Lexicon of Arguments

 

II XV
Logical Omniscience/Hintikka: thesis: logical omniscience is only a supposed problem.
ChomskyVsHintikka: Hintikka has given the alleged paradox as the reason for his rejection of any model-theoretical semantics for propositional attitudes.
HintikkaVsChomsky: Chomsky's problem has been solved long ago.
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II 21
Omniscience/solution/Hintikka: we must allow individuals to not exist in every possible world. Otherwise, all world lines would have to be ad libitum extendable, then everyone would have to know what an individual would be in any world (in whatever disguise), namely on the basis of the form of knowledge + indirect W-question.
II 23
Logical Omniscience/epistemic logic/model theory/Hintikka: problem: suppose (S1 > S2). That is, all S1 models are S2 models.
Then all the epistemic alternatives in which S1 is true are those in which S2 is true.
Problem: it follows that for each knowing person b and every scenario applies:
(3.1) {b} KS1> {b} K S2.
That is, one must also know all the logical consequences of one's knowledge.
This has led some to reject model theory.
Model Theory/HintikkaVsVs: model theory follows only if one cannot avoid omniscience, and one can avoid it.
>Model theory.
Solution: one can find a subset of logical consequences (S1 > S2) for which (3.1) applies.
(i) This subset can be restricted syntactically. The number of free individual symbols together with the number of layers of quantifiers limit the number of individuals that can be considered in a set S (or in an argument).
Solution: this number (parameter) should not be greater than the one in S1 or S2 at any point in the argument.
Problem: there is no simple axiomatic-deductive system for this.