# Alfred Tarski

Alfred Tarski (Jan. 14, 1901 – Oct. 26, 1983) was a Polish logician, mathematician and philosopher. He served as Professor at the University of California, Berkeley. He is known for his work on model theory, metamathematics, and algebraic logic. He also made significant contributions to abstract algebra, topology, geometry, measure theory, mathematical logic, set theory, and analytic philosophy.

## Quotes

* The present article is almost wholly devoted to a single problem—the definition of truth. Its task is to construct—with reference to a given language—a materially adequate and formally correct definition of the term 'true sentence'. This problem, which belongs to the classical problems of philosophy, raises considerable difficulties. For although the meaning of the term 'true sentence' in colloquial language seems to be quite clear and intelligible, all attempts to define this meaning more precisely have hitherto been fruitless, and many investigations in which this term has been used and which started with apparently evident premisses have often led to paradoxes and antinomies (for which, however, a more or less satisfactory solution has been found). The concept of truth shares in this respect the fate of other analogous concepts in the domain of the semantics of language.
** "The Concept of Truth in Formalized Languages" (1931) in Logic, Semantics, Metamathematics: Papers from 1923 to 1938 (1956) Tr. J. H. Woodger.
* Logic is justly considered the basis of all other sciences, even if only for the reason that in every argument we employ concepts taken from the field of logic, and that ever correct inference proceeds in accordance with its laws.
** Introduction to Logic: and to the Methodology of Deductive Sciences. (1941/2013) Tr. Olaf Helmer, pp. 108-110.
* There can be no doubt that the knowledge of logic is of considerable practical importance for everyone who desires to think and infer correctly.
** Introduction to Logic: and to the Methodology of Deductive Sciences. (1941/2013) Tr. Olaf Helmer, p. 109.

### The Semantic Conception of Truth (1952)

    reprinted in L. Linsky (ed.), Semantics and the Philosophy of Language, Urbana 1952, unless otherwise noted.
* It is perhaps worth while saying that semantics as conceived in this paper (and in former papers of the author) is a sober and modest discipline which has no pretensions to being a universal patent-medicine for all the ills and diseases of mankind, whether imaginary or real. You will not find in semantics any remedy for decayed teeth or illusions of grandeur or class conflicts. Nor is semantics a device for establishing that everyone except the speaker and his friends is speaking nonsense.
** p. 17; as cited in: Adam Schaff (1962). Introduction to semantics, p. 90.
* If a mathematician wishes to disparage the work of one of his colleagues, say, A, the most effective method he finds for doing this is to ask where the results can be applied. The hard pressed man, with his back against the wall, finally unearths the researches of another mathematician B as the locus of the application of his own results. If next B is plagued with a similar question, he will refer to another mathematician C. After a few steps of this kind we find ourselves referred back to the researches of A, and in this way the chain closes.
** p. 41.
* For reasons mentioned at the beginning of this section, we cannot offer here a precise structural definition of semantical category and will content ourselves with the following approximate formulation: two expressions belong to the same semantical category if (I) there is a sentential function which contains one of these expressions, and if (2) no sentential function which contains one of these expressions ceases to be a sentential function if this expression is replaced in it by the other. It follows from this that the relation of belonging to the same category is reflective, symmetrical and transitive. By applying the principle of abstraction, all the expressions of the language which are parts of sentential functions can be divided into mutually exclusive classes, for two expressions are put into one and the same class if and only if they belong to the same semantical category, and each of these classes is called a semantical category. Among the simplest examples of semantical categories it suffices to mention the category of the sentential functions, together with the categories which include respectively the names of individuals, of classes of individuals, of two-termed relations between individuals, and so on. Variables (or expressions with variables) which represent names of the given categories likewise belong to the same category.
** p. 45; as cited in: Schaff (1962) pp. 36-37.

## Quotes about Alfred Tarski

* It's interesting... Tarski, although his English was weak, had a very good sense of language and he kept on asking me "Is that really good English?" Not in the sense of being grammatically correct, but, well for example, Helmer was very fond of using the word "tantamount" and Tarski got the feeling that somehow it's not a word used very often. Actually his instincts for language were extremely good. I suppose that was connected with his general work on formalizations and metalanguages. Anyway, I was just a proofreader.
** Kenneth Arrow, in interview with J. S. Kelly, "An Interview with Kenneth J. Arrow", Social Choice and Welfare (1987)
* In 1931, Tarski proved quite simply that... there is no complete language of science. ...Tarski's proof... essentially consists in showing that, as soon as you not only exhibit the statements but add to them the statement, "is true," you are in trouble because you are bound to be landed in contradictions like the one which arises in the Epimenides paradox.
** Jacob Bronowski, The Origins of Knowledge and Imagination (1978) Ref: Tarski, "The Concept of Truth in Formalized Languages" (1931) Tr. J. H. Woodger in Tarski, Logic, Semantics, Metamathematics (1956)
* I think that I have learned more from you than from any other living thinker, except perhaps Alfred Tarski... but not even excepting Russell.
** Karl Popper, in a letter to Friedrich Hayek (1944); cited in: A. Ebenstein (2016). Hayek's Journey: The Mind of Friedrich Hayek. p. 182

## External links

* Alfred Tarski, MacTutor History of Mathematics archive.
* Stanford Encyclopedia of Philosophy:
** Tarski's Truth Definitions by Wilfred Hodges.
** Alfred Tarski by Mario Gómez-Torrente.
** Propositional Consequence Relations and Algebraic Logic by Ramon Jansana. Includes a fairly detailed discussion of Tarski's work on these topics.
* Tarski's Revolution: A New History, an Erc Starting Grant Project, Vrije Universiteit Amsterdam.
* Tarski's Semantic Theory on the Internet Encyclopedia of Philosophy.
Mathematics :
| Mathematicians (by country) | Abel • Anaxagoras • Archimedes • Aristarchus of Samos • Averroes • Arnold • Banach • Cantor • Cartan • Chern • Cohen • Descartes • Diophantus • Erdős • Euclid • Euler • Fourier • Gauss • Gödel • Grassmann • Grothendieck • Hamilton • Hilbert • Hypatia • Lagrange • Laplace • Leibniz • Milnor • Newton • von Neumann • Noether • Penrose • Perelman • Poincaré • Pólya • Pythagoras • Riemann • Russell • Schwartz • Serre • Tao • Tarski • Thales • Turing • Weil • Weyl • Wiles • Witten |
| Numbers | 1 • 23 • 360 • e • π • Fibonacci numbers • Irrational number • Negative number • Number • Prime number • Quaternion • Octonion |
| Concepts | Abstraction • Algorithms • Axiomatic system • Completeness • Deductive reasoning • Differential equation • Dimension • Ellipse • Elliptic curve • Exponential growth • Infinity • Integration • Geodesic • Induction • Proof • Partial differential equation • Principle of least action • Prisoner's dilemma • Probability • Randomness • Theorem • Topological space • Wave equation |
| Results | Euler's identity • Fermat's Last Theorem |
| Pure math | Abstract algebra • Algebra • Analysis • Algebraic geometry (Sheaf theory) • Algebraic topology • Arithmetic • Calculus • Category theory • Combinatorics • Commutative algebra • Complex analysis • Differential calculus • Differential geometry • Differential topology • Ergodic theory • Foundations of mathematics • Functional analysis • Game theory • Geometry • Global analysis • Graph theory • Group theory • Harmonic analysis • Homological algebra • Invariant theory • Logic • Non-Euclidean geometry • Nonstandard analysis • Number theory • Numerical analysis • Operations research • Representation theory • Ring theory • Set theory • Sheaf theory • Statistics • Symplectic geometry • Topology |
| Applied math | Computational fluid dynamics • Econometrics • Fluid mechanics • Mathematical physics • Science |
| History of math | Ancient Greek mathematics • Euclid's Elements • History of algebra • History of calculus • History of logarithms • Indian mathematics • Principia Mathematica |
| Other | Mathematics and mysticism • Mathematics education • Mathematics, from the points of view of the Mathematician and of the Physicist • Philosophy of mathematics • Unification in science and mathematics |