Phillip Kitcher has contributed significantly to a wide range of philosophical topics. Much of his work is tied to naturalism, especially his work on mathematics. His particular brand of mathematical naturalism is sketched in clear terms: “Our present body of mathematical beliefs is justified in virtue of its relation to a prior body of beliefs; that prior body of beliefs is justified in virtue of its relation to a yet earlier corpus; and so it goes.” He continues, “Somewhere, of course, the chain must be grounded. Here, perhaps, we discover a type of mathematics about which Mill was right, a state of rudimentary mathematical knowledge in which people are justified through their perceptual experiences in situations where they manipulate their environments (for example, by shuffling small groups of objects)” (Kitcher 1988, 299). An important footnote immediately qualifies this:

[B]ecause the chain is so long it seems misleading to emphasize the empirical character of the foundation. Indeed, it seems to me to be possible that the roots of primitive mathematical knowledge may lie so deep in prehistory that our first mathematical knowledge may be coeval with our first propositional knowledge of any kind. Thus, as we envision the evolution of human thought (or hominid thought, or primate thought) from a state in which there is no propositional knowledge to a state in which some of our ancestors know some propositions, elements of mathematical knowledge may emerge with the first elements of the system of representation. Of course, this is extremely speculative. (1988, 321n10)