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.