Animal Test

In this discussion note, I aim to reconstruct and assess Korsgaard's recent attempt to extend her regress argument. I begin, in section 1, with a brief recapitulation of the regress argument. Then, in section 2, I turn to the extension. I argue that the extension does not work because Korsgaard cannot rule out the possibility--a possibility for which there is both empirical evidence and argumentative pressure coming directly from the original regress--that we value animality in ourselves qua animality of rational (...) beings. (shrink)

What can we infer from numerical cognition about mathematical realism? In this paper, I will consider one aspect of numerical cognition that has received little attention in the literature: the remarkable similarities of numerical cognitive capacities across many animal species. This Invariantism in Numerical Cognition (INC) indicates that mathematics and morality are disanalogous in an important respect: proto-moral beliefs differ substantially between animal species, whereas proto-mathematical beliefs (at least in the animals studied) seem to show more similarities. This makes moral (...) beliefs more susceptible to a contingency challenge from evolution compared to mathematical beliefs, and indicates that mathematical beliefs might be less vulnerable to evolutionary debunking arguments. I will then examine to what extent INC can be used to flesh out a positive case for mathematical realism. Finally, I will review two forms of mathematical realism that are promising in the light of the evolutionary evidence about numerical cognition, ante rem structuralism and Millean empiricism. (shrink)