Cassatio, part 1

In March, a group of us met every Friday to read through Paul of Venice’s treatise on insolubles. During discussion one morning, the cassatio solution came up, and I realized how very little I knew of it. During the meeting, I remember briefly looking some things up, and then filing this away under “maybe I’ll write blog post on it sometime”.

The other day, I came across a paper by Laurence Goldstein, “Fibonacci, yablo, and the Cassationist Approach to Paradox”, Mind 115, no. 460 (2006): 867-890, which had this fascinating claim in the abstract:

The solution to the semantical paradoxes offered here revises the mediaeval cassatio appraoch, one that largely disappeared due to its incomprehending rejection by influential contemporary writers such as William Shyreswood and Thomas Bradwardine (p. 867).

Three immediate points upon reading this: (1) Sherwood and Bradwardine weren’t contemporaries, really. (2) I knew Bradwardine discussed cassatio but hadn’t realized Sherwood had, in fact, I thought Sherwood’s discussion of sophistical reasoning was relatively Aristotelian, but it’s been a long time since I’ve read that chapter of the Introductiones. (3) This makes it sound like cassatio was a viable and wide-spread account prior to its rejection by Sherwood, Bradwardine, and others; but what I remember of the little I found looking things up during the reading group was that cassatio was a view many people love to reject but few espouse.

Goldstein mentions Sherwood in one other place in his paper:

All of these paradoxes belong together in a family and, if the cassationist solution is good for one, it ought to be good for all. (‘Cassatio’ is the name of a proposed solution, popular in the early mediaeval period that was dismissed by influential authors such as William Shyreswood and Thomas Bradwardine (whose writings give no indication that they had given the view the serious attention that it merits). As P. V. Spade (1987) has documented, the proposed solution had virtually died out by the first quarter of the thirteenth century. According to the cassantes, attempted uses of paradoxical sentences to make statements are nullified, so that, although such sentences have meaning, no proposition or content gets to be expressed by them, and hence they lack truth-value (p. 880).

No explicit reference to the rejection by Sherwood or Bradwardine is given, and I suspect Goldstein didn’t look at the original medieval texts but relied on Spade (his ‘Five Early Theories in the Mediaeval Insolubilia-Literature’, Vivarium 25 (1987): 24-46). There is no discussion of cassatio in either the Introduction to Logic or the Syncategoremata — while the former discusses sophistical reasoning, neither the Liar paradox nor solutions to it feature in it. So the likely source for Sherwood’s views on cassatio is the treatise De insolubilibus in Paris Lat. MS 16.617; it is in this MS that the Introductiones and the Syncategoremata are preserved, but the treatise on insolubles is not explicitly attributed to him there.

That’s as far as I’ve gotten for part 1 of this discussion, more to come in the future.