In Post. Anal. A4, Aristotle enumerates four Kinds of "Per Se" which designate four kinds of necessity between subject and predicate. Many commentators exclude the last two "Per Se" from their concern as irrelevant to Aristotle's inquiry of the demonstrative theory. I think, however, that, as far as a necessary S-P relation, all four kinds of "Per Se" are, for Aristotle, indispensable to his theory of demonstration. In this paper, I try to investigate his true thought when he manifests four "Per Se" and to show the principal role of each of the last "neglected" two as follows. 1. implies tautological necessity which we acquire from the linguistical point of view. This must be relevant for positing a genus which each science has as its domain. 2. implies causal necessity such as is valid, in fields of nonmathematical sciences.