Is mathematics invented or discovered?

[anon50609448]

@LemoUtan

But the concept of addition/augmentation itself doesn’t seem to have to bother itself with confinement or boundaries and thus need not concern itself with a ‘noticing mind’.

I think addition necessarily has something to do with noticing. The universe having any properties beyond merely being there (where “being there” isn’t something we can rightly comprehend) seems to have something to do with noticing. According to some physics experiment I’m familiar with, even things simply existing appears to have something to do with noticing.

@dug

The operating principles of the universe might not be “mathematics” but their tractability to mathematical modelling surely points to something like it.

If you think about the chaos of base reality, as best we understand it, with fundamental particles existing in probability clouds exerting a handful of forces on one another, and consider that somehow out of that which 10²⁷ or 10²⁸ of those particles are working together to detect other things made of similar numbers of particles to ingest them and somehow continue the functioning of the collective, and that happened by pure chance, the fact that mathematics could have likewise evolved to be good as describing things we observe doesn’t actually seem very impressive, as least it doesn’t to me.

@GulliverFoyle

It could well be that the very axioms of mathematics which we’ve happened as a species to analyze the universe with are in no way special to the universe, and that there are other axiomatic systems which yield equally valid descriptions.

The question I would then have is whether there is a more fundamental logic that can show different mathematical systems to be logically related. If not, we’d have to face the possibility that different axiomatic mathematical systems describing what we think of as the same natural universe might be fundamentally incompatible, which then casts doubt on our concept of a unified reality.

I think mathematics as we use it is a fundamental logic that allows comparison between different sets of axioms. And it’s easy enough to prove that the set of axioms that that would result in systems isomorphic to any mathematical system is infinite, and that at the same time, from a perspective of attempting to model something that really is - that has properties whether we successfully model them or not - these systems are all deficient in different ways.

In mathematics we only care about what can be proven, and one of the things we can prove is that we can’t prove everything. If there is something that is, no model will ever be the whole thing. And with the universe there is also a physical constraint - the model would have the be larger than the universe.

You were talking about considering whether to consider things the same because they are in the same category in a computer simulation. But for everyone but platonists, the 3 I just typed is different from the 3 I just typed. We consider them the same because it’s hard for us to imagine why one three is different from another, but is cosmic radiation corrupts the physical memory device that they are stored on on some server hosting the BB forums, then could matter that one was in one place and the other in another.

We pretend away real differences in the underlying substance of the universe when we try to make mathematics the universe, but the fact that each bit of matter is different from each other bit of matter is why we are alive or dead. Fundamental particles being agitated by energy emissions can give us cancer, it’s not a quibble that can be overlooked. When I wrote down proofs on my exams in university, I was writing the “same proof” as the person next to me, but they were on different pieces of paper written by different ink. I have the “same genes” encoding how to make hemoglobin as they do, but a more precise description of underlying reality is probably that each of us has trillions of little molecules that - if left alone in an arbitrary part of the universe - mean nothing and just are.

I don’t just think it’s possible we can’t know reality, I think it’s obvious we can’t know reality.

@Wanderfound

Tangent: I’ve seen it seriously argued by professional philosophers and historians that a decent chunk of Descarte’s philosophy was deliberately bad, on the basis that he was trying to discredit popular positions that he disagreed with. They couldn’t believe that such a talented thinker would push things they viewed as obviously daft (e.g. Cartesian dualism).

I’ve heard people advance arguments like this about other dead philosophers too. It kind of hurts my head. Sometimes there is real evidence that someone was being satirical or trying to make push someone into a revelation by making a false claim, but unless you can give some historical context to explain it you’re just putting them up on a pedestal. There’s no amount of intelligence that lets you escape the time you were born in, you can only really build new good ideas adjacent to the ideas that have already been developed. If you are more than a few years ahead of your time you just seem insane.

And that aside, if we have a book from hundreds of years ago, that’s a better indication that the author was wealthy than intelligent.