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(2005) Activity and sign, Dordrecht, Springer.
It is not sufficient to supply an instance of Tarski's schema, ⌈"p" is true if and only if p⌉ for a certain statement in order to get a definition of truth for this statement and thus fix a truth-condition for it. A definition of the truth of a statement x of a language L is a bi-conditional whose two members are two statements of a meta-language L". Tarski's schema simply suggests that a definition of truth for a certain segment x of a language L consists in a statement of the form: ⌈v(x) is true if and only if τ(x)⌉, where ⌈v(x)⌉ is the name of x in L" and τ(x) is a function τ: S → S" (S and S" being the sets of the statements respectively of L end L") which associates to x the statement of L" expressed by the same sentence as that which expresses x in L. In order to get a definition of truth for x and thus fix a truth-condition for it, one has thus to specify the function τ. A conception of truth for a certain class X of mathematical statements is a general condition imposed on the truth-conditions for the statements of this class. It is advanced when the nature of the function τ is specified for the statements belonging to X. It is sober when there is no need to appeal to a controversial ontology in order to describe the conditions under which the statement τ(x) is assertible. Four sober conceptions of truth are presented and discussed.
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Full citation:
Panza, M. (2005)., Some sober conceptions of mathematical truth, in M. H. G. . Hoffmann, J. Lenhard & F. Seeger (eds.), Activity and sign, Dordrecht, Springer, pp. 335-347.
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