Oxford Studies in Ancient Philosophy, Volume 61 by Victor Caston;

Author:Victor Caston; [Caston, Victor]
Language: eng
Format: epub
ISBN: 9780192688354
Publisher: Oxford University Press USA
Published: 2022-08-02T00:00:00+00:00

6. Problems for the parts interpretation

6.1. Weakness of motivations

As we have seen, the parts interpretation’s principal motivation is the tension between (i) Aristotle’s supposed rejection of Inherent Properties and commitment to Imprecision in Metaphysics Β. 2 and (ii) his claims elsewhere that geometrical objects belong somehow to the sensible realm.

But as with most of the aporiai Aristotle raises, his Book Β treatment simply describes the difficulty as it currently stands and problematizes certain positions but does not yet develop a solution. Thus, Β. 2 taken on its own will not allow us to determine whether Aristotle really (i) rejects Inherent Properties and endorses Imprecision.100 It must rather be taken together with Aristotle’s resolution of this part of the fifth aporia—a resolution we do not come to until Metaphysics Μ. 3. And when we consider Β. 2 and Μ. 3 together, the supposed tension motivating the parts interpretation disappears.

In Μ. 3, Aristotle resolves the aporia by employing a familiar strategy: he introduces a distinction that allows him to accept a qualified version of one claim (Imprecision) that is compatible with the other (Inherent Properties). In this case he distinguishes between sensible magnitudes qua sensible (ᾗ αἰσθητά) and sensible magnitudes just insofar as they have a certain quality or attribute (μὴ ᾗ αἰσθητὰ ἀλλ’ ᾗ τοιαδί, 1077b20–2)—as we have seen in Section 3.3. Further, he claims that there can be propositions and demonstrations (λόγοι καὶ ἀποδείξεις) that are still about sensible magnitudes (περὶ τῶν αἰσθητῶν μεγεθῶν) even when they are about them not as sensible.101 This distinction allows him to resolve the aporia by limiting the scope of Imprecision: insofar as they are sensible, sensible objects (and specifically sensible magnitudes) are imprecise and so cannot be what mathematical statements are about; but insofar as they have (that is, really have) mathematical properties, certain sensible objects are adequate to the task. That is, Aristotle distinguishes between:

Thoroughgoing Imprecision: Sensible objects are imprecise, while geometrical statements and theorems are about perfectly precise objects; hence, sensible things cannot be the objects of geometry in any respect.

Sensible Imprecision: Sensible objects qua sensible are imprecise, while geometrical statements and theorems are about perfectly precise objects; hence, sensible things qua sensible cannot be the objects of geometry.

Aristotle rejects Thoroughgoing Imprecision but accepts Sensible Imprecision: while sensible objects fail to be perfectly precise qua sensible,102 in a different respect—qua quantitative and continuous, but not qua sensible—certain sensibles are parent subjects for kooky objects that are precise and so adequate.

But this immediately raises a new question: which sensible objects—even not qua sensible—could possibly be adequate to the task? Since Aristotle aims to explain how it is that geometers speak rightly (Μ. 3, 1078a29), and geometers often make statements about the precise construction drawings they produce in the course of their research, it would have been natural for him to identify these construction drawings as the special sensible objects of the geometer. This is especially likely given that Aristotle would have directly observed the strong practical, banausic element of geometrical practice.103 If

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