Find counter arguments by entering NameVs… or …VsName.
The author or concept searched is found in the following 6 entries.
| Disputed term/author/ism | Author |
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Reference |
|---|---|---|---|
| Attributes | Quine | VII (d) 75ff Attribute/Quine: an attribute may eventually be introduced in a second step: e.g. "squareness" according to geometrical definition, but then the name also requires substitutability, i.e. an abstract entity > Universals. X 7ff Attribute/Quine: an attribute corresponds to properties, predicates are not the same as attributes. >Predicates/Quine. IX 178ff Attribute/(s): an attribute corresponds to the quantity of those x for which a particular condition applies: {x: x ε a} all objects that are mortal. Predicate: "x is mortal", is not a quantity, but a propositional function. The denomination forms refer "φx", "φ(x,y)" to the attribution. >Propositional Function/Quine. XII 38 Attributary Attitude/Quine: E.g. hunting, needing, catching, fearing, missing. Important to note here is that e.g. "lion hunt" does not require lions as individuals but as a species - > Introduction of properties. IX 177 Attributes/Ontology/Russell: for Russell, the universe consisted of individuals, attributes and relations of them, attributes and relations of such attributes and relations, etc. IX 178f Extensionality/Quine: extensionality is what distinguishes attributes and classes. >Extensionality/Quine So Russell has more to do with attributes than with classes. Two attributes can be of different order and are therefore certainly different, and yet the things that each have one or the other attribute are the same. For example the attribute "φ(φ^x <> φy) where "φ" has the order 1, an attribute only from y. For example the attribute ∀χ(χ^x <> χy), where "χ" has order 2, again one attribute only from y, but one attribute has order 2, the other has order 3. (> Classes/ >Quantities/ >Properties). XIII 22 Class/set/property/Quine: whatever you say about a thing seems to attribute a property to it. Property/Attribute/Tradition/Quine: in earlier times one used to say that an attribute is only called a property if it is specific to that thing. (a peculiarity of this object is...). New: today these two expressions (attribute, property) are interchangeable. "Attribute"/Quine: I do not use this term. Instead I use "property". Identity/equality/difference/properties/Quine: if it makes sense to speak of properties, then it also makes sense to speak of their equality or difference. Problem: but it does not make sense! Problem: if everything that has this one property, also has the other. Shall we say that it is simply the same quality? Very well. But people do not talk like that. For example to have a heart/kidney: is not the same, even if it also applies to the same living beings. Coextensivity/Quine: two properties are not sufficient for their identity. Identity/properties/possible solution: is there a necessary coextensiveness? >Coextensive/Quine Vs: Necessity is too unclear as a term. Properties/Quine: We only get along so well with the term property because identity is not so important for their identification or differentiation. XIII 23 Solution/Quine: we are talking about classes instead of properties, then we have also solved the problem e.g. heart/kidneys. Classes/Quine: are defined by their elements. That is the way of saying it, but unwisely, because the misunderstanding might arise that the elements cause the classes in a different way than objects cause their. Def Singleton/Singleton/Single Class: class with only one element. Def Class/Quine: (in useful use of the word): is simply a property in the everyday sense, without distinguishing coextensive cases. XIII 24 Class/Russell/Quine: it struck like a bomb when Russell discovered the platitude that each containment condition (condition of containment, element relationship) establishes a class. (see paradoxes, see impredictiveness). Russell's Paradox/Quine: applies to classes as well as to properties. It also shatters the platitude that anything said about a thing attributes a property. Properties/Classes/Quine: all restrictions we impose on classes to avoid paradoxes must also be imposed on properties. Property/Quine: we have to tolerate the term in everyday language. Mathematics: here we can talk about classes instead, because coextensiveness is not the problem. (see Definition, > Numbers). Properties/Science/Quine: in the sciences we do not talk about properties. |
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 |
| Correctness | Tarski | Berka I 489 Correctness/domain/Tarski: according to the sentences 14-16 (or Lemma I) there is for each natural number k such a statement that is true in any area with k elements and in any area of the other thickness. In contrast: Every statementthat is true in an infinite range is also true in any other infinite domain. Properties/classes: so we conclude that the object language allows us to express such a property of classes of individuals, such as the existence of exactly k elements. There is no means for designating any specific type of infinity (e.g. countability) and we cannot distinguish by means of a single or a finite number of statements... I 490 ...two such properties of classes such as finiteness, infinity from each other. >Infinity. I 491 Truth (in the domain): depends on the scope in the finite case, not in the infinite. I 491 Correctness in the doamin/provability/Tarski: if we add the statement a (every nonempty class contains a singleton class as a part) to the axiom system correctness and provability will be coextensive terms. >Provability. N.B.: this does not work in the logical algebra, because here a is not satisfied in all interpretations. I 516 "In every correct domain"/Tarski: this term stands according to the extent in the middle between the provable sentence and the true statement, but is narrower than the class of all true statements generally. It does not contain statements whose validity depends on how big the total number of individuals is.(1) 1. A.Tarski, Der Wahrheitsbegriff in den formalisierten Sprachen, Commentarii Societatis philosophicae Polonorum. Vol 1, Lemberg 1935 |
Tarski I A. Tarski Logic, Semantics, Metamathematics: Papers from 1923-38 Indianapolis 1983 Berka I Karel Berka Lothar Kreiser Logik Texte Berlin 1983 |
| Decision Tree | Norvig | Norvig I 698 Def Decision tree/Norvig/Russell: A decision tree represents a function DECISION TREE that takes as input a vector of attribute values and returns a “decision”—a single output value. The input and output values can be discrete or continuous. A decision tree reaches its decision by performing a sequence of tests. Each internal node in the tree corresponds to a test of the value of one of the input attributes, Ai, and the branches from the node are labeled with the possible values of the attribute, Ai =vik. Each leaf node in the tree specifies a value to be returned by the function. A Boolean decision tree is logically equivalent to the assertion that the goal attribute is true if and only if the input attributes satisfy one of the paths leading to a leaf with value true. Writing this out in propositional logic, we have Goal ⇔ (Path1 ∨ Path2 ∨ · · ·) , where each Path is a conjunction of attribute-value tests required to follow that path. Thus, the whole expression is equivalent to disjunctive normal form. ((s) >Normal form/logic.) Unfortunately, no matter how we measure size, it is an intractable problem to find the smallest consistent tree; there is no way to efficiently search through the 22n trees. With some simple heuristics, however, we can find a good approximate solution: a small (but not smallest) consistent tree. The decision tree learning algorithm adopts a greedy divide-and-conquer strategy: always test the most important attribute first. This test divides the problem up into smaller subproblems that can then be solved recursively. “Most important attribute”: the one that makes the most difference to the classification of an example. Decision tree learning algorithm: see Norvig I 702. Norvig I 705 Problems: the decision tree learning algorithm will generate a large tree when there is actually no pattern to be found. Overfitting: algorithm will seize on any pattern it can find in the input. If it turns out that there are 2 rolls of a 7-gram blue die with fingers crossed and they both come out 6, then the algorithm may construct a path that predicts 6 in that case. Solution: decision tree pruning combats overfitting. Pruning works by eliminating nodes that are not clearly relevant. Norvig I 706 Missing data: In many domains, not all the attribute values will be known for every example. Norvig I 707 Multivalued attributes: When an attribute has many possible values, the information gain measure gives an inappropriate indication of the attribute’s usefulness. In the extreme case, an attribute such as exact time has a different value for every example, which means each subset of examples is a singleton with a unique classification, and the information gain measure would have its highest value for this attribute. Continuous and integer-valued input attributes: Continuous or integer-valued attributes such as height and weight, have an infinite set of possible values. Rather than generate infinitely many branches, decision-tree learning algorithms typically find the split point that gives the highest information gain. Continuous-valued output attributes: If we are trying to predict a numerical output value, such as the price of an apartment, then we need a regression tree rather than a classification tree. A regression tree has at each leaf a linear function of some subset of numerical attributes, rather than a single value. >Learning/AI Research. Norvig I 758 History: The first notable use of decision trees was in EPAM, the “Elementary Perceiver And Memorizer” (Feigenbaum, 1961)(1), which was a simulation of human concept learning. ID3 (Quinlan, 1979)(2) added the crucial idea of choosing the attribute with maximum entropy; it is the basis for the decision tree algorithm in this chapter. Information theory was developed by Claude Shannon to aid in the study of communication (Shannon and Weaver, 1949)(3). (Shannon also contributed one of the earliest examples of machine learning, a mechanical mouse named Theseus that learned to navigate through a maze by trial and error.) The χ2 method of tree pruning was described by Quinlan (1986)(4). C4.5, an industrial-strength decision tree package, can be found in Quinlan (1993)(5). An independent tradition of decision tree learning exists in the statistical literature. Classification and Regression Trees (Breiman et al., 1984)(6), known as the “CART book,” is the principal reference. 1. Feigenbaum, E. A. (1961). The simulation of verbal learning behavior. Proc. Western Joint Computer Conference, 19, 121-131. 2. Quinlan, J. R. (1979). Discovering rules from large collections of examples: A case study. In Michie, D. (Ed.), Expert Systems in the Microelectronic Age. Edinburgh University Press. 3. Shannon, C. E. and Weaver, W. (1949). The Mathematical Theory of Communication. University of Illinois Press. 4. Quinlan, J. R. (1986). Induction of decision trees. Machine Learning, 1, 81-106. 5. Quinlan, J. R. (1993). C4.5: Programs for machine learning. Morgan Kaufmann. 6. Breiman, L., Friedman, J., Olshen, R. A., and Stone, C. J. (1984). Classification and Regression Trees. Wadsworth International Group. |
Norvig I Peter Norvig Stuart J. Russell Artificial Intelligence: A Modern Approach Upper Saddle River, NJ 2010 |
| Mereology | Lewis | Schwarz I 79f Mereology: quantities are not the sums of their elements - sum of a single thing A is A the thing itself - but the singleton set {A} is never identical with A. >Singleton, >Unit set. IV 44 Counterpart/Couples/Mereology/Lewis: Example twin brothers Dee and Dum in the actual world. Their pair can be seen as a mereological sum. The couple as mereological sum is a possible individual, not a quantity. Then the counterpart theory can be applied without modification. V 258 Event/Mereology/Logic/Part/Logical Relation/Lewis: we have seen that an event in one sense can be part of another event. 1. then, as I suggest, they have a mereology like they all have classes: the parts of classes are the subclasses. (>Subsets). 2. in another sense they have another mereology: regions can be spatiotemporal parts of other regions. Events are classes of regions, the mereology of the elements transfers to the classes, in the sense that events can also be spatiotemporal parts of each other. V 260 Def Overlap/Event/Mereology/Lewis: two events overlap when they have an event as a common part. An atomistic event has no events except itself as part. Def mereological sum/event/mereology/Lewis: an event e is the mS of events f1,f2... then and only if e overlaps all and only those events that overlap at least one of the fs. Principles/Mereology/Event/Lewis: Question: are the principles here a) the same as that of the unlimited mereology of individuals, in which individual individuals always have a different individual as their sum? Or is it b) the limited mereology of e.g. chairs, in which several chairs rarely or never have another chair than their sum? (>subset/>Sets. Lewis: Thesis: Events have a more accessible mereology than e.g. chairs: For example a war can be a mereological sum of battles, For example, a conference the sum of its meetings. But we leave open whether events, however diverse, must always have other events as parts. It depends on whether one allows unlimited sums, so that there is no limit to how large and non-uniform an event may be, or whether one demands a certain unity for it (limited mereological sum). Perhaps the sum provides a property that is formally suitable for regions, but not an event. This is hard to decide. Our events should serve as causes and effects. |
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 |
| Syntax | Quine | VII (a) 15 Syntax/Quine: their rules are meaningful in contrast to their notation. VI 69 Syntax/translation/indeterminacy/Quine: many of my readers have mistakenly assumed that uncertainty also extends to syntax. There was a subtle reason for this: in word and object(1) (pp. 107, 129 136) it says: VI 70 that also the specific apparatus of reification and object reference, which we make use of, is subject to indeterminacy. To this apparatus belong the pronomina, the "=", (equal sign) the plural endings and whatever performs the tasks of the logical quantifiers. But it is wrong to assume that these mechanisms belonged to syntax! >Equal sign, >Quantifiers, >Pronouns, >Indeterminacy. VI 97 Spelling/Quine: resolves the syntax and lexicon of each content sentence and merges it with the interpreter's language. It then has no more complicated syntax than the addition sign. 1. Quine, W. V. (1960). Word and Object. MIT Press VII (a) 15 Syntax/Quine/Goodman: their rules are meaningful as opposed to the notation itself. XI 114 Language/Syntax/Lauener: Language cannot be regarded purely syntactically as the set of all correctly formed expressions, because an uninterpreted system is a mere formalism. ((s) This is not truthful). XI 116 Lauener: it is a mistake to think that the language contributes the syntax but the theory contributes the empirical content. Therefore, one cannot say that an absolute theory can be formulated in different languages, or vice versa, that different (even contradictory) theories can be expressed in one language. XI 136 Mathematics/QuineVsHilbert/Lauener: Mathematics is more than just syntax. Quine reluctantly professes Platonism. XII 58 The problem of the inscrutability of the reference reaches much deeper than that of the indeterminacy of the translation: e.g. protosyntax. >Inscrutability. Protosyntax/Uncertainty/Quine: the language here is a formalized system of proof theory of the first level, whose subject area consists only of expressions, i.e. of character strings of a certain alphabet. Expressions: are types here, not tokens! (no occurrences). Each expression is the set of all its occurrences. (Summarized due to similarity of inscriptions). For example, the concatenation x^y is the set of all inscriptions that consist of two parts. These parts are tokens of x and y. Problem: it can happen that x^y is the empty set ((s) the combination does not occur) although both x and y are not empty. XII 59 The probability of this problem increases with increasing length of x and y! N.B.: this violates a law of protosyntax that says: x = z, if x^y = z^y. Solution: then you will not understand the objects as sets of inscriptions. But then you can still consider its atoms, the single characters as a set of inscriptions. Then there is no danger that the set is empty. ((s) Because the atoms have to be there, even if not every combination). N.B.: instead of interpreting the strings as sets of inscriptions, they can be regarded as a (mathematical) sequence (of characters). Character String/Expression: is then a finite set of pairs of a sign and a number. Vs: this is very artificial and complicated. Simpler: Goedel numbers themselves (the characters disappear). Problem: Question: How clear is it here that we have just started to talk about numbers instead of expressions? The only thing that is reasonably clear is that we want to fulfill laws with artificial models that are supposed to fulfill expressions in a non-explicit sense. XIII 199 Syntax/Quine: "glamour" and "grammar" were originally one and the same word. XIII 200 Later, the meaning also included magic. Grammar: (in the narrower sense) said which chains of words or phonemes were coherent and which were not. Always related to a particular language. Grammar: (wider sense): "The art of speaking" (in relation to the established use). >Grammar. Syntax/Quine: for the narrower sense we do not really need the word "grammar", but "syntax". It is about which character strings belong to the language and which do not. Problem: this is indefinite in two ways: 1. How the individuals are specified (formally, by components or phonemes) and 2. What qualifies them for the specification XIII 201 Recognizability is too indeterminate (liberal). Problem: ungrammatical forms are used by many people and are not incomprehensible. A language that excludes these forms would be the dialect of a very small elite. Problem: merely possible utterances in imaginable but not actual situations that are not themselves linguistic in nature. Solution: Def ungrammatic/William Haas/Quine: a form that would not make sense in any imaginable fictitious situation. Rules/Syntax/syntactic rules/Quine: are abstractions of the syntactic from long practice. They are the fulfillment of the first task (see above) to recognize which chains are grammatical. XIII 202 Solution: this is mainly done by recursion, similar to family trees. It starts with words that are the simplest chains and then moves on to more complex constructions. It divides the growing repertoire into categories. Parts of speech/Quine: there are eight: Nouns, pronouns, verb, adjective, adverb, preposition, conjunction, sentence. Further subdivisions: transitive/intransitive, gender, etc. But this is hardly a beginning. Nomina: even abstract ones like cognizance (of) and exception (to) are syntactically quite different, they stand with different prepositions. Recursion/syntax/Quine: if we wanted to win the whole syntax by recursion, it would have to be so narrow that two chains would never be counted as belonging to the same speech part, unless they could be replaced in all contexts salva congruitate. >Recursion. Def Replaceability salva congruitate/Geach/Quine: preserves grammaticality, never returns ungrammatical forms. VsRecursion/Problem: if speech parts were so narrowly defined, e.g. Nomina, which stand with different prepositions, they would then have to be counted among different kinds of speech parts. And these prepositions e.g. of and to, should not fall into the same category either! Then there would be too many kinds of speech parts, perhaps hundreds. Of which some would also be singletons ((s) singletons = categories with only one element). Solution: to give up recursion after having the roughest divisions. |
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 |
| Unit Set | Stalnaker | I 37 Unit set/singletons/unit class/Stalnaker/(s): advantage: when we have a unit set, all things are of the same kind.) (s)> Quine's set theory. Stalnaker: advantage here: we have compositionality and can define consistency. Cf. >Unit set/Quine, >Compositionality, >Consistency. |
Stalnaker I R. Stalnaker Ways a World may be Oxford New York 2003 |
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| Disputed term/author/ism | Author Vs Author |
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| Field, H. | Lewis Vs Field, H. | Schwarz I 75 Ontology/Science/Mathematics/Lewis: Philosophy needs to accept the results of established sciences. It would be absurd to reject mathematics because of philosophical reasons. LewisVsField. Lewis: It is about a systematic description, which should be as simple as possible, of the mathematical part of reality. Solution: Reduction on set theory. Set Theory/Mereology/Lewis: (Parts of Classes, 1991)(1): Are sets simply mereological sums? As such set theory manifests itself as mereologically expanded arithmetic, with successor relation, a set relation between object A and its singleton {A}. With a structural analysis of this relation, Lewis establishes the thesis: All mathematics are based on the assumption that there many objects. >Sets/Lewis, >mereology/Lewis. 1. D. Lewis [1991]: Parts of Classes. Oxford: Blackwell |
Lewis I David K. Lewis Die Identität von Körper und Geist Frankfurt 1989 Lewis I (a) David K. Lewis An Argument for the Identity Theory, in: Journal of Philosophy 63 (1966) In Die Identität von Körper und Geist, Frankfurt/M. 1989 Lewis I (b) David K. Lewis Psychophysical and Theoretical Identifications, in: Australasian Journal of Philosophy 50 (1972) In Die Identität von Körper und Geist, Frankfurt/M. 1989 Lewis I (c) David K. Lewis Mad Pain and Martian Pain, Readings in Philosophy of Psychology, Vol. 1, Ned Block (ed.) Harvard University Press, 1980 In Die Identität von Körper und Geist, Frankfurt/M. 1989 Lewis II David K. Lewis "Languages and Language", in: K. Gunderson (Ed.), Minnesota Studies in the Philosophy of Science, Vol. VII, Language, Mind, and Knowledge, Minneapolis 1975, pp. 3-35 In Handlung, Kommunikation, Bedeutung, Georg Meggle Frankfurt/M. 1979 Lewis IV David K. Lewis Philosophical Papers Bd I New York Oxford 1983 Lewis V David K. Lewis Philosophical Papers Bd II New York Oxford 1986 Lewis VI David K. Lewis Convention. A Philosophical Study, Cambridge/MA 1969 German Edition: Konventionen Berlin 1975 LewisCl Clarence Irving Lewis Collected Papers of Clarence Irving Lewis Stanford 1970 LewisCl I Clarence Irving Lewis Mind and the World Order: Outline of a Theory of Knowledge (Dover Books on Western Philosophy) 1991 Schw I W. Schwarz David Lewis Bielefeld 2005 |
| Possibilia | Lewis Vs Possibilia | Schwarz I 87 Possibilia/Possible World/possible worlds/possibilistic structuralism/Lewis/Schwarz: (1991(1),1993d(2)) here Lewis assumed, thesis: that there are clearly less inhabitants of possible worlds (Possibilia) than sets. Set theory: so for them additional entities had to be accepted besides the Possibilia. These additional entities should then contain the sets (and classes) required by the 5th condition (see above). Lewis later: accepts that there are at least as many Possibilia as sets. Then one could do without the additional mathematical entities (Lewis pro). Then we delete condition five. Then "many" inhabitants of possible worlds must be sets. Schwarz I 88 Because Lewis assumes that there are more sets than individuals. Because if there are "many" individuals, then also "many" individual atoms, atoms of individuals exist. But there are more sums of individual atoms than individual atoms. Then there are also more individuals than atoms at all and then, according to conditions (1) and (3), more units than atoms, in contradiction to (2). Possibilia/Lewis/Schwarz: if they have no cardinality, not all Possibilia can be individuals. Def possibilistic structuralism/Lewis/Schwarz: mathematical statements are not only about mathematical entities anyway, but partly also about Possibilia. Then why not just these? Pro: not only does he get along without primitive mathematical vocabulary, but also without primitive mathematical ontology. Questions about their origin and our epistemic approach are thus resolved. If mathematical statements are about Possibilia, it results in a modal state from the logic of unlimited modality: For unlimited modal statements truth, possibility and necessity coincide.(see section 3.6 above). Lewis: can't just delete the mathematical entities. (LewisVsField): Problem: mixed sums. For example, if some atoms in Caesar's brain are classified as single sets and others as individuals, then Caesar is a mixed sum. Mixed Sum/Mereology/Lewis: is neither individual nor class. Class: Sum of single sets. Schwarz I 89 Mixed sums: are not elements of sets in Lewis' original system either. Schwarz: that is unmotivated in terms of set theory: according to the iterative view, absolutely everything has a single set. Lewis usually ignores mixed sums anyway. Problem: not under every single set relationship is there a single set of Caesar. Solution: a) also allow a mixed sums single set. Vs: there are more mixed sums than single sets, so that doesn't work. b) Requirement: that all "small" mixed sums have a single set. c) More elegant: settle mixed sums by forbidding individuals. If you identify classes with ordinary Possibilia, you could treat each atom as a single set. For example, Caesar is then always a class, his single set is the object of pure set theory. LewisVs: this does not work in his set theory (unlike ZFC). Because we need at least one individual as an empty set. Single set/Lewis/Schwarz: since a single individual atom is sufficient, instead of (1) (3) single set relationships, one could also determine arbitrary unambiguous images of small things in all atoms except one. This one atom is then the empty set relative to the respective single set relationship. (> QuineVsRussell: several empty sets, there depending on type). Solution/Daniel Nolan: (2001, Kaß 7, 2004): VsLewis, VsZermelo: empty set as real part of units: Def "Esingleton" by A/Nolan: {A} consists of 0 and a thing {A} - 0 . (Terminology: "Singleton": only card of one color). Esingleton/Nolan: similar assumptions apply to them as in Lewis' single sets. Mixed Sum/Nolan: this problem becomes that of sums of 0 and atoms other than Esingletons. In Nolan, these are never elements of sets. Object/Nolan: (2004.§4): only certain "big" things can be considered as 0. So all "small" things are allowed as elements of classes. Individual/Nolan: many "little" things are individuals according to him among all Esingleton relationships. Empty Set/Schwarz: all these approaches are not flawless. The treatment of the empty set is always somewhat artificial. Schwarz I 90 Empty Set/Lewis/Schwarz: set of all individuals (see above): There is a good reason for this! ((s) So there are no individuals and the empty set is needed to express that.). Subset/Lewis/Schwarz: is then defined as disjunctive: once for classes and once for the empty set. Possibilistic structuralism/Schwarz: is elegant. Vs: it prevents set-theoretical constructions of possible worlds (e.g. as sentence sets). If you reduce truths about sets to those about Possibilia, you can no longer reduce Possibilia to sets. 1. David Lewis [1991]: Parts of Classes. Oxford: Blackwell 2. David Lewis [1993d]: “Mathematics is Megethology”. Philosophia Mathematica, 3: 3–23. In [Lewis 1998a] |
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 |
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