Logic as the Foundation of Knowledge

Ockham distinguishes three levels of language: mental, spoken, and written. Mental language is the most fundamental — it is the system of concepts by which the mind thinks, and it is the same in all human beings regardless of what spoken language they use. Spoken language is conventional: it consists of sounds that mean what they mean by social agreement. Written language is doubly conventional: it represents spoken sounds, which represent mental concepts. This hierarchy has consequences: misunderstandings due to ambiguous spoken or written terms can always in principle be resolved by returning to the mental term they are supposed to express.

One of the most technically sophisticated parts of the Summa Logicae is its theory of supposition: the study of what terms refer to in different contexts. A term in a proposition can "stand for" its significate in different ways. "Personal supposition" is when a term stands for the individual things it signifies (in "A man is running," the term "man" stands for a particular man). "Simple supposition" is when a term stands for the concept itself ("Man is a species"). "Material supposition" is when a term stands for itself as a word ("Man is a monosyllable"). Confusion between these modes of supposition, Ockham argues, is the source of many apparent metaphysical puzzles — including the puzzle of universals.

Ockham treats logic as a discipline complete in itself — not dependent on metaphysics for its foundations, as some of his predecessors had maintained. The principles of inference are not grounded in the structure of reality but in the structure of mental language itself. This positions logic as prior to and independent of ontology: we can determine what follows from what without first settling what kinds of things exist. This independence is important for Ockham's larger project: it allows him to accept nominalism about universals without any threat to the validity of the logical syllogisms that use universal terms.

The Summa Logicae was one of the most read logic texts of the fourteenth and fifteenth centuries and was printed repeatedly after the invention of the printing press. Its account of supposition theory and its defence of nominalism against realism shaped the "via moderna" (the modern way) — the nominalist tradition in late medieval university philosophy that included Gabriel Biel, Jean Buridan, and others.