[pfortuny]

Oh, dear. Truth being the operating word… There is no truth in a set of axioms we cannot even conceive properly (any infinite set has properties beyond what seems reasonable, even “just” the Natural numbers). From that comes arithmetic, the “most elementary” form of mathematics which cannot be proved consistent…

We (I am a working mathematician) do not understand our objects, we can just make do. Only finite graph theory has a chance of being “real”. And it stops being finite very soon.

And we certainly should be honest enough to admit that our “science” says very little about the “real” world, where truth lies.

Maths is just a tool. Funny, exciting and even in some sense beautiful. But “truth” does it not contain. Except, I insist, in very specific finite constructions.

Statements hold but they are not “true” because they do not relate to the real world (otherwise, Frodo reaching Mount Doom would also be “true”).

There are no continuous functions out there. Bolzano’s theorem is not “true”.

[whatshisface]

I would contend that A -> B can be true even if A is not true or more relevantly to this discussion if A is unknown. That's math's version of objective truth, where "A" is filled by our various axioms and rules of inference.

[macrolocal]

In ~300 BCE, Euclid decides to work with morphisms not objects.

[meroes]

How can you explain appealing to these “unreal objects” (real numbers, set theory, arithmetic) * does* help science? (Effectiveness maybe)

I see you are also a non realist about science.

But even the methodological naturalist (one who takes natural empirical science to be the best method but not an ontology) must wonder how we are uncovering and putting more precision to more and more of the world.

I don’t think we can currently explain why this made up tool “works”.

[zmgsabst]

The enduring appeal of both triangles and Frodo is that they relate a truth that is hard to see, because it’s diffuse and abstract.

But that “abstract truth” is why your pizza doesn’t flop if you fold it or Amazon can’t make a good LOTR.

[VirusNewbie]

> From that comes arithmetic, the “most elementary” form of mathematics which cannot be proved consistent…

This is kind of wrong. Are you familiar with Godel's thoughts on this?

[uoaei]

...are you?

[VirusNewbie]

Very much so.

[uoaei]

So lording esoteric knowledge over the anonymous rabble is more productive than just explaining what is the issue?

[VirusNewbie]

ok fair enough. There is no issue with proving arithmetic consistency on a finite number of symbols. Incompleteness entirely relies on the unbounded induction step.