Programme
Stephen Read
University of St Andrews
“Everything True Will Be False”: Paul of Venice’s Two Solutions to Insolubles
In his Quadratura, Paul of Venice considers a sophism involving time and tense which appears to show that there is a valid inference which is also invalid. His argument runs as follows: consider the inference concerning some proposition A: A will signify only that everything true will be false, so A will be false. Call this inference B. Then B is valid because the opposite of its conclusion is incompatible with its premise. In accordance with the standard doctrine of ampliation, Paul takes A to be equivalent to ‘Everything that is or will be true will be false’. But he proceeds to argue that it is possible that B’s premise (‘A will signify only that everything true will be false’) could be true and its conclusion false, so B is not only valid but also invalid. Thus A is the basis of an insoluble. Throughout the fourteenth century, many solutions to the insolubles claimed that insolubles had an additional implicit signification which rendered them false. For example, Bradwardine argued that any proposition signifying its own falsehood also signified (implicitly) its own truth; Heytesbury, that there must be a hidden meaning to insolubles, but its exact nature need not be identified; John of Holland and John Hunter, along with a set of teaching modules at Oxford (the Logica Oxoniensis), otherwise following Heytesbury’s diagnosis, that the additional meaning is indeed an assertion of the insoluble’s truth; Rimini and Ailly, respectively, that insolubles involve a clash, or equivocation, involving an additional mental proposition asserting the falsehood of another; Buridan and Albert of Saxony that in fact all propositions assert or at least imply their own truth. Swyneshed was one of the few standing out against this “multiple-meanings” approach in offering a solution that took insolubles at face value, meaning no more than is explicit in what they say: insolubles imply their own falsity, and in so falsifying themselves, are false. In the treatise on insolubles in his Logica Magna, and in the final sophism of his Sophismata, drawn from it, Paul develops and endorses Swyneshed’s solution, with its familiar radical consequences, such as the claim that a valid inference can have true premises and false conclusion. In his Logica Parva and in the Quadratura, self-confessedly elementary texts aimed at students and not necessarily representing his own view, Paul follows the Logica Oxoniensis in identifying an implicit assertion of its own truth in insolubles like A. We consider how both types of solution apply to A and how they complement each other. On both, B is valid. But on one (following Swyneshed), B has true premises and false conclusion, and contradictories can be false together; on the other (following the Logica Oxoniensis), the counterexample is rejected.