Pondering Postulative Thinking (The Necessity of Postulates in Mathematics)

          The explanation given by Euclid that Axiomatic / Postulative thinking is the only method of acquiring any concrete truth is that any proof is based on either another proof or an assumption.  This in itself makes itself logically redundant, as obviously is show that either it is based on a fundamental assumption (as by its own logic, any proof can be shown to be derived from some previous assumption), in which case it may be taken to not represent a fact, or it is in fact a proof that does not require a former assumption, in which case it contradicts itself by providing evidence that it is not necessarily the truth.

           What this implies is not that this method is incorrect, but that it is not necessarily true, and there may be other methods.  Thus we cannot prove that our logic is the most suitable, only measure how closely it relates to reality, and refine it until it becomes a satisfactory model that can make future predictions on the behaviour of our environment.  Now that rant's over I'll get back to the maths!