It might seem quite commonplace to say that Aristotle identifies fire, air, water and earth as the στοιχεῖα, or ‘elements’ – or, to be more precise, as the elements of bodies that are subject to generation and corruption. Yet there is a tradition of interpretation, already evident in the work of the sixth-century commentator John Philoponus and widespread, indeed prevalent, today, according to which Aristotle does not really believe that fire, air, water and earth are truly elemental. The basic premise (...) of this interpretation is that Aristotle takes fire, air, water and earth to be, in some sense, composite bodies and, as such, analysable into simpler constituents. But, of course, an element of bodies is defined by Aristotle himself as something into which bodies can be analysed, and which does not admit further analysis . So if fire, air, water and earth can be analysed into simpler or more basic constituents, then it would seem to follow that the latter ought to be considered Aristotle's true elements. These are usually identified as the primary contraries hot and cold, dry and wet; many, perhaps most, commentators would insist also upon prime matter as the subject upon which these contraries act. (shrink)

Aristotelian ideas have in the past been applied with mixed fortunes to quantum mechanics. One of the most persistent criticisms is that Aristotle’s notions of potentiality and actuality are burdened with a teleological character long ago abandoned in the natural sciences. Recently this criticism has been met with a model of the actualization of quantum potentialities in light of Aristotle’s doctrine of ‘spontaneous events’. This presumably restores the nowadays acceptable idea of efficient causation in place of Aristotle’s original doctrine of (...) the ‘four causes’. In this article I challenge the model by arguing that when properly scrutinized Aristotle’s final cause poses no problems for an Aristotelian reading of quantum mechanics. Final causes in fact provide a better ontology for quantum mechanics than spontaneous causation. The idea of ‘spontaneity’ is unanalyzable and therefore of little use in quantum mechanics. In addition, it is ontologically sterile in the context of quantum measurement, as shown by a historical and conceptual review of the role of efficient causation in experimental physics. (shrink)

The symbolism introduced earlier provides a convenient vehicle for examining the status and consistency of Aristotle's three diverse justifications and for explaining how he means to avoid Protagorean relativism without embracing Platonic absolutism. When the variables ‘ x ’ and ‘ y ’ are allowed to range over the groups of free men in a given polis as well as over individual free men, the formula for the Aristotelian conception of justice expresses the major premiss of Aristotle's three justifications: (1) (...) (∀ x )(∀ y ) (P(x)·W(x)/P(y)·W(y)=V(T(x))/V(T(y)))Democracy is justified by adding a minor premiss to the effect that as a group the many ( m ) are superior (>) in virtue and wealth to the few best men ( f ): 85 (2 d ) (P(m) · W(m)) > (P(f) · W(f)) (3 d ) V(T(m))>V(T(f))Absolute kingship is justified when a godlike man ( g ) appears in a polis who is incommensurably superior (≫) in virtue and wealth to all the remaining free men ( r ): (2 k ) (P(g) · W(g)) ≫ (P(r) · W(r)) (3 k ) V(T(g)) ≫ V(T(r))True aristocracy requires a more complex justification, which was symbolized in Section 4. These justifications are compatible with each other since they apply to different situations. The polises where democracy and true aristocracy are justified contain no godlike men, and the polis in which democracy is justified differs from that in which true aristocracy is justified in containing a large group of free men who individually have little virtue ( Pol. III.11.1281b23-25, 1282a25-26). Each of the justifications is a valid deductive argument. Aristotle affirms the major premiss they share on the basis of a twofold appeal to nature. The principle of distributive justice, the concept as distinguished from the various conceptions of distributive justice, is itself according to nature ( Pol. VII.3.1325b7-10) and so too is one particular standard of worth, the standard of the best polis. Consequently, the question of the status of these three justifications, whether they are purely hypothetical or not, is a question about the minor premiss or premisses of each. In the case of the democratic premiss Aristotle's answer is straightforward: it is sometimes but not always true ( Pol. III.11.1281bl5-21). Hence the justification of democracy is not purely hypothetical. Nor is the justification of absolute kingship. The man who is “like a god among men” ( Pol. III.13.1284a10-11) would be a man of heroic virtue (see VII.14.1332bl6-27); and such a man, Aristotle says, is “rare” ( σπávιoη ) (not nonexistent) ( E.N. VII.1.1145a27-28). The minor premisses of the aristocratic argument describe a situation where all of the free men in a given polis have sufficient wealth for the exercise of the moral and intellectual virtues and where all of the older free men of the polis are men of practical wisdom. In the Politics Aristotle makes only the modest claim that such a situation is possible: It is not possible for the best constitution to come into being without appropriate equipment [that is, the appropriate quality and quantity of territory and of citizens and noncitizens]. Hence one must presuppose many things as one would wish them to be, though none of them must be impossible ( Pol. VII.4.1325b37-38; see also II.6.1265al7-18). But Aristotle appears to subscribe to the principle that every possibility is realized at some moment of time ( Top. 11.11.115bl7-18, Met. Θ.4.1047b3-6, N.2.1088b23-25). This principle together with the claim that the situation described is possible entails that the situation sometimes occurs. Thus even Aristotle's justification of true aristocracy is not purely hypothetical. The final question is Aristotle's way of avoiding Protagorean relativism without embracing Platonic absolutism. The relativist, along with everyone else ( E.N. V.3.1131a13-14, Pol. III.12.1282bl8), can accept the principle of distributive justice: Q(x)/Q(y) = V(T(x))/V(T(y)) And he can concede that particular instances of this principle, particular conceptions of justice, accurately describe the modes of distributing political authority that appear just to particular polises and to particular philosophers. What he denies is that there is any basis for ranking these various conceptions of justice or for singling one out as the best (Plato, Theaet. 172A-B). Aristotle, following in Plato's track ( Laws X.888D7-890D8), maintains against the relativist that nature provides such a basis. But he departs from Plato in his conception of nature. For Plato “the just by nature” ( τó ρυσει δίκ↑oν }) ( Rep. VI.501B2) is the Form of justice, an incorporeal entity ( Phdo. 65D4-5, Soph. 246B8) that exists beyond time and space ( Tim. 37C6-38C3, 51E6-52B2), whereas for Aristotle the sensible world is the realm of nature ( Met. A.1.1069a30-b2). Thus in appealing to nature Aristotle does not appeal to a transcendent standard. Nor does he appeal to his main criterion of the natural, namely, happening always or for the most part. Aristotle's theory of justice is anchored to nature by means of the polis described in Politics VII and VIII, and he regards this polis as natural because it fosters the true end of human life and because its social and political structure reflects the natural hierarchy of human beings and the natural stages of life. Thus the nature that Aristotle's theory of justice is ultimately founded on is human nature. (shrink)