Alfred Tarski

“Tarski's Semantic Theory on the Internet Encyclopedia of Philosophy.”

“Tarski's Revolution: A New History, an Erc Starting Grant Project, Vrije Universiteit Amsterdam.”

“{{w|Stanford Encyclopedia of Philosophy}}:”

“Alfred Tarski, MacTutor History of Mathematics archive.”

“I think that I have learned more from you than from any other living thinker, except perhaps Alfred Tarski... but not even excepting Russell.”

“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 {{w|Epimenides paradox}}.”

“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.”

“Tarski tried to publish his theorem (the equivalence between AC and "every infinite set A has the same cardinality as A × A") in Comptes Rendus, but Fréchet and Lebesgue refused to present it. Fréchet wrote that an implication between two well known (true) propositions is not a new result, and Lebesgue wrote that an implication between two false propositions is of no interest. And Tarski said that after this misadventure he never tried to publish in the Comptes Rendus.”

“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.”

“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.”

“There can be no doubt that the knowledge of logic is of considerable practical importance for everyone who desires to think and infer correctly.”

“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.”