A trio of questions from Z:
It is not immediately clear that the rationalism you describe is conscious of its historicity, of the way particular ‘rational’ subjects and knowledge practices are historically constituted — and therefore it appears to be unconscious of its limitations. The “rhetoric of transcendence” further suggests this inattention. Again, the question here is not one of intellectual imperialism, but about how, whether, and with what limitations you can know. Is a rationality that transcends the standpoints of particular rational subjects possible? Can it be practiced by these subjects? Are the tools being relied upon, whether maths or something else, capable or sufficient of producing knowledge that transcends given subjects’ limitations?
Yes, yes and yes, otherwise we might as well pack up and go home. But the trap’s in the word “transcendence”, which implies a magic trick that one could always remain unpersuaded had actually been performed. Actually, the notion that “the standpoints of particular…subjects” constrain rationality in such a way that it must somehow escape them in order to function as the rationality it thinks it is, is fatally question-begging. Such “transcendence” is in fact an everyday occurrence, banal and unmagical: it takes place every time you or I take up an argumentative form and commit ourselves to reasoning consequentially according to its rubric.
There is no fact of the matter about my standpoint that can have any bearing whatsoever on the validity of a mathematical proof: if I am able to know that the proof has been performed successfully, it is because I am able to follow it through. If I am able to detect an error, it is because in the process of following the proof through I have stumbled upon an invalidating condition (usually a contradiction of some kind). Formalisms enable us to get to places that are not prescribed or localised by our immediate situations as users-of-form. That is, in fact, precisely what we use them for.
Most of the things we know, we don’t know in quite that kind of way of course. Much of the time, what we know or think we know is stabilised as knowledge against a backdrop of assumptions and heuristics supplied by our “standpoints”, which is one of the reasons why we misunderstand each other so often and so deeply. So I’m not suggesting that we take proof-following reasoning as a model for reasoning in general, or that knowers in general are not situated and not simultaneously enabled and constrained by situational constraints and affordances. What I do want to argue is that our image of a knower’s “situation” as wholly-localised and wholly-limiting is false: we are in fact situated within view, and within reach, of a rich variety of navigational affordances which enable us to reason from context to context. Reason is not an instantaneous ascent into the empyrean heights, from whence the whole terrain is visible at once: it involves traversals, translations, the construction of linkages from context to context, and whereabouts you start on the map is often significant. The crux I think is that it’s significant but not wholly determining: we don’t have to have perfect, godlike freedom in order to have some degrees of freedom.