There are many different kinds of proof. But none of them are absolute. We know this because Goedel showed us that no system can be both complete and consistent, which means that we are always going to need axioms.
The strongest kind of “proof”, I would say, is mathematical. This is a proof by which having accepted a postulate, every step we take is logically rigorous. The conclusion is therefore an unarguable consequence of the premise. The only weakness, therefore, is the fact that it all has to start somewhere, so we need to accept some axioms (eg axiom of choice/Zorn’s Lemma) to build the theory up.
Scientific proof isn’t bad, but it’s far less rigorous because it is deductive rather than inductive. We accept that a zillion observations proves the case. There is, however, always the chink in the armour - maybe the sun will not come up tomorrow and the whole system will come crashing down around our ears.
There is, of course, a further chink in observational proof. We must rely on measuring devices - even if these are just our eyes and ears. Any image of a thing is not the thing, and the brain can be fooled into thinking something is there when actually it is not. Light, gravity, even our very existence could just be a mass hallucination. We assume not, for otherwise we could get nowhere. But the doubt must always be there.
Then there are situations in which we have less than the optimum number of observations anyway. The data so far agrees with the predictive model. Today. But will it tomorrow? We can only wait and see.
But mathematics and science are only two epistimological systems. There are other ways of evaluating knowledge - religion is one. Like science and maths, religion can never be both complete and consistent. It could be argued that unlike science and maths, which strive for consistency and accept a lack of completion, religion strives for completion and accepts a lack of consistency. This is still a valid approach. What consititutes a proof under the religious epistimological system I cannot guess.
But I could submit the epistimology “Every sentence that starts with a vowel is true”. This is then the (necessary) axiom of the epistomology (which of course is neither consistent nor complete). Under this epistomolgy proofs are very simple indeed. If a sentence begins with a vowel, it is proved true. As epistimologies go this one is useless. But you cannot prove that it is a definitively incorrect system of evaluation - Goedel showed us that. It seems to offer us nothing, so we reject it. But we are, in essence, using the science epistimology even to do this.
So what constitutes “proof”? Everything and nothing. After the layers of the onion have been peeled, there is nothing left to prove. Which is why you have to have belief, even if that belief is that what you see is what you get.
pan
