Did Tarski commit “Tarski's fallacy”?

• Published in: The Journal of symbolic logic 1996-06, Vol.61 (2), p.653-686
• Main Author: Sher, G. Y.
• Format: Article
• Language: English
• Subjects: Denotational semantics; Language; Logical givens; Mathematical logic; Mathematical set theory; Metaphysics; Model theory; Semantics; Truth
• ISSN: 0022-4812; 1943-5886
• DOI: 10.2307/2275681

In his 1936 paper, On the Concept of Logical Consequence , Tarski introduced the celebrated definition of logical consequence : “ The sentence σ follows logically from the sentences of the class Γ if and only if every model of the class Γ is also a model of the sentence σ .” [55, p. 417] This definition, Tarski said, is based on two very basic intuitions, “essential for the proper concept of consequence” [55, p. 415] and reflecting common linguistic usage: “Consider any class Γ of sentences and a sentence which follows from the sentences of this class. From an intuitive standpoint it can never happen that both the class Γ consists only of true sentences and the sentence σ is false. Moreover, … we are concerned here with the concept of logical, i.e., formal , consequence.” [55, p. 414] Tarski believed his definition of logical consequence captured the intuitive notion: “It seems to me that everyone who understands the content of the above definition must admit that it agrees quite well with common usage. … In particular, it can be proved, on the basis of this definition, that every consequence of true sentences must be true.” [55, p. 417] The formality of Tarskian consequences can also be proven. Tarski's definition of logical consequence had a key role in the development of the model-theoretic semantics of modern logic and has stayed at its center ever since.