Ebert P (2016) A framework for implicit definitions and the a priori. In: Ebert P & Rossberg M (eds.) Abstractionism: Essays in the Philosophy of Mathematics. Oxford: Oxford University Press, pp. 133-160. https://global.oup.com/academic/product/abstractionism-9780199645268?q=abstractionism〈=en&cc=gb
The so called traditional connection – a position defended by Bob Hale and Crispin Wright – aims to account for our knowledge of arithmetic by appeal to the idea of implicit definitions and stipulations. The resulting picture is one that does not draw on epistemic support from empirical evidence or from pragmatic considerations and regards our arithmetical knowledge as genuinely a priori. In this paper, I will offer a general framework for a theory of implicit definitions and locate the main tenets of the traditional connection while also highlighting the main challenges this approach faces.
a priori knowledge; implicit definitions; Neo-Fregeanism; Abstractionism; traditional-connection