Find counter arguments by entering NameVs… or …VsName.
| Disputed term/author/ism | Author Vs Author |
Entry |
Reference |
|---|---|---|---|
| Church, A. | Quine Vs Church, A. | I 368 QuineVsChurch: The subject does not need to speak the language of the object sentence. There is a German phrase of which is true that the mouse, which is afraid of the cat, fears it. But in a certain way they remain language relative (Church). Ex A sentence in a given concrete translation might have a slightly different meaning. For Church this is even likely, because he also accepts all sorts of artificial languages. So we improve: (7) Thomas true-believes in German "Cicero..." I 369 According to Church, we would then have to make all other possible translations as well (8) Thomas believes true in German "Cicero has denounced Catiline." But an Englishman who does not speak German would find other information in (8) than in a full translation. (9) Thomas believes that Cicero denounced Catiline (in English). However, since (8) reflects the meaning of (7), (9) must miss the meaning of (7). QuineVsChurch: not necessarily because a certain concept of meaning is required. Quine: (7) not satisfactory because of the dependence on a language. Such relations of a sentence, a person and a language cannot be linked with the propositional attitudes. I 370 Sheffler + about expressions and degrees XI 55 Identity/Necessity/Church: the values of the variables could be reduced to intensions and thereby make all the true identity statements necessary. QuineVsChurch: it is a mistake to think that the quantified modal logic can tolerate only intentions, but no classes or individuals. Proof: Specification/Quine: every thing x, even an intention is, if it can at all be specified, specifiable in random matching manner. ((s) >indeterminacy of translation, indefinite >reference, >inscrutability of reference). XI 56 Suppose x is determined as the only thing by the condition "φx", so it is also determined as the only one by the conjunction "p u φx". Now you select any truth for "p" that is not implied by "φx", and both specifications contingently turn out to be consistent. So you gain nothing by taking intentions as values of the variables. Should we try again with necessary identity? Identity/Necessary Identity/Necessity/Quine/Lauener: let us consider the following postulate (1) ((w)(Fx w = x) u (w)(Gw w = x))> N(w) (Fw Gw) The demands that if there are always two open sentences that determine the same thing x as the only thing, they should be necessarily equivalent. Although this would repeal the referential opacity of the rules - it would also repeal modal distinctions themselves at the same time! (... + ...) |
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 |
| Dummett, M. | Schiffer Vs Dummett, M. | I 221 Verificanistical semantics/Dummett/Schiffer: (not truth-theoretical): verification conditions instead of truth conditions. Dummett: (like Davidson): we must ask what form a meaning theory (m.th.) would have to take to find out what meaning is. This M.Th. should be able to specify the meaning of all words and propositions. (Dummett 1975, p. 97). Dummett: pro compositionality (with Wittgenstein): no systematic meaning theory is possible without explaining the understanding of infinitely many sentences. Therefore one must, like Chomsky and Wittgenstein, accept that we have an implicit capture some general principles. (Dummett 1978, p. 451). DummettVsDavidson: the meaning theory does not have to contain any truth theory (tr.th.). Verification condition/verification conditions/Dummett: (for propositions) the verification conditions are also recursively specified. Schiffer: but that does not follow that a compositional truth-theoretic semantics does not exist as well. I 222 Dummett: with the specification of the verification conditions the meaning theory could at the same time specify the truth conditions (Dummett 1978 Foreword). Verification conditions/SchifferVsDummett: it is not clear how the verification conditions should look like. Relation theory/meaning theory/Schiffer: when I argued VsRelation theory, I had a standard meaning theory in mind. The relation theory for belief is wrong when languages have no compositional truth-theoretical semantics (tr.th.sem.). Otherwise, it would be true!. Verificationist meaning theory/Verif. m.th./relation theory/Dummett/Schiffer: with a verificationist meaning theory could the relation theory maybe also be true?. I 225 Use theory/Dummett/Schiffer: for Dummett the point of use theory is: "the meaning of a word is uniquely determined by the observable characteristics of its linguistic use". (Dummett 1976, 135). SchifferVsDummett: but what counts as "observable characteristic" and what as "openly shown" ?. Does Dummett think that a description of the use in purely behavioral, non-semantic and non-psychological terms would be sufficient that a word has a specific meaning? That would be too implausible as that Dummett would accept that. Still, he notes that the description should not use any psychological or semantic terms. Meaning/Dummett/Schiffer: should therefore also become understandable for beings who have no semantic or psychological concepts themselves! So even for Marsians. (Also McDowell understands him like this, 1981, 237). McDowellVsDummett: according to Dummett it must be possible to give a description of our language behavior that is understandable for extraterrestrials. That does not work, because the intentional "(content-determining) is not reducible to the non-intentional. Content/McDowellVsDummett/SchifferVsDummett: is not detectable for extraterrestrials. ((s) Not "speechless", but only those who do not share our intentional vocabulary). I 226 Ad. 4: ("To know which recognizable circumstances determine a proposition as true or false"). Schiffer: that means how do we get from behaviorism to anti-realism?. Manifestation/SchifferVsDummett: this one makes do here even with pronounced psychological terms!. 1. Recognizing (that the conditions are met) is itself a form of knowledge, which in turn contains belief. You cannot describe that non-psychologically. 2. How can one then achieve the further conclusion that a purified attribution should ascribe a skill that can only be "openly shown"? (The showing understood behavioristically). Behaviorism/Dummett/Schiffer: However, I am not ascribing any behaviorism to Dummett, I ascribe him nothing, I just wonder what his position is. meaning theory/m.th./Dummett: thinks that natural languages have a m.th.! Their core will be recursively definable verif. cond.. Anti-Realism/Schiffer: here Dummett is uncertain whether the m.th. should have falsification conditions, but that will not affect my subsequent criticism. 1. Whether the knowledge that a state of affair exists, counts as verification of a proposition. I 227 Could depend on extralinguistic knowledge and not by the understanding of the proposition! We usually need background information. Understanding/SchifferVsDummett: then it should not be about verification conditions!. Direct verification conditions/Dummett: has to exist for each single proposition!. QuineVsDummett/Schiffer: (Quine 1953b): direct verification conditions cannot exist for every proposition. ((s) ~Theories are not verifiable proposition by proposition). 2. Surely there are meaningful propositions that have no recognizable conditions that would turn out this proposition as true or false. Dummett/Schiffer: insists, however, that a proposition must be shown as true or false and in fact "conclusively" (conclusive verifiability). (1978, 379). This leads to anti-realism. ((s) Def anti-realism/Dummett/(s): is exactly to demand that the verification must be performed in order to understand a proposition. The realism would waive the verification.) Anti-realism/Dummett: you still should not rely too heavily on the anti-realism! Because often a "conclusive verification" is not to obtain!. Schiffer: so Dummett itself holds the verification conditions contestable!. I 228 Pain/Verification/Wittgenstein/Dummett/Schiffer: Dummett quotes Wittgenstein with consent: that pain behaviors can be refuted. (Dummett 1978, S. XXXV) SchifferVsDummett: then the m.th. needs contestable criteria as well as contestable conditions!. Problem: this applies to most empirical judgments E.g. "That is a dog". 3. We know what kind of semantic values we must attribute to the non-logical constants (predicates and singular term) in the conditional sentences in a truth-theoretic semantics. But how shall that look like in the alternative with verification conditions instead of truth conditions?. Solution/Dummett: the verificationist semantics will make every predicate an effective means available, so that it can be determined for each object whether the predicate applies to the object or the singular term references to the object. I 230 Relation theory/SchifferVsDummett: the by me disapproved relation theory for propositional attitudes (belief as a relation to belief objects) seems inevitable for Dummett. ((s) because of the relation of predicates to objects to which they must apply verifiable). Problem: that can only happen in a finite theory, and for propositional attitude it would have to be infinite, because for each prop the VB would have to be found individually. Relation theory/Schiffer: has to assume propositional attitude as E.g. "believes that Australians drink too much" as semantically primitive - namely, 2-figure predicate between believer and content). |
Schi I St. Schiffer Remnants of Meaning Cambridge 1987 |
| Modal Logic | Quine Vs Modal Logic | Chisholm II 185 QuineVsModal Logic: instead space time points as quadruples. Reason: permanent objects (continuants) seem to threaten the extensionality. SimonsVsQuine: the Achilles heel is that we must have doubts whether anyone could learn a language that refers not to permanent objects (continuants). --- Lewis IV 32 QuineVsModal Logic: which properties are necessary or accidental, is then dependent on the description. Definition essentialism/Aristotle: essential qualities are not dependent on description. QuineVs: that is as congenial as the whole modal logic. LewisVsQuine: that really is congenial. --- I 338 But modal logic has nothing to do with it. Here, totally impersonal. The modal logic, as we know it, begins with Clarence Lewis "A survey of Symbolic Logic" in 1918. His interpretation of the necessity that Carnap formulates even more sharply later is: Definition necessity/Carnap: A sentence that starts with "it is necessary that", is true if and only if the remaining sentence is analytic. Quine provisionally useful, despite our reservations about analyticity. --- I 339 (1) It is necessary that 9 > 4 it is then explained as follows: (2) "9 > 4" is analytically. It is questionable whether Lewis would ever have engaged in this matter, if not Russell and Whitehead (Frege following) had made the mistake, the philonic construction: "If p then q" as "~ (p and ~ q)" if they so designate this construction as a material implication instead of as a material conditional. C.I.Lewis: protested and said that such a defined material implication must not only be true, but must also be analytical, if you wanted to consider it rightly as an "implication". This led to his concept of "strict implication". Quine: It is best to view one "implies" and "is analytical" as general terms which are predicated by sentences by adding them predicatively to names (i.e. quotations) of sentences. Unlike "and", "not", "if so" which are not terms but operators. Whitehead and Russell, who took the distinction between use and mention lightly, wrote "p implies q" (in the material sense) as it was with "If p, then q" (in the material sense) interchangeable. --- I 339 Material implication "p implies q" not equal to "p > q" (>mention/>use) "implies" and "analytical" better most general terms than operators. Lewis did the same, he wrote "p strictly implies q" and explained it as "It is necessary that not (p and not q)". Hence it is that he developed a modal logic, in which "necessary" is sentence-related operator. If we explain (1) in the form of (2), then the question is why we need modal logic at all. --- I 340 An apparent advantage is the ability to quantify in modal positions. Because we know that we cannot quantify into quotes, and in (2) a quotation is used. This was also certainly Lewis' intention. But is it legitimate? --- I 341 It is safe that (1) is true at any plausible interpretation and the following is false: (3) It is necessary that the number of planets > 4 Since 9 = the number of planets, we can conclude that the position of "9" in (1) is not purely indicative and the necessity operator is therefore opaque. The recalcitrance of 9 is based on the fact that it can be specified in various ways, who lack the necessary equivalence. (E.g. as a number of planets, and the successor to the 8) so that at a specification various features follow necessarily (something "greater than 4 ") and not in the other. Postulate: Whenever any of two sentences determines the object x clearly, the two sentences in question are necessary equivalent. (4) If Fx and only x and Gx and exclusively x, it is necessary that (w)(Fw if and only if when Gw). --- I 342 (This makes any sentence p to a necessary sentence) However, this postulate nullifies modal distinctions: because we can derive the validity of "It is necessary that p" that it plays no role which true sentence we use for "p". Argument: "p" stands for any true sentence, y is any object, and x = y. Then what applies clearly is: (5) (p and x = y) and exclusively x as (6) x = y and x exclusively then we can conclude on the basis of (4) from (5) and (6): (7) It is necessary that (w) (p and w = y) if and only if w = y) However, the quantification in (7) implies in particular "(p and y = y) if and only if y = y" which in turn implies "p"; and so we conclude from (7) that it is necessary that p. --- I 343 The modal logic systems by Barcan and Fitch allow absolute quantification in modal contexts. How such a theory can be interpreted without the disastrous assumption (4), is far from clear. --- I 343 Modal Logic: Church/Frege: modal sentence = Proposition Church's system is structured differently: He restricts the quantification indirectly by reinterpreting variables and other symbols into modal positions. For him (as for Frege) a sentence designated then, to which a modal operator is superior, a proposition. The operator is a predicate that is applied to the proposition. If we treat the modalities like the propositional attitude before, then we could first (1) reinterpret (8) [9 > 4] is necessary (Brackets for class) and attach the opacity of intensional abstraction. One would therefore interpret propositions as that what is necessary and possible. --- I 344 Then we could pursue the model from § 35 and try to reproduce the modality selectively transparent, by passing selectively from propositions to properties: (9) x (x > 4) is necessary in terms 9. This is so far opposed to (8) as "9" here receives a purely designated position in one can quantify and in one can replace "9" by "the number of planets". This seemed to be worth in the case of en, as we e.g. wanted to be able to say (§ 31), there would be someone, of whom is believed, he was a spy (> II). But in the case of modal expressions something very amazing comes out. The manner of speaking of a difference of necessary and contingent properties of an object. E.g. One could say that mathematicians are necessarily rational and not necessarily two-legged, while cyclist are necessarily two-legged but not necessarily rational. But how can a bicycling mathematician be classified? Insofar as we are talking purely indicatively of the object, it is not even suggestively useful to speak of some of its properties as a contingent and of others as necessary. --- I 344 Properties/Quine: no necessary or contingent properties (VsModal Logic) only more or less important properties Of course, some of its properties are considered essential and others unimportant, some permanently and others temporary, but there are none which are necessary or contingent. Curiously, exactly this distinction has philosophical tradition. It lives on in the terms "nature" and "accident". One attributes this distinction to Aristotle. (Probably some scholars are going to protest, but that is the penalty for attributing something to Aristotle.) --- I 345 But however venerable this distinction may be, it certainly cannot be justified. And thus the construction (9) which carries out this distinction so elegantly, also fails. We cannot blame the analyticity the diverse infirmities of modality. There is no alternative yet for (1) and (2) that at least sets us a little on something like modal logic. We can define "P is necessary" as "P = ((x) (x = x))". Whether (8) thereby becomes true, or whether it is at all in accordance with the equation of (1) and (2), will depend on how closely we construct the propositions in terms of their identity. They cannot be constructed so tightly that they are appropriate to the propositional properties. But how particularly the definition may be, something will be the result that a modal logic without quantifiers is isomorphic. --- VI 41 Abstract objects/modal logic/Putnam/Parsons: modal operators can save abstract objects. QuineVsModal Logic: instead quantification (postulating of objects) thus we streamline the truth functions. Modal logic/Putnam/Parsons/Quine: Putnam and Charles Parsons have shown how abstract objects can be saved in the recourse to possibility operators. Quine: without modal operators: E.g. "Everything is such that unless it is a cat and eats spoiled fish, and it gets sick, will avoid fish in the future." ((s) logical form/(s): (x) ((Fx u Gx u Hx)> Vx). Thus, the postulation of objects can streamline our only loosely binding truth functions, without us having to resort to modal operators. --- VI 102 Necessity/opportunity/Quine: are insofar intensional, as they do not fit the substitutivity of identity. Again, vary between de re and de dicto. --- VI 103 Counterfactual conditionals, unreal conditionals/Quine: are true, if their consequent follows logically from the antecedent in conjunction with background assumptions. Necessity/Quine: by sentence constellations, which are accepted by groups. (Goes beyond the individual sentence). --- VI 104 QuineVsModal logic: its friends want to give the necessity an objective sense. --- XI 52 QuineVsModal Logic/Lauener: it is not clear here on what objects we are referring to. --- XI 53 Necessesity/Quine/Lauener: ("Three Grades of Modal Involvement"): 3 progressive usages: 1. as a predicate for names of sentences: E.g. "N "p"": "p is necessarily true". (N: = square, box). This is harmless, simply equate it with analyticity. 2. as an operator which extends to close sentence: E.g. "N p": "it is necessarily true that p" 3. as an operator, too, for open sentences: E.g. "N Fx": through existence generalization: "(Ex) N Fx". |
Quine XIII Willard Van Orman Quine Quiddities Cambridge/London 1987 Chisholm I R. Chisholm The First Person. Theory of Reference and Intentionality, Minneapolis 1981 German Edition: Die erste Person Frankfurt 1992 Chisholm II Roderick Chisholm In Philosophische Aufsäze zu Ehren von Roderick M. Ch, Marian David/Leopold Stubenberg Amsterdam 1986 Chisholm III Roderick M. Chisholm Theory of knowledge, Englewood Cliffs 1989 German Edition: Erkenntnistheorie Graz 2004 Lewis I David K. Lewis Die Identität von Körper und Geist Frankfurt 1989 Lewis I (a) David K. Lewis An Argument for the Identity Theory, in: Journal of Philosophy 63 (1966) In Die Identität von Körper und Geist, Frankfurt/M. 1989 Lewis I (b) David K. Lewis Psychophysical and Theoretical Identifications, in: Australasian Journal of Philosophy 50 (1972) In Die Identität von Körper und Geist, Frankfurt/M. 1989 Lewis I (c) David K. Lewis Mad Pain and Martian Pain, Readings in Philosophy of Psychology, Vol. 1, Ned Block (ed.) Harvard University Press, 1980 In Die Identität von Körper und Geist, Frankfurt/M. 1989 Lewis II David K. Lewis "Languages and Language", in: K. Gunderson (Ed.), Minnesota Studies in the Philosophy of Science, Vol. VII, Language, Mind, and Knowledge, Minneapolis 1975, pp. 3-35 In Handlung, Kommunikation, Bedeutung, Georg Meggle Frankfurt/M. 1979 Lewis IV David K. Lewis Philosophical Papers Bd I New York Oxford 1983 Lewis V David K. Lewis Philosophical Papers Bd II New York Oxford 1986 Lewis VI David K. Lewis Convention. A Philosophical Study, Cambridge/MA 1969 German Edition: Konventionen Berlin 1975 LewisCl Clarence Irving Lewis Collected Papers of Clarence Irving Lewis Stanford 1970 LewisCl I Clarence Irving Lewis Mind and the World Order: Outline of a Theory of Knowledge (Dover Books on Western Philosophy) 1991 |
| Quine, W.V.O. | Quine Vs Quine, W.V.O. | II 131 Def Unfounded/Quine: is a class if it contains an element that contains an element.... ad infinitum without ever reaching firm ground. QuineVsQuine: self-criticism: my "New Foundations" and "Mathematical Logic" both contain unfounded classes. I could argue that there is no principle of individuation for such classes. They are identical as long as their elements are identical, and they are identical as long as their elements are identical ..., without stopping. Our study shed light on a strange comparison between three degrees of stringency. a) table, b) with Russell's definition we can define the identity of properties, however, c) the individuation of properties is still not okay. This suggests that a) specification makes the most stringent demands, b) individuation is less strict, and c) the mere definition of identity is even more undemanding. |
Quine XIII Willard Van Orman Quine Quiddities Cambridge/London 1987 |
| Strawson, P. F. | Tugendhat Vs Strawson, P. F. | Wolf II 20 Identification/TugendhatVsStrawson: he underestimates the importance of the space-time system for identification. Most basic statements: those with perception predicates. I 387/388 StrawsonVsRussell: logical proper names are only fictitious. "This" is not an ambiguous proper name but has a uniform meaning as a deictic expression and designates a different object depending on the situation of use. TugendhatVsStrawson: but you cannot oblige Russell to use this word as we use it in our natural language. Russell fails because he does not take into account another peculiarity: the same object for which a deictic expression is used in the perceptual situation can be designated outside that situation by other expressions. (Substitutability). I 389 TugendhatVsStrawson: what StrawsonVsRussell argues does not actually contradict his theory, but seems to presuppose it. I 433 Learning: the child does not learn to attach labels to objects, but it is the demonstrative expressions that point beyond the situation! The demonstrative expressions are not names, one knows that it is to be replaced by other deictic expressions, if one refers from other situations to the same. (TugendhatVsRussell and StrawsonVsRussell). I 384 StrawsonVsRussell: Example "The present King of France is bald" (King-Example). It depends on what time such an assertion is made. So it is sometimes true. I 385 Example "The present king of France is bald" has a meaning, but no truth value itself. (>expression, >utterance): RussellVsStrawson: that would have nothing to do with the problem at all, one could have added a year. StrawsonVsRussell: if someone is of the opinion that the prerequisite for existence is wrong, he will not speak of truth or falsehood. RussellVsStrawson: it does not matter whether you say one or the other in colloquial language, moreover, there are enough examples that people speak more of falsity in colloquial language. I 386 TugendhatVsStrawson: he did not realize that he had already accepted Russell's theory. It is not about the difference between ideal language and colloquial language. This leads to the Oxford School with the ordinary language philosophy. It is not about nuances of colloquial language as fact, but, as with philosophy in general, about possibility. I 387/388 StrawsonVsRussell: logical proper names are only fictitious. "This" is not an ambiguous proper name but has a uniform meaning as a deictic expression and designates a different object depending on the situation of use. TugendhatVsStrawson: but you cannot oblige Russell to use this word as we use it in our natural language.) Russell fails because he does not take into account another peculiarity: the same object for which a deictic expression is used in the perceptual situation can be designated outside that situation by other expressions. (Substitutability). I 389 TugendhatVsStrawson: what StrawsonVsRussell argues does not actually contradict his theory, but seems to presuppose it. I 395 Identification/TugendhatVsStrawson: uses identification in the narrower sense. Tugendhat: my own term "specification" (which of all objects is meant) is superior to this term. "To pick put" is Strawson's expression. (Taken from Searle). (>Quine: "to specify"). I 397/398 TugendhatVsStrawson: example "The highest mountain" is no identification at all: which one is the highest? Something must be added, an ostension, or a name, or a location. For example, someone can be blindfolded and led to the highest mountain. He will also not know more. I 399 Identification/Strawson: distinguishes between two types of identification a) Direct pointing b) Description by marking. Space-time locations. Relative position to all other possible locations and all possible objects (in the world). I 400 TugendhatVsStrawson: he overlooked the fact that demonstrative identification in turn presupposes non-demonstrative, spatio-temporal identification. Therefore, there are no two steps. Strawson had accepted Russell's theory of the direct relation so far that he could not see it. ((s) > Brandom: Deixis presupposes anaphora.) I 415 TugendhatVsStrawson: he has overlooked the fact that the system of spatio-temporal relations is not only demonstratively perceptively anchored, but is also a system of possible positions of perception, and thus a system of demonstrative specifications. I 419 TugendhatVsStrawson: he did not ask how the meaning of singular terms is explained or how it is determined which object a singular term specifies. This is determined with different objects in very different ways, sometimes by going through all possible cases. |
Tu I E. Tugendhat Vorlesungen zur Einführung in die Sprachanalytische Philosophie Frankfurt 1976 Tu II E. Tugendhat Philosophische Aufsätze Frankfurt 1992 K II siehe Wol I U. Wolf (Hg) Eigennamen Frankfurt 1993 |
| Type Theory | Quine Vs Type Theory | III 315 Type Theory/TT/Quine: U1, U2 ... etc. logical types. Meaningless are expressions like "x e x", etc. "e2 may only stand between variables of successive type." III 316 With that we avoid confusion of constants. Example: we do not identify the number 12, which contains the class A of the Apostles, with the number 12, which contains a certain class consisting of a dozen classes. Because one is of the type U2, the other of type U3. Every type has a new number 12. ((s) Elsewhere: therefore VsType Theory: infinitely many numbers 1,2,3, etc.). Number/Existence/Ontology/Quine: that there are these numbers no longer depends on whether there are so many individuals. Type Theory/TT/Russell/Quine: Reason: we can derive an incorrect sentence without the separation of types: by simplifying the scheme (A) to (A'): (A’) (Ey)(x)(x ε y . ↔ Fx) If we then introduce the predicate «[1] ε [1]» for "F": we get the Russell antinomy/Russell paradoxy/logical form: (1) (Ey)(x)[x ε y . ↔ ~x ε x)] (2) (x)(x ε y . ↔ ~(x ε x)] (1) y (3) y ε y . ↔ ~(y ε y) (2) (4) (Ey)[y ε y . ↔ ~y ε y)]. Solution/Zermelo/VsType Theory/Quine: simpler: some predicates have classes as extension, others don't. (A') is thus considered as valid for some, but not all sentences. E.g. the predicate "[1] ε [1]" has no class as an extension. Zermelo: here (A') is assumed for the case in which the sentence has the form of a conjunction "x ε z. Gx" instead of "Fx". Then (A') becomes: (Ey)(x)( x ε y . ↔ . x ε z . Gx). Zermelo calls this the Def axiom schema of specification. To any given class z this law supplies other classes that are all sub-classes of z. But by itself it supplies at first no non-empty classes z. (...) III 318 Layers/Layered/Zermelo: (...) Sets/Classes/von Neumann/Quine: (...) Classes are not sets... III 319 Axioms/Stronger/Weaker/Quine: (...) you can seek strength or weakness. VII (e) 91 QuineVsType Theory: unnatural and uncomfortable disadvantages: 1) Universal class: because the TT only allows uniform types as members of a class, the universal class V leads to an infinite series of quasi universal classes, each for one type. 2) Negation: ~x ceases to comprise all non-elements of x, and only comprises those non-elements that do not belong to the next lower level! VII (e) 92 3) Zero class: even that accordingly leads to an infinite number of zero classes. ((s) for each level its own zero class). ((s) Absurd: we cannot distinguish different zero classes.) 4) Boolean class algebra: is no longer applicable to classes in general, but is reproduced at each level. 5) Relational calculus: accordingly. to be re-established at each level. 6) Arithmetic: the numbers cease to be uniform! at each level (type) appears a new 0, new 1, new 2, and so on! Quine: instead counterproposal: QuineVsType Theory: Solution: Instead: variables with unlimited range, the concept of hierarchical formulas only survives in one point where we write numbers for variables and, without any reference to type theory, we replace R3 by the weaker: R3' If φ is stratified and does not contain "x", then (Ex)(y) ((y ε x) ↔ φ) is a theorem. Negation: ~x then contains everything that is not part of x. Zero class: there is only one zero class. Universal class: there is similarly only one universal class that contains absolutely everything, including itself. Relation, arithmetic, numbers: everything works out again comes in this way. VII (e) 93 Only difference between R3 and R3': R3' lacks a guarantee for the existence of such classes as: y^ (y ε y), y^~(y ε y), etc. In the case of some non-hierarchical formulas the existence of appropriate classes is still to be demonstrated through absurd consequences: R3' results in: (Ex)(y) ((y ε x) ↔ ((z ε y) l (y ε w))) and by inserting this results in subsitution inference (1) (Ex)(y) ((y ε x) ↔ ((z ε y) l (y ε z))) through the other rules What asserts the existence of a class y^ ((z ε y) l (y ε z)) whose generating formula is not hierarchical. But probably we cannot prove its existence. (From these follows inter alia Russell's paradox). Within a system, we can explicitly use such contradictions to take their existence ad absurdum. That (1) can be demonstrated, in turn, shows that the derivation strength of our system "NF" (New Foundations, Quine) exceeds the Principia Mathematica(1). 1. Whitehead, A.N. and Russel, B. (1910). Principia Mathematica. Cambridge: Cambridge University Press. |
Quine XIII Willard Van Orman Quine Quiddities Cambridge/London 1987 |
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