If one had all the true particular statements that there are would such a collection be deficient for the purpose of science? In particular, would we still require a type of explanation that requires irreducible appeal to universals, and modalities. An argument to this conclusion is examined. In the situation envisaged, the realists needed distinctions such as between accidental and essential properties, or generalizations that are accidently true and those that are lawful and true, cannot be made. The argument then is rejected: appeal to universals, and the need for explanations td tell us what might have happened , cannot be secured when science no longer need discover the truth about the world. Particulars maintain their claim to epistemological and ontological priority over universals.

The following questions arising in connection with the géométrisation of modern physics are discussed: is the physical theory a bicomponent one (physical objects plus geometry) or everything can be reduced to space? Whether the hypothesis of the macroscopic nature of space and time deals with the theoretical or empirical structure of physical theory? Is there géométrisation of quanta or quantisation of geometry?

Science is a historically evolved and developed system, which does not include every construction. If a new construction is to become part of scientific knowledge, it must (1) fit into a certain paradigm (during the extensive growth of science) or meet the conformity princilple (during intensive growth) and (2) comply with certain general "rules of the game" (such as, e.g., the principle of repeatability, simplicity, etc., as well as "maxims" of the type "God is insidious but not rancorous"). These two aspects constitute the systemic principle, which thus works as a sort of a metaregulative.

The paper is concerned with three basic factors - the factor of historical determination, syetemic appropriateness and ontologico-gnoseological presuppositions which according to the view of the author determine the possibility and limits of mathematisation in science. This topic ia exemplified by an analysis of axiomatisation and quantification in the contemporary measurement theory.