Yet I felt slightly guilty every time I tried to explain to a person that studying maths meant that I would not become an accountant because mathematics is not really about calculations with numbers at all, but concepts. Mathematics is a glorious ensemble of concepts with which the mathematician plays. Oh, it's work alright, but it's beautiful, much like composing music. What made me feel slightly guilty was the lingering idea that it's all made up (although this doesn't bother students of music too much, somehow it plagues a mathematician a little more, because one is supposed to be, after all, in the science 'half' of the university). Is maths true, in the real world? Or is it merely internally consistent? The mathematical existence of both Euclidean and non-Euclidean geometry really didn't help (it makes maths somewhat relativistic as regards corresponding to the world).
Well, passing from my favourite analogy of music, I propose that maths is like a literary genre. It makes reference to the world, but not necessarily in a one-to-one correspondance. Literature cannot be reduced to propositional facts - that is if one does so, it ceases to be literature and loses much of its value. Each literary genre constrains the presentation of the truth and furthers it - "...every genre works out its own ad hoc arrangement with regard to the word-world relation... Some genres (e.g., history, reporting) add to our stock of propositional knowledge [savoir]; other genres (e.e., poetry, novel) increase our knowledge by deepening or intensifying our awareness of what we already know. [connaître] ... Neither genre is "truer" than the other, each aims for its own kind of engagement with reality and its own kind of precision." (Vanhoozer).
I submit that in this way, the various disciplines are like literary genres. Each genre offers its own language, its own culture, and both author and reader recogise and agree to this. Literature is no less true than mathematics, nor the abstractions of mathematics more or less true than their applications in engineering or chemistry. So what Vanhoozer at one point concludes about literary genre, I propose we may conclude about the various disciplines themselves, insofar as the various academic disciplines act as descriptive frameworks:
In conclusion, genres engage the reader and render reality in different ways. The presence of rules and conventions does not preclude real reference, though the way in which a text 'maps' the world varies from genre to genre. Texts have many kinds of objects and can render them in many different ways. The diversity of genres is yet another confirmation of critical realism. No one form of discourse, no one descriptive framework, exhausts all that can be said about the world, humanity, or God. ...
(See also the post God loves maths. And arts. And science.)
[Quotations of Vanhoozer are from Is there meaning in this text?, IVP 1998]