On Finding Compactness in Aristotle

Jonathan Lear has suggested that Aristotle attempts to demonstrate a proof-theoretic analogue of a compactness theorem in Posterior analyticsI, chs. 19?22. Aristotle argues in these chapters that there cannot be in finite series of predications of terms. Lear's analysis of Aristotle's arguments are shown to be based on confusions about the nature of infinite orderings. Three distinct confusions are identified. In final remarks, it is suggested that a compactness claim is irrelevant to the issues which motivate Aristotle's arguments