- Treatise on Consequences by John Buridan
John Buridan was the greatest of the medieval logicians. His massive logical text, the Summulae de Dialectica, has been available in a first rate English translation for well over a decade. Now it is joined by his other major logical work, the Treatise on Consequences. The translation provided here runs about a hundred pages. Chapters 1 and 3 concern consequences involving non-modal propositions, and chapters 2 and 4 concern modals. Buridan is a very clear writer, and Read has provided a translation that is both accurate and readable. The book has a helpful introduction.
A consequence is a proposition in conditional form such that (roughly) things cannot be as its antecedent signifies without also being as its consequent signifies. It is formal if changing its terms to others always yields a consequence. A (good) syllogism is a kind of formal consequence whose antecedent is a conjunction.
On Buridan’s account, consequences obey principles that will be familiar to current logicians. For example, “From every impossible proposition any other follows [as a consequence] and every necessary proposition follows [as a consequence] from any other” (75).
Syllogistic: Aristotle’s syllogistic is based on the dictum of All and None: “Whatever is predicated of (denied of) all of a whole is predicated of (denied of) each of its members.” Buridan adds a two-part principle he considers equally fundamental: “Whatever are the same as one and the same are the same as each other,” and “Two things are not the same as each other if one is the same as something and the other is not.” (This principle appears widely in logic texts in the next few centuries, but it drops out in the 1800s.) He then develops some general “principles of distribution” which may have been original with him, and which have been widely applied in expositions of syllogistic up to and including the present day. The first distribution principle is that the middle term in a syllogism must be distributed in at least one premise; if this does not hold, the syllogism is not valid. He argues for this as follows: If C is not distributed in either premise, then the premises only entail that some C be the same as (or different from) an A, and another C be the same as (or different from) a B. In this case the basic criterion above does not apply, and the purported syllogism is not valid. The other distribution principle is that a term that is not distributed in a premise cannot be distributed in the conclusion of a valid syllogism. This is argued in chapter 1 to hold for single-premised arguments, based on a discussion of the causes of the truth of propositions. That conclusion is carried over in chapter 3 to the two-premise case, using reasoning that is not clear to this reviewer.
Modals: Following tradition, Buridan distinguishes between composite and divided modal propositions. A proposition is composite when a modal word applies to the rest, as in “Possibly some horse is running.” This has what we call the de dicto reading; it attributes possibility to a proposition. A proposition is divided when the modal word comes in between the parts, as in “Some horse possibly is running”; this yields something like our de re reading, except that the modal word ampliates the subject, yielding a reading something like “Some actual-or-possible-horse is a possible-runner.” This ampliation yields readings that differ from [End Page 163] what we take for granted today. For example, “Some B is necessarily A” does not entail “Some B is A” because the former can be true if some possible B is a necessary A even if there are no actual B’s. The result of ampliation is typically a proposition with the same overall form as a non-modal proposition of the form “Some F is a G.” This results in a theory in which (divided) modal propositions are subject to all of the...