[FOM] FOM Condition beta of Tarski's Convention T.

John Corcoran corcoran at buffalo.edu
Wed Jun 20 11:43:30 EDT 2012

I am looking for published and unpublished discussions of condition beta of
Tarski's Convention T. 
  Tarski's Convention T-which defines "adequate definition of
truth"-contains two conditions, alpha and beta, that are separately
necessary and jointly sufficient, LOGIC, SEMANTICS, METAMATHEMATICS [=LSM],
pp. 187-8. Alpha requires that all instances of the T Schema be provable-a
condition elsewhere called "material adequacy", LSM, p. 404.  Beta requires
in effect the provability of 'every truth is a sentence'. Beta is one way of
recognizing a fact repeatedly emphasized by Tarski: sentences-as opposed to
"pre-sentences" having free occurrences of variables-exhaust the range of
applicability of true; it is part of the meaning of true that attribution of
true to a given thing presupposes the thing is a sentence, LSM, pp. 186-8,
195-7. The necessity of beta is highlighted by the fact that alpha is
satisfied by the recursively definable concept of being satisfied by every
sequence, which Tarski rejects as inadequate, LSM, p.189 and which he
supplements with the condition of being a sentence in the famous
truth-definition, LSM, p.195.

John Corcoran
University of Buffalo
Buffalo NY 14260-4150

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