Naturalism, James Robert Brown explains, is a cluster concept. Its main ingredients are: knowledge is based on sensory experience, it is something we discover, it lacks a foundation, and it is acquired by a fallible process using only the methods of the natural science; what exists is what true science says exists; and norms and values must either be eliminated or reduced to factual statements (pp. 32-34). Brown pits naturalism against what he calls a Platonic alternative, which is similarly multi-dimensional: mathematical objects are real, mind-independent existents outside of space and time and thus abstract in the now-standard sense (though not in an older one); most importantly for Brown, these objects are intuitable; mathematical statements have objective truth-values independent of us; mathematical statements are necessary and knowable a priori, but not knowable...

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