Heavy!

My current forays into the history of Mathematics brought back to me the memory of
Euclid's Elements, one of my fondest moments from High School ( the worst was
Biology which I dropped for Physics; Save the Frogs!). I thoroughly enjoyed all the
problems but, as I recall, the introduction to the work was awesome and somewhat
mysterious. Let us look again at the Axioms and Postulates:

Today, both concepts are defined as self-evident truths but what is the difference 

between them. The clue to the issue comes from Aristotle, in whose work on 

Logic the Organon, axioms are referred to as primary notions with which one 

builds demonstrations. Postulates, in turn, define the field of study: it comes from 

asking for, here a line, a point, a circle, parallels. The statement of the fifth postulate is 

cleverly presented, ie those lines where angle deviation from the parallel

will be on the same side. Euclid comes a bit later than Aristotle, but his influence 

here is clear as well. He thought that logical connections came from experience 

itself,  whose richness informed the mind, because there was just too much otherwise.

Interestingly, the followers of Aristotle quickly came to the view that he had been 

right, and that all one needed to do was to understand him, a view that prevailed to 

the Renaissance. Ironic and misguided: philosophy is an acitvity. Plato knew that 

and Aristotle himself wrote on the dialectic. Perhaps it was the heaviness of the 

written word that came to prevail...