I was talking to a friend of mine one day and he told me atheists do not exist. I asked him how can you say that if he himself is an atheist.
Sounds like your friend is an idiot. If he is an atheist, then necessarily, at least one atheist exists, and atheism as well. Moreover, there are plenty of atheists besides him (myself included), so that atheists exist is indisputable.
He told me that an atheist is someone who reject god or the existence of god and how can one reject what they cannot prove exist yet alone prove does not exist. So by declaring oneself an atheist he or she is making a logical absurdity.
Not at all. The problem of "negative existentials", or, the problem of proving a negative (i.e. what does NOT exist), was solved with the discovery of the predicate calculus. Proving a negative is not very difficult.
Moreover, one needn't need to
prove something in order to be justified in believing it, or to know it; proof, in the strict sense, is
only possible in the domains of math and logic. All science, and all inductive knowledge, cannot be proved- but is still knowledge, is still true, and is still science nonetheless.
I cannot
prove that the sun will rise tomorrow, but believing that it will is reasonable, justified, and supported by sufficient evidence to count as knowledge.
Belief in the non-existence of God and/or gods is the same.
Because an atheist can cloud his or her disposition by holding strong to science they are also holding strong to scientific principles. Meaning to declare the unknown that is not known is a fallacy in thought.
It is not a fallacy, but even if it were, saying it is wouldn't be enough- you have to
show the fallacy- show how it leads to a contradiction. (since this is what a fallacy is, in logic)
Hence no such thing as atheism occurs in the normal sense. Atheists often take a strong stance saying "god does not exist" and will ramble on and on about cosmological sciences when they themselves are a fool by default for ignoring their very own source of reason.
You've made yourself a fool by making this unsubstantiated and hopelessly vague accusation.
I believe the only proper way of making a logical definition for atheism is to change the definition itself. I
Atheism is the knowledge that God and/or gods do not exist.