/sci/ - Science & Math

>>12489599
The definitions of topology, by its simple base axioms, incidentally through out a lot of the nice order theoretical properties that this subset of the powerset would have.
I think he's making a valid case that the simple topology axioms are a ruse, since most theorems end up demanding particular properties anyway (e.g., most notably, being Housdorff and others), so it's a ruse to say "oh topology is so simple, look at those nice 3 axioms."
There's many fields of mathematicans which go on to cast "ostensible topology" into metric theory, combinators, graph theory, lattice theory, locale theory to to their thing anyway.

But David Rodgers in the comments seems to be also a bit triggered that he's not giving pretopoi it's due, which already seem to capture half of the abstraction. I don't know enough about it.

What's worse, lem [math] \vdash A \lor \neg A [/math] or explosion [math] A \land \neg A \vdash [/math].

Can we boycott the logical or? It just leads to shit. Especially [math] A \vdash A \lor B [/math]. I may ask like this: Is there a relevant logic with something like an easy to understand semantics.

>>10489137
The answer is one that applies to many similar questions:
We try to model physical phenomena using frameworks that we are able to solve.

Say there's a much better non-linear theory. It might be hard to find and even if found, hard to solve. We are glad we find a linear theory that still works.
Same spiel applies with "conservation of energy" and integrate systems. Those are the ones we are able to solve and so people desperately try to find theories that fall into that framework. E.g. when the nuclear physics theory broke conservation of energy, the neutrino was hypothesized to add another particle that made conservation of energy work out after all, and in that case it worked out and new experiments could be explained with that theory.
Of course for every theory that works out, there are 1000 that don't. Consider e.g. these list of 80 or so post 1900 bust still classical theories of gravity that turned out not to make it
https://en.wikipedia.org/wiki/Alternatives_to_general_relativity

tl;dr we know of theories that are comparatively simple by the nature of us being able to deal with them