The modal status of mathematical statements (in Polish) (Diametros, 2011)
The paper contains an analysis of three counterexamples to the view that all mathematical statements are necessary, i.e. necessarily true or necessarily false: an argument from contingent, relational, empirical properties, an argument from properties based on conventional representations and an argument from model relativity. The first and the second argument can be rejected easily, while to answer the third argument one has to adopt a quite strong set-theoretic realism.
Keywords: mathematical statements; necessity; John Stuart Mill; continuum hypothesis; set-theoretic realism