First of all, as Plato pointed out long ago, knowledge is not just true belief. Since a guess is a true belief, and a guess is not knowledge. Suppose I believe that Obama is using the bathroom at this moment, and suppose that is true. Do I know that he is using the bathroom? Of course not. I believe he is and he is. But I have no justification for my belief. I have no good reason to believe what I believe. Therefore, it is a true belief, but it is not knowledge. So there is a difference between true belief and knowledge, and there is also, of course, a difference between false belief and knowledge, so we know there is a differerence between belief and knowledge. All knowledge is belief, but some beliefs are not knowledge.

In the second place, we have to distinguish between knowledge and certainty.

I know when I have a justified belief which is not false. I am certain when I have cannot have a belief, and that belief be false. Therefore, I know that pigs cannot fly, because I believe that pigs cannot fly, that belief is adequately justified, and, of course, that belief is true. But, I am not certain that pigs cannot fly, because it is not impossible that I should believe that pigs cannot fly, and it still might be true that they can fly. For, as you say, I cannot prove (in the sense of demonstrate the certainty) of the proposition that pigs cannot fly. But that does not mean that I do not know that pigs cannot fly. My evidence is sufficient for knowledge, but not for certainty.

You ask whether Descartes's Cogito is certain? That is, you ask whether we are certain that we exist. Is it possible for us to believe that we exist and be mistaken, is what you are really asking. That is a difficult question, and certainly, the Cogito is a prime candidate for certainty if anything is. The argument is, of course, that you cannot believe anything, let alone that you exist, and be mistaken, since in order to believe anything, it is necessary that you exist. And, it is necessary that you exist even in order to be mistaken. In fact, it is necessary that if anything has a property, that thing must exist. So, if I walk, then I exist. For how could I walk, and not exist? In fact, predicate logic enshrines this principle into what is called, "existential generalization". (x) (Fx > Ex). Whatever has property, F, exists. There have been counter-arguments, of course. So, all I can say is to repeat what I said just earlier. I am not sure whether "I exist" is certain, but if anything is, it is.

But, whether it is certain or not, we all know that we, ourselves, exist. We need not be certain in order to know.

Thank you, that is reassuring. But that principle is largely based on how your non-existence, is a paradox. So can that technique of prooving the paradox of one, thus the certainty of its opposite, be used for other things in life, like mathematics for instance?

Sorry, I have no idea what you are asking. And, I have no idea what it is you are saying is reassuring. What principle is based on my non-existence? Let me assure you that if it is, it will soon fall to the ground, for I exist.

Lol...It isn't based on your non-existence, its based on the impossibility of your non-existence. What I am asking, is "can that type of argument be used to create certainty in other things?" So just as, questioning your existence prooves you exist, and your not existing and yet being able to question it would be contradictory, and there is only one other option, that you exist, so by demonstrating the paradox of one, you proove the certainty of it's opposite. Can this be done for other questions besides the question of one's existence?

Sure. Suppose I say, "I am dead", or, "I cannot speak a word of English", or, "I am in a coma". But those are really not formal contradictions. They are what are called, "pragmatic contradictions". Another interesting one is, "I believe it is raining, but it isn't raining". There is no contradiction there, since I can certainly believe it is raining, and it not be raining. (That was invented by the great English philosopher, G.E. Moore. It is called, "Moore's Paradox".