Aristotle invented this word, deriving it from Gr. 'axios,' meaning worth. Remember Axiology? Refers to VALUE judgments. The philosopher decided that axioms are those concepts of such worth, that they are essential as the cornerstones of science. He also added that each science needs its proper axioms. Euclid, in Geometry, searched for its proper axioms, like, 'a straight line is the shortest distance...' The Euclidean axioms have been called also postulates, creating a lot of confusion and a vast irrelevant literature. I have chosen, as a philosopher on my own right, to state that analogical thinking is the basis for postulates, which --as such-- need to be proved. Thus one can state: 'I postulate, on the basis of a and b observations, which are analogical to c and d existing facts, that there is a high probability of such and such idea of mine to be true. Now, this postulate of mine needs to be proved or disproved.'
One of Einstein's postulates was that a massive body attracts light. His assumption, quite probably based on analogical thinking, was confirmed. In fact, I really do not know if it was based on analogical thinking. Could somebody give the facts?
Now, each science needs its own axioms, which, 'axiomatically' are considered by all the people to be absolute truths. They may be improved upon, of course, like when quantum mechanics added to Newtonian mechanics. In Biology, a basic science of prime importance in medicine (an applied science) an axiom says, 'Living organisms grow, multiply, and die.'
Therefore, axioms are to be related to as if indeed they represent absolute truths, even though they may be improved upon, because we cannot function as intelligent beings without their support. Consider the following: There are cells that can be made immortal in the lab. Does this mean that the axiom on living organisms is not absolute truth? Remember, I'm reasoning as a DSP developer, attempting to clarify what at present is confusing. Do not demand from me to be a purist! I shall --in another essay-- write about the Truth, the Good, and the Beauty, the three Platonic Pillars, as interpreted by the DSP.