: Metaphysics B considers two sets of views that hypostatize mathematicals. Aristotle discusses the first in his B.2 treatment of aporia 5, and the second in his B.5 treatment of aporia 12. The former has attracted considerable attention; the latter has not. I show that aporia 12 is more significant than the literature suggests, and specifically that it is directly addressed in M.2 – an indication of its importance. There is an immediate problem: Aristotle spends most of M.2 refuting the (...) view that mathematicals are separate; but the B.5 mathematicals are inherent. I argue that the B.5 inherence is compatible with the M.2 separateness, and further, that aporia 12 is more than just a puzzle about the hypostatization of mathematicals. It is also a puzzle about the ontological status of mathematicals relative to sensibles. (shrink)

This paper examines Aristotle’s notion of priority with the specific aim of capturing the sort of priority that characterizes the primacy of substances in his metaphysics. I reject the traditional interpretation, which understands the ontological priority of substances in terms of independent existence. But there are rather two sorts of priority: the ontological priority of substances should be understood in terms of completeness, whereas the ontological priority of “substances-of-something” (the essences) is a causal-explanatory priority. Furthermore, an important piece of Aristotle’s (...) argument against Platonism is that these two sorts of priority – namely, the completeness priority and the causal-explanatory priority – should be kept distinct. (shrink)

Eu examino cada meandro do esforço de Aristóteles identificar vários usos de termos filosóficos essenciais em sua Metafísica, V.9-17.

Ontological separation plays a key role in Aristotle’s metaphysical project: substances alone are ontologically χωριστόν. The standard view identifies Aristotelian ontological separation with ontological independence, so that ontological separation is a non-symmetric relation. I argue that there is strong textual evidence that Aristotle employs an asymmetric notion of separation in the Metaphysics—one that involves the dependence of other entities on the independent entity. I argue that this notion allows Aristotle to prevent the proliferation of substance-kinds and thus to secure the (...) unity of his metaphysical system. (shrink)

Books M and N of Aristotle's Metaphysics receive relatively little careful attention. Even scholars who give detailed analyses of the arguments in M-N dismiss many of them as hopelessly flawed and biased, and find Aristotle's critique to be riddled with mistakes and question-begging. This assessment of the quality of Aristotle's critique of his predecessors (and of the Platonists in particular), is widespread. The series of arguments in M 2 (1077a14-b11) that targets separate mathematical objects is the subject of particularly strong (...) criticism by Annas and Ross. Two related arguments in this series (1077a14-20 and 1077a24-31) will serve as cases in point. The principal charges made against these arguments (that Aristotle misunderstands or misrepresents his opponents' views, and that he engages in question-begging because he presupposes his own metaphysical views) are frequently made against Aristotle's critique of Platonist positions more generally. If, as I argue, these charges are false for our two test case arguments, then there is good reason to think that they might also be false when they are leveled against the other arguments in this M 2 series. And, although presenting an argument for this is beyond the scope of this paper, this suggests that these two charges are more often than not false when applied to Aristotle's critique of Platonist mathematical views in M-N and beyond. (shrink)

Aristotle is often taken to define priority in being in Metaphysics Δ.11, where he says that those things are prior in being which “admit of being without other things, while these others cannot be without them: a division which Plato used” (1019a3-4). But Aristotle’s pattern of arguments about priority – some of which use Plato’s Test and others of which use distinct, causal tests – looks puzzling if Plato’s Test is his definition. This paper offers a new interpretation of Δ.11 (...) on which it offers a guide to the Aristotelian use of Plato’s Test, given that being is said in many ways, rather than endorsing it as Aristotle’s own definition of priority. This reading illuminates Aristotle’s pattern of arguments in the corpus – explaining why Aristotle uses Plato’s Test in some cases and departs from it in others – and suggests a plausible story about how these arguments were shaped by engaging with Plato. (shrink)

In Metaphysics Λ7 1072b30–1073a3, Aristotle introduces a Speusippean theory according to which ‘what is most beautiful and best is not en archēi’. Through a detailed analysis of the passage, I argue that Aristotle’s refutation of Speusippus’ thesis is favoured by the introduction of the seed example, which conflates both ontological and temporal priority. The elements gathered from the analysis of Aristotle’s polemical strategy will support a broader conclusion: Speusippus’ reason not to characterise his principle(s) as (the) good is related to (...) the problematic relationship Forms and sensibles had within Plato’s account, or, in other words, participation. (shrink)