Abstract

Theories which born during interior development of mathematics later obtain empirical interpretation and become a part of applied science. The reasons for this are still not clear, although many mathematicians and philosophers put forward their hypotheses. We believe that solution the problem should involve investigation of mathematics as a sort of evolving system. Two systems may be subordinated; that is, if the first one is a primary and fundamental one, then the other one is secondary and adjusted to the first. We propose that substantial sciences are primary and formal sciences are secondary. There are reasons to think that mathematics in its interior development has intention to physics. Secondary system may have changes of two sorts: those which are requested by the primary system, and those which are free of the requests of the primary system. Analyzing biological systems we see that interior changes of the system, which are not caused by its current needs, are determined by its further purposes. Each living system carries a “model of future” in itself, and it tends to this future by its free changes. We think that the living systems development logic may be transferred to conceptual systems, also. If we consider mathematics as a conceptual system which is secondary in relation to physics, then we receive a natural explanation of the possibility of mathematical anticipation.