Perhaps we should start admitting to ourselves that infinity is not really something that actually exists but instead it's just an imaginary concept that we created but that has no correspondence to anything that makes sense in our universe?

Or at least, some versions of infinity (I will leave which ones, exactly, to the experts).

Hence all the paradoxes that derive from it.

I mean, perhaps we can work with some version(s) of infinity, without creating a plethora of paradoxes.

The natural numbers, for example, might be something that is infinite and makes sense. However, perhaps talking about a single set that contains an infinite amount of natural numbers might not make sense (or perhaps it still might?). Or perhaps we just need a new language for talking about infinite things without re-using the language we use for describing (finite) sets, so that we don't try to reuse concepts from finite objects with infinite objects.

Or perhaps the only objects that exist (and can be meaningfully talked about) are the computable ones. And/or perhaps "computable function" is one that can use infinite amounts of time but only finite amounts of storage (rather than infinite amounts of storage).

Would it make sense to go back to classical finitism and re-evaluate some of the choices that were made along the way to where we are now?

I can't help but think about the many paradoxes that arise from the very (supposed) existence of infinity.

For example, everybody thinks the halting problem is undecidable. The halting problem is clearly not undecidable on finite-state machines (i.e. real computers), it's only undecidable if you use imaginary Turing machines (which supposedly can have literally infinite state) as a model. But of course, Turing machines cannot exist in our universe.

So it's rather ironic that people say the Halting problem is undecidable, when this is only true for (impossible to construct) imaginary machines but it's not true for the real machines that we actually have and that are possible to construct.

Or think about Hilbert's paradox of the Grand Hotel.

Or the Banach-Tarski paradox.

Or Galileo's paradox.

Or other such paradoxes that only exist if you believe that imaginary infinite objects could possibly exist.

Most people will tell you "well, it's just that our intuition doesn't work for infinite things", but in this specific instance, it's really hard for me to believe that it's our intuitions that are mistaken rather than that we actually made some conceptual mistakes along the way. To me, this argument sounds more like gaslighting rather than a real convincing argument.

I'm not saying our intuition is always correct, though. For example, the quantum properties of our universe are clearly not intuitive but it's hard to argue that our universe is not quantum, after all the scientific experiments that have clearly verified this to be true.

I don't think that invalidates my argument, though, because the convincing argument in that case is not "sorry, you must believe my theory that the universe is quantum" despite not existing any evidence that this was true, but rather, "sorry, but here's all this real evidence that our universe truly is quantum".

Am I crazy here?