## Kripkenstein from the mathematical point of view: a preliminary survey

##### Abstract

This paper deals with the problem of the impact of Kripke’s skeptical
paradox on the philosophy of mathematics. By perceiving mathematics as
a huge rule-following discipline, one could argue that the Kripkean nonfactualist
thesis should be adopted within the philosophy of mathematics
en bloc to imply a refutation of objectivity and an enforcement of a
particular view on the nature of mathematics. In this paper I will discuss
this claim. According to Kripke’s skeptical solution we should reject the
notion of fact and adopt the use theory of meaning that could be stated as
follows: ’One understands the concepts embodied in a language to the
extent that one knows how to use the language correctly.’ [Shapiro
1991, 211] [Kripke 1982]. Focusing on mathematical discourse, we
should ask: what are the implications of the use theory of meaning for
the philosophy of mathematics? Furthermore, is the answer to the
skeptical paradox consistent with selected views in philosophy of
mathematics? The supposed answer to the first question is that it
demands the view that mathematics should be perceived as a strictly
pragmatic discipline and the rules of mathematical discourse are mere
conventions. But this is too simplistic a view and the matter at hand is far
more complicated.

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