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The author or concept searched is found in the following 2 entries.
| Disputed term/author/ism | Author |
Entry |
Reference |
|---|---|---|---|
| Kripke Semantics | Hintikka | II XIII Kripke Semantics/HintikkaVsKripke: Kripke semantics is not a viable model for the theory of logical modalities (logical necessity and logical possibility). Problem: the right logic cannot be axiomatized. Solution: to interpret Kripke semantics as a non-standard semantics,... II XIV ...in the sense of Henkin's non-standard interpretation of the logic of higher levels, while the correct semantics for logical modalities would be analogous to a standard interpretation. >Logical possibility, >Logical necessity, >Modal logic, >Modalities. --- II 1 Kripke Semantics/Hintikka: Kripke semantics is a modern model-theoretic approach that is misleadingly called Kripke semantics. E.g.: F: is a framework consisting of SF: a set of models or possible worlds and R: a two-digit relation, a kind of alternative relation. Possible Worlds: w1 is supposed to be an alternative, which could legitimately be realized instead of w0 (the actual world). R: the only limitation we impose on it is reflexivity. Truth Conditions/modal logic/Kripke semantics/Hintikka: the truth conditions for modal sentences are then: II 2 (TN) Given a frame F, Np is true in w0 ε SF iff. P is true in every alternative wi ∈ SF to w0. (T.M) Given a frame F, Mp is true in w0 ε SF iff. P is true in at least one alternative wi ∈ SF to w0. Model Theory/modal logic/Hintikka: Kanger, Guillaume and later Kripke have seen that when we add reflexivity, transitivity, and symmetry, we get a model theory for axiom systems of the Lewis type for modal propositional logic. Kripke Semantics/modal logic/logical possibility/logical necessity/HintikkaVsKripke/HintikkaVsKripke semantics: problem: if we interpret the operators N, P as expressing logical modalities, they are inadequate: we need more than one arbitrary selection for logical possibility and necessity of possible worlds. We need truth in every logically possible world. But in the Kripke semantics it is not necessary that all such logically possible worlds are contained in the set of alternatives ((s) that is, there may be logically possible worlds that are not considered). (See below the logical possibility forms the largest class of possibilities). Problem: Kripke semantics is therefore inadequate for logical modalities. II 12 Kripke/Hintikka: Kripke has avoided epistemic logic and the logic of propositional attitudes, concentrating on pure modalities. >Epistemic logic. Therefore, it is strange that he uses non-standard logic. But somehow it seems clear to him that this is not possible for logical modalities. Metaphysical Possibility/Kripke/HintikkaVsKripke: Kripke has never explained what these mystical possibilities actually are. II 13 Worse: Kripke has not even shown that they are so restrictive that he can use his extremely liberal non-standard semantics. |
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 |
| Kripke Semantics | Bigelow | Bigelow I 109 Kripke Semantics/Bigelow/Pargetter: has only recently shown that K, D, T B are the right preliminary stages for S4 and S5. Before, they thought it was S1, S2 and S3. >Systems S4/S5, >S.A. Kripke, >Logic, >Accessibility relation, >Axioms, >Axiom systems, >Semantics. |
Big I J. Bigelow, R. Pargetter Science and Necessity Cambridge 1990 |
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| Disputed term/author/ism | Author Vs Author |
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Reference |
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| Kripke, S. A. | Hintikka Vs Kripke, S. A. | II XIII Possible Worlds/Semantics/Hintikka: the term is misleading. (Began in the late 50s). Kripke Semantics/HintikkaVsKripke: is not a viable model for the theory of logical rules (logical necessity and logical possibility). (Essay 1). Problem: the correct logic cannot be axiomatized. Solution: interpreting Kripke semantics as non-standard semantics, II XIV in the sense of Henkin’s non-standard interpretation of higher-level logic, while the correct semantics for logical modalities would be analogous to a standard interpretation. Possible Worlds/HintikkaVsQuine: we do not have to give them up entirely, but there will probably never be a complete theory. My theory is related to Kant. I call them "epistemology of logic". II XVI Cross World Identity/Hintikka: Quine: considers it a hopeless problem HintikkaVsKripke: he underestimates the problem and considers it as guaranteed. He cheats. World Line/Cross World Identity/Hintikka: 1) We need to allow that some objects in certain possible worlds do not only exist, but that their existence is unthinkable there! I.e. world lines can cease to exist - what is more: it may be that they are not defined in certain possible worlds. Problem: in the usual knowledge logic (logic of belief) this is not permitted. 2) world lines can be drawn in two ways: a) object-centered b) agent-centered. (Essay 8). Analogy: this can be related to Russell’s distinction between knowledge by acquaintance and by description. (Essay 11) II 2 Kripke Semantics/Modal Logic/Logical Possibility/Logical Necessity/HintikkaVsKripke/HintikkaVsKripke Semantics: Problem: if we interpreted the operators N, P so that they express logical modalities, they are inadequate: for logical possibility and necessity we need more than an arbitrary selection of possible worlds. We need truth in every logically possible world. But Kripke semantics does not require all such logically possible worlds to be included in the set of alternatives. ((s) I.e. there may be logically possible worlds that are not considered). (see below logical possibility forms the broadest category of options). Problem: Kripke semantics is therefore inadequate for logical modalities. Modal Logic/Hintikka: the historically earliest purpose for which it was developed was precisely dealing with logical modalities. This was the purpose for which the Lewis systems were developed. HintikkaVsKripke: does not only have a skeleton in the closet, but said skeleton haunts the entire house. Equivalence Relation/Hintikka: if R is required to be reflexive, symmetrical, and transitive, it does not provide the solution: it still does not guarantee that all logically possible worlds are contained in the set. It can (possibly together with with connectedness) only guarantee that w0 has a maximum number of sets as its alternatives that are, so to speak, already in SF. II 3 KripkeVsVs/Hintikka: It could be argued that this does not yet show that Kripke semantics is wrong. It just needs to be reinforced. E.g. Nino Cocchiarella: Cocchiarella: additional condition: all models (in the usual 1st order sense) with the same domain of individuals do (w0) must occur among the alternative possible worlds to w0. ((s) No new individuals may be added or removed with regard to the original possible world w0). Hintikka: technically it is of course possible. "Old": (= Kripke semantics): non-standard semantics. new: F must include all models that have the same individuals domain do(w0) of well-defined individuals as w0. Individual/Individuals/Modal/Hintikka: an individual must be well-defined, but it does not have to exist! ((s) I.e. it can be expressed then that it is missing, E.g. the hero has no sister in a possible world). Domain of Individuals: for each possible world is then a subset of the domain D. II 4 HintikkaVs: Problem: this is unrealistically interpretative: this flexible approach namely allows non-well-shaped individuals. Then there is no point in asking whether this individual exists or not. Fusion/Fission: a flexible semantics must also allow fission and fusion between one possible world and the another. Def Well-Defined/Individual/Hintikka: an individual is well-defined, if it can be singled out by name at a node of the world line. World Line: can link non-existent incarnations of individuals, as long as they are well-defined for all possible worlds in which a node of the world line can be located. Truth Conditions: are then simple: (Ex) p(x) is true iff there is an individual there, E.g. named z, so that p(z) is true in w. Modal Semantics/Hintikka. About a so defined (new) semantics a lot can be said: Kripke Semantics/Hintikka: corresponds to a non-standard semantics, while the "new" semantics (with a fixed domain of individuals) corresponds to a standard semantics. (For higher-order logic). Standard Semantics/higher level: we get this by demanding that the higher level quantifiers go over all extensionally possible entities of the appropriate logical type (higher than individuals) like quantifiers in the standard semantics for modal logic should go over all extensionally possible worlds. This is a parallelism that is even stronger than an analogy: Decision problem: for 2nd order logic this is reduced to the 1st order standard modal logic. Standard: does the same job in the latter sense as in the former sense. Quantified 1st Order Standard Modal Logic/Hintikka: all of this leads to this logic being very strong, comparable in strength with 2nd order logic. It follows that it is not axiomatizable. (see above HintikkaVsKripke). The stronger a logic, the less manageable it is. II 12 Kripke/Hintikka: has avoided epistemic logic and the logic of propositional attitudes and focuses on pure modalities. Therefore, it is strange that he uses non-standard logic. But somehow it seems to be clear to him that this is not possible for logical modalities. Metaphysical Possibility/Kripke/HintikkaVsKripke: has never explained what these mystical possibilities actually are. II 13 Worse: he has not shown that they are so restrictive that he can use his extremely liberal non-standard semantics. II 77 Object/Thing/Object/Kripke/Hintikka: Kripke Thesis: the existence of permanent (endurant) objects must simply be provided as a basic concept. HintikkaVsKripke: this requirement is not well founded. Maybe you have to presuppose the criteria of identification and identity only for traditional logic and logical semantics. But that also does not mean that the problem of identification was not an enduring problem for the philosophers. II 84 KIripkeVsHintikka: Problem: the solutions of these differential equations need not be analytic functions or features that allow an explicit definition of the objects. Hintikka: it seems that Kripke presupposes, however, that you always have to be able to define the relations embodied by the world lines. HintikkaVsKripke: that is too strict. World Line: we allow instead that they are implicitly defined by the solutions of the differential equations. II 86 HintikkaVsKripke: our model makes it possible that we do not necessarily have to presuppose objects as guaranteed like Kripke. ((s) it may be that a curve is not closed in a time section). II 116 Cross World identity/Rigidity/HintikkaVsKripke: it’s more about the way of identification (public/perspective, see above) than about rigidity or non-rigidity. The manner of identification decides what counts as one and the same individual. HitikkaVsKripke: his concept of rigidity is silently based on Russell’s concept of the logical proper name. But there is no outstanding class of rigid designation expressions. Proper Names/Names/HintikkaVsKripke: are not always rigid. E.g. it may be that I do not know to whom the name N.N. refers. Then I have different epistemic alternatives with different references. Therefore, it makes sense to ask "Who is N.N.?". Public/Perspective/Identification/Russell/Kripke/Hintikka: Russell: focuses on the perspective II 117 Kripke: on public identification. II 195 Identity/Individuals/Hintikka: it is much less clear how the identity for certain individuals can fail in the transition to another possible world. I.e. world lines can branch (fission). Separation/KripkeVsFission/SI/Hintikka: Kripke excludes fission, because for him the (SI) applies. A fission, according to him, would violate the transitivity of identity. After a fission, the individuals would by no means be identical, even if it should be after the transitivity. Therefore, for Kripke the (SI) is inviolable. HintikkaVsKripke: that is circular: Transitivity of Identity/Hintikka: can mean two things: a) transitivity within a possible world. b) between possible worlds. The plausibility of transitivity is part of the former, not the latter. To require transitivity of identity between possible worlds simply means to exclude fission. This is what is circular about Kripke’s argument. II 196 Possible World/Individuals Domain/HintikkaVsKripke: it should not be required that the individuals remain the same when changing from possible world to possible world. Talk about possible worlds is empty if there are no possible experiences that might distinguish them. ((s) is that not possible with a constant domain? Also properties could be partly (not completely) exchanged). Possible World/Hintikka: should best be determined as the associated possible totalities of experience. And then fission cannot be ruled out. II 209 Re-Identification/Hintikka: also with this problem situation semantics and possible worlds semantics are sitting in the same boat. Situation semantics: rather obscures the problem. In overlapping situations, E.g. it assumes that the overlapping part remains the same. Re-Identification/Quine/Hintikka: deems it hopeless, because it is impossible to explain how it works. Re-Identification/Kripke/Hintikka: Kripke ditto, but that’s why we should simply postulate it, at least for physical objects. HintikkaVsQuine/HintikkaVsKripke: that is either too pessimistic or too optimistic. But mistaking the problem would mean to neglect one of the greatest philosophical problems. |
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 |
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