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Barcan-Formula | Stalnaker | I 150 Barcan formula/BF/Stalnaker: the Barcan formula involves the interaction of the universal quantifier with the necessity operator: (BF) " NF x ^ > N " x ^ F. Conversely: (CBF) N " F ^ x > " x ^ NF (Kripke 1963)(1): Kripke's semantics showed that semantic assumptions are also needed. He also showed a fallacy in the proofs that they supposedly deduced, in which these assumptions were missing. It is valid if wuU, Du < Dw, i.e. if the subject matter of the accessible possible world is a subset of the range of the output possible world - vice versa for the converse. Qualified converse of Barcan-Formula/Stalnaker: a qualified converse with the Barcon-Formula is made with the existence adoption: ( QCBF ) N "x ^ F> " x ^ N ex > F). Existence predicate e: Ey ^ (x = y ). I 151 Barcan-Formula/qualified converse/Stalnaker: if in possible world w it is necessary that everything satisfies F, then everything that must exist in w, must satisfy F in any accessible possible world, in which this individual exists. That is valid in our semantics but it is not a theorem because it is a variant of the invalid semantics. This is what we examine here. 1. S. A. Kripke, 1963. Semantical Analysis of Modal Logic I Normal Modal Propositional Calculi. Mathematical Logic Quarterly Volume 9, Issue 5‐6 |
Stalnaker I R. Stalnaker Ways a World may be Oxford New York 2003 |
Existence Predicate | Stalnaker | I 150f Barcan formula/BF/Stalnaker: the Barcan formula involves the interaction of the universal quantifier with the necessity operator: (BF) "x^NF > N"x^F A (CBF) N"x^F > x^NF. Kripke (1963)(1): Kripke's semantics showed which semantic assumptions are needed additionally. He showed a fallacy in the evidence that was allegedly derived, in lacking these assumptions - it is valid if wRu, Du < Dw. >Domains, >Converse. That is, if the domain of the accessible worlds is a subset of the domain of departing worlds. This applies vice versa for the converse. Qualified converse of Barcan formula/Stalnaker: a qualified converse of the Barcan formula is made with the existence assumption (QCBF) N"x^F > x^N Ex > F). Existence predicate e: Ey ^ (x = y ). >Existence predicate, >Barcan-formula. 1. S. A. Kripke, 1963. Semantical Analysis of Modal Logic I Normal Modal Propositional Calculi. Mathematical Logic Quarterly Volume 9, Issue 5‐6 |
Stalnaker I R. Stalnaker Ways a World may be Oxford New York 2003 |
Logical Necessity | Field | I 255 Mathematics/physics/necessity/Field: e.g. Laplace equation: physical equation - holds not with logical necessity - even if the mathematics is valid. >Physics, >Mathematics, >Facts, >Natural laws. Solution: separation in a purely mathematical and a purely physical part. - The equation does not have to be preceded by a necessity operator - but probably a by chance operator. >Equations, >Chance, >Probability. Problem: that still does not allow to preserve Platonic physics. >Platonism. |
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 |
Modal Logic | Quine | II 152 Modal Logic/Quine: The entire modal logic is context-dependent - what is the role of someone or something? It is on the same level as essential properties. (Essentialism). VII (h) 151 Modal Logic/ontology/Quine: instead of Venus as a material object we now have three objects: Venus term, morning star term, evening star term - avoiding opaque contexts: class names as objects rather than classes, numerical names as objects instead of numbers - number concept/number of planets concept: a term is not larger/smaller than another one - reason: necessity is not satisfied by physical objects (> Necessity/Hume). - Necessity/possibility: is only introduced by way of reference, not by the objects - necessity concerns relations, not objects (not existence) - Frege: "sense (meaning) of names" Quine: Problem: individuation requires analyticity and synonymy - E.g. (s) "The term Morning Star necessarily includes the appearance on the morning sky. VII (h) 151f Modal Logic/Quine: makes essentialism necessary, i.e. you cannot do without necessary traits of the objects themselves, because you cannot do without quantification - QuineVsModal Logic: actually there is nothing necessary to the objects "themselves", but only in the way of reference. VII (h) 151 Modal Logic/Ontology/Quine: the condition that two names for x must be synonymous is not a condition for objects, but for singular terms - no necessity de re - Venus does not decide about morning star/evening star. - ((s) The conditions are equivalent not the objects. > necessity. VII (h) 154 Modal Logic/Church/Quine: quantified variables should be limited to intensional values - Proposition: complex names of intensional objects - then instead of necessity operator for whole sentences: Necessity predicate is based on complex names ("propositions") - no modal logic in the narrower sense. >Propositions/Quine. VII (h) 154 Modal Logic/Smullyan/Quine: there is a strict separation of proper names and (overt or covert) descriptions - names which denote the same objects are always synonymous (if x = y, then nec. x = y.) - In this case, sentences like (number of the planets = 9) which do not have a substitutable identity must be analyzed by descriptions rather than through proper names (Quine pro). - QuineVs: one must still consider opaque contexts, even if descriptions and other singular terms are eliminated all together. >Proper Names/Quine. VII (h) 154 Modal Logic/Necessity/Planet Example/Quine: the only hope is to accept the situation as described in (33): there are exactly x planets) and still insist that the object x in question is necessarily more than 7! (> Essentialism). - An object itself, regardless by what it is named or not named, must be considered in a way that it has some traits necessarily and others by chance! And notwithstanding the fact that the random traits stem from a way of reference, as well as the necessary ones from other modes of reference - ~nec. [p. (x = x)] where "p" stands for any random truth. VII (h) 156 Modal Logic/Quine: one must accept an Aristotelian essentialism, if one wants to permit quantified modal logic. VII (h) 156 Modal Logic/planet/Quine: the property of being bigger than 9 = the property of being bigger than 9 - but wrong: the property of exceeding the number of planets = the property of being bigger than 9 (s) New: although now the number is the same, the property is not the same - (E.g.) (x = The property of being greater than x = the property to be greater than 9) - any non-truth-functional language leads to opaque contexts. X 107 Modality/modal/Quine: Problem: extension-identical (coextensive) predicates are not interchangeable salva veritate. >Modalities/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 |
Modalities | Church | Quine VII 153 Modality/Modal Logic/Ontology/Church: (1943)(1) Proposal: the quantified variables should be limited to intensional values. >Intensions, >Intensionality, cf. >Extension, >Extensionality. Carnap: took this in extreme form for his entire system. He himself presented this as a complicated double interpretation of his variables. QuineVsChurch, QuineVsCarnap: see above. Proposition/Church: (late): complex names of certain intensional objects. >Propositions. Intensional Logic/Church: later: instead of a necessity generator (related to whole sentences): New: Necessity predicate: which is related to complex names of certain intensional objects, called "propositions". >Intensional logic, >Operators, >Necessity operator. VII 154 In these propositions, the constants and variables of the corresponding propositions no longer appear (otherwise circular). >Names of sentences, >Circular reasoning, >Levels, >Constants, >Variables. This reflects the interplay between events inside and outside the modal contexts. Church did not call this modal logic, nor should we. Cf. >Modal Logic. Modal logic in the narrower sense has to do with the modal operator in relation to whole sentences. >Modal operators. 1. Church, Alonzo. The Journal of Symbolic Logic, vol. 8, no. 1, 1943, pp. 31–32. JSTOR, https://doi.org/10.2307/2267985. Accessed 18 Nov. 2022. |
Chur I A. Church The Calculi of Lambda Conversion. (Am-6)(Annals of Mathematics Studies) Princeton 1985 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 |
Models | Stalnaker | I 146 Model/Stalnaker: a model is a pair consisting of an object domain D and a valuation function V. >Valuation function, >Domains. I 149 Model: For our modal predicate logic is then a quadruple ‹W,R,D,v›. D is the range function of W on the sets of individuals. For w ε W, Dw is the range of the world w. Valuation function: the valuation function attributes intensions to descriptive expressions. Intension: the intension here is a function of possible worlds on extensions. >Intensions, >Extensions. Necessity operator: The semantic rule of the necessity operator remains unchanged. >Operators. I 150 The rules for predicate logic are generalizations of the extensional rules. We only add an index for the worlds. E.g. rule for Universal quantification/universal quantifier/Stalnaker: IF Φ has the form ∀F, then is νs w (Φ) = 1 gdw. νs w(F) = D w. otherwise = 0. >Quantification, >Universal quantification. |
Stalnaker I R. Stalnaker Ways a World may be Oxford New York 2003 |
Operators | Hintikka | II 9 Backwards Operator/retrospective/Hintikka: (literature: "Rome paper", 1955): "retrospective" operators can make quantified standard modal logic extremely strong. One can say that the absence of such operators in modal logic is only a coincidence and should be inserted. II 13 Necessity Operator/Hintikka: a necessity operator interpreted as standard performs exactly the same as a standard interpreted universal quantifier of a higher level. |
Hintikka I Jaakko Hintikka Merrill B. Hintikka Investigating Wittgenstein German Edition: Untersuchungen zu Wittgenstein Frankfurt 1996 Hintikka II Jaakko Hintikka Merrill B. Hintikka The Logic of Epistemology and the Epistemology of Logic Dordrecht 1989 |
Scope | Scope, range, logic, philosophy: range is a property of quantifiers or operators to be able to be applied to a larger or smaller range. For example, the necessity operator N may be at different points of a logical formula. Depending on the positioning, the resulting statement has a considerably changed meaning. E.g. great range "It is necessary that there is an object that ..." or small range "There is an object that is necessarily ....". See also quantifiers, operators, general invariability, stronger/weaker, necessity, Barcan Formula. |
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Modal Logic | Quine Vs Modal Logic | Chisholm II 185 QuineVsModal Logic: instead space time points as quadruples. Reason: permanent objects (continuants) seem to threaten the extensionality. SimonsVsQuine: the Achilles heel is that we must have doubts whether anyone could learn a language that refers not to permanent objects (continuants). --- Lewis IV 32 QuineVsModal Logic: which properties are necessary or accidental, is then dependent on the description. Definition essentialism/Aristotle: essential qualities are not dependent on description. QuineVs: that is as congenial as the whole modal logic. LewisVsQuine: that really is congenial. --- I 338 But modal logic has nothing to do with it. Here, totally impersonal. The modal logic, as we know it, begins with Clarence Lewis "A survey of Symbolic Logic" in 1918. His interpretation of the necessity that Carnap formulates even more sharply later is: Definition necessity/Carnap: A sentence that starts with "it is necessary that", is true if and only if the remaining sentence is analytic. Quine provisionally useful, despite our reservations about analyticity. --- I 339 (1) It is necessary that 9 > 4 it is then explained as follows: (2) "9 > 4" is analytically. It is questionable whether Lewis would ever have engaged in this matter, if not Russell and Whitehead (Frege following) had made the mistake, the philonic construction: "If p then q" as "~ (p and ~ q)" if they so designate this construction as a material implication instead of as a material conditional. C.I.Lewis: protested and said that such a defined material implication must not only be true, but must also be analytical, if you wanted to consider it rightly as an "implication". This led to his concept of "strict implication". Quine: It is best to view one "implies" and "is analytical" as general terms which are predicated by sentences by adding them predicatively to names (i.e. quotations) of sentences. Unlike "and", "not", "if so" which are not terms but operators. Whitehead and Russell, who took the distinction between use and mention lightly, wrote "p implies q" (in the material sense) as it was with "If p, then q" (in the material sense) interchangeable. --- I 339 Material implication "p implies q" not equal to "p > q" (>mention/>use) "implies" and "analytical" better most general terms than operators. Lewis did the same, he wrote "p strictly implies q" and explained it as "It is necessary that not (p and not q)". Hence it is that he developed a modal logic, in which "necessary" is sentence-related operator. If we explain (1) in the form of (2), then the question is why we need modal logic at all. --- I 340 An apparent advantage is the ability to quantify in modal positions. Because we know that we cannot quantify into quotes, and in (2) a quotation is used. This was also certainly Lewis' intention. But is it legitimate? --- I 341 It is safe that (1) is true at any plausible interpretation and the following is false: (3) It is necessary that the number of planets > 4 Since 9 = the number of planets, we can conclude that the position of "9" in (1) is not purely indicative and the necessity operator is therefore opaque. The recalcitrance of 9 is based on the fact that it can be specified in various ways, who lack the necessary equivalence. (E.g. as a number of planets, and the successor to the 8) so that at a specification various features follow necessarily (something "greater than 4 ") and not in the other. Postulate: Whenever any of two sentences determines the object x clearly, the two sentences in question are necessary equivalent. (4) If Fx and only x and Gx and exclusively x, it is necessary that (w)(Fw if and only if when Gw). --- I 342 (This makes any sentence p to a necessary sentence) However, this postulate nullifies modal distinctions: because we can derive the validity of "It is necessary that p" that it plays no role which true sentence we use for "p". Argument: "p" stands for any true sentence, y is any object, and x = y. Then what applies clearly is: (5) (p and x = y) and exclusively x as (6) x = y and x exclusively then we can conclude on the basis of (4) from (5) and (6): (7) It is necessary that (w) (p and w = y) if and only if w = y) However, the quantification in (7) implies in particular "(p and y = y) if and only if y = y" which in turn implies "p"; and so we conclude from (7) that it is necessary that p. --- I 343 The modal logic systems by Barcan and Fitch allow absolute quantification in modal contexts. How such a theory can be interpreted without the disastrous assumption (4), is far from clear. --- I 343 Modal Logic: Church/Frege: modal sentence = Proposition Church's system is structured differently: He restricts the quantification indirectly by reinterpreting variables and other symbols into modal positions. For him (as for Frege) a sentence designated then, to which a modal operator is superior, a proposition. The operator is a predicate that is applied to the proposition. If we treat the modalities like the propositional attitude before, then we could first (1) reinterpret (8) [9 > 4] is necessary (Brackets for class) and attach the opacity of intensional abstraction. One would therefore interpret propositions as that what is necessary and possible. --- I 344 Then we could pursue the model from § 35 and try to reproduce the modality selectively transparent, by passing selectively from propositions to properties: (9) x (x > 4) is necessary in terms 9. This is so far opposed to (8) as "9" here receives a purely designated position in one can quantify and in one can replace "9" by "the number of planets". This seemed to be worth in the case of en, as we e.g. wanted to be able to say (§ 31), there would be someone, of whom is believed, he was a spy (> II). But in the case of modal expressions something very amazing comes out. The manner of speaking of a difference of necessary and contingent properties of an object. E.g. One could say that mathematicians are necessarily rational and not necessarily two-legged, while cyclist are necessarily two-legged but not necessarily rational. But how can a bicycling mathematician be classified? Insofar as we are talking purely indicatively of the object, it is not even suggestively useful to speak of some of its properties as a contingent and of others as necessary. --- I 344 Properties/Quine: no necessary or contingent properties (VsModal Logic) only more or less important properties Of course, some of its properties are considered essential and others unimportant, some permanently and others temporary, but there are none which are necessary or contingent. Curiously, exactly this distinction has philosophical tradition. It lives on in the terms "nature" and "accident". One attributes this distinction to Aristotle. (Probably some scholars are going to protest, but that is the penalty for attributing something to Aristotle.) --- I 345 But however venerable this distinction may be, it certainly cannot be justified. And thus the construction (9) which carries out this distinction so elegantly, also fails. We cannot blame the analyticity the diverse infirmities of modality. There is no alternative yet for (1) and (2) that at least sets us a little on something like modal logic. We can define "P is necessary" as "P = ((x) (x = x))". Whether (8) thereby becomes true, or whether it is at all in accordance with the equation of (1) and (2), will depend on how closely we construct the propositions in terms of their identity. They cannot be constructed so tightly that they are appropriate to the propositional properties. But how particularly the definition may be, something will be the result that a modal logic without quantifiers is isomorphic. --- VI 41 Abstract objects/modal logic/Putnam/Parsons: modal operators can save abstract objects. QuineVsModal Logic: instead quantification (postulating of objects) thus we streamline the truth functions. Modal logic/Putnam/Parsons/Quine: Putnam and Charles Parsons have shown how abstract objects can be saved in the recourse to possibility operators. Quine: without modal operators: E.g. "Everything is such that unless it is a cat and eats spoiled fish, and it gets sick, will avoid fish in the future." ((s) logical form/(s): (x) ((Fx u Gx u Hx)> Vx). Thus, the postulation of objects can streamline our only loosely binding truth functions, without us having to resort to modal operators. --- VI 102 Necessity/opportunity/Quine: are insofar intensional, as they do not fit the substitutivity of identity. Again, vary between de re and de dicto. --- VI 103 Counterfactual conditionals, unreal conditionals/Quine: are true, if their consequent follows logically from the antecedent in conjunction with background assumptions. Necessity/Quine: by sentence constellations, which are accepted by groups. (Goes beyond the individual sentence). --- VI 104 QuineVsModal logic: its friends want to give the necessity an objective sense. --- XI 52 QuineVsModal Logic/Lauener: it is not clear here on what objects we are referring to. --- XI 53 Necessesity/Quine/Lauener: ("Three Grades of Modal Involvement"): 3 progressive usages: 1. as a predicate for names of sentences: E.g. "N "p"": "p is necessarily true". (N: = square, box). This is harmless, simply equate it with analyticity. 2. as an operator which extends to close sentence: E.g. "N p": "it is necessarily true that p" 3. as an operator, too, for open sentences: E.g. "N Fx": through existence generalization: "(Ex) N Fx". |
Quine I W.V.O. Quine Word and Object, Cambridge/MA 1960 German Edition: Wort und Gegenstand Stuttgart 1980 Quine 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 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 |
Stalnaker, R. | Williamson Vs Stalnaker, R. | I 159 Identity/Indistinguishability/Timothy WilliamsonVsStalnaker: (1996): Actuality Operator/@/Williamson: if we add it to K, we can prove the necessity of diversity from the necessary identity. I.e. actual different things are then necessarily different: Logical form: I- @ (∀x)(∀y)(x ≠ y > Nx ≠ y). I 160 Stalnaker: my independence argument above for necessary diversity was based on two assumptions 1. the extensional logic of identity is the same as the logic of indistinguishability, but 2. in a modal semantics without symmetry condition for the accessibility relation, individuals can be distinguishable in a possible world while they are not in another possible world. If one cannot "look back", the information about the distinction may be lost. Actuality Operator/Williamson: preserves the information because you can always look back to the actual world. General: the information about every possible world accessible from the actual world is reflected in the actual world and thus also in every other possible world in the model. Williamson: general thesis: I- Ni (x ≠ y > Nj x ≠ y) In our classical system, the universal generalization is invalid and unprovable with this (∀x)(∀y)(Ni (x ≠ y > Nj x ≠ y) because the predication implies existence and thus the negation of an identity statement can be true, not because the expressions refer to different things, but because these do not exist at all. But: the version with the quantifiers within the necessity operator Ni (∀x)(∀y) (x ≠ y > Nj x ≠ y) Will be valid even if the equal sign is defined as indistinguishable. But it will not be provable. Reason: K + @ is an incomplete quantified modal logic. Actuality Operator/Stalnaker: Problem: the semantic limitations for its interpretation have consequences that are not reflected in the propositional logic for this operator, consequences that occur when the range may change from possible worlds to possible worlds. There are propositions without identity which are valid but not provable, e.g. I- @ N (∀x)(Fx > @MFx) Counterpart Semantics/counterpart theory/necessity diversity/Stalnaker: the absence of the need of diversity in the counterpart theory. I 161 Is not connected with the limits of the expressiveness of modal logic (it is even missing in S5). The necessary identity is valid and provable here. Rather, the necessary difference cannot be proven with or without the actuality operator. StalnakerVsWilliamson: therefore I think that his argument does not threaten the thesis, Thesis: the necessity (or essentiality) of identity is more central in identity logic than the necessity of diversity. |
EconWillO Oliver E. Williamson Peak-load pricing and optimal capacity under indivisibility constraints 1966 |
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