Ontic Indeterminacy and Change in Ancient Metaphysics: Plato and Aristotle

My aim is to present and discuss the ancient idea that some specific objects within the ontology are indeterminate or indefinite ‘beings’ (the inverted commas are important here since ancient philosophers draw a sharp distinction between being and becoming), namely those in motion or in process of changing. The view was held, albeit in quite different ways, by Heraclitus (and, maybe, by alleged or so-called proponents of Heraclitus’ theory of flux as Protagoras or, but it is also a vexed question, as the Cyrenaics), Pythagoreans, Plato and Aristotle. I shall expound their positions in turn with an emphasis on Plato and Aristotle (roughly: Plato’s kinematical passages in the Parmenides leaves open the possibility that there are objects that only partially participate in the idea of Being, whereas, for Aristotle, an object can have properties by degree and, more famously, objects in motion are neither completely virtual nor fully actual in all respects, see Physics, 3.1-3 and Metaphysics, K.9). Obviously, such an idea – moving objects are indefinite entities (at least in some respects) – clashes with the Parmenidean ideology, for the Eleatic stance claims, first, that being is not a qualification which admits degree or indefiniteness, and, second, that nothing changes or moves. I will reconstruct the discussion between Parmenidean zealots and their opponents by putting together these two lines of thought: the Eleatics support the denial of change because being is always determinate (remind the Eleatic challenge that things cannot go in and out of being, given that something can come-to-be neither from what is already nor from nothing, and the Megarian view in Metaphysics, Θ.3), while the other philosophers (Heraclitus, Pythagoreans, Plato, Aristotle) argue that change is real and, consequently, that there are indeterminate beings within the natural world. Such a discussion will drive us from metaphysics to logic with some closing remarks on the Principle of Non-Contradiction (PNC), change and indeterminacy (in fact to some remarks about the PNC and its companion, at least in classical and ancient logics, the Principle of Excluded-Middle (PEM) for indeterminacy can be understood either as underdeterminacy – for a predicate X, an item is neither determinately X nor determinately not-X – or as overdeterminacy – for a predicate X, an item is both determinately X and determinately not-X, see Aristotle’s Metaphysics, Γ.4-8 for such a difference in a discussion of PNC and PEM: according to Aristotle and classical logic, the rejection of the first leads to trivialism – Heraclitus’ processualism –, the denial of the second to nihilism – Anaxagoras’ mixture as interpreted in Metaphysics, Γ.7 –, that is, to two very different kinds of ontological indeterminacy). Indeed, on the one hand, the Parmenidean commitment to the truth of the Principle of Non-Contradiction grounds the Eleatic changeless worldview; and, on the other hand, following Plato’s Theaetetus, Aristotle explicitly argues that it is a commonplace view that Heraclitus’ theory of flux (everything is always changing in every respect) entails the denial of the Principle of Non-Contradiction which itself entails ontological indeterminacy (Metaphysics, Γ.5 1010a7-b1, cf. Theaetetus, 182c-e and Cratylus, 439d-e + Priest 1995: 12-17). However, equipped with his account of change as ‘actuality of what is virtually-X insofar as it is virtually-X’, Aristotle is able both to break these entailments (that is, to keep the truth of the Principle of Non-Contradiction in a restless world) and to explain what means to be indeterminate for an item in motion (that is, to make ontological indeterminacy understandable and intelligible: roughly, Aristotle does that by equating ‘to be indeterminately-X’ and ‘to be virtually-X’) without falling in Heraclitus’ deeply inconsistent and indeterminate abysses. To sum up, my paper will move from metaphysics (change and indeterminacy) to logic (Principle of Non-Contradiction, change, and indeterminacy, in that order) by means of meta-ontology (definiteness/indefiniteness of being, indeterminacy, and change, in that order) in order to better understand the commonplace idea in ancient philosophy that change implies indeterminacy.