Arithmetical Certainties: A Few Exceptions Among Countless Knowledge- Statements

Abstract

In this paper I disagree with Kusch (2016) on three issues concerning expressions of arithmetical certainties - in Wittgenstein's sense - and regular uses of arithmetical expressions. Specifically, I explain why calculations do not turn into certainties by the fact that they have been proved; I argue that proved calculations constitute knowledge-statements; and, last but not least, I conclude from this that such proved calculations are sayable, whilst arithmetical certainties are ineffable or unsayable.