let me try to escape from the paradox, byron, which you stated in a syloogism.
i make the assumption that only that which is either true or false is subject to proof.
statements of an analytic-apriori nature fall within the set of that which can be proven.
for example, in euclidian geometry, one can prove base angles of an isoceles triangle are equal. the proof does not involve the senses.
when you perceive, the result has some probability of being true and a probability of being false. thus perceptions cannot be proven true or false.
in the empirical world (experience) absolute proof is not possible.
in the world of the abstract, it is possible.
there are many other examples in trigonometry, boolean algebra, calculus, num,ber theory, which are subject to proof.
the problem with preception is that one can never say the perception is true, with certainty.
one may have confidence in one's perceptions and act on them, but one can never be sure that one's perceptions are true.
confirmation by others, if the sample is large, can lead to confidence, but not truth.