The present paper is an attempt to clear up some of the problems involved in the traditional theory of analogy as presented by the Thomistic school. The two main ideas behind the formal developments offered here are (1) analogy is an important discovery, worthy of a thorough examination and further development, (2) contemporary mathematical logic supplies excellent tools for such work. This paper is, as far as the author knows, the first of its kind¹; it deals with a difficult subject in a sketchy way; what it contains is, therefore, not meant to be definitive truths, but rather proposals for discussion.