To add some nuance, the boundary between science and philosophy is always changing as we get more information about how the world works. Philosophical truths help us make better decisions about the future.

DNA and quantum mechanics are 2 areas where the boundary between philosophy and science has shifted over time. All the modern talk about multiverses, universe simulations, and AGI seem philosophical, but might become scientific in the future. But people who believe in these concepts will take different actions than people who don’t, so you can’t say it just doesn’t matter because we can’t prove it yet.

I wasn’t trying to lump math and science together and agree they’re very different, although both based on core propositional truths that are taken on faith.

At the cost of being extremely annoying for the second time today, what does "a truth we can't empirically prove" look like?

> All the modern talk about multiverses, universe simulations, and AGI

None of the things you mention are "philosophical truths". The first is one of many interpretations of QM, the second is a meme, the third is a vague, unclear teleological goal of computer science. I'm not objecting to the fact that you can speculate, I myself said that pointing to new things, as vague and undefined they may be, is generally useful and stimulating. I'm objecting to the idea that you can have "truths you can't prove".

> I wasn’t trying to lump math and science together and agree they’re very different, although both based on core propositional truths that are taken on faith.

Sorry, my fault. Tomato, tomato.

> what does "a truth we can't empirically prove" look like?

Law of causation, Doomsday argument, complex processes that can't be recreated, historical processes which leave faint empirical markers, etc.

Wasn't the black hole a truth you can't prove for a pretty long time? Scientists 'believed' that they are true and tried to prove their existence. See: https://www.sciencefocus.com/space/who-really-discovered-bla...

There's a difference between making a definite claim and pointing out that Newton's model allows the existence of such an object. I'm not going into "quid est veritas?" type of discussions because it's a bottomless pit that leads nowhere, but it seems to me like "black holes could exist" is a statement much like "an artificial general intelligence could exist". It's not ruled out by the model, but a-priori we have no idea.

Much of mathematics isn’t empirically provable, except in a very fuzzy sort of way. You prove math... with math. Not by conjuring up physical experiments. That’s called, well, physics.