Ontological Assumptions Structuralistic Approach for the Axiomatization of Non-relativistic Point Mechanics

Abstract

In the article different ontological assumptions for two fundamentally different approaches for the axiomatizaton of non-relativistic point mechanics are discussed. The first approach, thatwe call KSA-axiomatization, non-definability mass in kinematical language is simply takenas the essential feature in the definition of theorecity, while the second, that we call SSA-aximatization, leads to a mathematically exact and satisfactory definition of this function. We would like to resolve the apparent contradiction by demonstrating that in the background of both kinds of axiomatizations diffrent ontologies are operative. The main difference between SSA axiom system and KSA-system is that SSA characterize a mechanical system by its set S of possible motions and not just by one single motion, as was done KSA. This means that SSA-system employ a much more powerful and richer language than KSA-system, and, for this reason, it is able to define concepts that are not definable in more austere axiomatizations. But in other words ᾿sets of possible motion᾽ is something one would not accept in a purely extensional language. Then the two different attitudes lead to two different approaches to mechanics. On the other side the definability of mass in kinematical language is founded in the ground of the realism about possible worlds and rather seems to be a theoretical achievement, and then we can strenghten the realism about possible worlds.