Frege's fallacy foiled: Independence-friendly logic

Jaakko Hintikka was a Finnish philosopher who developed important new methods and systems in mathematical and philosophical logic. Over a distinguished career in universities in Finland and the USA, he was one of the most cited analytic philosophers and published prolifically in mathematical and philosophical logic, philosophy of language, formal epistemology, philosophy of science and history of philosophy. Hintikka was a pioneer of possible-worlds semantics, epistemic logic, inductive logic, game-theoretical semantics, the interrogative approach to inquiry and independence-friendly logic. He was an expert on Aristotle, Leibniz, Kant, Peirce and Wittgenstein. He also influenced philosophy as a successful teacher and the long-time editor of the journal Synthese.

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Some combinatorics of imperfect information

Journal of Symbolic Logic ◽

10.2307/2695036 ◽

2001 ◽

Vol 66 (2) ◽

pp. 673-684 ◽

Cited By ~ 21

Author(s):

Peter Cameron ◽

Wilfrid Hodges

Keyword(s):

Imperfect Information ◽

Free Variable ◽

Not Given ◽

Compositional Semantics ◽

Truth Conditions ◽

Impossibility Proof ◽

Independence Friendly Logic

We can use the compositional semantics of Hodges [9] to show that any compositional semantics for logics of imperfect information must obey certain constraints on the number of semantically inequivalent formulas. As a corollary, there is no compositional semantics for the ‘independence-friendly’ logic of Hintikka and Sandu (henceforth IF) in which the interpretation in a structure A of each 1 -ary formula is a subset of the domain of A (Corollary 6.2 below proves this and more). After a fashion, this rescues a claim of Hintikka and provides the proof which he lacked:… there is no realistic hope of formulating compositional truth-conditions for [sentences of IF], even though I have not given a strict impossibility proof to that effect.(Hintikka [6] page 110ff.) One curious spinoff is that there is a structure of cardinality 6 on which the logic of Hintikka and Sandu gives nearly eight million inequivalent formulas in one free variable (which is more than the population of Finland).We thank the referee for a sensible change of notation, and Joel Berman and Stan Burris for bringing us up to date with the computation of Dedekind's function (see section 4). Our own calculations, utterly trivial by comparison, were done with Maple V.The paper Hodges [9] (cf. [10]) gave a compositional semantics for a language with some devices of imperfect information. The language was complicated, because it allowed imperfect information both at quantifiers and at conjunctions and disjunctions.

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