In order to make reliable predictions in any region of human activity, it is necessary to distinguish clearly what is based on experience and what is a construction of intellect. The theory of knowledge developed in the present paper is an attempt to devise a set of axioms that demarcate experience, as the only source of our knowledge of the external world, from the ideas, scientific models, and theories by means of which the scientific predictions are made. After a discussion of the causality in relation to the laws of nature, the axioms of the expounded theory are formulated in the formalism of set theory. The theory is then applied to some problems in physics to demonstrate its usefulness.