I am making my way through Brian Rotman’s Mathematics as Sign, slowly, non-linearly, and on-and-off-ly. Although I haven’t read it all, something/s need to be said at the moment:
Rotman criticizes the Fregean-contemporary (is it still popular/dominant?) version of Platonist philosophy of mathematics for many reasons. Here’s one point Rotman makes: Fregean Platonism posits “thought” as something eternal and unchanging that can be “apprehended” by thinking thinkers (people, more or less) but it “is incapable of giving a coherent account of knowing” (33). Rotman quotes Frege: “‘The apprehension of a thought presupposes someone who apprehends it, who thinks it. He is the bearer of the thinking but not of the thought. Althought the thought does not belong to the thinkers consciousness yet something in his consciousness must be aimed at that thought. But this should not be conufsed with the thought itself’ (Frege 1967, 35)” (33 emphasis mine). Rotman finds this problemaic because it leaves knowing, “the means by which we manage to apprehend [thoughts] in total mystery” (33).
Rotman then attempts to salvage this conception of math by translating it into semiotic terms. Luckily, for Rotman, this attempt at reform fails and, better yet, points up a more *constructive* way to re-theorize mathematics. I hope to return to Rotman’s constructive re-construction at a later date. For now, I’d like to wonder, briefly, about another response to Frege’s frigg-up.
Can Nietzsche come to Frege’s rescue? (After all, he is Superman, right?) Maybe Frege’s mistake is not that he leaves out the process by which the thinker and his (sic) thinking gets at the thought. Maybe the problem is that, for Frege, “The apprehension… presupposes someone who apprehends it, who thinks it (emphasis mine),” that, for Frege, the thinking must be born of a (masculine) thinker.
What if we follow Nietzsche’s line (one that runs to me through Judith Butler): ~”there is no doer behind the deed; there is no thinker behind the thought”~? If we approach the thinker as only (an) after-thought, maybe we can save something else or something more from Fregean Platonism than Rotman does…?
But what? And/or why?
I want to come back to this, but for now, I will just suggest that the answer to “why” has something to do with Brouwer’s conception of the solipsistic subject, expressivist composition pedagogy, and/or the religiosity/faith that some have identified (re)surfacing in/around/through poststructuralist/postmodern theory (the body of work that Rotman calls something like contemporary Post thought).
