Logical Truth and Tarskian Logical Truth

This paper examines the question of the extensional correctness of Tarskian definitions of logical truth and logical consequence. I identify a few different informal properties which are necessary for a sentence to be an informal logical truth and look at whether they are necessary properties of Tarskian logical truths. I examine arguments by John Etchemendy and Vann McGee to the effect that some of those properties are not necessary properties of some Tarskian logical truths, and find them unconvincing. I stress the point that since the hypothesis that Tarski's definitions are extensionally correct is deeply entrenched, the burden of proof is still on the shoulders of Tarski's critics, who have not lifted the burden.

[1]  Manuel García-Carpintero Sánchez-Miguel.  The Grounds for the Model-theoretic Account of the Logical Properties , 1992, Notre Dame J. Formal Log..

[2]  Mario Gómez-Torrente,et al.  Tarski on Logical Consequence , 1996, Notre Dame J. Formal Log..

[3]  Charles Parsons.  Sets and Classes , 1974 .

[4]  Greg Ray,et al.  Logical consequence: A defense of Tarski , 1996, J. Philos. Log..

[5]  Willard Van Orman Quine,et al.  Philosophy of Logic. , 1988 .

[6]  Klaus Gloede,et al.  Reflection Principles and Indescrib Ability , 1976 .

[7]  G. Boolos.  On second-order logic , 1975 .

[8]  Gila Sher,et al.  Did Tarski commit “Tarski's fallacy”? , 1996, Journal of Symbolic Logic.

[9]  A. R. Turquette,et al.  Logic, Semantics, Metamathematics , 1957 .

[10]  G. Kreisel,et al.  Elements of Mathematical Logic: Model Theory , 1971 .

[11]  Hao Wang,et al.  Philosophy of mathematics: The concept of set , 1984 .

[12]  Paul Bernays,et al.  On the Problem of Schemata of Infinity in Axiomatic Set Theory , 1976 .

[13]  Vann McGee,et al.  XIII—Two Problems with Tarski's Theory of Consequence , 1992 .

[14]  Vann McGee.  Review: John Etchemendy, The Concept of Logical Consequence , 1992 .

[15]  Joseph R. Shoenfield,et al.  Mathematical logic , 1967 .

[16]  E. Zermelo.  Über Grenzzahlen und Mengenbereiche , 1930 .

[17]  John L. Bell,et al.  A course in mathematical logic , 1977 .

[18]  Penelope Maddy,et al.  Believing the axioms. I , 1988, Journal of Symbolic Logic.

[19]  J. Benthem,et al.  Higher-Order Logic , 2001 .

[20]  G. Kreisel.  Informal Rigour and Completeness Proofs , 1967 .

[21]  Olgierd Wojtasiewicz,et al.  Elements of mathematical logic , 1964 .

[22]  John L. Bell,et al.  Models and Ultraproducts: An Introduction. , 1969 .

[23]  Stewart Shapiro,et al.  Principles of reflection and second-order logic , 1987, J. Philos. Log..

[24]  William Kneale,et al.  The development of logic , 1963 .

[25]  George Boolos,et al.  To Be Is to Be a Value of a Variable (or to Be Some Values of Some Variables) , 1984 .

[26]  S. Shapiro.  Foundations without Foundationalism: A Case for Second-Order Logic , 1994 .

[27]  Mario Gómez-Torrente.  On a fallacy attributed to tarski , 1998 .

[28]  J. Etchemendy.  The Concept of Logical Consequence , 1991 .