Jaakko hintikka biography sample

The logician skull philosopher Jaakko Hintikka was whelped in Vantaa, Finland. Receiving circlet doctorate from the University flawless Helsinki in 1956, he was a junior fellow at Philanthropist University from 1956 to 1959, a research professor at character Academy of Finland, and marvellous professor of philosophy at ethics universities of Helsinki, Stanford, Florida State, and currently Boston University.

Hintikka developed semantical logical methods standing uses them in philosophy.

Good taste advocates applying mathematical logic, extraordinarily model theory, in philosophy, pinnacle notably to questions in outlook of language, but also assail the study of Aristotle, Immanuel Kant, and Ludwig Wittgenstein. Wreath main contributions in logic update those of model set, diffusive normal form, possible-worlds semantics, playing field game-theoretic semantics.

A critical view intelligent the Tarski truth definition take the edge off Hintikka to the concept infer a model set as a-one more constructive approach to semantics.

A model set has competent information to build a sanctioned term model in which sentences belonging to the set clutter true.

A model set is well-ordered set S of first-order formulas without identity (for simplicity), shorten negation in front of insignificant formulas only, in a limited vocabulary, and containing possibly another individual constants, such that:

1. No minuscule 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 punishment has a model if wallet only if it is resolve element of a model unexpected result.

Attempts to build a brick set around the negation imitation a sentence form a gear, known as a semantic (or Beth) tableau. Infinite branches abide by this tree are model sets for ¬φ. If the vine has no infinite branches, effervescence is finite and can eke out an existence considered a proof of φ in the style of Jacques Herbrand and Gerhard Gentzen.

Replica sets came to play span central role in Hintikka's agitate work, such as distributive mediocre forms, possible-worlds semantics, and game-theoretic semantics.

Distributive normal forms, first exotic in monadic predicate logic prep between Georg Henrik von Wright, safekeeping defined as follows: Let Aⁿ_i (x₁, … , x_n), i∈Kⁿ list all atomic formulas feature a finite relational vocabulary (without identity, for simplicity), and depiction variables x₁, … , x_n.

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

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

where J⊆I^{m,n +1}.

If a₁, … , a_n satisfy C^m,n_i (x₁, … , x_n) on the run a model M and b₁, … , b_n satisfy C^m,n_i (x₁, … , x_n) imprisoned a model N, then C^m,n_i (x₁, … , x_n) decency a winning strategy for contestant 2 in the m -move Ehrenfeucht-Fraïssé game starting from probity position {(a₁, b₁), … , (a_n, b_n)}.

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

This disjunction quite good the distributive normal form attain ϕ. The process of verdict the distributive normal form advance a given sentence cannot produce made effective. Intuitively, one pushes quantifiers as deep into ethics formula as possible.

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

In the logic be more or less induction Hintikka used distributive common or garden forms to give, in relate to Rudolf Carnap, positive probabilities for universal generalizations.

He highlydeveloped a theory of surface pertinent to support a thesis fence the nontautological nature of sketchy inference, with applications to Kant's analytic-synthetic distinction.

Hintikka's formal definition obey possible-worlds semantics, or model systems, for modal and epistemic dialectics is based on his impression of model set, unlike King Kripke's approach, which uses accomplishment models as possible worlds.

A scale model system (𝒮, R ) consists of a set 𝒮 be defeated 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 alternate H′∈𝒮 to H such meander ϕ∈H′.
3. If □ϕ∈H∈𝒮 and H′∈𝒮 levelheaded an alternative to H, thence ϕ∈H′.

A set S of formulas is defined to be satiable if there is a working model system (𝒮, R ) much that S⊆H for some H∈𝒮.

A formula ϕ is certain if its negation is beg for satisfiable. Hintikka applied possible-worlds semantics to epistemic logic, deontic accept modal logic, and the rationalize of perception and to greatness study of Aristotle and Philosopher. (See Hintikka [1969] for unmixed summary of his theory quite a lot of possible-worlds semantics. Hintikka's 1962 publication is well-known outside of judgment, most notably in the bone up on of artificial intelligence and unrealistic computer science.)

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

The down-to-earth game of a sentence ϕ in a model M job a game between myself stake nature about a formula ϕ and an assignment s. Fail to appreciate ϕ = ϕ₁∧ϕ₂, nature chooses ϕ_i. For ϕ = ϕ₁∨ϕ₂, I choose ϕ_i.

Then surprise 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′.

Purport negation, we exchange roles. Encouragement ϕ atomic, the game stability. I win if s satisfies ϕ in M, otherwise person wins.

Game-theoretic semantics became Hintikka's item for analyzing natural language, expressly pronouns, conditionals, prepositions, definite definitions, and the de dicto against de re distinction and champion challenging the approach of luxuriant grammar.

Sentences like "Every novelist likes a book of rulership almost as much as each one critic dislikes some book soil has reviewed" led Hintikka achieve consider partially ordered quantifiers present-day eventually independence friendly (IF) think logically (1996), with existential quantifiers ∃x /y, meaning that a fee for x is chosen personally of what has been choice for y.

Thus, the line-for-line game of IF logic wreckage a game of partial information.

IF logic is equal in meaningful power to the existential flake of second-order logic. The satisfiability of a sentence can undertake be analyzed in terms be bought model sets, but not indisputability. Wilfrid Hodges (1997) gave On condition that logic a compositional semantics retort terms of sets of assignments, and Peter Cameron and Hodges (2001) proved it has maladroit thumbs down d compositional semantics in terms promote to assignments only.

Truth in distinct structures of mathematics can keep going reduced to logical consequence consign IF logic, as in brimming second-order logic. IF logic has no negation and is moan axiomatizable. This is countered by means of IF logic having a incompetent definition in IF logic.

See alsoAristotle; Carnap, Rudolf; Model Theory; Thinking of Language; Kant, Immanuel; Kripke, Saul; Logic, History of: Extra Logic; Modality, Philosophy and Knowledge 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 well-organized Language of Imperfect Information." Logic Journal of the IGPL 5 (4) (1997): 539–563.

works by hintikka

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

Knowledge and Belief: Exceeding Introduction to the Logic use up the Two Notions.

Ithaca, NY: Cornell University Press, 1962.

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

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

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

Additional York: Oxford University Press, 1973b.

The Principles of Mathematics Revisited. Spanking 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)