The Meaning of Axioms

An axiom is a basic statement which is self-evident since it makes sense. Out of the insightfull statements of an axiom, one can activate the consequences implied in it. Scientifically relevant axioms are not unchecked factual pronouncements, but rather rational criteria which help us to judge states of affairs. (To be distinguished from principles and axioms from data I/A2). Something problematic should never be the content of an axiom. On the contrary, one should solve problems with the help of unproblematic axioms. Such a fruitfull basic statement, which help us to cope - think and act - with the most common experiences, is the mechanical statement of that all non-living things, called by me objects, distinguish themselves from living beings by the preservation of their state. This is a basic statement, not a factual pronouncement, since it is not thought that such an ideal, unperturbed state, really could exist. Therefore no refutation is possible, but only the question how rational it is. Descartes wrightly called it "The first law of nature"; Newton limitted in his mechanics the universal principle of conservation to the state of an object, so that conservation appears as a kind of persistence/endurance. His first law of motion states: "Each object persist in his state of rest or of uniform, rectilinear motion, so long externally applied forces do not compell to change it". (Translation by George Galeczki). He shows that the motion of a non-influenced object is a forcefree state, which needs no foreign causes and can have no consequences, solong the motion doesn't lead to encounters with other bodies. It became superfluous to assume the existence of spiritual beings, like angels, to maintain celestial motions. Newton's first law of motion shows that unaccelerated motion is a natural one and represents no physical problem, therefore it needs no explanation, neither through "impressed forces", nor as attempted by Newton - a natural philosoph with of faith in God - through "distance masses of fixed stars" (Einstein's Mach principle). Both attempts of explanation are evidence for a doctrinaire thought. However, since the force-free motion is not problematic, Newton the physicist was entitled to implement is as first axiom and put it at the fundament of his mechanics. And by showing how a persistence by its own appears as force when an encounter occurs, he defines the force (2nd axiom) as the factor changing motion. Were both an invariable state and its change consequences of force actions, the concept of force and the entire mechanics would remain without foundation. It would be equally impossible to base it "on massless mass" receiving its inertia from other ("far"), also inertialess masses, since nobody can give something which he doesn't have. If somebody denies, that an object has inertia from its own, makes ou of reality an "as-if-appearence" and out of physics a number in thin air. If such a contradictory something like a "massless mass" is not frightening, means that one accepts to be overwhelmed by a deterministic zeitgeist (spirit of the age).

Bodies (and in my opinion other physical entities) possess not only inertia, but also the force responsible for gravity. Due to the implied interaction with all physical objects, this confers a permanent dynamical property, though without another interacting physical reality one cannot speak about "force". The axioms show that the nothing is a force for itself and that nothing can be "inert", or "heavy" without interaction. Mass is, consequently only the measure of a mechanical resistance due to interaction. Nothing can be refered to an observer as "moving", or "resting". Only the scientist, who recognizes its role in the research process - and takes this into account - knows the he "in Niels' words, is both spectator and actor in the big drama of existence" (Heisenberg) and could gain knowledge. Only who, who considers himself as part of his perceptions, actually "perceives" and is not merely a technician and performer who forgets to refer his work to himself. The meaning of the formulated axiom is exactly to arouse this deeper understanding and to convey real knowledge. Its goal is:

To make the things to be explained as matter of course, through explanation.
Surely, intellect is presupposed/required.

translated by Dr. Georg Galeczki (Cologne/Germany)

© HILLE 1996-2001

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