The term ‘possible’, in Aristotle's view, is ambiguous. It has two senses, known as one-sided possibility and two-sided possibility (or contingency). Being two-sided possible means being neither impossible nor necessary, and being one-sided possible simply means being not impossible. Aristotle defines the two senses in Prior Analytics 1.13 (32a18–21). This definition is followed by a controversial passage which states several equivalences between modal expressions (32a21–28). It is often thought that this passage is spurious and should be excised even though it is found in all manuscripts. I argue that the passage is not spurious, but contains a coherent argument justifying the one-sided sense of ‘possible’ (Section 1). This argument follows a pattern of proof explained by Aristotle elsewhere in the Prior Analytics and De caelo (Section 2). Moreover, it is closely related to a similar argument concerning one-sided possibility in De interpretatione 13 (Section 3). Examining this latter argument will help us better understand the controversial passage in Prior Analytics 1.13 (Section 4).

The Problematic Passage

At the beginning of Prior Analytics 1.13, Aristotle introduces the two senses of ‘possible’ as follows:

In point [i] of this passage, Aristotle characterizes two-sided possibility. Something is two-sided possible just in case it is not necessary and nothing impossible results from putting it as being the case. This characterization involves the term ‘impossible’. Unlike ‘possible’, ‘impossible’ is not ambiguous in the Prior Analytics but is consistently used in the sense of ‘not one-sided possible’ as opposed to ‘not two-sided possible’. Aristotle takes the condition that nothing impossible results from putting X as being the case to be equivalent to the condition that X is not impossible. Thus, he holds that something is two-sided possible just in case it is neither necessary nor impossible.

In point [ii] of the passage, Aristotle turns to one-sided possibility. He does not offer an explicit definition of one-sided possibility, but characterizes it by pointing out the specific case of application that distinguishes it from two-sided possibility.