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Here's some reason to doubt any proof:

  • Dissent – The uncertainty demonstrated by the differences of opinions among philosophers and people in general.
  • Progress ad infinitum – All proof rests on matters themselves in need of proof, and so on to infinity.
  • Relation – All things are changed as their relations become changed, or, as they are looked upon from different points of view.
  • Assumption – The truth asserted is based on an unsupported assumption.
  • Circularity – the truth asserted involves a circularity of proofs

Source: https://en.m.wikipedia.org/wiki/Agrippa_the_Skeptic

https://en.m.wikipedia.org/wiki/M%C3%BCnchhausen_trilemma

We can doubts anything even someone doubt existence of self, God, mind, external reality, time, consistency, etc.

But why in first place we think that even something can be proved without proof?

So question is is there any proof of assertion that "assertion can be proved"?

To express more clearly:

Assertion: a confident and forceful statement of fact or belief.

Proof: the action of establishing the truth of a statement.

Action: the fact or process of doing something, typically to achieve an aim.

And it is in metaphysical sense.

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    The proof of the pudding is in the eating, and the proof of provability, if any, is in the specific proofs given. Inspecting them is far more productive than abstractly wondering about provability. Agrippa's trilemma you quote relies on the absolutist standard of proof that even skeptics themselves do not follow in practice. And on the human standards that actually matter, many assumptions are unproblematic and readily accepted without much dissent, as currency of proofs in science, law, etc., attests. "Let us not pretend to doubt in philosophy what we do not doubt in our hearts", Peirce.
    – Conifold
    Nov 29 '20 at 6:00
  • Does this answer your question? How far can/should one press philosophical doubt?
    – Conifold
    Nov 29 '20 at 6:03
  • @Conifold Proof of pudding is in eating, but people can doubt it by saying like really qualia exists, or is real? Many people has doubted qualia, and even some says consciousness is illusion even among scientists. And many people who has experienced God, also think same proof of pudding in eating, like who has experienced God can sure that God exists. But people usually don't accept anything as proof of God, so may be fundamentally because there is problem with proof in first place. Nov 29 '20 at 6:06
  • @Conifold Sorry but I want to know how there are proof proposed for proof itself and if can itself can be proved. Somewhat Different from doubting everything. Nov 29 '20 at 6:09
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    The problem lies in choosing a proof standard appropriate in a specific context, but nothing cogent can be said about it in abstract generality. If you want informative answers you'll have to make the question more specific.
    – Conifold
    Nov 29 '20 at 6:13
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It’s certainly true that much less is “proven” than we intuitively like to think. We can still formulate local concepts in maths like “proof in classical axiomatic set theory ZFC”. These embrace the “Assumptions” objection by wearing the Axioms of a given proof clearly on their sleeves - yes, this proof relies on some assumptions, but they are assumptions that are clearly stated and that you don’t have to believe uncritically to be true in order to appreciate that some construction is, indeed, a valid proof in that system.

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In On Certainty Wittgenstein explains how systematic doubt is impractical. Even solipsists who claim every one around them is just a product of their imagination continue to interact with them as if they were real. If they did not, they would soon run put of food, clothes, a place to live...

Similarly, one can affect to doubt that logic is even real and pretend that nothing can be proved. They can say they doubt the Pythagorean theorem and its demonstration and consequences. But still, remains the fact that each time they will draw a rectangle of sides 3, 4 and 5, the angle between 3 and 4 will always be 90 degrees. And that at the end of the day, they prefer to live in soundly built houses, with parallel walls and a straight ceiling.

Some demonstrations just work. If I can observe a fact A (my wheel is of diameter 1) and a fact B (each turn of the wheel my chariot advances by more or less 3.14) , have a demonstration that a circle circumference is diameter times Pi, and all the while each time I try to measure any wheel I find the same result, it is only practical to admit that something is valid here.

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  • One question: If we accept something because live or behaves as believing it to true, then people should believe in free will, as most are live as free will exists. But if still very intelligent people not believe free will, then people can believe free will doesn't exists and behaves or continue to act as free will exists, then it will oppose claims. Someone can behaves different to what he believes, and it shouldn't affect truth of what is there. So truth or belief in truth can be different to how he act, and because of it, point still remains? Nov 29 '20 at 18:24
  • What would be the behavior of a non believer in free will as opposed to a believer ? I personaly dont believe in it and it hasn't changed my day to day life. It's more an attitude shift, from a self beating "how i wish i did things differently!" to a forward looking "how can i make things happen differently next time?" I think the main difference would be that the pythagorean theorem and its demonstration can be reliably tested, while free will is probably going to remain unsolved forever.
    – armand
    Nov 29 '20 at 23:31
  • As for your question, even if capital T Truth remains inaccessible to us, and i agree with you that what we believe or how we act won't affect it, it remains that some things work and some dont, and it's a good heuristic to consider the things that work to be closer to the truth.
    – armand
    Nov 29 '20 at 23:32
  • Isn't this attitude shift very much visible in behavior? And shouldn't we take the fact that it "works" as evidence of free will's existence?
    – Conifold
    Nov 30 '20 at 2:58
  • Although it's marking against my team, I wouldn't say so, because this shift in attitude is valuable even for advocates of free will: beating oneself up about how things could have been different is unproductive anyway (unless one believes the past can be changed by wishing strong enough). It's just easier to shift once you consider that things could not have gone differently in the first place.
    – armand
    Nov 30 '20 at 3:45

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