 In Metaphysics 4.4, Aristotle notes that some people consider it possible for the same thing to be and not to be, and for someone to believe so (he refers to a range of positions, all of which in some way are related to denial of the Principle of Non-Contradiction; see Castagnoli 2010, I.5.4). Against this, Aristotle says it is the firmest of principles that things cannot be and not be at the same time. To deny this shows a lack of training. With adequate training, one recognizes for which things proof should be sought, and for which it ought not to be sought (see also An. Post. I.3). It is impossible that there be demonstration for everything. Otherwise demonstration would go on ad infinitum. Scholars often refer to this point when discussing the skeptical modes of argument. The skeptics might be guilty of what, from Aristotle’s perspective, would be a mistake of exactly this kind (on this theme in later Aristotelian logic, cf. Malink 2020).