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The author or concept searched is found in the following 3 entries.
| Disputed term/author/ism | Author |
Entry |
Reference |
|---|---|---|---|
| Decidability | Hintikka | I 7 Standard Semantics/Kripke Semantics/Hintikka: what differences are there? The ditch between them is much deeper than it first appears. Cocchiarella: Cocchiarella has shown, however, that even in the simplest quantifying case, of the monadic predicate logic, the standard logic is radically different from its Kripkean cousin. Decidability: monadic predicate logic is, as Kripke has shown, decidable. Kripke semantics: Kripke semantics is undecidable. Decidability: decidability implies axiomatizability. I 208 Decision Problem/predicate calculus/Hao Wang: thesis: the problem corresponds to the task of completely filling the Euclidean surface with square dominoes of different sizes. At least one stone of each size must be used. E.g. logical omniscience now comes in in the following way: At certain points I can truthfully say according to my perception: (5) I see that this Domino task is impossible to solve. In other cases, I cannot say that truthfully. >Logical omniscience. Problem/HintikkaVsBarwise/HintikkaVsSituation Semantics/Hintikka: according to Barwise/Perry, it should be true of any unsolvable Domino problem that I see the unsolvability immediately as soon as I see the forms of available stones because the unsolvability follows logically from the visual information. Solution/semantics of possible worlds/Hintikka: according to the urn model there is no problem. >Possible world semantics. I 209 Omniscience/symmetry/Hintikka: situational semantics: situational semantics needs the urn model to solve the second problem of logical omniscience. Semantics of possible worlds: on the other hand, it needs situational semantics itself to solve the first problem. >Situation 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 |
| Necessity | Peacocke | II 313 Necessity/necessary/modification of predicates/Wiggins/Peacocke: Problem: 'big' cannot modify like 'nec' predicates of any fine degree. ((s) "nec" : Operator for necessary"). >Operators. That means, we get a finite axiomatized theory for 'big' but not for 'nec'. - There can only be an infinite number of modifications here. >Axioms, >Axiom systems, >Axiomatizability. Problem: 'nec' can be iterated in the object language, but Grandy's representational content cannot treat the iterations because the performance is not defined. Solution: 1. syntactical variabel 't>' is about series of terms of the form (t1 ... tn) 2. separate recursion for abstracts of the object language in the theory, that specifies inductively the conditions under which a sequence has the property correlated with the abstract('Corr'). II 316 Then the truth conditions turn the predications into sequences - so the theory is not entirely homophonic. >Homophony, >Truth conditions, >Predication. II 324 Necessity/satisfaction/language/Peacocke: the satisfaction and evaluation axioms not only express contingent truths about the language - necessarily in German each sequence fulfils x1 'is greater than Hesperus' in L, if their first element is greater than Hesperus. >Satisfaction. |
Peacocke I Chr. R. Peacocke Sense and Content Oxford 1983 Peacocke II Christopher Peacocke "Truth Definitions and Actual Languges" In Truth and Meaning, G. Evans/J. McDowell Oxford 1976 |
| Strength of Theories | Hintikka | II 7 Standard Semantics/Kripke Semantics/Hintikka: what differences are there? The ditch between standard semantics and Kripke semantics is much deeper than it first appears. Cocchiarella: Cocchiarella has shown, however, that even in the simplest quantifying case of the monadic predicate logic, the standard logic is radically different from its Kripke cousin. Decidability: monadic predicate logic is, as Kripke has shown, decidable. Kripke semantics: Kripke semantics is undecidable. Decisibility: Decisibility implies axiomatizability. Stronger/weaker/Hintikka: as soon as we go beyond monadic predicate logic, we have a logic of considerable strength, complexity, and unruliness. Quantified standard modal logic of the 1. level/Hintikka: the quantified standard modal logic of the 1. level is in a sense more powerful than the 2. level logic (with standard semantics). The latter is, of course, already very strong, so that some of the most difficult unresolved logical and quantum-theoretical problems can be expressed in terms of logical truth (or fulfillment) in logical formulas of the second level. Def equally strong/stronger/weaker/Hintikka: (here): the terms "stronger" and "weaker" are used to show an equally difficult decision-making problem. Decision problem: the standard logic of the 2. level can be reduced to that for quantified standard modal logic of the 1. level. Reduction: this reduction is weaker than translatability. II 9 Quantified standard modal logic of the 1. level/Hintikka: this logic is very strong, comparable in strength with the 2. level logic. It follows that it is not axiomatizable (HintikkaVsKripke). The stronger a logic is, the less manageable it is. II 28 Branching Quantifiers/stronger/weaker/Hintikka: E.g. branching here: 1. Branch: there is an x and b knows... 2. Branch: b knows there is an x ... Quantification with branched quantifiers is extremely strong, almost as strong as 2. level logic. Therefore, it cannot be completely axiomatized (quantified epistemic logic with unlimited independence). II 29 Variant: variants are simpler cases where the independence refers to ignorance, combined with a move with a single, non-negated operator {b} K. Here, an explicit treatment is possible. II 118 Seeing/stronger/weaker/logical form/Hintikka: a) stronger: recognizing, recognizing as, seeing as. b) weaker: to look at, to keep a glance on, etc. Weaker/logical form/seeing/knowing/Hintikka: e.g. (Perspective, "Ex") (15) (Ex) ((x = b) & (Ey) John sees that (x = y)). (16) (Ex)(x = b & (Ey) John remembers that x = y)) (17) (Ex)(x = b & (Ey) KJohn (x = y)) Acquaintance/N.B.: in (17) b can be John's acquaintance even if John does not know b as b! ((S) because of y). II 123 Everyday Language/ambiguity/Hintikka: the following expression is ambiguous: (32) I see d Stronger: (33) (Ex) I see that (d = x) That says the same as (31) if the information is visual or weaker: (34) (Ex) (d = x & (Ey) I see that (x = y)) This is the most natural translation of (32). Weaker: for the truth of (34) it is enough that my eyes simply rest on the object d. I do not need to recognize it as d. |
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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