Charles Sanders Peirce regarded mathematics as “the only one of the sciences which does not concern itself to inquire what the actual facts are, but studies hypotheses exclusively” (RLT, 114). Since, by contrast, “[w]e must begin with all the prejudices which we actually have when we enter upon the study of philosophy” (CP 5.265), the presuppositionless status of mathematics makes it more primitive than anything found in philosophy. Given that phenomenology falls under philosophy (CP 1.280), we get the result that mathematics is prior to phenomenology.

Yet, Peirce also held that “every deductive inference is performed, and can only be performed, by imagining an instance in which the premises are true and observing by contemplation of the image that the conclusion is true” (NEM III/2, 968).

We thus have two conflicting arguments:

On the one hand, one could argue that mathematics is prior to phenomenology because mathematics makes even less presuppositions than phenomenology.

On the other hand, one could argue that phenomenology is prior to mathematics because whatever happens during mathematical inquiry must perforce appear before (some)one.

Peirce's pronouncements notwithstanding, it is not obvious to me why the first argument should trump the second. In fact, I find considerations about the inevitability of appearing in mathematics to be decisive.

What do you think?

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