Event: Larwill Lecture in Philosophy: Graham Priest

Date: February 25th 2013

Location: Higley Auditorium

Correspondent: Andrew Stewart

Professor Graham Priest of the University of Melbourne and the CUNY Graduate Center visited Kenyon this week, giving a Philosophy Department Larwill Lecture. His visit, significantly hyped in philosophy and math circles here at Kenyon, did not disappoint.

Priest is well-known (and infamous) for his work in paraconsistent logic. Such systems oppose the “explosive” theory of logic, which is associated with the so-called “classical” (early-20th century) logic currently taught in textbooks. According to the explosive theory, say that some contradiction, “A and not-A,” is true. Using the rules of classical logic, one can use this premise to prove any proposition at all, including that the world is round, the world is flat, and 3+4=128. Consequently, classical logicians feel they have good reason to avoid contradictions at all costs. Paraconsistent systems of logic oppose the explosive theory. Within such systems, it is not the case that any old contradiction can be used to prove absolutely anything. In a typical paraconsistent system, propositions have one of three truth-values: “True,” “False,” or “True and False.” Yes, you read me right: there are systems of logic that actually allow (some) contradictions.

Considering Priest advocates a departure from classical logic that is, at least at first glance, so radical, it is not surprising that Priest’s lecture topic was “Revising Logic.” He began his talk by reassuring the audience that there would be “no squiggles involved” and that no background in formal logic was necessary to understand what he had to say. This was a talk in the philosophy of logic, not logic proper. He kept his promise: there were no squiggles! Nevertheless, a bit more background in epistemology and semantics would have been helpful for understanding his finer points, as some of his concluding arguments went a bit over my head.

A common move in contemporary debates on logic is to claim that logic cannot be revised. Priest argued that revision has happened in the past and continues to be possible. He discussed the potential for revision in three different types of logic: logica docens (what is taught in logic textbooks), logica utens (what we actually use), and logica ens (logic in itself: the “truth” about logic). Priest’s first contention was that Western logic has, in fact, changed a great deal over time, particularly during chunks of activity in ancient Greece, the Middle Ages, and the early 20th century. The concept of explosion, for example, does not go all the way back the ancient Greeks: it was first articulated during the Middle Ages, neglected, and then rediscovered in the 20th century.

Priest argued that many past revisions to logics extended their application and relevance. For future revisions to be rational, logicians should remember that a given logica docens is essentially a theory to compare to other logics. Changes ought to be based on criteria such as unifying power, adequacy to data, and simplicity. As for logica utens–the use of logic–it should stay in line as much as possible with the theory provided by logica docens. Some particular situations, though, might call for use of a slightly different logic for practical reasons. As for logica ens, or the truth of logic, Priest claimed that it might be revisable, or perhaps not, depending on one’s standard for what constitutes validity.

I would imagine that lectures on logic have a tendency to become dry, but Priest’s talk was both accessible and captivating. He was enthusiastic, articulate, and relaxed. Rather than doing injustice to intricate issues by trying to provide all of the answers in a short time, he presented an appropriate amount of material, leaving many questions open. Though his talk was fairly general and did not get into the details of alternative logics, I think his topic is critical to a clearer understanding of academic discourse. Very often, we think of logic as a set of unchanging rules to which one must appeal to produce a valid argument. The notion that there can be revision and progress in logic might change the relationship of other disciplines to it. Revision also reveals that the particular discipline of logic has just as much of a demand for innovation as other fields. More broadly, revision might also challenge certain things we thought we could take for granted about the connections between language, mathematics, and the structure of the universe. Or maybe not. Or maybe both.