TOWARD AN AXIOMATIC PREGEOMETRY OF SPACE-TIME

We present a deductive theory of space-time which is realistic, object ive, and relational. It is realistic because it assumes the existence of physical things endowed with concrete properties. It is objective b ecause it can be formulated without any reference to knowing subjects or sensorial fields. Finally, it is relational because it assumes that space-time is not a thing, but a complex of relations among things. I n this way, the original program of Leibniz is consummated, in the sen se that space is ultimately an order of coexistents, and time is an or der of successives. In this context, we show that the metric and topol ogical properties of Minkowskian space-time are reduced to relational properties of concrete things. We also sketch how our theory can be ex tended to encompass a Riemannian space-time.