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. Second paper: For a formula S in the simple theory of types, a formula r(S) is constructed such that: (i) r(S) is satisfiable if S is satisfiable; (ii)r(S) is of the form (∃X) F(X) where “X” is a second-order formula which does not contain any second-order quantifiers. 274 Annotated Bibliography of Jaakko Hintikka Papers “Notes on Quantification Theory”, Societas Scientiarum Fennicae, Commentationes Physico-Mathematicae 17, no. 12, (1955), 13pp. 1956 Papers (a) “Identity, Variables, and Impredicative Definitions”, The Journal of Symbolic Logic 21, (1956), 225-245. (b) “Loogisen kielentutkimuksen näköaloja”, Ajatus 19, (1956), 81-96. (“Perspectives on the Logical Study of Language”.) 1957 Papers (a) “Arvokäsitteistä sosiaalitieteiden metodiopissa”, Ajatus 20, (1957), 27-47. (“On Value-Concepts in the Methodology of the Social Sciences”.) (b) “Modality as Referential Multiplicity”, Ajatus 20, (1957), 49-64. Problems of intensional context can be handled by assuming that they involve a multiplicity of different situations (worlds, models) in which the references of our singular terms can be different. (Note: This paper seems to be the first philosophical statement of the basic ideas of possible-worlds semantics in the literature. The problems of cross-identification are nevertheless overlooked in it. They make their appearance in Knowledge and Belief: An Introduction to the Logic of the Two Notions, (1962(a)).) (c) “Necessity, Universality, and Time in Aristotle”, Ajatus 20, (1957), 65-90. (d) “Quantifiers in Deontic Logic”, Societas Scientaiarum Fennicae, Commentationes Humanarum Litterarum 23, no. 4, (1957), 21 pp. (e) “Vicious Circle Principle and the Paradoxes”, The Journal of Symbolic Logic 22, (1957), 245-249. 1958 Papers (a) “On Wittgenstein’s ‘Solipsism’”, Mind 67, (1958), 88-91. (b) “Remarks on a Paradox”, Archiv für Rechts- und Sozialphilosophie 44, (1958), 514-516. (c) “Towards a Theory of Definite Descriptions”, Analysis 19, (1958), 79-85. The methods used in the new theory of descriptions illustrate the virtues of our new quantification theory which dispenses with existential presuppositions. This system is superior to Russell’s. 1959 Papers (a) “Aristotle and the Ambiguity of Ambiguity”, Inquiry 2, (1959), 137-151. Annotated Bibliography of Jaakko Hintikka 275 (b) “An Aristotelian Dilemma”, Ajatus 22, (1959), 87-92. (An expanded version under the title “On Aristotle’s Modal Syllogistic” appears in Jaakko Hintikka, Time and Necessity: Studies in Aristotle’s Theory of Modality, Clarendon Press, Oxford, 1973, 135-146.) (c) “Existential Presuppositions and Existential Commitments”, The Journal of Philosophy 56, (1959), 125-137. The usual quantification theory can be modified in such a way as to allow individual constants to be empty. What is needed is a suitable change in the quantifier rules. (Note: Together with the paper by Leblanc and Hailperin in the Philosophical Review in 1959, this paper seems to have been the first explicit treatment of a logic without existence assumptions in the literature.) (d) “Filosofian ajankohtaisista ja ajattomista tehtävistä”, Suomalainen Suomi 27, (1959), 538-542. (“On the Timely and Timeless Tasks of Philosophy”.) (e) “Kantin oppi matematiikasta: tutkimuksia sen peruskäsitteistä, rakenteesta ja esikuvista”, Ajatus 22, (1959), 5-85. (“Kant’s Theory of Mathematics: Studies in its Basic Concepts, Structure, and Precedents”.) 1960 Papers (a) “Aristotle’s Different Possibilities”, Inquiry 3, (1960), 17-28. 1961 Papers (a) “Cogito, ergo sum, 1-11”, Nya Argus 54, (1961), 143-146 and 159-162. (An early Swedish version of “Cogito ergo sum: Inference or Performance?”, Philosophical Review 71, (1962), 3-32.) (b) “Filosofia ja maailmankatsomukset”, Uusi Suomi, (22 October 1961). (“Philosophy and Weltanschauungen”.) (c) “Käsitteilläkin on kohtalonsa”, Suomalainen Suomi 29, (1961), 459-464. (“Concepts Have Their Fates, Too”.) (d) “Modality and Quantification”, Theoria 27, (1961), 119-128. (An expanded version appears in Jaakko Hintikka, Models for Modalities, D. Reidel Publishing Co., Dordrecht, 1969, 57-70.) Satisfiability may be defined for sets of formulas containing modal operators and quantifiers by means of the notion of model set (in short, m.s.; for a definition see JSL XX362): λ is satisfiable if and only if there is a model system Ω and a m.s. µ∈Ω such that λ⊆µ. Model system is defined as a set Ω of m.s.’s together with a reflexive dyadic relation (called the relation of alternativeness) on Ω which satisfies the following conditions: (1) if Mf ∈υ∈Ω, then there is in Ω at least one alternative υ1 to υ such that f ∈υ1; (2) If Nf ∈υ∈Ω and if υ1∈ Ω is an alternative to υ, then f∈υ1. 276 Annotated Bibliography of Jaakko Hintikka The resulting system corresponds to von Wright’s M in that a quantifier-free f is provable in M if and only if {~f} is not satisfiable. If the relation of alternativeness is stipulated to be transitive, the resulting system will similarly correspond to Lewis’s S4; if transitive and symmetric, to S5. Most of the usual difficulties can be avoided by specifying whether and when free individual symbols (say a, b,… are transferable from a m.s. to another in a model system. If no transfer is permitted, (2) has to be replaced by a weaker condition obtained by adding: “provided that each free individual symbol a of f occurs in some of the other formulas of υ1.” (Condition (3).) However, we may (if we choose) permit transfer from a m.s. to its alternatives (in the old deductive systems the corresponding assumption is sometimes made unwittingly). Then (2) is acceptable, but one of the defining conditions of m.s.’s has to be strengthened to read: (4) If (x)f∈µ, then f(a/x)∈µ for every a occurring in any λ∈Ω to which µ bears the ancestral of the alternativeness relation. (f(a/x) results from f by replacing x by a.) However, if empty domains are disqualified (e.g. by the condition (5): if (x)f∈µ (µ being a m.s.), then f(a/x)∈µ for at least one a), then it suffices to strengthen (3) to (2). If we also want to permit the converse transfer (thus in effect permitting arbitrary transfer), it can be done by adopting an additional condition (6) obrained from (4) by reversing the roles of λ and µ. If identities are admitted to the formalism, the conditions of their transfer must likewise be carefully defined. 1962 Books (a) Knowledge and Belief: An Introduction to the Logic of the Two Notions, Cornell University Press, Ithaca, 1962, pp. x+179. An explicit logic is developed for knowledge and belief (knowing that and believing that), formulated by means of the author’s model set method. The problem of “logical omniscience” (one apparently necessarily knows all the logical consequences of what one knows) is dealt with by reinterpreting the metalogical notion of provability. An analysis is presented of knowing wh-constructions in terms of “knowing that” plus quantifiers, and the interplay of knowledge and quantifiers is studied. The approach is applied to selected conceptual problems, especially to Moore’s paradox of saying and disbelieving and to the notion of “knowing that one knows.” Papers (a) “Cogito, ergo sum: Inference or Performance?”, Philosophical Review 71, (1962), 3-32. Annotated Bibliography of Jaakko Hintikka 277 Descartes’ cogito ergo sum is not an inference from cogito to sum. Its special character is due to the self-defeating character of an attempt to think that I don’t exist, analogous to the self-defeating character of the assertion “I don’t exist.” Hence “cogito” does not express a premise, but refers to the act through which the self-defeating or self-verifying character of certain thought-acts is manifested. This throws light on several aspects of the cogito in Descartes, e.g., its curiously momentary character. (b) “Huomioita kreikkalaisten ajankäsityksestä”, Ajatus 24, (1962), 39-65. (“Observations on the Concept of Time in Ancient Greek Philosophy”.) (c) “Johdonmukaisen järkevyyden ihanteet: 90-vuotias Bertrand Russell”, Uusi Suomi, (18 May, 1962). (“The Ideals of Consistent Reasonableness: Bertrand Russell at Ninety”.) (d) “Kaksi Spengleriä?” Suomalainen Suomi 30, (1962), 86-92. (“Spengler Against Himself?”) (e) “Kepler ja Galilei”, Suomalainen Suomi 30, (1962), 278-281.