This argument completely ignores the observer which is bound by the same limits of our processing - indeed they are paired together.
Entering purely theoretical space here: On the timescale of eternity this might be a local pocket of some logical organization but there is no fundamental logic governing everything. Our observation is limited so we can’t perceive chaos, instead evolved to only recognize patterns. Over infinity, pure chaos does not preclude long pockets of what looks like order. What we consider fundamental rules could very well be local phenomenon, which we are a product of.
Of course this purely theoretical - all I’m saying is that intuitism could be true while also math being useful to predict things right now. We could also only exist for an instant and all our memories just construct, but that’s not very useful. It’s more useful to believe in scientific method because what’s repeatable is provable, whereas chaos is by its nature unprovable - which doesn’t make it impossible.
Well, not a possibility I considered, but nothing in the argument depends on the regularity being a permanent feature of the cosmos, just that systematic human endeavours, such as mathematics or indeed meaningful debate, depend on it, so when it goes they go. In that sense, if you wish to consider this conversation meaningful you are kind of ceding the point that for now chaos doesn't, in fact, reign. If you don't consider it meaningful, then why are you having it? :)
Not arguing anything - it's more an interesting thought experiment. This view doesn't change much other than never finding the "true unified theory of everything", which I'm not sure how many people think is truly possible (at least anytime soon) anyway.
It is useful to focus on repeating things, and useless to focus on randomness. But I don't think it's necessarily true that randomness (probably a better word than chaotic since chaotic systems are complex mathematical interactions) doesn't reign. We evolved to take advantage of repeatable things, our sense organs and perception are all focused on things that are repeatable. Our definition of usefulness (what is useful/what isn't) depends on repeatable things. I believe there's a pretty high likelihood that we are blind to anything outside of that, such as true randomness. IE, we literally cannot conceive of true randomness since we are products of an environment that rewarded it.
To your point, I guess this isn't exactly Intuitionism, since Intuitionism says it's a totally human construct, and mathematics has provenly predicted things in nature from purely theoretical models, whereas I just find the part that supposes mathematics isn't a fundamental part of objective reality possible.
Either way, I don't think it changes anything about how we do math or science or anything - how could you even study this? By definition understanding and using things depends on repeatability. If there truly were cracks in it, they by definition couldn't be repeatable. It certainly won't help us get food.
EDIT
> If you don't consider it meaningful, then why are you having it?
I just find it interesting since I've had this thought before and seeing what other people think of it.
Something to consider in the context of "repetition", is that it requires abstraction, and possibly memory. As noted before, I do not see any kind of repetition (identical things, counting) in nature. I think abstraction and memory are both emergent properties from human brains (or machines, brains in other mammals, octopuses, etc.) My pet theory also initially discards "things", because that again requires abstraction.
For reference, my views are somewhat related to "emergentism", "connectionism", and "realism", but I haven't found a school of philosophy that I feel comfortable with.
> how could you even study this?
This is indeed the biggest challenge. I am currently studying this from a conceptual art perspective, because philosophy and science do not seem adequately equipped for this kind of problem.
Entering purely theoretical space here: On the timescale of eternity this might be a local pocket of some logical organization but there is no fundamental logic governing everything. Our observation is limited so we can’t perceive chaos, instead evolved to only recognize patterns. Over infinity, pure chaos does not preclude long pockets of what looks like order. What we consider fundamental rules could very well be local phenomenon, which we are a product of.
Of course this purely theoretical - all I’m saying is that intuitism could be true while also math being useful to predict things right now. We could also only exist for an instant and all our memories just construct, but that’s not very useful. It’s more useful to believe in scientific method because what’s repeatable is provable, whereas chaos is by its nature unprovable - which doesn’t make it impossible.