that they cannot play at the same time. I 67 On the other hand, some of the other things that Barwise and Perry ask for from situations behave like worlds! For example: Mollie barks e*: = in I, Mollie, yes. That describes a situation e iff e* < e. ((s) Subset of situations where Mollie barks otherwise? Or where Mollie exists and someone barks?). Def Generation property/terminology/Cresswell: (generation property): sentences that describe a situation have a situation property ((s) that is part of a set of situations). A sentence ? has the generation property in terms of a context u, iff there is a situation e*, so that u[[φ]] e iff e* < e. ((s) If there is a sentence that is more general than the sentence "Mollie barks in the space-time situation I" Or: Generation property is the property that embeds the sentence in the context, because proposition as sets of worlds must not be limited to a single situation.) The sentence φ has the generation property (simpliciter) iff it has it in every context. Atomic sentence/Barwise/Perry: Thesis: all atomic sentences have the generation property. >Atomic sentences. Cresswell: if situations are to be understood as proposition, all sentences should have the generation property. And that is because the generating situation e* can be understood as the proposition expressed by the sentence ? in context u. In fact, we do not need the other situations at all! We can say that e* is the only situation described by φ in u. But that doesn't matter, because each e* determines the only class of e's, so e* < e, and each class generated by an e* determines that e* uniquely. 1. Jon Barwise & John Perry (1983). Situations and Attitudes. Cambridge, Mass.: MIT Press. Edited by John Perry 2. M. J. Cresswell (1985a) Situations and Attitudes. Philosophical Review 94 (2):293 3. M. J. Cresswell (1985b). Structured meanings. MIT Press 4. Jon Barwise & John Perry (1981). Semantic Innocence and Uncompromising Situations. Midwest Studies in Philosophy (1981), 6 : 387 https://doi.org/10.1111/j.1475-4975.1981.tb00447.x |
Barw I J. Barwise Situations and Attitudes Chicago 1999 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 |
| Skepticism | Descartes | Stroud I 4 Descartes/Skepticism/Knowledge/Stroud: Descartes wants to establish principles, a general method for the investigation of our knowledge. >Principles, >Knowledge. 1) Meditation: in the end, Descartes finds that there is no reason to believe anything about the world around him. Stroud I 16 Senses/Knowledge/Descartes: E.g. if he knows that he is sitting at the fireplace, he thinks that he knows it due to his senses. >Perception, >Sensory impressions. But he also knows that it is compatible with the fact that he is only dreaming. VsDescartes: If we allow a dreaming person to know something (e.g. mathematics, mathematical truths), does this not show that Descartes is wrong with his skepticism? VsVs: This is not shown with that. Stroud I 37 Descartes/Stroud: From the beginning, his skepticism was directed against everyday knowledge. >Certainty. |
Stroud I B. Stroud The Significance of philosophical scepticism Oxford 1984 |
| Truth | Kripke | I 47/48 Necessary and a priori are not obviously synonymous. They are not even coextensive: there are both: necessary truths from posteriori and probably contingent truths a priori! >Necessary/Kripke, >necessary a posteriori, >necessary de re/Kripke, >a priori/Kripke. Many people have thought that these two things should mean the same thing because they imagine we would go through all possible worlds in our minds and then be able to recognize them a priori. But that is not so clear! I 50 Description: if we call Nixon "the man who won the 1988 election", it will of course be a necessary truth. >Description/Kripke. I 66 Prototype meter/standard meter: someone who thinks that everything you know a priori is necessary might think: "This is the definition of a meter. This is a necessary truth." Kripke: however, he/she does not use this definition to specify the meaning, but to define the reference. >Standard meter, >Speaker reference, >Reference/Kripke. I 68 Rigid: a meter is rigid ((s) "rigid" means that the reference is the same in all possible worlds). Non-rigid: the length of S at time t is non-rigid. The "definition" does not say that the two expressions are synonymous, but rather that we have determined the reference of the expression "one metre" by fixing that it is to be a rigid expression of designations, which in fact has the length S. The term "one metre" is not synonymous with the term "one metre". So it is no necessary truth! And that is because under certain circumstances it would not have been one metre long. One expression is rigid and the other is not. The truth he/she knows is contingent. So I prefer not to call them "analytical." >Analytic/synthetic, >Rigidity, >Contingency. I 77 E.g. a thesis may be true because it is simply a definition. >Definition/Kripke. I 153ff Reference of proper names: Definition of the reference: is given a priori (contingent) - this is not the same as synonymy. Meaning: the meaning is analytical (necessary). Definition: defines reference and expresses truth a priori. I 156 E.g. necessary truth: "Cats are animals". I 175 The phrase "heat is the movement of molecules" expresses a truth a posteriori. I 181 A posteriori: one can experience a mathematical truth a posteriori by looking at a computer or by asking a mathematician. The philosophical analysis tells us that it was not contingent and therefore any empirical knowledge of its truth is automatically an empirical knowledge of its necessity. --- III 409 Truth/formal languages: understanding the meta language > explicit truth-definition > truth conditions > understanding of the language examined. >Truth conditions, >Understanding. |
Kripke I S.A. Kripke Naming and Necessity, Dordrecht/Boston 1972 German Edition: Name und Notwendigkeit Frankfurt 1981 Kripke II Saul A. Kripke "Speaker’s Reference and Semantic Reference", in: Midwest Studies in Philosophy 2 (1977) 255-276 In Eigennamen, Ursula Wolf Frankfurt/M. 1993 Kripke III Saul A. Kripke Is there a problem with substitutional quantification? In Truth and Meaning, G. Evans/J McDowell Oxford 1976 Kripke IV S. A. Kripke Outline of a Theory of Truth (1975) In Recent Essays on Truth and the Liar Paradox, R. L. Martin (Hg) Oxford/NY 1984 |
| Understanding | Deutsch | I 149 Understanding: for the reality to be understandable, the laws of nature must be incorporated in another object: the one, that understands - I 240 Understanding: While everything is understandable in physical reality, the intelligible mathematical truths are a tiny minority, which coincidentally corresponds to a physical truth! >Laws of nature, >Reality, >Mathematics, >World/thinking. Brockman I 123 Understanding/Deutsch: In the broadest sense, a person’s quest for understanding is indeed a search problem, in an abstract space of ideas far too large to be searched exhaustively. But there is no predetermined objective of this search. There is, as Popper put it, no criterion of truth, nor of probable truth, especially in regard to explanatory knowledge. Objectives are ideas like any others—created as part of the search and continually modified and improved. >Criteria/Popper, >Artificial General Intelligence/Deutsch. Deutsch, D. “Beyond Reward and Punishment” in: Brockman, John (ed.) 2019. Twenty-Five Ways of Looking at AI. New York: Penguin Press. |
Deutsch I D. Deutsch Fabric of Reality, Harmondsworth 1997 German Edition: Die Physik der Welterkenntnis München 2000 Brockman I John Brockman Possible Minds: Twenty-Five Ways of Looking at AI New York 2019 |
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| Disputed term/author/ism | Author Vs Author |
Entry |
Reference |
|---|---|---|---|
| Artificial Intelligence | Gödel Vs Artificial Intelligence | Dennett I 603 Library of BabelGodel / Turing: showed that this set belongs to a different set in the Library of Babel: the set of all possible computers. Each Turing machine in which happens to be a consistent algorithm runs for evidence of mathematical truths is associated with a Godel s theorem, an arithmetic truth that they can not prove. Dennett: So what? Mind / Godel: it shows that the mind can not simply be like machines. People can do things which machines can t. DennettVs! DennettVsGödel: problem: how can you find out, whether a mathematician proved a theorem, or has only made a noise like a parrot? (> Behavior). |
Göd II Kurt Gödel Collected Works: Volume II: Publications 1938-1974 Oxford 1990 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 |
| Artificial Intelligence | Penrose Vs Artificial Intelligence | Dennett I 617 PenroseVsAI/PenroseVsArtificial Intelligence: x can perfectly achieve a checkmate There is no algorithm for chess. Therefore, the good performance of x can not be explained by the fact that x can run an algorithm. Dennett I 619 Penrose: if you take any single algorithm, it can not be the method by which human mathematicians insure mathematical truths. Therefore they use no algorithms at all. I 621 DennettVsPenrose: thus is not shown that the human brain does not operate algorithmically. On the contrary, it makes clear how the cranes of culture, the community of mathematicians can exploit without recognizable boundaries in distributed algorithmic processes. |
Penr I R. Penrose The Road to Reality: A Complete Guide to the Laws of the Universe 2005 Dennett I D. Dennett Darwin’s Dangerous Idea, New York 1995 German Edition: Darwins gefährliches Erbe Hamburg 1997 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 |
| Benacerraf, P. | Lewis Vs Benacerraf, P. | Field I 231 Example (2) if most mathematicians accept "p" as an axiom, then p. I 232 VsPlatonism: he has a problem if he cannot explain (2). This is a reformulation of the famous problem of Benacerraf in "Mathematical truth". (see above). (>Benacerraf here departs from a causal theory of truth). Field: our current approach does not depend on that, though. I 233 Knowledge/Mathematics/Field: our approach does not depend on the givenness of necessary and sufficient conditions for knowledge. Instead: Reliability Theory/Knowledge/Field: the view that we should be skeptical if the reliability of our knowledge is not explainable in principle. Mathematics/LewisVsBenacerraf: (Lewis, 1986, p.111 12): Benacerraf's case is not a problem for mathematics because most mathematical facts necessarily apply. Reliability Theory/Lewis: then we also need an explanation of the reliable relationship, e.g., between facts about electrons and our "electron" belief states and we even have them! In this case, it is the causal approach, according to which the "electron" beliefs counterfactually (>counterfactual conditionals) depend on the existence and nature of electrons. Explanation/Lewis: now it's precisely the contingent existence and nature of electrons, which makes the question of their existence and nature meaningful. Lewis: nothing can counterfactually depend on non-contingent things. E.g. nothing can counterfactually depend on which mathematical entities there are. Nothing meaningful can be said about which of our opinions would be different if the number 17 did not exist. Stalnaker I 41 Mathematics/Benacerraf/Stalnaker: for mathematics we should expect a semantics that is a continuation of general semantics. We should interpret existence statements about numbers, functions and sets with the same truth-conditional semantics as propositions about tables, quarks, etc. I 42 Knowledge/Mathematics/Reality/Stalnaker: On the other hand, we should also expect that the access to our mathematical knowledge is continuous to the to everyday knowledge. The procedures by which we evaluate and justify mathematical statements should be explained by a general approach to knowledge, together with a representation of mathematical knowledge. Platonism/Mathematics/Benacerraf: Thesis: he gives natural semantics, but does not allow plausible epistemology. ((s) that does not explain how we come to knowledge). Combinatorial Approach/Combinatorial/Terminology/Benacerraf: Example conventionalism, example formalism: they show mathematical procedures, but do not tell us what the corresponding confirmed mathematical statements tell us. Benacerraf/Stalnaker: he himself does not offer any solution. Reference/Benacerraf: Thesis: true reference needs a causal link. Knowledge/Possible Worlds/Poss.W./Solution/LewisVsBenacerraf: pro Platonism but Vs causal link for reference. |
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 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 Stalnaker I R. Stalnaker Ways a World may be Oxford New York 2003 |
| Carnap, R. | Putnam Vs Carnap, R. | Goodman II Putnam Foreword V Carnap/Putnam: according to Putnam Carnap has the constant tendency to identify terms with their syntactic representations (> Putnam I (a) 48). Carnap suggested that a predicate can also be disjunctive or non-disjunctive in itself, PutnamVsCarnap: E.g. "logical sky" e.g. "is to tell us" e.g. "metaphysical pointer". >Disjunctive predicate. Lewis IV 85 Partial Interpretation/PutnamVsCarnap: theories with false observation consequences have no interpretation! Because they have no "model" that is "standard" with respect to the observation concepts. IV 85/86 Putnam: such interpretations are wrong then, not pointless! Sense/Theory/LewisVsPutnam: the theoretical concept are also not meaningless here, but denotation-less (without denotation): their sense is given by their denotation in those possible worlds in which the theory is uniquely implemented and thus has no wrong consequences there. They have a sense as well as the reference-less term "Nicholas". Putnam V 244 Pain/Physical Object/Putnam: It is difficult to understand that the statement that a table stands in front of someone is easier to accept than the statement that someone is in pain. Popper/Carnap: would respond: the methodological difference consists in that one of them is public and the other is private. PutnamVsPopper/VsCarnap: both exaggerate the extent to which observations of physical objects are always publicly verifiable. >Observability. V 250 Method/Science/PutnamVsCarnap: many philosophers believed (wrongly) that science proceeded by a method (e.g. Carnap). Putnam I (a) 42 Carnap/Putnam: (Logischer Aufbau der Welt) Final Chapter: brings a sketch of the relation between object language to sensation language which is not a translation! PutnamVsCarnap/PutnamVsPhenomenology: this amounts to the old assertion that we would pick out the object theory that is the "easiest" and most useful. There is no evidence as to why a positivist is entitled to quantify over material things (or to refer to them). Phenomenology/Putnam: after their failure there were two reactions: 1) theories were no longer to be construed as statements systems that would need to have a perfectly understandable interpretation, they are now construed as calculi with the aim to make predictions. I 43 2) Transition from the phenomenalistic language to "language of observable things" as the basis of the reduction. I.e. one seeks an interpretation of physical theories in the "language of things", not in the "sensation language". Putnam I (a) 46 Simplicity/Putnam: gains nothing here: the conjunction of simple theories need not be simple. Def Truth/Theory/Carnap: the truth of a theory is the truth of its Ramsey sentence. PutnamVsCarnap: this again is not the same property as "truth"! (I 46 +: Hilbert's ε, formalization of Carnap: two theories with the same term). I (a) 48 Language/Syntax/Semantics/PutnamVsCarnap: he has the constant tendency to identify concepts with their syntactic representations, e.g. mathematical truth with the property of being a theorem. I (a) 49 Had he been successful with his formal language, it would have been successful because it would have corresponded to a reasonable degree of probability over the set of facts; However, it is precisely that which positivism did not allow him to say! |
Putnam I Hilary Putnam Von einem Realistischen Standpunkt In Von einem realistischen Standpunkt, Vincent C. Müller Frankfurt 1993 Putnam I (a) Hilary Putnam Explanation and Reference, In: Glenn Pearce & Patrick Maynard (eds.), Conceptual Change. D. Reidel. pp. 196--214 (1973) In Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993 Putnam I (b) Hilary Putnam Language and Reality, in: Mind, Language and Reality: Philosophical Papers, Volume 2. Cambridge University Press. pp. 272-90 (1995 In Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993 Putnam I (c) Hilary Putnam What is Realism? in: Proceedings of the Aristotelian Society 76 (1975):pp. 177 - 194. In Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993 Putnam I (d) Hilary Putnam Models and Reality, Journal of Symbolic Logic 45 (3), 1980:pp. 464-482. In Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993 Putnam I (e) Hilary Putnam Reference and Truth In Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993 Putnam I (f) Hilary Putnam How to Be an Internal Realist and a Transcendental Idealist (at the Same Time) in: R. Haller/W. Grassl (eds): Sprache, Logik und Philosophie, Akten des 4. Internationalen Wittgenstein-Symposiums, 1979 In Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993 Putnam I (g) Hilary Putnam Why there isn’t a ready-made world, Synthese 51 (2):205--228 (1982) In Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993 Putnam I (h) Hilary Putnam Pourqui les Philosophes? in: A: Jacob (ed.) L’Encyclopédie PHilosophieque Universelle, Paris 1986 In Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993 Putnam I (i) Hilary Putnam Realism with a Human Face, Cambridge/MA 1990 In Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993 Putnam I (k) Hilary Putnam "Irrealism and Deconstruction", 6. Giford Lecture, St. Andrews 1990, in: H. Putnam, Renewing Philosophy (The Gifford Lectures), Cambridge/MA 1992, pp. 108-133 In Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993 Putnam II Hilary Putnam Representation and Reality, Cambridge/MA 1988 German Edition: Repräsentation und Realität Frankfurt 1999 Putnam III Hilary Putnam Renewing Philosophy (The Gifford Lectures), Cambridge/MA 1992 German Edition: Für eine Erneuerung der Philosophie Stuttgart 1997 Putnam IV Hilary Putnam "Minds and Machines", in: Sidney Hook (ed.) Dimensions of Mind, New York 1960, pp. 138-164 In Künstliche Intelligenz, Walther Ch. Zimmerli/Stefan Wolf Stuttgart 1994 Putnam V Hilary Putnam Reason, Truth and History, Cambridge/MA 1981 German Edition: Vernunft, Wahrheit und Geschichte Frankfurt 1990 Putnam VI Hilary Putnam "Realism and Reason", Proceedings of the American Philosophical Association (1976) pp. 483-98 In Truth and Meaning, Paul Horwich Aldershot 1994 Putnam VII Hilary Putnam "A Defense of Internal Realism" in: James Conant (ed.)Realism with a Human Face, Cambridge/MA 1990 pp. 30-43 In Theories of Truth, Paul Horwich Aldershot 1994 SocPut I Robert D. Putnam Bowling Alone: The Collapse and Revival of American Community New York 2000 Lewis I David K. Lewis Die Identität von Körper und Geist Frankfurt 1989 LewisCl I Clarence Irving Lewis Mind and the World Order: Outline of a Theory of Knowledge (Dover Books on Western Philosophy) 1991 |
| Counterfactual Conditional | Schwarz Vs Counterfactual Conditional | Schwarz I 131 Similarity criteria/VsLewis: but even so a counterfactual dependence without causality would be possible: E.g. the halting problem would be solvable, were the PL decidable (because counterfactual conditionals with a false antecedent is always true with Lewis) but that one is not the cause of the other. Vs counterfactual conditional/Vs co.co: Problem: after the previous analysis every event would also cause itself: it would not happen, then it would not have happened! E.g. Jaegwon Kim (1973(1), 1974(2)): if Socrates had not died, Xanthippe would not have become a widow, e.g. had I not turned the window handle, I would not have opened the window, e.g. had I not written "rr", I would not have written "Larry". Everything counterfactual relations without causality. Solution/Lewis: we must limit the Relata A and B: they may neither be mathematical truths nor be identical to each other. Allowed are only contingent, non-overlapping single events. Overlapping/Schwarz: "Non-overlapping" is weaker than "not identical". ((s) "overlapping" can also be "not identical". This excludes that e.g. a football match caused its first half..) ((s)> Hume: Only between non-identical events causality can be effective). LewisVsKim: so also its examples are done: partly the entities Kim considered, are no events (e.g. Xanthippe) partly it is a single event, described by two identifiers (e.g. window), or two events that are not completely separated (E.g. Larry). (1981c(3), 124). 1. Jaegwon Kim [1973]: “Causes and Counterfactuals”. Journal of Philosophy, 70: 570–572 2. Jaegwon Kim [1974]: “Noncausal Connections”. Nous, 8: 41–52. In [Kim 1993] 3. David Lewis [1981c]: “Nachwort (1978) zu ‘Kausalität’ ”. In Güuter Posch (ed.), Kausalität: Neue Texte, Stuttgart: Reclam, 124–126 |
Schw I W. Schwarz David Lewis Bielefeld 2005 |
| Goedel, K. | Dennett Vs Goedel, K. | I 603 Gödel number/Dennett: Goedel numbers make it possible to arrange all possible axiom systems in alphabetical order. Goedel/Turing: showed that this set belongs to a different set in the Library of Babel: the set of all possible computers. Each Turing machine in which happens that a consistent algorithm runs for proving mathematical truths is associated with a Godel s theorem - with an arithmetic truth that it can not prove. Dennett: So what? Mind/Goedel: it shows that the mind can not simply be like machines. People can do things which may not be performed by machines. DennettVs! DennettVsGödel: problem: how can you find out, whether a mathematician has proved a theorem, or has only made a noise like a parrot? (> Proofs). |
Dennett I D. Dennett Darwin’s Dangerous Idea, New York 1995 German Edition: Darwins gefährliches Erbe Hamburg 1997 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 |
| Hume, D. | Kripke Vs Hume, D. | Apriori: Some philosophers modify the modalities in this characterization somehow from "may" to "shall". They think that if something belongs to the realm of a priori knowledge it is impossible to recognize it empirically.(Hume). This is wrong! (KripkeVsHume). E.g. The computer can give an answer to the question of whether particular numbers are primes. Nobody has calculated or proved this, but the computer gave the answer. I 45 A posteriori: A mathematical truth can be known a posteriori by looking at a computer or by asking a mathematician (e.g. naturally a posteriori). The philosophical analysis tells us that it could not be contingent and therefore all empirical knowledge of its truth is automatically an empirical knowledge of its necessity.(KripkeVsHume, KripkeVsKant) I 181 |
Kripke I S.A. Kripke Naming and Necessity, Dordrecht/Boston 1972 German Edition: Name und Notwendigkeit Frankfurt 1981 Kripke II Saul A. Kripke "Speaker’s Reference and Semantic Reference", in: Midwest Studies in Philosophy 2 (1977) 255-276 In Eigennamen, Ursula Wolf Frankfurt/M. 1993 Kripke III Saul A. Kripke Is there a problem with substitutional quantification? In Truth and Meaning, G. Evans/J McDowell Oxford 1976 Kripke IV S. A. Kripke Outline of a Theory of Truth (1975) In Recent Essays on Truth and the Liar Paradox, R. L. Martin (Hg) Oxford/NY 1984 |
| Indispensability | Field Vs Indispensability | I 14 Indispensability Argument/Field: here it’s all about purposes - such an argument must be based on the best explanation (BE). I 17 FieldVsIndispensability Argument: we can show that there are good theories that do without mathematical entities - Justification/Field: is gradual. FieldVsIndispensability Argument: two points which together make it seem untenable: 1) if we can show that there are equally good theories that do not involve ME. I believe that we can show that in the case of ME, but not in the case of electrons! (Lit.Field: "Science without Numbers"). At the moment, we do not yet know exactly how to eliminate ME, and our method of ((s) complete) induction gives us some confidence in mathematical entities 2) Justification is not a question of all or nothing! (justification gradual) I 29 Indispensability Argument/Field: Might even be explained by way of evolutionary theory: that evolutionary pressure finally led us to find the empirically indispensable mathematical assumptions plausible. FieldVsVsBenacerraf:. Problem: the scope of mathematics which is used in empirical science is relatively small! That means that only this small portion could be confirmed as reliable by empiricism. And inferences on the rest of mathematics are not sustainable, there are simply too many possible answers to questions about large cardinals or the continuum hypothesis or even about the axiom of choice. These work well enough to provide us with the simpler "application mathematics". ((s) That means that we cannot infer a specific answer to the questions of the higher levels from application mathematics.) II 328 Utility/Truth/Mathematics/Putnam/Field: (Putnam 1971 locus classicus, unlike 1980): Thesis: we must consider mathematics as true in order to be able to explain its utility (benefit) in other fields. E.g. in science and metalogic. (i.e. the theory of logical consequence). Modality/Modal/Mathematics/Field: this is in contrast to his former view that we can use modality instead of mathematical objects to explain mathematical truth. II 329 Modal Explanation: will not work for other disciplines such as physics, however. (FieldVsPutnam, Field 1989/91: 252-69). Putnam/Field: the general form of his argument is this: (i) we must speak in terms of mathematical entities in order to study science, metalogic, etc. (ii) If need them for such important purposes, we have reason to believe that this kind of entities exists. VsPutnam/Field: there are two possible strategies against this: 1) Vs: "foolhardy" strategy: requires us to substantially change premise (i): we want to show that we basically do not need to make any assumptions which require mathematical entities. I.e. we could study physics and metalogic "nominalistically". Problem: in a practical sense, we still need the mathematical entities for physics and metalogic. We need to explain this practical indispensability. "foolhardy" strategyVs: in order to explain them, we just have to show that mathematical entities are only intended to facilitate inferences between nominalistic premises. And if this facilitation of inference is the only role of mathematical entities, then (ii) fails. Solution: In that case, something much weaker than truth (E.g. "conservatism") suffices as an explanation for this limited kind of utility. FieldVs: Unfortunately, the project of nominalization is not trivial. (Field 1980 for physics, 1991 for metalogic). At that time I found only few followers, but I am too stubborn to admit defeat. 2) Vs ("less foolhardy strategy"): questions (ii) more profoundly: it denies that we can move from the theoretical indispensability of existence assumptions to a rational belief in their truth. That is what Putnam calls "indispensability argument". Putnam pro. FieldVsPutnam: that requires some restrictions and ManyVsPutnam: these restrictions ultimately prevent an application in mathematics. And ultimately, because mathematical entities are simply not causally involved in physical effects. II 330 FieldVsPutnam: that’s plausible. PutnamVsVs: If mathematical entities are theoretically indispensable in causal explanations (such as (i) claims), however, there seems to be a sense in which they are very well causally involved. Conversely, it would have to be explained why they should not be causally involved. FieldVs: a closer look should reveal that the role of mathematical entities is not causal. And that it supports no indispensability argument. E.g. the role of quantities in physics was simply to allow us to assert the local compactness of physical space. Other E.g. role of quantities in physics. Allow us to accept (Cp) instead of (Cs). (Field, 1989) 1, 136-7). ... + ... |
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 |
| James, W. | Rorty Vs James, W. | Horwich I 443 Truth/James/Rorty: Thesis: no truth theory (TT) can explain a correspondence relation. I 444 Correspondence/James: does not exist as as something neutral between perceptual, theoretical, moral or mathematical truths. Correspondence cannot take on an explanatory role. Truth/VsJames: theories are not true, because they work, but vice versa. They work, because they are true. JamesVsVs: these critics miss the point: Thesis: "true" is a term of respect. Truth/Justification/RortyVsJames: Unfortunately, James did not confine himself to this negative point, but he concluded from a false premise: If we have a concept of "justified", we do not need the concept of truth". "True" needs to mean something like "justifiable". This is a form of the idealistic error of inferring. We cannot get any sense out of the concept of truth as correspondence. Truth must exist in an ideal consistency. >Coherence. RortyVsJames: the mistake is to assume that "true" requires a definition, and then the fact that they cannot be defined as a relation of beliefs to non-beliefs on the view that it would have to be defined as a relation between beliefs. Naturalistic Fallacy/PutnamVsJames: E.g. "it could be true, but not X" is always useful, no matter what is inserted for X. (Moore asserted the same in connection with "good".) Truth/RortyVsPeirce: it was a mistake to identify it with the "end point of our examination". |
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 Horwich I P. Horwich (Ed.) Theories of Truth Aldershot 1994 |
| Kant | Kripke Vs Kant | I 135Kant: "All analytic judgments are based entirely on the principle of contradiction and by their nature are a priori knowledge, the definitions on which they are based on may be empirical or not. Since the predicate has been thought of in terms of the subject, it cannot be negated by the first." I 181 That is precisely why all analytic propositions are a priori judgments even though their terms are empirical. E.g. gold is a yellow metal. In order to know this, I need no further experience beyond my definition of gold. If that makes up my definition, I am only able to segment my definition, I cannot look anywhere else for it. Kripke: Kant seems to say that gold means simply yellow metal. KripkeVsKant: Is Kant right? According to scientists, it is very difficult to define what a metal is. We also need to know the periodic table. One might think that there are actually two definitions, a phenomenological and a scientific one, where the latter replaces the former. Phenomenological: Stretchable, deformable, scientific: Periodic table. (KripkeVs). A posteriori: one can learn a mathematical truth a posteriori by looking at a computer or by asking a mathematician. (e.g. naturally a posteriori). The philosophical analysis tells us that it could not be contingent, and therefore any empirical knowledge of its truth is automatically an empirical knowledge of its necessity.(KripkeVsHume, KripkeVsKant) |
Kripke I S.A. Kripke Naming and Necessity, Dordrecht/Boston 1972 German Edition: Name und Notwendigkeit Frankfurt 1981 Kripke IV S. A. Kripke Outline of a Theory of Truth (1975) In Recent Essays on Truth and the Liar Paradox, R. L. Martin (Hg) Oxford/NY 1984 |
| Lewis, C.I. | Schwarz Vs Lewis, C.I. | Schwarz I 31 Personal identity/SchwarzVsLewis: his criterion is not accurate and provides in interesting cases no answer. E.g. continuity after brain surgery, etc. But Lewis does not want that. Our (vague) everyday term should only be made explicitly. Beaming/Teleportation/Doubling/Lewis: all this is allowed by his theory. Schwarz I 60 Identity/Lewis/Centered world/Possible world/Schwarz: my desire to be someone else, does not refer to the whole world, but only to my position in the world. E.g. Twin Earth/Schwarz: one of the two planets is blown tomorrow, the two options (that we are on the one or the other) do however not correspond to two possible worlds! Detailed knowledge would not help out where we are, because they are equal. ((s) so no "centered world"). Actually, we want to know where we ourselves are in the world. (1979a(1),1983b(2),1986e(3):231 233). SchwarzVsLewis: says too little about these perspective possibilities. It is not enough here to allow multiple counterparts (c.p.) in a world. It should not just be possible that Humphrey is exactly as the actual Nixon, he should also to be allowed to be different. Humphrey may not be a GS of himself. (> Irreflexive counterpart relation,> see below Section 9.2. "Doxastic counterparts". Similarity relation. No matter what aspects you emphasize: Nixon will never be more similar to Humphrey than to himself. Schwarz I 100 Fundamental properties/SchwarzVsLewis: this seems to waver whether he should form the fE to the conceptual basis for the reduction of all predicates and ultimately all truths, or only a metaphysical basis, on which all truths supervene. (>Supervenience, >Reduction). Schwarz I 102 Naturalness/Natural/Property/Content/Lewis: the actual content is then the most natural candidate that matches the behavior. "Toxic" is not a perfectly natural property (p.n.p.), but more natural than "more than 3.78 light years away" and healthy and less removed and toxic". Naturalness/Degree/Lewis: (1986e(3):, 61,63,67 1984b(4):66): the naturalness of a property is determined by the complexity or length of their definition by perfectly natural properties. PnE: are always intrinsically and all their Boolean combinations remain there. Problem: extrinsic own sheep threaten to look unnatural. Also would e.g. "Red or breakfast" be much more complicated to explain than e.g. "has charge -1 or a mass, whose value is a prime number in kg. (Although it seems to be unnatural by definition). Naturalness/Property/Lewis: (1983c(5), 49): a property is, the more natural the more it belongs to surrounding things. Vs: then e.g. "cloud" less natural than e.g. "table in the vicinity of a nuclear power plant or clock showing 7:23". Schw I 103 Naturalness/Properties/Lewis: (1983c(5): 13f): naturalness could be attributed to similarity between characteristics: E.g. a class is more natural, the more the properties of its elements resemble each other. Similarity: Lewis refers to Armstrong: similarity between universals 1978b(6),§16.2,§21, 1989b(7): §5.111997 §4.1). Ultimately LewisVs. Naturalness/Lewis/Schwarz: (2001a(8):§4,§6): proposing test for naturalness, based on similarity between individual things: coordinate system: "intrinsic" and "extrinsic" axis. A property is then the more natural, the more dense and more compact the appropriate region is. Problem: 1. that presupposes gradual similarity and therefore cannot be well used to define gradual naturalness. 2. the pnE come out quite unnatural, because the instances often do not strongly resemble each other. E.g. if a certain mass property is perfect, of course, then all things with this mass build a perfectly natural class, no matter how dissimilar they are today. SchwarzVsLewis: it shows distinctions between natural and less natural properties in different areas, but does not show that the distinction is always the same. Naturalness/SchwarzVsLewis: could also depend on interests and biological expression. And yet, can in various ways the different types of natural - be determined by perfect naturalness. That is not much, because at Lewis all, by definition, by the distribution of p.n.p. is determined. ((s)>Mosaic). Schwarz I 122 Naturalness/SchwarzVsLewis: not reasonable to assume that it was objectively, regardless of how naturally it appears to us. Lewis introduced objective naturalness as a metaphysical basis for qualitative, intrinsic similarity and difference, as some things resemble each other like eggs and others do not. (see above 5.2). Intrinsic Similarity: also qualitative character and duplication: these terms are intended to be our familiar terms by Lewis. SchwarzVsLewis: but if objective naturalness is to explain the distinction of our opinions about similarity, one cannot ask with sense the question whether the distinction serves exactly this. So although there are possible beings (or worlds) whose predicates express relatively unnatural properties and therefore are wrong about natural laws, without being able to discover the error. But we can be sure a priori that we do not belong to them. Problem: the other beings may themselves believe a priori to be sure that their physical predicates are relatively natural. Solution: but they (and not we) were subject to this mistake, provided "natural" means in their mouth the same as with us. ((s) but we also could just believe that they are not subject to error. Respectively, we do not know whether we are "we" or "they"). Schwarz: here is a tension in our concept of natural law (NL): a) on the one hand it is clear that we can recognize them empirically. b) on the other hand they should be objective in a strong sense, regardless of our standards and terms. Problem: Being with other standards can come up with the same empirical data to all other judgments of NL. Schwarz I 134 Event/SchwarzVsLewis: perhaps better: events but as the regions themselves or the things in the regions: then we can distinguish e.g. the flight from the rotation of the ball. Lewis appears to be later also inclined to this. (2004d)(9). Lewis: E.g. the death of a man who is thrown into a completely empty space is not caused by something that happens in this room, because there is nothing. But when events are classes of RZ regions, an event could also include an empty region. Def Qua thing/Lewis/Schwarz: later theory: “Qua-things” (2003)(10): E.g. „Russell qua Philosoph“: (1986d(9a),247): classes of counterpieces – versus: LewisVsLewis: (2003)(10) Russell qua Philosoph and Russell qua Politician and Russell are identical. Then the difference in counterfactual contexts is due to the determined by the respective description counterpart relation. These are then intensional contexts. (Similar to 1971(11)). counterfactual asymmetry/Lewis/Schwarz: Lewis' analysis assumes similarity between possible worlds. HorwichVsLewis: (1987(15),172) should explain why he is interested in this baroque dependence. Problem/SchwarzVsLewis: so far, the analysis still delivers incorrect results E.g. causation later by earlier events. Schwarz I 139 Conjunctive events/SchwarzVsLewis: he does not see that the same is true for conjunctive events. Examples A, B, C, D are arbitrary events, so that A caused B and C caused D. If there is an event B&C, which exactly occurs when both B and C happen, then A is the cause of D: without A, B would not have happened, neither B&C. Likewise D would not have happened without B&C. Because causation is transitive, thus any cause causes any effect. Note: according to requirement D would not happen without C, but maybe the next possible world, in which B&C are missing, is one in which C is still taking place? According to Lewis the next possible world should however be one where the lack of cause is completely extinguished. Schwarz: you cannot exclude any conjunctive events safely. E.g. a conversation or e.g. a war is made up of many events and may still be as a whole a cause or effect. Lewis (2000a(13), 193) even used quite unnatural conjunctions of events in order to avoid objections: E.g. conjunction from the state of brain of a person and a decision of another person. Absence/Lewis/Schwarz: because Lewis finds no harmless entities that are in line as absences, he denies their existence: they are no events, they are nothing at all, since there is nothing relevant. (200a, 195). SchwarzVsLewis: But how does that fit together with the Moore's facts? How can a relationship be instantiated whose referents do not exist?. Moore's facts/Schwarz: E.g. that absences often are causes and effects. Something to deny that only philosopher comes to mind. I 142 Influence/SchwarzVsLewis: Problem: influence of past events by future. Example had I drunk from the cup already half a minute ago, then now a little less tea would be in the cup, and depending on how much tea I had drunk half a minute ago, how warm the tea was then, where I then had put the cup, depending on it the current situation would be a little different. After Lewis' analysis my future tea drinking is therefore a cause of how the tea now stands before me. (? Because Ai and Bi?). Since the drinking incidents are each likely to be similar, the impact is greater. But he is not the cause, in contrast to the moon. Schwarz I 160 Know how/SchwarzVsLewis: it is not entirely correct, that the phenomenal character must be causal effect if the Mary and Zombie pass arguments. For causal efficacy, it is sufficient if Mary would react differently to a phenomenally different experience ((s) >Counterfactual conditional). Dualism/Schwarz: which can be accepted as a dualist. Then you can understand phenomenal properties like fundamental physical properties. That it then (as above Example charge 1 and charge 1 switch roles in possible worlds: is possible that in different possible worlds the phenomenal properties have their roles changed, does not mean that they are causally irrelevant! On the contrary, a particle with exchanged charge would behave differently. Solution: because a possible world, in which the particle has a different charge and this charge plays a different role, is very unlike to our real world! Because there prevail other laws of nature. ((s) is essential here that besides the amended charge also additionally the roles were reversed? See above: >Quidditism). SchwarzVsLewis: this must only accept that differences in fundamental characteristics do not always find themselves in causal differences. More one must not also accept to concede Mary the acquisition of new information. Schwarz I 178 Content/Individuation/Solution/LewisVsStalnaker: (1983b(2), 375, Fn2, 1986e(3), 34f), a person may sometimes have several different opinion systems! E.g. split brain patients: For an explanation of hand movements to an object which the patient denies to see. Then you can understand arithmetic and logical inference as merging separate conviction fragments. Knowledge/Belief/Necessary truth/Omniscience/SchwarzVsLewis/SchwarzVsFragmentation: Problem: even within Lewis' theory fragmentation is not so easy to get, because the folk psychology does not prefer it. Schwarz I 179 E.g. at inconsequent behavior or lie we do not accept a fragmented system of beliefs. We assume rather that someone changes his beliefs or someone wants to mislead intentionally. E.g. if someone does not make their best move, it must not be the result of fragmentation. One would assume real ignorance contingent truths instead of seeming ignorance of necessary truths. Fragmentation does not help with mathematical truths that must be true in each fragment: Frieda learns nothing new when she finally finds out that 34 is the root of the 1156. That they denied the corresponding proposition previously, was due to a limitation of their cognitive architecture. Knowledge/Schwarz: in whatever way our brain works, whether in the form of cards, records or neural networks - it sometimes requires some extra effort to retrieve the stored information. Omniscience/Vs possible world/Content/VsLewis/Schwarz: the objection of logical omniscience is the most common objection to the modeling mental and linguistic content by possible worlds or possible situations. SchwarzVsVs: here only a problem arises particularly, applicable to all other approaches as well. Schwarz I 186 Value/Moral/Ethics/VsLewis/Schwarz: The biggest disadvantage of his theory: its latent relativism. What people want in circumstances is contingent. There are possible beings who do not want happiness. Many authors have the intuition that value judgments should be more objective. Solution/Lewis: not only we, but all sorts of people should value under ideal conditions the same. E.g. then if anyone approves of slavery, it should be because the matter is not really clear in mind. Moral disagreements would then in principle be always solvable. ((s)>Cognitive deficiency/Wright). LewisVsLewis: that meets our intuitions better, but unfortunately there is no such defined values. People with other dispositions are possible. Analogy with the situation at objective probability (see above 6.5): There is nothing that meets all of our assumptions about real values, but there is something close to that, and that's good enough. (1989b(7), 90 94). Value/Actual world/Act.wrld./Lewis: it is completely unclear whether there are people in the actual world with completely different value are dispositions. But that does not mean that we could not convince them. Relativism/Values/Morals/Ethics/Lewis/Schwarz: Lewis however welcomes a different kind of relativism: desired content can be in perspective. The fate of my neighbor can be more important to me than the fate of a strangers. (1989b(14), 73f). Schwarz I 232 Truthmaker principle/SchwarzVsLewis: here is something rotten, the truth maker principle has a syntax error from the outset: we do not want "the world as it is", as truth-makers, because that is not an explanation, we want to explain how the world makes the truth such as the present makes propositions about the past true. Schwarz I 233 Explanation/Schwarz: should distinguish necessary implication and analysis. For reductive metaphysics necessary implication is of limited interest. SchwarzVsLewis: he overlooks this when he wrote: "A supervenience thesis is in the broader sense reductionist". (1983,29). Elsewhere he sees the difference: E.g. LewisVsArmstrong: this has an unusual concept of analysis: for him it is not looking for definitions, but for truth-makers ". 1. David Lewis [1979a]: “Attitudes De Dicto and De Se”. Philosophical Review, 88: 513–543. 2. David Lewis [1983b]: “Individuation by Acquaintance and by Stipulation”. Philosophical Review, 92: 3–32. 3. David Lewis [1986e]: On the Plurality of Worlds. Malden (Mass.): Blackwell 4. David Lewis [1984b]: “Putnam’s Paradox”. Australasian Journal of Philosophy, 61: 343–377 5. David Lewis [1983c]: “New Work for a Theory of Universals”. Australasian Journal of Philosophy, 61: 343–377. 6. David M. Armstrong [1978b]: Universals and Scientific Realism II: A Theory of Universals. Cambridge: Cambridge University Press 7. David M. Armstrong [1989b]: Universals: An Opinionated Introduction. Boulder: Westview Press 8. David Lewis [2001a]: “Redefining ‘Intrinsic’ ”. Philosophy and Phenomenological Research, 63: 381-398 9. David Lewis [2004d]: “Void and Object”. In [Collins et al. 2004], 277–291 9a. David Lewis [1986d]: “Events”. In [Lewis 1986f]: 241–269 10. David Lewis [2003]: “Things qua Truthmakers”. Mit einem Postscript von David Lewis und Gideon Rosen. In Hallvard Lillehammer und Gonzalo Rodriguez-Pereyra (Hg.), Real Metaphysics: Essays in Honour of D.H. Mellor, London: Routledge, 25–38. 11. David Lewis [1971]: “Counterparts of Persons and Their Bodies”. Journal of Philosophy, 68: 203–211. 12. David Lewis [1987]: “The Punishment that Leaves Something to Chance”. Proceedings of the Russellian Society, 12: 81–97. 13. David Lewis [2000a]: “Causation as Influence”. Journal of Philosophy, 97: 182–197. Gekürzte Fassung von [Lewis 2004a] 14. David Lewis [1989b]: “Dispositional Theories of Value”. Proceedings of the Aristotelian Society, Suppl. Vol. 63: 113-137. 15. Paul Horwich [1987]: Asymmetries in Time. Cambridge (Mass.): MIT Press |
Schw I W. Schwarz David Lewis Bielefeld 2005 |
| Modal Realism | Stalnaker Vs Modal Realism | Stalnaker I 36 Proposition/closeness/Stalnaker: whatever propositions are, if there are any at all, there are also sets of them. And for each set of propositions it is definitely true or false, that all of its elements are true. And this is of course again a proposition. (W5) Closeness-condition: for each set of propositions G there is a proposition A so that G implies A and A implies every element of G. Stalnaker: that means that for each set of propositions there is a proposition that says that every proposition in the set is true. So I suppose that the world-stories-theorists wants to add (W5) to his theory. (W6) Equivalent propositions are identical. Problem: the problems of (W6) are known. ((s) > hyperintensionalism/ hyperintensionality): propositions that are true in the same worlds are indistinguishable, VsPossible worlds semantics). I 40 modal realism/MR/Lewis/Stalnaker: by Lewis the actual world (act. wrld.) is only a real part of a reality which consists of many parallel universes which are spatially and temporally separated. Actual world/Lewis/Stalnaker: is then indexically defined as the part that is related to us. Unrealized possibilities/Possibilia/Lewis/Stalnaker: then actually exists, but in another part of the reality. Its non-actuality only exists in its localisation somewhere else. ((s) This is only a polemical presentation: Localization must be more than "somewhere else". Localization may be not carried out by us for areas that do are not related to us because we have then no knowledge.) Modal Realism/MR/Stalnaker: divides into 1. semantic thesis: assertions about what is possible and necessary, should be analyzed in concepts about what is true in some or all parts of reality 2. metaphysical thesis: about the existence of possible worlds (poss.w.). Semantic MR/Stalnaker: problem: VsMR it could be argued that it is not possible to know the metaphysical facts about it even if the semantic part was true. I 41 Lewis: there is a parallel here to Benacerraf's dilemma of mathematical truth and knowledge. I 42 EpistemologyVsModal Realism/Stalnaker: the representatives of the epistemological argument against the MR reject the parallel between mathematical objects and realistically construed possibilia. They insist that reference and knowledge require causal relation of concrete things even if that does not apply for abstract things (numbers etc.). Knowledge/LewisVs: why should the limit between what for knowledge and reference requires a causal relation to be made in concepts of the distinction abstract/concrete? Knowledge/Lewis: instead we should say that reference and knowledge require a causal relation of contigent facts but not the one of modal reality (knowledge about what is possible and necessary). Modal Realism/knowledge/Lewis: thesis: in the context of MR, we can say that indexical knowledge requires causal relation, but impersonal knowledge does not. I 43 Platonism/mathematics/Stalnaker: pro Lewis: here knowledge does not have to be based on a causal relation. Then Benacerraf's dilemma can be solved. EpistemologyVsModal realism/Stalnaker: but I still feel the force of the epistemological argument VsMR. Reference/knowledge/Stalnaker: problem: to explain the difference between knowledge and reference to numbers, sets and cabbages and so on. I 49 Possible worlds/pos.w./MR/Vsmodal realism/knowledge/verificationism/StalnakerVsLewis: the modal realist can cite no verificationist principles for what he calls his knowledge. Conclusion: problem: the MR cannot say on the one hand that poss.w. things are of the same kind (contingent physical objects) like the real world and say on the other side that poss.w. things are of what we know in the same kind as of numbers, sets, functions. ((s) The latter are not "real" things). |
Stalnaker I R. Stalnaker Ways a World may be Oxford New York 2003 |
| Penrose, R. | Dennett Vs Penrose, R. | I 614 Gödel/Toshiba Library/Dennett: "there is no single algorithm that can prove all truths of arithmetics." Dennett: But Gödel says nothing about all the other algorithms in the library! I 617/618 In particular, he says nothing about whether or not there are algorithms in the library for very the impressive performance "to call sentences true"! "Mathematical intuition", risky, heuristic algorithms, etc. DennettVsPenrose: he makes the very mistake of ignoring this group of possible algorithms and of focusing solely on those whose impossibility Gödel had demonstrated. Or about which Gödel says anything at all. Dennett: an algorithm can bring forth "mathematical insight", although it was not an "algorithm for mathematical insight"! I 615 PenroseVsArtificial Intelligence: x can perfectly achieve a checkmate - there is no algorithm for chess. Therefore, the good performance of x cannot be explained with the fact that x can run an algorithm. I 617 DennettVsPenrose: that’s wrong. The level of the algorithm is obviously the correct explanation level. X wins, because he has the better algorithm! I 619 Fallacy: If the mind is an algorithm, then it certainly cannot be seen or accessed by those whose mind it generates. E.g. There is no specific algorithm for distinguishing italics from bold print, but that does not mean that it cannot be distinguished. E.g. Suppose in the Library of Babel there is a single book which contains the alphabetic order of all New Yorker participants whose net worth is over $ 1 million. ("Megaphone Book"). Now we can prove multiple statements about this book: 1) The first letter on the first page is an A. 2) The first letter on the last page is not A. E.g. The fact that we cannot find any remains of the "mitochondrial Eve" does not mean that we cannot derive any statements about it. I 619 Penrose: if you take any single algorithm, it cannot be the method by which human mathematicians ensure mathematical truths. Accordingly, they do not use an algorithm at all. I 621 DennettVsPenrose: this does not show that a human brain does not operate algorithmically. On the contrary, it makes clear how the cranes of culture can exploit the community of mathematicians with no apparent limits in decentralized algorithmic processes. I 623 DennettVsPenrose: he says that the brain is not a Turing machine, but he does not say that the brain is not well represented by a Turing machine. I 625/626 Penrose: even a quantum computer would be a Turing machine which can only calculate functions that are proven to be computable. But Penrose also wishes to advance further than that: with "quantum gravity". I 628 DennettVsPenrose: why he thinks such a theory should not be computable? Because otherwise AI would be possible! That’s all. (Fallacy). DennettVsPenrose: The idea with microtubules is unconvincing: Suppose he was right, then even cockroaches would have a wayward spirit. Because they have microtubules like us. |
Dennett I D. Dennett Darwin’s Dangerous Idea, New York 1995 German Edition: Darwins gefährliches Erbe Hamburg 1997 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 |
| Putnam, H. | Field Vs Putnam, H. | III 113 Pure Mathematics/Putnam: should be interpreted in a way that it asserts the possible existence of physical structures that satisfy the mathematical axioms. FieldVsPutnam: pure mathematics should not be interpreted at all. I 211 Properties/Relations/Putnam: (1970): are predicative, according to them we have a few basic physical prop and rel from which all others are derived: 1st order: Allows no reference to a totality of physical objects when a new property is constructed. 2nd order: Allows reference to the totality of the properties of the 1st order. 3rd order: Allows reference to the totality of the properties of the 1st and 2nd order. - Every physical property appears on any level of the hierarchy -> functionalism. Functional properties are 2nd or higher order properties - the prop that the role has may differ from person to person. I 214 FieldVsPutnam: instead of properties provide instantiations of properties with steps. I 268 Mathematics/Ontology/Putnam: ("Mathematics without foundations", 1976b, 1975 "What is mathematical truth?"): Field: Putnam Thesis: the mathematical realist does not have to accept the "mathematical object picture". He can formulate his views in purely modal terms. And that not as an alternative, but only as another formulation of the same view. I 269 Indispensability Argument/Putnam: appear in the subsequent text. Field: If "Mathematics as a modal" logic was really an equivalent description of mathematics in terms of mathematical objects (MO), then it should also be possible to reformulate the Indispensability Argument so that there is a prima facie argument for one or the other kind of modalized mathematics and mathematical objects. FieldVsPutnam: but Section 6 and 7 show that we cannot formulate the indispensability argument like that: it requires MO and modalized mathematics does not bring them forth. VSVs: but beware: I have not studied all the possibilities. I 269 FieldVsPutnam: his mathematical realism seems puzzling: Mathematics/Ontology/Putnam: Thesis: there is a modal translation of pure mathematics: he presents a translation procedure that turns mathematical statements into modal statements, one that transforms acceptable mathematical statements (E.g. axioms of set theory) into true modal assertions that include no quantification, unless it is modalized away. (I.e. no mathematical entities (ME) in the modal statements). I 270 FieldVsPutnam: two general questions: 1) what kind modality is involved here? 2) what benefit is the translation to have? ad 1): Putnam thinks that the "object-image" (the starting position) and its modal translation are equivalent at a deeper level. FieldVs: that’s really not interesting: "mathematically possible" should coincide with "logically possible" in any reasonable view (this is stated by conservatism). ((s) contrary to the above). Important argument: if A is not mathematically possible, then "~A" is a consequence of mathematics - i.e. if A (and then also its negation) are purely non-mathematically, then "~A" is logically true. If Putnam now says that his modal translation involves a "strong and clear mathematical sense of possibility", then a mathematical possibility operator must be applied to sentences that contain ME. However, such a sentence A could also be a mixed sentence (see above, with purely mathematical and purely physical components). I 271 FieldVsPutnam: for purely mathematical sentences mathematical possibility and truth coincide! But then the "modal translations" are just as ontologically committed as the mathematical assertions. FieldVs"Mathematical Possibility"/FieldVsPutnam: we had better ignore it. Maybe it was about 2nd order logical possibility as opposed to 1st order for Putnam? I 271 FieldVsPutnam: what benefits does his modal translation have? Does it provide a truth transfer (as opposed to the transmission of mere acceptability)? And what value has it to say that the mathematical statements are both true and acceptable? Etc. Mathematics/Realism/Putnam/Field: Putnam describes himself as "mathematical realist": Difference to Field’s definition of realism: he does not consider ME as mind-independent and language-independent, but (1975): Putnam: you can be a realist without being obliged to mathematical objects. I 272 The question is the one that Kreisel formulated long ago: the question of the objectivity of mathematics and not the question the existence of mathematical objects. FieldVsPutnam: this is puzzling. I 277 Model Theory/Intended Model/Putnam/Field: this morality can be strengthened: there is no reason to consider "∈" as fixed! Putnam says that in "Models and Reality": the only thing that could fix the "intended interpretation" would be the acceptance of sentences that contain "∈" through the person or the community. Putnam then extends this to non-mathematical predicates. ((s)> Löwenheim-Skolem). FieldVsPutnam: this is misleading: it is based on the confusion of the view that the reference is determined, E.g. by causal reasoning with the view that it is defined by a description theory (description theory, (labeling theory?), in which descriptions (labels?) that contain the word "cause" should play a prominent role. (> Glymour, 1982, Devitt, 1983, Lewis 1984). |
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 |
| Swinburne, R. | Mackie Vs Swinburne, R. | Stegmüller IV 405 Proof for the existence of God/confirmation/MackieVsSwinburne: 1. How can we assert an output probability indicating that there is a God, if no such universe existed? The data have to be taken from background knowledge. IV 406 Then the background knowledge only contains logical and mathematical truths. How should they make the God hypothesis more likely? Swinburne: seemingly only compares two competing hypotheses: a) That there is no specific cause and no further explanation for the complex universe b) That there is a God. Both hypothesis assume that there is the universe. Background knowledge/Swinburne: our background knowledge includes all the knowledge about the world, but not religious assumptions. Then it is more likely that God exists than not. proof of the existence of God/confirmation/MackieVsSwinburne: 2. The fact that the uncaused universe cannot be explained further, does not justify Swinburne's notion that it is "strange and surprising" or "very unlikely". A hypothesis involving a divine creation is, on the other hand, quite unlikely! If there were a God in the sense of traditional theism, it would certainly be very likely; but this is about the existence and not to the actions of an existing God. IV 407 proof of the existence of God/Swinburne/Stegmüller: leans on considerations of simplicity: to accept omnipotence, infinite knowledge and infinite goodness means as much as "to assume the simplest kind of person"! MackieVs: contradictions between theists. greatness (Anselm) Vs simplicity. MackieVsSwinburne: 1. The simplicity is achieved through the adoption of a series of actual infinities. 2. The peculiarity is not eliminated, but merely covered: why had God the preference, to create exactly this world? 3. A disembodied spirit is very unlikely. (And especially Swinburne workes with his scientific background and probabilities). IV 408 4. If one wants to explain the order of the natural world by a divine plan, one has to explain the order in the divine plan! MackieVsSwinburne: doesn't call for complete explicability and universal intelligibility of the world (as did Leibniz). But he still demands explicability. He attempts to reduce the inexplicable part. Hew ants to do so without relying on a "sufficient reason" or "essential existence". Unfortunately, it turns out that then he has nothing to justify that by adding God we explain something more. IV 425/426 Explanation/MackieVsSwinburne: we as philosophers do not have the right to, first, mentally isolate and/or idealise that simple relation that interests us and is known to us from a truly very complicated procedure, and second to use this as a familiar model. (Argument). SwinburneVsMackie: might reply that it could belong to God's abilities to elicit the appropriate intentions in us. Stegmüller: but that is highly mysterious. Explanation/Theism/MackieVsSwinburne: the personal explanation is not even a competitor but a special case of causal explanation! 1. It is just as fantastic and unlikely as the evolutionary explanation. 2. If each body soul relationship were to be explained, that would be a relapse into occasionalism 3. Locke: if divine omnipotence gave humans the ability to think, then why not also the stones? (> Thinking stones). |
Macki I J. L. Mackie Ethics: Inventing Right and Wrong 1977 Carnap V W. Stegmüller Rudolf Carnap und der Wiener Kreis In Hauptströmungen der Gegenwartsphilosophie Bd I, München 1987 St I W. Stegmüller Hauptströmungen der Gegenwartsphilosophie Bd I Stuttgart 1989 St II W. Stegmüller Hauptströmungen der Gegenwartsphilosophie Bd 2 Stuttgart 1987 St III W. Stegmüller Hauptströmungen der Gegenwartsphilosophie Bd 3 Stuttgart 1987 St IV W. Stegmüller Hauptströmungen der Gegenwartsphilosophie Bd 4 Stuttgart 1989 |
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The author or concept searched is found in the following 3 theses of the more related field of specialization.
| Disputed term/author/ism | Author |
Entry |
Reference |
|---|---|---|---|
| Mathematics | Putnam, H. | Field II 319 Putnam: Thesis: there are many properties and relations in which these mathematical entities can stand to each other. And there is not much to say about what such properties and relations for which we use our mathematical predicates should stand, apart from making the mathematical propositions we accept true. II 321 Truth/Mathematics/Putnam: Thesis: Truth is too easy to attain ((s) by reinterpretation) to limit our choice of axioms. (However, only as long as there are (infinitely many) mathematical objects). II 328 Usefulness/truth/mathematics/Putnam/Field: (Putnam 1971 locus classicus, unlike 1980): Thesis: We must regard mathematics as true in order to be able to explain its usefulness in other fields. E.g. in science and meta logic. (i.e. the theory of the logical sequence). Modality/modal/mathematics/Field: this contrasts with his earlier view that we can use modality instead of mathematical objects to explain mathematical truth. II 329 Modal explanation: will not work for other disciplines like physics. (FieldVsPutnam, Field 1989/91: 252-69). Putnam/Field: the general form of its argument goes like this: (i) we must speak in terms of mathematical entities in order to practice science, meta logic, etc.. (ii) if we need them for such important purposes, we have reason to believe that this kind of entities exists. VsPutnam/Field: ... + |
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 |
| Possible World | Stalnaker, R. | Field II 100 Possibility/stronger/weaker/real/epistemic/Stalnaker/Field: Stalnaker thinks that thesis worlds are possible in a stronger sense: in which not only denial of logical truths are impossible, but also denial of mathematical truth (pp. 73-7), and even denial of a posteriori identity between name and denial of certain "essentialist" assertions. Field: the assumption that these possible worlds are possible in a stronger sense aggravates the problem. But I do not see what should be solved with it either. In any case, it is essential for Stalnaker that logical falsities are absolutely impossible. That is the condition for not being able to believe them. Staln passim Possible world/Stalnaker: to know how the world could have been. |
Field I H. Field Realism, Mathematics and Modality Oxford New York 1989 |
| Possibility | Stalnaker, R. | Field II 100 Possibility/stronger/weaker/real/epistemic/Stalnaker/Field: Stalnaker thinks worlds are possible in a stronger sense: in which not only denial of logical truths are impossible, but also denial of mathematical truth (pp. 73-7), and even denial of a posteriori identity between name and denial of certain "essentialist" assertions. II 103 FieldVsStalnaker: Thesis: There is no plausible way to describe apparent cases of inconsistent beliefs (e.g. Cantor) so that they match Stalnaker's image. I 40 Possibility/Stalnaker: 1. Semantic Thesis: claims about what is possible and necessary should be analysed in terms of what is true in some or all parts of reality. 2. Metaphysical Thesis: about the existence of worlds. |
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 |
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