Philosophy Now Forum

alan1000 wrote: ↑Thu May 08, 2025 3:04 pm And all of this is thought to be a debate in mathematics, is it? I guess the moderators are asleep, which would be par for the course.

Your remark discloses first of all that you are ignorant about the philosophy of mathematics. What exactly is "truth" and "proof" in mathematics, are obviously core questions in its epistemology. But then again, if you do not like that kind of debates, who has actually forced you to participate in it? You are obviously free to leave the debate as fast as you can make it out of here!

Wait!

"If it were possible to prove that you saw something, then jsCoq would happily verify and accept your proof"

Indeed, but proof of what you saw jsCoq demonstrate could only ever be known by you.

If you were to write the statement, "i saw jsCoq verify a proof that i saw something," nobody could verify that this was true and you're fucked.

You can not see a proof that what you saw is real if you have to see it to do so for you would then need another proof... and you'd have to see that one too!

Are we all stuck in our own solipsistic nightmares?

promethean75 wrote: ↑Sun May 18, 2025 1:04 am You can not see a proof that what you saw is real if you have to see it to do so for you would then need another proof... and you'd have to see that one too!

Are we all stuck in our own solipsistic nightmares?

Not really. What we see, is truth, but not proof. When we communicate, we will trust each other (to some extent) for telling the truth. So, human interaction is largely based on trust.

godelian wrote: ↑Sat May 03, 2025 2:48 am Look around you.

You may, for example, see a chair or a table or something else. Now take a piece of paper and write down an irrefutable argument that you did see what you saw. Will the verifier of your argument consider it to be irrefutable?

No, the verifier won't.

What you have seen is true (to you) but unprovable (to others).

In other words, the physical universe is entirely Godelian, i.e. true but not provable.

The abstract Platonic universe of mathematical objects, on the other hand, is overwhelmingly Godelian but not entirely. Some of it, is both true and provable.

True but not provable, is the norm, and not the exception.

Binary> Noun is not a verb, a relative is not a correlative, a quality can never be a quantity, etc,, a boundary can never be the material within a boundary.

I.e. as Plato stated, the perceptible can never be intelligible, nor can the intelligible ever be perceptible.
Or in computer jargon, the processing in a computer can never be the product of a computer, and the product of a computer can never be the processing of the computer.
or again, the 0, or limit, can never be a 1, the material difference between limits.
So, the proof is the simplest one possible, the definition of a thing, As Aristotle tried to explain Plato in simple terms, one part of a definition must play the part of material, while the other that of form.
A thing is defined as the combination of material and form, one can never be the other. So, the very fact that things exist, and this is just another thing, if you comprehend it, a definition, is comprised of two elements, and all you have done is repeat Plato, neither element in of itself can be proven, only named, a definition is the combination of a thing's elements.