There occurs in Aristotle a thesis which is symbolised in I. M. Bocheński's La Logique de Théophraste, Chapter V, by the formula EMpMNp. We might read this as “It is possible that P (Mp) if and only if (E) it is possible that not P (MNp).” But as Bocheński explains, Aristotle is here using the word “possible” to mean, not merely “not impossible”, but “neither necessary nor impossible”. And if we take “ It is impossible that P” to mean “It is necessary that not P”, Aristotle's thesis seems evidently true. For “It is neither necessary nor impossible that P” (Mp) amounts to “It is not necessary that P, and it is not necessary that not P” (KNSpNSNp, where S is the symbol for “It is necessary that”); and “It is neither necessary nor impossible that not P” (MNp) amounts to “It is not necessary that not P, and it is not necessary that not not P” (KNSNpNSNNp); and this reduces easily to the other by the law of double negation (ENNpp) and the commutativeness of conjunction (EKpqKqp).

Despite the apparently unexceptionable character of this thesis EMpMNp, when properly understood, Bocheński informs us, in paragraph 42 of this chapter, that Łukasiewicz has shown that it “implies a contradiction”. He goes on to explain that what he means by this is that it follows from this thesis, together with the assumption that some propositions are “possible” in the Aristotelian sense, that any proposition whatever is “possible” (in that sense). And this, when one thinks what it means, is a most extraordinary contention.