Infinity, Continuity, and Composition: The Contribution of Gregory of Rimini
Cross, Richard (Oriel College, Oxford)
Medieval Philosophy and Theology 7 (1998)
Gregory of Rimini (1300–1358) occupies an important place in the fourteenth- century indivisibilist controversy, offering by far the most sophisticated accounts of both infinity and continuity to emerge from scholasticism. As is well known, Gregory holds that a continuum is composed of an actual infinity of parts.
Less well known, however, are Gregory’s motivations for accepting this view, and indeed how precisely he understands it. Gregory explicitly opposes two different but related views: that of the Aristotelians who claim that a continuum is composed of a potential infinity of divisible parts, and that of Henry of Harclay who claims that a continuum is composed of actually infinitely many indivisible points. As Gregory sees it, the views he opposes are united in their claim that, if a continuum is composed of actually infinitely many parts, then each part must be immediately adjacent to at least one and at most two other parts.