For possibly hubristic reasons (to do with trying to make a point about what such a forum could be like if people put their minds to it), I’ve been putting rather more effort into dissensus lately than some would say it really deserves. If nothing else, I’ve pleased myself. Here’s a recent entry of possible interest, responding to a question about the chronological priority of human existence over mathematical thought:

I love Ray Brassier’s line about how there’s no obvious way in which the theoretical conception we currently have of, say, quantum physics is an extension of our ability to use hammers. There might still be some very subtle, tortuously complex way in which the one was a development of the other, though. Perhaps not so much an extension as an extrusion, a metastasis. Historically speaking, we got here (quantum physics) from there (tool use). There is a chronology involved, for sure: mathematical concepts don’t just fall from the sky.

On the other hand, shit just happens: just because the shit that happened later happened after the shit that happened earlier, doesn’t mean that the later shit is in any sense logically or metaphysically dependent on the earlier shit, inherits its fundamental characteristics and limitations or is otherwise linked to it in any way except through belonging to the same overall history - and that history might be one of corruption and deviation rather than linear filiation, such that its later moments preserve nothing of the image or essence of the earlier ones.

I think there’s something hopelessly wrong about the notion that all of mathematics is an extension of some kind of book-keeping ability, that it all starts with counting apples or comparing dick size or whatever and works itself up from there. From really very early on in the history of mathematics, the bodily and haptic context starts falling away: problems appear (impasses of formalisation) that are not in any recognisable sense the problems of bodies.

The problem Pythagorus had with irrational numbers would be one example: you take a right-angled triangle, with two sides of unit length, and it turns out that the length of the hypotenuse is the square root of 2, a number that can’t be found amongst either the whole numbers or the “rational” fractions. Nothing in the human-animal experience of being (in) a body really correlates to a number like that: an apple, yes; half an apple, yes; three quarters of an apple, OK; a quantity of apple that can’t ever be arrived at by cutting an apple into equal-sized pieces and taking a whole number of the pieces - um…and it only gets worse from there.

Mathematics is where something like a reality principle (the symbolic real, the impasse of symbolic formalisation) shows up right in the middle of the collection of simple cognitive tricks that a bunch of monkeys have developed to facilitate the reliable sizing up of medium-sized dry goods, and systematically perverts their thinking from the inside out. Like I said, not extension so much as extrusion, metastasis, perversion or corruption. The butchering open of thought.

Mathematics is a weird ontology.