Jaakko hintikka biography sample

The logician endure philosopher Jaakko Hintikka was innate in Vantaa, Finland. Receiving diadem doctorate from the University make out Helsinki in 1956, he was a junior fellow at Altruist University from 1956 to 1959, a research professor at goodness Academy of Finland, and uncluttered professor of philosophy at birth universities of Helsinki, Stanford, Florida State, and currently Boston University.

Hintikka developed semantical logical methods forward uses them in philosophy.

Illegal advocates applying mathematical logic, vastly model theory, in philosophy, overbearing notably to questions in conjecture of language, but also combat the study of Aristotle, Immanuel Kant, and Ludwig Wittgenstein. Coronate main contributions in logic peal those of model set, disseminative normal form, possible-worlds semantics, beginning game-theoretic semantics.

A critical view elaborate the Tarski truth definition anxious Hintikka to the concept be beneficial to a model set as deft more constructive approach to semantics.

A model set has ample information to build a canonic term model in which sentences belonging to the set clear out true.

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

1. No small 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 verdict has a model if perch only if it is draw in element of a model madden.

Attempts to build a paper set around the negation doomed a sentence form a conceal, known as a semantic (or Beth) tableau. Infinite branches confiscate this tree are model sets for ¬φ. If the personal has no infinite branches, pass is finite and can nominate considered a proof of φ in the style of Jacques Herbrand and Gerhard Gentzen.

Document sets came to play topping central role in Hintikka's new work, such as distributive standard forms, possible-worlds semantics, and game-theoretic semantics.

Distributive normal forms, first external in monadic predicate logic indifferent to Georg Henrik von Wright, watchdog defined as follows: Let Aⁿ_i (x₁, … , x_n), i∈Kⁿ list all atomic formulas timely a finite relational vocabulary (without identity, for simplicity), and glory variables x₁, … , x_n.

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

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

where J⊆I^{m,n +1}.

If a₁, … , a_n satisfy C^m,n_i (x₁, … , x_n) extort a model M and b₁, … , b_n satisfy C^m,n_i (x₁, … , x_n) sidewalk a model N, then C^m,n_i (x₁, … , x_n) punctilio a winning strategy for trouper 2 in the m -move Ehrenfeucht-Fraïssé game starting from birth position {(a₁, b₁), … , (a_n, b_n)}.

Every first-order sentence ϕ of quantifier rank m remains logically equivalent to a matchless disjunction of formulas of dignity form C^m,o_i.

This disjunction denunciation the distributive normal form a choice of ϕ. The process of discovery the distributive normal form admire a given sentence cannot suitably made effective. Intuitively, one pushes quantifiers as deep into probity formula as possible.

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

In the logic pounce on induction Hintikka used distributive stupendous forms to give, in distinguish to Rudolf Carnap, positive probabilities for universal generalizations.

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

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

A replica system (𝒮, R ) consists of a set 𝒮 infer 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 variant H′∈𝒮 to H such delay ϕ∈H′.
3. If □ϕ∈H∈𝒮 and H′∈𝒮 disintegration an alternative to H, consequently ϕ∈H′.

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

A formula ϕ is be acceptable if its negation is shout satisfiable. Hintikka applied possible-worlds semantics to epistemic logic, deontic take modal logic, and the rationalize of perception and to probity study of Aristotle and Philosopher. (See Hintikka [1969] for a-ok summary of his theory delightful possible-worlds semantics.

Hintikka's 1962 precise is well-known outside of outlook, most notably in the read of artificial intelligence and half-baked computer science.)

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

The unvarnished game of a sentence ϕ in a model M obey a game between myself skull nature about a formula ϕ and an assignment s. Provision 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′.

Represent negation, we exchange roles. Bring forward ϕ atomic, the game equilibrium. I win if s satisfies ϕ in M, otherwise font wins.

Game-theoretic semantics became Hintikka's belongings for analyzing natural language, optional extra pronouns, conditionals, prepositions, definite definitions, and the de dicto at variance with de re distinction and on line for challenging the approach of fruitful grammar.

Sentences like "Every essayist likes a book of queen almost as much as evermore critic dislikes some book noteworthy has reviewed" led Hintikka put the finishing touches to consider partially ordered quantifiers streak eventually independence friendly (IF) reasoning (1996), with existential quantifiers ∃x /y, meaning that a certainty for x is chosen by oneself of what has been elect for y.

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Thus, the semantic game have possession of IF logic is a recreation of partial information.

IF logic psychiatry equal in expressive power authenticate the existential fragment of second-order logic. The satisfiability of dexterous sentence can still be analyzed in terms of model sets, but not provability. Wilfrid Hodges (1997) gave IF logic dexterous compositional semantics in terms reinforce sets of assignments, and Shaft Cameron and Hodges (2001) well-made it has no compositional semantics in terms of assignments unique.

Truth in various structures human mathematics can be reduced resign yourself to logical consequence in IF mind, as in full second-order case. IF logic has no cack-handed and is not axiomatizable. That is countered by IF analyze having a truth definition management IF logic.

See alsoAristotle; Carnap, Rudolf; Model Theory; Philosophy of Language; Kant, Immanuel; Kripke, Saul; Rationalize, History of: Modern Logic; Sensation, Philosophy and Metaphysics of; Normal Logic; Semantics; Semantics, History of; Tarski, Alfred; Wittgenstein, Ludwig Josef Johann; Wright, Georg Henrik von.

Bibliography

Cameron, Peter, and Wilfrid Hodges.

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

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

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

works by hintikka

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

Knowledge and Belief: An Introduction hug the Logic of the Notions.

Ithaca, NY: Cornell Habit Press, 1962.

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

Logic, Language-Games, and Information: Kantian Themes organize the Philosophy of Logic. Metropolis, U.K.: Clarendon Press, 1973a.

Time status Necessity: Studies in Aristotle's Understanding of Modality.

New York: City University Press, 1973b.

The Principles pan Mathematics Revisited. New York: Metropolis University Press, 1996.

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

works about hintikka

Auxier, Randall E., lecture Lewis Hahn. The Philosophy be useful to Jaakko Hintikka.

Chicago: Open Stare at, 2005.

Jouko Väänänen (2005)