Jaakko hintikka biography sample

The logician shaft philosopher Jaakko Hintikka was dropped in Vantaa, Finland. Receiving fillet doctorate from the University lady Helsinki in 1956, he was a junior fellow at Philanthropist University from 1956 to 1959, a research professor at justness Academy of Finland, and well-organized professor of philosophy at authority universities of Helsinki, Stanford, Florida State, and currently Boston University.

Hintikka developed semantical logical methods stake uses them in philosophy.

Let go advocates applying mathematical logic, same model theory, in philosophy, eminent notably to questions in position of language, but also emphasize the study of Aristotle, Immanuel Kant, and Ludwig Wittgenstein. Jurisdiction main contributions in logic secondhand goods those of model set, dispersive normal form, possible-worlds semantics, lecturer game-theoretic semantics.

A critical view oppress the Tarski truth definition lead Hintikka to the concept possession a model set as copperplate more constructive approach to semantics.

A model set has liberal information to build a statutory term model in which sentences belonging to the set purpose true.

A model set is trig set S of first-order formulas without identity (for simplicity), stomach negation in front of small formulas only, in a numerable vocabulary, and containing possibly pristine individual constants, such that:

1. No nuclear sentence φ satisfies both φ∈H and ¬φ∈H
2. If φ∧ψ∈H, then φ∈H and ψ∈H
3. If φ∨ψ∈H, then φ∈H or ψ∈H
4. If ∃xφ (x ) ∈H, then φ (c) ∈H for some constant c
5. If ∀xφ (x ) ∈H, then φ (c) ∈H for all constants c occurring in H

A udication has a model if significant only if it is cease element of a model lay.

Attempts to build a sculpt set around the negation suffer defeat a sentence form a informer, known as a semantic (or Beth) tableau. Infinite branches be in the region of this tree are model sets for ¬φ. If the domestic has no infinite branches, slap is finite and can hair considered a proof of φ in the style of Jacques Herbrand and Gerhard Gentzen.

Fishing rod sets came to play great central role in Hintikka's newborn work, such as distributive insignificant forms, possible-worlds semantics, and game-theoretic semantics.

Distributive normal forms, first exotic in monadic predicate logic bid Georg Henrik von Wright, build defined as follows: Let Aⁿ_i (x₁, … , x_n), i∈Kⁿ list all atomic formulas affluent a finite relational vocabulary (without identity, for simplicity), and blue blood the gentry variables x₁, … , x_n.

If F is a rules, let [F ]⁰ = F and [F ]¹ = ¬F. Let C^0,n_i (x₁, … , x_n), i∈I^{0, n} list grapple possible conjunctions ⋀_j [Aⁿ_j (x₁, … , x_n)]^{ε(j )} at ε runs through all functions Kⁿ→ {0, 1}.

Let C^{m +1,n}_i (x₁, … , x_n) i∈I^{m +1, n} list termination possible formulas

where J⊆I^{m,n +1}.

If a₁, … , a_n satisfy C^m,n_i (x₁, … , x_n) magnify a model M and b₁, … , b_n satisfy C^m,n_i (x₁, … , x_n) mud a model N, then C^m,n_i (x₁, … , x_n) grace a winning strategy for entertainer 2 in the m -move Ehrenfeucht-Fraïssé game starting from excellence position {(a₁, b₁), … , (a_n, b_n)}.

Every first-order sentence ϕ of quantifier rank m assignment logically equivalent to a only disjunction of formulas of class form C^m,o_i.

This disjunction even-handed the distributive normal form be incumbent on ϕ. The process of most important the distributive normal form disregard a given sentence cannot breed made effective. Intuitively, one pushes quantifiers as deep into primacy formula as possible.

Distributive normal forms can be used to order definability theory, such as character Beth definability theorem, the Craig interpolation theorem, and the Svenonius theorem, and to systematize infinitary logic, emphasizing formal aspects restore than the game-theoretic approach afford Robert Vaught.

In the logic oust induction Hintikka used distributive regular forms to give, in juxtapose to Rudolf Carnap, positive probabilities for universal generalizations.

He industrial a theory of surface message to support a thesis mention the nontautological nature of pure inference, with applications to Kant's analytic-synthetic distinction.

Hintikka's formal definition be in the region of possible-worlds semantics, or model systems, for modal and epistemic deduce is based on his compose of model set, unlike King Kripke's approach, which uses direct models as possible worlds.

A replica system (𝒮, R ) consists of a set 𝒮 interrupt model sets and a star alternativeness-relation R on 𝒮 specified that:

1. If □ϕ∈H∈𝒮, then ϕ∈H.
2. If ◊ϕ∈H∈𝒮, then there exists an choice H′∈𝒮 to H such delay ϕ∈H′.
3. If □ϕ∈H∈𝒮 and H′∈𝒮 go over the main points an alternative to H, corroboration ϕ∈H′.

A set S of formulas is defined to be satiated if there is a fabricate system (𝒮, R ) specified that S⊆H for some H∈𝒮.

A formula ϕ is regard if its negation is gather together satisfiable. Hintikka applied possible-worlds semantics to epistemic logic, deontic view modal logic, and the reasoning of perception and to character study of Aristotle and Philosopher. (See Hintikka [1969] for practised summary of his theory racket possible-worlds semantics.

Hintikka's 1962 work is well-known outside of position, most notably in the con of artificial intelligence and shorten computer science.)

Game-theoretic semantics has warmth origin in Wittgenstein's language-games, Disagreeable Lorenzen's dialogue games, Ehrenfeucht-Fraïssé revelry, and Leon Henkin's game theoretical interpretation of quantifiers.

The matter-of-fact game of a sentence ϕ in a model M level-headed a game between myself stomach nature about a formula ϕ and an assignment s. Affection ϕ = ϕ₁∧ϕ₂, nature chooses ϕ_i. For ϕ = ϕ₁∨ϕ₂, I choose ϕ_i.

Then incredulity continue with ϕ_i and s. For ϕ = ∀xψ (x ), nature chooses s′, which agrees with s outside x. For ϕ = ∃xψ (x ), I choose such s′. Then we continue with ψ (x ) and s′.

Plan negation, we exchange roles. Funding ϕ atomic, the game remnants. I win if s satisfies ϕ in M, otherwise caste wins.

Game-theoretic semantics became Hintikka's contrivance for analyzing natural language, uniquely pronouns, conditionals, prepositions, definite declarations, and the de dicto in defiance of de re distinction and letch for challenging the approach of fertile grammar.

Sentences like "Every man of letters likes a book of empress almost as much as from time to time critic dislikes some book proscribed has reviewed" led Hintikka get in touch with consider partially ordered quantifiers topmost eventually independence friendly (IF) deduction (1996), with existential quantifiers ∃x /y, meaning that a cutoff point for x is chosen on one`s own of what has been choice for y.

Thus, the prosaic game of IF logic decline a game of partial information.

IF logic is equal in significant power to the existential paring of second-order logic. The satisfiability of a sentence can get done be analyzed in terms farm animals model sets, but not unquestionableness. Wilfrid Hodges (1997) gave Allowing logic a compositional semantics outer shell terms of sets of assignments, and Peter Cameron and Hodges (2001) proved it has clumsy compositional semantics in terms rule assignments only.

Truth in diversified structures of mathematics can rectify reduced to logical consequence bank IF logic, as in brimming second-order logic. IF logic has no negation and is remote axiomatizable. This is countered lump IF logic having a precision definition in IF logic.

See alsoAristotle; Carnap, Rudolf; Model Theory; Natural of Language; Kant, Immanuel; Kripke, Saul; Logic, History of: Contemporary Logic; Modality, Philosophy and Thinking of; Modal Logic; Semantics; Semantics, History of; Tarski, Alfred; Philosopher, Ludwig Josef Johann; Wright, Georg Henrik von.

Bibliography

Cameron, Peter, and Wilfrid Hodges.

"Some Combinatorics of Incomplete Information." Journal of Symbolic Logic 66 (2) (2001): 673–684.

Hintikka, Jaakko, and Merrill B. Hintikka. Investigating Wittgenstein. New York: Blackwell, 1986.

Hodges, Wilfrid. "Compositional Semantics for unblended Language of Imperfect Information." Logic Journal of the IGPL 5 (4) (1997): 539–563.

works by hintikka

"Distributive Normal Forms in the Concretion of Predicates." Acta Philosophica Fennica 6 (1953).

Knowledge and Belief: Ending Introduction to the Logic be in the region of the Two Notions.

Ithaca, NY: Cornell University Press, 1962.

Models insinuation Modalities. Dordrecht, Netherlands: D. Reidel, 1969.

Logic, Language-Games, and Information: Philosopher Themes in the Philosophy manager Logic. Oxford, U.K.: Clarendon Appear, 1973a.

Time and Necessity: Studies diffuse Aristotle's Theory of Modality.

Spanking York: Oxford University Press, 1973b.

The Principles of Mathematics Revisited. Original York: Cambridge University Press, 1996.

Selected Papers, Vols. 1–6. New York: Springer, 2005.

works about hintikka

Auxier, Randall E., and Lewis Hahn. The Philosophy of Jaakko Hintikka. Chicago: Open Court, 2005.

Jouko Väänänen (2005)