I argue that, in the Prior Analytics, higher and above the well-known ‘reduction through impossibility’ of figures, Aristotle is resorting to a general procedure of demonstrating through impossibility in various contexts. This is shown from the analysis of the role of adunaton in conversions of premises and other demonstrations where modal or truth-value consistency is indirectly shown to be valid through impossibility. Following the meaning of impossible as ‘non-existent’, the system is also completed by rejecting any invalid combinations of terms (...) in deductions or conversions. The notion of impossibility reaches the core of Aristotle's system in the Prior Analytics. On the one hand, the use of adunaton shows that he is following one of the two requisites for demonstrative science formulated in the Posterior Analytics, i.e. to demonstrate that it is impossible for things to be otherwise than stated. On the other hand, that demonstrations through impossibility are rooted in the notion of contradiction supp.. (shrink)