## Philosophy Lexicon of Arguments | |||

Author | Item | Excerpt | Meta data |
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Books on Amazon |
I 7 Standard semantics/Kripke semantics/Hintikka: what differences are there? The ditch between them is much deeper than it first appears. Cocchiarella: he 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 1. level/Hintikka: the quantified standard modal logic of 1. level is in a sense more powerful than 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. Definition equally strong/stronger/weaker/Hintikka: (here): to show an equally difficult decision-making problem. Decision problem: for standard logic 2. level can be reduced to that for quantified standard modal logic 1. level. Reduction: this reduction is weaker than translatability. --- I 9 Quantified standard modal logic 1. level/Hintikka: this logic is very strong, comparable in strength with 2. level logic. It follows that it is not axiomatizable. (HintikkaVsKripke). The stronger a logic is, the less manageable it is. --- I 28 Branched quantifiers/branching/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). --- I 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. --- I 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 even John's acquaintance even if John does not know b as b! ((S) because of y). --- I 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. |
Hin I Jaakko and Merrill B. Hintikka The Logic of Epistemology and the Epistemology of Logic Dordrecht 1989 W I J. Hintikka/M. B. Hintikka Untersuchungen zu Wittgenstein Frankfurt 1996 |

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Ed. Martin Schulz, access date 2017-05-26