Abstract

MENDEZ PINTO, Emilio. Is It Necessarily True that if a Geometric Statement Is True, It Is Necessarily True?. Diánoia [online]. 2019, vol.64, n.82, pp.61-84.  Epub May 12, 2020. ISSN 0185-2450.  https://doi.org/10.22201/iifs.18704913e.2019.82.1635.

In this essay I respond negatively to the question of the title by arguing that the statement “The sum of the internal angles of a triangle is equal to 180◦” is contingently true. For this, I try to refute Ramsey’s thesis that geometric truths are necessarily necessary truths (Ramsey 2013, p. 13), as well as Kripke’s thesis that there can be no contingently true mathematical propositions (Kripke 2005, p. 156). In addition, by appealing to the Fregean conception of the a priori and the a posteriori (Frege 1980, p. 5), I argue that there are geometric truths that can be a priori without having to be a priori.

Keywords : mathematical truth; geometric truths; contingent geometric truths; a priori contingent geometric truths; a posteriori necessary geometric truths.