Absolute logical proof is only possible in the abstract mathematical realm where we precisely state and agree on the rules ahead of time. In math-land, I can absolutely prove that 2+2=4. I can absolutely prove that there are no even prime numbers larger than 2. It has also been rigorously proven that no map can be drawn that can't be colored with only 4 colors, or that no integers a, b, c, and n, a, b, and c > 0 and n > 2, such that a^n + b^n = c^n (though those proofs are way beyond me). In the realm where it's truly possible to prove anything, it is possible to prove a negative, though it may be more difficult than disproving a negative by providing a counterexample.
In the real world, there are no axioms. There are only working hypotheses and heuristics that we generally agree on, and we often find that when we try to state them exactly we don't agree on them. And there is no truly absolute evidence; all observational data is subject to fallible perceptions and fallible memory. If I interview your plates and they speak and tell me that yes, they are in fact trying to kill you, that doesn't actually prove the platist proposition -- they could be lying, or I could be nuts.
Much more vexing, though, is the fact that human beings don't evaluate and maintain their beliefs through pure logic. We filter evidence that is offered to us based on how it fits with what we already believe and how much we want it to be valid. The more emotionally invested we are in a position, the less likely we are to honestly consider something that appears to contradict our position. And there are few questions that we're more emotionally invested in than the existence and nature of a deity.
no subject
In the real world, there are no axioms. There are only working hypotheses and heuristics that we generally agree on, and we often find that when we try to state them exactly we don't agree on them. And there is no truly absolute evidence; all observational data is subject to fallible perceptions and fallible memory. If I interview your plates and they speak and tell me that yes, they are in fact trying to kill you, that doesn't actually prove the platist proposition -- they could be lying, or I could be nuts.
Much more vexing, though, is the fact that human beings don't evaluate and maintain their beliefs through pure logic. We filter evidence that is offered to us based on how it fits with what we already believe and how much we want it to be valid. The more emotionally invested we are in a position, the less likely we are to honestly consider something that appears to contradict our position. And there are few questions that we're more emotionally invested in than the existence and nature of a deity.