Annotated Bibliography of Jaakko Hintikka
ANNOTATED BIBLIOGRAPHY OF JAAKKO HINTIKKA 1953 Books (a) Distributive Normal Forms in the Calculus of Predicates, Acta Philosophica Fennica 6, (1953), 71pp. By distributing quantifiers deeper and deeper into the formulas of a finite first-order language, with or without identity, at the same time as truth-functions are transformed into a propositional normal form, we obtain a simple normal form for such formulas. This refutes the conjecture of Hilbert and Bernays that “a simply characterizable normal form is not obtainable in this way in general.” The basic properties of these distributive normal forms are established, including a set of sufficient conditions of inconsistency. Papers (a) “A New Approach to Sentential Logic”, Societas Scientiarum Fennica, Commentationes Physico-Mathematicae 17, no. 3, (1953), 13pp. 1954 Papers (a) “An Application of Logic to Algebra”, Mathematica Scandinavia 2, (1954), 243-246. 1955 Books (a) Two Papers on Symbolic Logic, Acta Philosophica Fennica 8, (1955), 115pp. (Includes “Form and Content in Quantification Theory”, 11-55, and “Reductions in the Theory of Types”, 57-115.) First paper: For a finite first-order language, the concept of a model set (m.s.) of formulas is defined by means of certain simple closure and compatibility conditions. Intuitively, a m.s. is a partial description of a possible world. A set of formulas is accordingly consistent if it can be embedded in some m.s.. A simple proof procedure is obtained by considering rules for an attempt to embed the negation of a sentence S in a m.s.. If such an attempt fails in all directions, a proof is obtained for S.
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