Hypothetical Syllogisms and Infinite Regress

In his commentary on Aristotle’s De interpretatione, Ammonius puts forward an argument for the priority of categorical over hypothetical syllogisms. The argument relies on two of the Five Modes of Agrippa, the modes from infinite regress and from hypothesis. Much of the argument, however, remains unclear and open to doubt. The present chapter sheds new light on the argument by considering it against the backdrop of two related arguments given by Pseudo-Ammonius and Alexander of Aphrodisias in their commentaries on the Prior Analytics. The chapter argues that all three arguments originate in Theophrastus’ discussion of Aristotle’s treatment of syllogisms from a hypothesis. They rely on the view that stating a hypothetical proposition If P, then Q does not amount to the unqualified assertion of a conditional proposition, but rather to a conditional assertion of Q on the supposition that P.

Conditional Propositions and Conditional Assertions

A comparison of accounts of indicative conditional statements that treat them as a distinctive kind of conditional speech act—qualified assertion of the consequent qualified by the supposition of the antecedent—and accounts that treat them as unqualified assertions of propositions that are a function of antecedent and consequent. The aim is to reconcile the two accounts by making them precise in a common pragmatic framework, and showing that the former can be seen to be equivalent to a limiting case of the latter. It is argued that this way of representing the conditional assertion account helps to explain the relation between indicative and subjunctive conditionals.

A Theory of Conditional Assertion

According to one tradition, uttering an indicative conditional involves performing a special sort of speech act: a conditional assertion. We introduce a formal framework that models this speech act. Using this framework, we show that any theory of conditional assertion validates several inferences in the logic of conditionals, including the False Antecedent inference (that not A implies if A, then C). Next, we determine the space of truth-conditional semantics for conditionals consistent with conditional assertion. The truth value of any such conditional is settled whenever the antecedent is false, and whenever the antecedent is true and the consequent is false. Then, we consider the space of dynamic meanings consistent with the theory of conditional assertion. We develop a new family of dynamic conditional-assertion operators that combine a traditional test operator with an update operation.