Agnostosticism is the belief that claims concerning God and certain accompanying religious or metaphysical beliefs cannot be proven either way. The truth is not known so it cannot be argued.
In the words of Jorge Luis Borges, a famous Argentinian writer and poet:
"Being an agnostic means all things are possible, even God, even the Holy Trinity. This world is so strange that anything may happen, or may not happen. Being an agnostic makes me live in a larger, a more fantastic kind of world, almost uncanny. It makes me more tolerant."
Many Atheists discover that the proper label for their beliefs would actually be Agnostic, while some Agnostics occasionally refer to themselves as Atheists, just to 'keep it simple'. Bertrand Russell (1872-1970), a British philosopher, mathematician and social critic is a good example of such an Atheist/Agnostic.
However, as in his essay 'Am I An Atheist Or An Agnostic?', under 'Proof of God' he clarifies:
"As a philosopher, if I were speaking to a purely philosophic audience I should say that I ought to describe myself as an Agnostic, because I do not think that there is a conclusive argument by which one [can] prove that there is not a God."
Read "Am I An Atheist Or An Agnostic?" by Bertrand Russell
Even though the term agnosticism is somewhat modern, coined by Thomas Henry Huxley who first mentioned it in his speech given in 1876, the concept of agnosticism is ancient!
One of the oldest texts to mention such a belief/philosophy is the Hindu Rigveda.
An excerpt from an ancient sacred text of Hinduism called Rigveda (~1700-1100 BCE), or more specifically the Nasadiya Sukta, a creation hymn, says:
"Who really knows? Who will here proclaim it? Whence was it produced?
Whence is this creation? The gods came afterwards, with the creation of the universe.
Who then knows whence it has arisen? Whence this creation has arisen-perhaps it formed itself, or perhaps it did not-the one who looks down on it, in the highest heaven, only He knows-or perhaps He does not know."
The ancient Greek philosopher Protagoras (~490-420 BCE) wrote:
"Concerning the gods, I have no means of knowing whether they exist or not or of what sort they may be,
because of the obscurity of the subject, and the brevity of human life."