The development of the distinction between formal and material consequence in medieval logic

Jacob Archambault (Fordham University)

19 Feb, 2pm, LH 302.

The idea of a conclusion following formally from a set of premises is central to our conception of logic today: logical consequence is often taken for the subject matter of logic, and ‘formal consequence’ and ‘logical consequence’ are routinely taken as synonyms. It would come as a surprise, then, to know that consequences generally and formal consequence in particular did not always hold this place of prominence: the first treatises specifically devoted to the study of consequences did not appear until the beginning of the fourteenth century – over 1600 years after the death of Aristotle; and the notion of formal consequence didn’t begin to take a shape resembling its modern successor until nearly a half century after these treatises appeared.
Prior to the later nineteenth century, the main developments of the concept of formal consequence as we know it occur in the following stages:

  1. The application of the form/matter distinction to logic;
  2. The earliest implicit appeals to a distinction between formal and material consequence;
  3. The appearance of the earliest treatises on consequences;
  4. The appearance of the first systematic attempts to parse a distinction between formal and material consequence;
  5. The identification of formal consequences with those holding for all permutations of categorematic terms;
  6. The identification of formal consequence with logical consequence;
  7. The identification of logical consequence as the subject matter of logic.

All but the first and last of these developments occur in a period of intense logical activity stretching from about 1285 to 1341, just over half a century. This talk provides an overview of the developments of this period. I begin with an outline of the topical tradition on which earlier treatises on consequences depended. Next, I detail the account of John Buridan, whose distinction between formal and material consequences is more familiar than others, both because it has been better researched and because of its basic similarity to modern model-theoretic accounts. From here, I move backward to the previous developments Buridan’s account relies on and engages with, particularly those of William of Ockham and Walter Burley.