Is there any knowledge in the world which is so certain that no reasonable man could doubt it?

Death.

Identity, non-contradiction, excluded middle.

If you deny these then you're unreasonable by definition, so it's a self-fulfilling prophecy anyway.

>excluded middle
lmao

Assume that all knowledge can be doubted. If so, then there is a possible contradiction if it can be shown that it is certain that all knowledge can be doubted.

Assume that we are uncertain if any knowledge can be doubted. If we can recognize our own uncertainty in this matter, and if we can show that we are certain that we are uncertain, then we will have found something which we are certain about.

Assume that we are uncertain that we are uncertain. If we are certain that we are uncertain that we are uncertain, then we will have found something we can be certain of.

But let's doubt that as well. Obviously this method of proof leads to an infinite regress of doubt, at least we can be certain of that, right?

Let's doubt that also. Assume that this method of questioning does not lead to an infinite regress of doubt. If that's the case, then isn't it implied that the doubting chain terminates because it is finite, and hence there is some point at which we are certain of our uncertainty?

Seems reasonable, and this is the point at which most reasonable individuals would stop. But I'm not very reasonable, or at least I'm not certain I'm reasonable or not, so let's keep going. I'm doubting the entire methodology of this proof to be honest, what if I'm convinced of what it's trying to show me, but in actuality I have been misled because I believe that this logical methodology will reveal certain truths?

Assume that logical systems can be trusted to reveal truth. Then we have the self-referential statement "This logical system reveals truth" as a true statement within a logical system. Is it certain that it is true? If it is, we've found our certain knowledge.

If we doubt that it is true, then we posit that "This logical system reveals truth" is false, ""This logical system reveals truth" is true" is false, both, or some other option we haven't considered that likewise causes us to doubt the certainty of the logical system.

Let's tackle these one by one. If "This logical system reveals truth" is false, then we have a piece of certain knowledge, that the logical system does not reveal truth. However, if it is true that ""This logical system reveals truth" is false," then we cannot trust the prior conclusion. Are we certain that we cannot trust the conclusion? Also, if ""This logical system reveals truth" is false" is true, can I be certain of it?

Most of those unreasonable individuals who make it to this point would say that we can be certain that we cannot trust the logical system (amounting to trust in the principle of non-contradiction), and would be uncertain of the second claim of the veracity of the logical system's truth revealing properties. I'm unsure if I'm unreasonable, and I'm unsure if I'm unsure if I'm unreasonable, ... etc (maybe), so I'm going to doubt the principle of non-contradiction...
..but then isn't this whole post worthless?
I can say that with absolute certainty, and now you know it too. Omeletto

Edit: thx 4 teh gold

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Hegel already doubted every single law of logic Aristotle said on. although he used this laws in his dialectics, but that's just because he thought it would follow in within logic of his dialectics.
You will realize this is a shallow answer if you knew existence of fourth law in logic. it is called the law of sufficient reason, named by Leibniz. Nobody considers we fundamentally and successfully followed that law.
Right now, even major mathematics took intuitionism(or their theoretical output) seriously. In Algebraic geometry they regularly use Grothendieck topos, which don't support the law of excluded middle.

>excluded middle
Not in math or quantum physics.

That this something, whatever it is, no matter what it is, unbeknownst of how or why it is, or if it's plural or One, or both—it is.

Mmmmmmm

Holy....i want more!

Quantum logic is constructed from standard logic. Intuitionism is a meme and no one uses it in reasonable(that was the initial criterion) math

The knowledge of one's own existence

Simple self-referencing propositions.
Such as, "this statement is true" or "this is a sentence"

Right "I think therefore I am" would fall into the class of self-referential statements A thing must exist in order to assert its own existence in the first place. The premise is the same object as the conclusion.

"I exist" is not a self-referential statement

>excluded middle
You can build entire mathematic systems without excluded middle, and they come up necessarily in a very general family of situations. Those mathematics even have applications to computer science.

The principle of identity only means you're restricting yourself to abstract entity that can be formally or operationally identified.

Non-contradiction as such is not universal to all system of logic.

The statement isn't referencing itself, but the utterer is referencing himself. I could have made that clearer.

That being is

>reasonable math
>implying you have authority to decide what is reasonable math
>iplying intuitionistic mathematics haven't proved themselves surprisingly relevant in the past decades
>implying the law of excluded middle makes sense from a point of view of reasonable implementability

Read more.

Nietzsche critique cogito argument with existence of implicit presupposition that needs self, so I think he would claim in "I exist" "exist" has implicit need to include self.

Read Decartes, Husserl and Ponty
You are welcome

honest answer
appropriate answer
redundant answer
I'm not sure that "we" can state anything at all—the individual can make definitive claims about his or her own being, but ultimately we can't extend that to a larger field of "we," I think
solid retort
unoriginal!

Could do the rest but reached the character limit and got tired.
The short version is that meta-meta-doubt cycles in on itself to reveal certainty. After going through the whole Gödelian thing and building up a logic without the assumption of non-contradiction (which Hegel did), the next stage is to doubt language itself a la Derrida, and if you're feeling frisky to doubt referentiality, signs, and signifiers a la Baudrillard, and after that you doubt the *possibility* of knowledge about knowledge (which, my guess is at least where OP is given the wording of the question, if he's not a grand master trying to guide others), and then you have a few options, Kierkegaardian "leap of faith" that it is possible to know something about knowledge or that an idea can be communicated, belief that it is impossible to communicate, both, or neither. (side note: continuing to write a post does not imply communicating or belief about communicating)
The issue is that any individual (assuming they exist, as plural, one, both, or neither) either now has a choice in the matter between faith, absolute lack of faith, simultaneous faith and lack, or something else, OR they have no choice in their orientation toward the possibility of knowledge, they both do and do not have a choice, or neither. "I" can internally verify this, and "I" can transcribe markings which may or may not be "external" to "me" (which is really just a rehash of Kierkegaard desu), but I can still doubt whether I have been convinced that choice either exists (and subsequently is absolute belief, absolute doubt, both, or neither), doesn't exist, both, or neither. Then we get into doubt about our awareness of mental states and phenomenology (destroying all the cogito ergo sumfags), doubt about existence and experience taking care of all the empiricists, and... wait a minute why am I doing your homework for you?

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That Man is the product of causes which had no prevision of the end they were achieving; that his origin, his growth, his hopes and fears, his loves and his beliefs, are but the outcome of accidental collocations of atoms; that no fire, no heroism, no intensity of thought and feeling, can preserve an individual life beyond the grave; that all the labours of the ages, all the devotion, all the inspiration, all the noonday brightness of human genius, are destined to extinction in the vast death of the solar system, and that the whole temple of Man's achievement must inevitably be buried beneath the debris of a universe in ruins--all these things, if not quite beyond dispute, are yet so nearly certain, that no philosophy which rejects them can hope to stand.