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알프레트 타르스키

VIS VITALIS 2017. 1. 10. 14:01

알프레트 타르스키

알프레트 타르스키(폴란드어: Alfred Tarski, 1901년 1월 14일 ~ 1983년 10월 26일)는 폴란드의 논리학자·수학자·철학자이다. 논리학과 수학기초론에 큰 영향을 끼쳤고, 20세기 논리학에서 쿠르트 괴델과 함께 쌍대를 이루는 학자였다.

생애[편집]

바르샤바에서 유대인 가정에서 태어났다. 본명은 알프레트 타이텔바움(폴란드어: Alfred Tajtelbaum)이었다. 1918년 바르샤바 대학교에 입학하여, 생물학을 공부하였다. 그러나 바르샤바 대학교 수학 교수 스타니스와프 레시니에프스키(폴란드어: Stanisław Leśniewski)는 타르스키의 재능을 알아보고, 타르스키를 수학과로 유치하려 노력하였다. 결국 타르스키는 생물학을 접고 수학을 공부하였다. 이후 타르스키는 레시니에프스키의 유일한 박사 지도 학생이 되었고, 바르샤바 대학교에서 최연소 졸업 박사가 되었다.

1923년에 타르스키는 성을 유대인식 이름 "타이텔바움"에서 "타르스키"로 개명하였고, 로마 가톨릭교회로 개종하였다. (개인적으로 타르스키는 무신론자였다고 한다.)

이후 타르스키는 바르샤바의 한 고등학교에서 수학을 가르쳤고, 1929년에 동료 교사 마리아 비트코프스카(폴란드어: Maria Witkowska)와 결혼하였다. 리비우 대학교와 포즈난 대학교 교수직에 지원하였으나 탈락하였다. 1939년 8월에 미국에 강연하러 배를 탔는데, 타르스키가 떠난 직후 나치 독일과 소련은 폴란드를 침공하였고, 타르스키는 가족을 남겨둔 채 미국에 머물러야만 했다. 제2차 세계 대전 동안 타르스키의 친척들은 나치 독일에 의해 죄다 학살당했지만, 유대인이 아니었던 아내 마리아는 살아남았다.

미국에서 타르스키는 하버드 대학교 (1939), 뉴욕 시립 대학 (1940), 프린스턴 고등연구소 (1942) 등에 머물렀고, 1942년에 캘리포니아 대학교 버클리의 수학 교수가 되었다. 1945년 미국 시민권을 획득하였다. 타르스키는 버클리에서 매우 뛰어나지만 매우 까다로운 교수로 유명하였다. 타르스키의 뉴욕 타임스 사망 기사에는 다음과 같은 묘사가 실려 있다.

“	버클리에서 그의 세미나는 빠르게 수리논리학계에서 유명해졌다. 타르스키의 학생들에 따르면, 타르스키는 오직 최고의 선명도와 정밀도의 학업만을 요구하고, 이를 위해 학생들을 항상 엄청난 에너지로 재촉하고 구슬렸다고 한다. (타르스키의 학생들 가운데 상당수는 이후 유명한 수학자가 되었다.) His seminars at Berkeley quickly became famous in the world of mathematical logic. His students, many of whom became distinguished mathematicians, noted the awesome energy with which he would coax and cajole their best work out of them, always demanding the highest standards of clarity and precision.	”
	— ^[1]

타르스키는 1968년 은퇴하였지만 1973년까지 강의를 계속하였고, 사망 직전까지 계속 박사 과정 학생들을 지도하였다. 타르스키 아래 총 24명의 학생들이 박사 학위를 취득하였고, 특히 그 가운데 5명은 여성이었다. 이는 당시 수학계에 여성들이 희귀했다는 점을 볼 때 놀라운 점이다.

1983년 버클리에서 사망하였다.

참고 문헌[편집]

이동↑ Obituary in Times, reproduced here

Feferman, Anita Burdman; Feferman, Solomon (2004). 《Alfred Tarski: Life and Logic》. Cambridge University Press. ISBN 978-0-521-80240-6. OCLC 54691904.
Givant, Steven, 1991. "A portrait of Alfred Tarski", Mathematical Intelligencer 13: 16-32.
Patterson, Douglas. Alfred Tarski: Philosophy of Language and Logic (Palgrave Macmillan; 2012) 262 pages; biography focused on his work from the late-1920s to the mid-1930s, with particular attention to influences from his teachers Stanislaw Lesniewski and Tadeusz Kotarbinski.

Alfred Tarski

Born	Alfred Teitelbaum January 14, 1901 Warsaw, Congress Poland
Died	October 26, 1983 (aged 82) Berkeley, California, United States
Citizenship	Polish American
Nationality	Polish
Fields	Mathematics, logic, philosophy of language
Institutions	University of Warsaw (1925-1939) University of California, Berkeley (1942-1983)
Alma mater	University of Warsaw
Doctoral advisor	Stanisław Leśniewski
Doctoral students	Solomon Feferman Haim Gaifman Bjarni Jónsson Howard Jerome Keisler Roger Maddux Richard Montague Andrzej Mostowski Julia Robinson Wanda Szmielew Robert Vaught
Known for	Work on the foundations of modern logic Formal notion of truth Development of model theory logic of relations Banach–Tarski paradox
Influences	Charles Sanders Peirce
Influenced	Kenneth Arrow Rudolf Carnap John Corcoran Donald Davidson Erich Leo Lehmann Karl Popper Willard Van Orman Quine Patrick Suppes

Alfred Tarski (/ˈtɑːrski/; January 14, 1901 – October 26, 1983) was a Polish logician, mathematician and philosopher. Educated at the University of Warsaw and a member of the Lwów–Warsaw school of logic and the Warsaw school of mathematics and philosophy, he immigrated to the USA in 1939 where he became a naturalized citizen in 1945, and taught and carried out research in mathematics at the University of California, Berkeley from 1942 until his death.^[1]

A prolific author best known for his work on model theory, metamathematics, and algebraic logic, he also contributed to abstract algebra, topology, geometry, measure theory, mathematical logic, set theory, and analytic philosophy.

His biographers Anita and Solomon Feferman state that, "Along with his contemporary, Kurt Gödel, he changed the face of logic in the twentieth century, especially through his work on the concept of truth and the theory of models."^[2]

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Semantic theory of truth

A semantic theory of truth is a theory of truth in the philosophy of language which holds that truth is a property of sentences.^[1]

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Origin[edit]

The semantic conception of truth, which is related in different ways to both the correspondence and deflationary conceptions, is due to work published by Polish logician Alfred Tarski in the 1930s. Tarski, in on the Concept of Truth in Formal Languages", attempted to formulate a new theory of truth in order to resolve the liar paradox. In the course of this he made several metamathematical discoveries, most notably Tarski's undefinability theorem using the same formal technique as Kurt Gödel used in his incompleteness theorems. Roughly, this states that a truth-predicate satisfying convention-T for the sentences of a given language cannot be defined within that language.

Tarski's theory[edit]

To formulate linguistic theories^[2] without semantic paradoxes like the liar paradox, it is generally necessary to distinguish the language that one is talking about (the object language) from the language that one is using to do the talking (the metalanguage). In the following, quoted text is use of the object language, while unquoted text is use of the metalanguage; a quoted sentence (such as "P") is always the metalanguage's name for a sentence, such that this name is simply the sentence P rendered in the object language. In this way, the metalanguage can be used to talk about the object language; Tarski demanded that the object language be contained in the metalanguage.

Tarski's material adequacy condition, also known as Convention T, holds that any viable theory of truth must entail, for every sentence "P", a sentence of the following form (known as "form (T)"):

(1) "P" is true if, and only if, P.

For example,

(2) 'snow is white' is true if and only if snow is white.

These sentences (1 and 2, etc.) have come to be called the "T-sentences". The reason they look trivial is that the object language and the metalanguage are both English; here is an example where the object language is German and the metalanguage is English:

(3) 'Schnee ist weiß' is true if and only if snow is white.

It is important to note that as Tarski originally formulated it, this theory applies only to formal languages. He gave a number of reasons for not extending his theory to natural languages, including the problem that there is no systematic way of deciding whether a given sentence of a natural language is well-formed, and that a natural language is closed (that is, it can describe the semantic characteristics of its own elements). But Tarski's approach was extended by Davidson into an approach to theories of meaning for natural languages, which involves treating "truth" as a primitive, rather than a defined concept. (See truth-conditional semantics.)

Tarski developed the theory to give an inductive definition of truth as follows.

For a language L containing ¬ ("not"), ∧ ("and"), ∨ ("or"), ∀ ("for all"), and ∃ ("there exists"), Tarski's inductive definition of truth looks like this:

(1) "A" is true if, and only if, A.
(2) "¬A" is true if, and only if, "A" is not true.
(3) "A∧B" is true if, and only if, A and B.
(4) "A∨B" is true if, and only if, A or B or (A and B).
(5) "∀x(Fx)" is true if, and only if, every object x satisfies the sentential function F.
(6) "∃x(Fx)" is true if, and only if, there is an object x which satisfies the sentential function F.

These explain how the truth conditions of complex sentences (built up from connectives and quantifiers) can be reduced to the truth conditions of their constituents. The simplest constituents are atomic sentences. A contemporary semantic definition of truth would define truth for the atomic sentences as follows:

An atomic sentence F(x1,...,xn) is true (relative to an assignment of values to the variables x1, ..., xn)) if the corresponding values of variables bear the relation expressed by the predicate F.

Tarski himself defined truth for atomic sentences in a variant way that does not use any technical terms from semantics, such as the "expressed by" above. This is because he wanted to define these semantic terms in terms of truth, so it would be circular were he to use one of them in the definition of truth itself. Tarski's semantic conception of truth plays an important role in modern logic and also in much contemporary philosophy of language. It is a rather controversial matter whether Tarski's semantic theory should be counted either as a correspondence theory or as a deflationary theory.^{[citation needed]}

References[edit]

Jump up^ Hale, Bob; Wright, Crispin, eds. (1999). "A Companion to the Philosophy of Language". A Companion to the Philosophy of Language. pp. 309–330. doi:10.1111/b.9780631213260.1999.00015.x. ISBN 9780631213260., p. 326
Jump up^ Parts of section is adapted from Kirkham, 1992.