Brian Rotman: signifier, signified, and referent

For Rotman, the signified meaning of mathematical signifiers “exists” in the mind of the scribbling/thinking mathematician-in-action. If we adopt this position and rigorously pursue it, I think we end up in a solipsistic position much more sophisticated than, but ultimately rather similar to, the one associated with Brouwer’s intuitionism. I don’t have time to make such a pursuit at the moment, nor do I actually know how that road goes… I have yet to map it. However:
The difference is that Rotman doesn’t deny the importance of mathematical language, the sign, the inseparable signifier-signified pair. Brouwer ignores the signifier to focus exclusively on, and give a very satisfying account of, the signified meaning. Rotman, on the other hand, acknowledges that the signifier is just as crucial since, as everyday experience proves, it is the means by which mathematics is a public, intersubjective experience.

This is wonderful. Thank you Brian Rotman. For how brilliant Brouwer seems to have been, I’m shocked by the stupidity of his claim that math has nothing to do with language.

So it’s great that Rotman points out that mathematical writing, signifiers, are important. Nevertheless, his account is problematic to me. This is, in part, because it doesn’t explain the relationship of signifier and signified. Nor does it explain the stability of the signifier over time, between semiotic agents, across various significations. It assumes but says nothing about the way in which mathematical signifiers carry their signified meaning along with them. It assumes but says nothing about the way in which signifiers “create” or “give rise to” the signified meaning “in” the mind or, to remain within Rotman’s terms, “in” the imagination of the person-doing-math (the Person? the Subject? both?).

Where/what is meaning?

This is a bit surprising to me since Rotman seems to know somethings about somethings: in particular, in this case, Derrida (and what he wrote about potential and not-coming-to-pass) and theories of situated, distributed cognition. What about all the potential meanings overflowing from detached/detachable and re-attachable, iterating and iterable mathematical signifiers? What about the flimsiness, pointed out by Thompson, Varela, Hutchins, Brooks, et. al., of an account of “knowledge in the mind”?

I have to return to these questions.

The other problem I have with Rotman’s approach—and this one is less surprising—is the way he (mis)treats and (dis)regards the referent. He accepts Umberto Eco’s (deconstructive?–don’t know; haven’t read it) critique of the sense/reference distinction, claiming that there is no such thing as a prelinguistic referent (31). If every referent is socio-historically constructed and contingent, there’s not much sense in talking about anything but sense, i.e. signification, i.e. the signified.

Why throw away the referent? Of course, it would be laughable to claim it’s prelinguistic. But what about a postlinguistic referent? What about the kind of referent Shoshana Felman posits into existence through her trinity of Don Juan-Austin-Lacan?

Another thing I have to return to…

P.S. I wanted to name this post B. Rotman & L.E.J. Brouwer: initial thoughts .