## Document Type

Book

## Publication Date

3-4-2005

## Abstract

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.

## Recommended Citation

Panza, M. (2005). Some Sober Conceptions of Mathematical Truth. In: Hoffmann, M.H., Lenhard, J., Seeger, F. (eds) Activity and Sign. Springer, Boston, MA. https://doi.org/10.1007/0-387-24270-8_29

## Copyright

Springer

#### Included in

Logic and Foundations Commons, Logic and Foundations of Mathematics Commons, Other Mathematics Commons

## Comments

This is a pre-copy-editing, author-produced PDF of a chapter accepted for publication in Michael H.G. Hoffmann, Johannes Lenhard, and Falk Seeger (Eds.),

Activity and Sign. Grounding Mathematics Education. This version may not exactly replicate the final published version.