Two weeks ago, I wrote about Ex impossibili sequitur quidlibet in the 12th C. Today, I come back to one of the promises there, namely, to look at part of Joke Spruyt’s “Thirteenth-Century Positions on the Rule ‘Ex Impossibili Sequitur Quidlibet‘”, in K. Jacobi, Argumentationstheorie (Brill): 161-193.
At the time of Spruyt’s writing, “not much attention [had] been paid to the thirteenth-century conceptions of the validity of consequences” (p. 161). (Since then, this has certainly changed, most notably with Catarina Dutilh Novaes’s Formalizing Medieval Logical Theories.) Looking at the Ex impossibili rule is one way to discern the specifics of various conceptions of validity in the 13th century.
The most basic definition of validity, in which “the antecedent cannot be true without the consequent” (p. 161), has Ex impossibili as an immediate consequence. But this can be accepted either as “the ultimate criterion for evaluating a consequence, or merely as one of the criteria that accompany other, equally important ones” (p. 162), and this is because this most basic definition can be specified in a variety of ways, and in particular depending on how consequences and conditional sentences are defined and distinguished from each other. One point of agreement amongst most 13th-century was that both conditionals and consequences express some sort of relationship between antecedent and consequent (p. 162); the nature of this relationship was a point of disagreement. Two common interpretations were that the relationship was one of causation or one of inclusion. If the relationship between the antecedent and the consequent is one of causation, the opponent of Ex impossibili can argue that “the impossible is nothing and thus cannot cause anything” (p. 162), in which case the rule must be rejected. The proponent of the rule, on the other hand “does not describe consequences in terms of a relationship between beings” (p. 163), but it is not clear to me how this still counts as a causal account of consequences or how it addresses the objection of the opponents. (Maybe if the relationship doesn’t relate beings but something else, then the impossible is something that can fall under that something else?).
13th-century discussions of the syncategorematic term si ‘if’ often included a variant of the question “Whether from the impossible anything follows”. Spruyt notes one exception, Roger Bacon’s treatise on syncategorematic words written between 1230 and 1240 (p. 163), which does not mention the rule at all. She argues, following Braakhuis, that this is a result of Bacon following Priscian’s definition of si as “a continuing conjunction which signifies an ordering of res (p. 163); the relationship which this continuing conjunction indicates is the ordering of prior to posterior. Thus, “the mind grasps two complex res and is affected by the ordering between the two” (p. 163), and as a result of this ordering, a unity is formed (p. 164). Because there are no impossible res, they cannot be related to anything to form a unity. (The relationship that is expressed by si is distinguished from that expressed by ergo. Ergo has the force of assertion, making the antecedent certain, while si lacks this force (p. 164).)
The rule is discussed extensively in an anonymous Distinctiones treatise from the first decade of the 13th century, where “it is presented as a rule defended by the nominales and rejected by the reales” (p. 165). The author himself follows the reales. Spruyt highlights one argument he gives against an argument in favor of the principle:
the conditional sentence ‘If Sortes is an ass, Sortes is a goat’ is true because (in virtue of the locus a parte disiunctiva) the conditional ‘If Sortes is an ass, Sortes is an ass or a goat’ is true. Now Sortes is not an ass, therefore he is a goat. So taking it from the beginning: ‘If Sortes is an ass, he is a goat’ (pp. 165-166).
The anonymous author rejects this inference as invalid because “two opposite species cannot be united in one and the same subject” (p. 166). So when it is posited that Sortes is an ass, this immediately denies that he is a goat.
The author must then modify the definition of validity in order to be able to exclude Ex impossibili:
In his opinion, the definition of a true conditional is meant to cover only those conditionals that contain an antecedent that, while not necessarily being true, is at least such that it can be true (p. 167).
Of course, such a modification directly blocks Ex impossibili, but it is also not a very satisfying one!
Spruyt’s article continues by looking at the positions in the Sophistaria wrongly attributed to Walter Burley, Peter of Spain’s Syncategoremata, and Henry of Ghent’s Syncategoremata, all of whom are opponents of the view. Then comes a section on the proponents, including Nicholas of Paris, Matthew of Orléans, and John le Page. We’ll cover these in another post (or two)!