I freaking love Big Bang Theory! No other show would've brought me to the summation of one of my most fundamental troubles with human truth and knowledge - the Münchhausen Trilemma.
I've pretty much always believed in the philosophical assertion that we can never prove anything. Science can only go as far as to increase the probability or confidence that a proposition is true by providing supporting evidence. Through repeated controlled experiments, we can establish a theory to be a 'true' law, but there is always the possibility that it can be falsified. But that's the limits of our human knowledge for you - this is as far as we can go to increase the confidence that a theory is probably right.
Science isn't the only way. We can also attempt to come to a conclusion of truth through logic. Rational reasons can replace statistical evidence to provide support for a proposition. Reductionism helps us break down a proposition into smaller subpropositions, which would strengthen the original proposition, in theory.
However, what makes up those subpropositions? Even smaller sub-subpropositions would have to be established, ad infinitum.
Hans Albert was the first to notice this and concretize the observation, and established three forms of dissatisfactory methods to prove any truth. Interestingly, the Münchhausen Trilemma is named after Baron Münchhausen, who allegedly pulled himself out of a swamp seizing himself by his hair. This trilemma rounds off the classical problem of justification in the theory of knowledge - that all attempts to get a certain justification must eventually fail when scrutinized fully.
The Münchhausen Trilemma essentially states that we have only three options when providing proof in any situation:
1) The circular argument, in which theory and proof support each other (e.g. we repeat ourselves at some point)
2) The regressive argument, in which each proof requires a further proof (e.g. we just keep giving proofs, presumably forever)
3) The axiomatic argument, which rests on accepted precepts (e.g. we reach some bedrock assumption or certainty)
The first two methods of reasoning are fundamentally weak, and because the Greek skeptics advocated deep questioning of all accepted values they refused to accept proofs of the third sort. The trilemma, then, represents the philosopher's difficulty in choosing among the three equally unsatisfying options.
I think this is yet another demonstration of our limits of human understanding and perception of truth. By virtue of the fact that we exist in a manifest world that is separate from the 'essential' source that we come from, we can only revolve in circles to try and hit a truth we somewhat perceive coming from a more fundamental and transcendental realm, but never come close enough. Only having five senses that perceive environmental input/stimuli within a limited scope (e.g. the light or sound frequencies that we are privvy to) is one good way of understanding this limit of ours. Some people (usually agnostics) see this as good reason to resign ourselves to not bothering because we can never get to the point or know what truth is, but on the contrary I think this disconnect is important and necessary because it will continue to drive us to seek the truth even against all odds. If we could see truth and easily recognize it then there would be no motivation for human endeavour, and truth wouldn't be all that valuable.
Which is why I think every method of truth-seeking is actually a leap of faith to be made, whether the skeptics or rationalists want to admit it or not. Beyond a certain point, science has to concede that something is there just because it is, even if the methods used to get at it still leave much to be desired. The gap can only be bridged by faith, both in terms of the presence of the truth and in terms of our methods of getting there.