Philosophy of mathematics has little to do with intent, in the performative sense. Intent is treated instead by philosophers of logic, as a field for categorisation and analysis. But if number is core to the philosophy of mathematics, then something is amiss. Because number is intent: number is nothing more than intent.
I don’t mean (well, maybe I do mean) to be provocative. If you’ve read my train of thought before, you might imagine I’m about to justify numerology as legitimate within the hagiography of Truth’s emergence or something to that effect.
I mean something very specific about number, irrespective of its framing within whatever dialectic its anthropological historicity is thrown. Ha ha.
I want to say number is nothing more than intent.
In the Cartesian philosophy game: that’s the scope of my statement. Take the meditations. Number, and its algebra, emerges post cogito as a priori indisputable reality. Intent of the subject to claim the territory the a a priori for itself.
Intent to emerge into something real, intent, desire, desire to expand, expound, prove the reality of the subject and the subject’s reality as Real. And by “prove the subject’s reality as Real”, of course we mean just speak — because, as everyone knows, metaphysics is a lie — and speech is all there is, language is all there is. “Reality” and the “Real” are, after all, just words being spoken, each with a particular intent, a weight determined by philosophy as a regulator of such signs. Their weight is nuclear: particularly when combined with the sign of the subject.
Note well: the first taste of “Reality” and the “Real” are felt in Descartes immediately after the Cogito. If I am at least certain I exist because I’m thinking, then what else follows? Number, hence mathematics. I know that there’s at least one of me. So hence “one”, an abstract, a priori, but certainly existent thing. But once I conceive of the successor to one, and the successor to the successor of one, and so on: I can’t say that these are imaginary or not Real, as they are definitely Real, by virtue of their relationship of successor to the Real one. Then functions and algebra and so on.
The argument is itself (a priori as it is), both the Cartesian Logicians own personal meditation, full of intent to be and to speak, in and of him or herself, but also the peculiar truth about the a priori space itself. There is a subject within that space. It is 0, nothing, but being. And from that 0, there is the a priori, existent concept of successorship. And from that 0 meets the Real, in s(0). But successorship is the first function and from that axioms, and mathematics and code, and language. The Cartesian meditation has both an undocumented psycho-anthropological aspect, as well as built upon a long ignored profoundly gnostic and mystical foundation, rooted in number as intent.