Halper-Aristotle on the Extension of Non-Contradiction

North American Philosophical Publications

Aristotle on the Extension of Non-ContradictionAuthor(s): Edward HalperSource: History of Philosophy Quarterly, Vol. 1, No. 4 (Oct., 1984), pp. 369-380Published by: University of Illinois Press on behalf of North American Philosophical PublicationsStable URL: http://www.jstor.org/stable/27743696 .Accessed: 22/01/2015 09:54

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp

.

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact [email protected].

.

University of Illinois Press and North American Philosophical Publications are collaborating with JSTOR todigitize, preserve and extend access to History of Philosophy Quarterly.

http://www.jstor.org

This content downloaded from 168.176.5.118 on Thu, 22 Jan 2015 09:54:46 AMAll use subject to JSTOR Terms and Conditions

History of Philosophy Quarterly Volume 1, Number 4, October 1984

ARISTOTLE ON THE EXTENSION OF NON-CONTRADICTION

Edward Halper

MOST discussions of Metaphysics T4-8 focus their attention on

presenting and evaluating Aristotle's arguments for what he calls the "firmest principle of all things" (1005bll-12), and what we generally call the "principle of non-contradiction."1 Aristotle surely is concerned to show that those who deny the principle implicitly or explicitly are reduced to incoherence. However, the view that this is his only concern in T4-8 presumes that this section is merely an island of logic in a sea of metaphysics. On this usual view, T4-8 is consistent with Aristotle's other concerns, but does not advance his metaphysical investigation. I will take a different approach here. It seems to me that Aristotle is using the discussion of non-contradiction in T4-8 to explain how metaphysics can include all beings (t

370 HISTORY OF PHILOSOPHY QUARTERLY

is what Aristotle had in mind, and there is no need to pursue this question further here. Let us simply assume that T3-8 uses "belongs" in a general, non-technical way. The principle of non-contradiction "belongs" to all

beings because it holds of all beings. Using more modern terminology, Aristotle might have spoken of the universal extension of the principle of non-contradiction. Or he could have said that each being is "subject to" or "falls under the scope of the principle, or that the principle "holds of or "is true of each being.

Just how, though, are we to understand the principle as extending universally to all beings? Consider one of Aristotle's formulations of the

principle: "the same (being) cannot belong and not belong to the same

(being) at the same time and in the same respect" (1005bl9-20). The

principle refers to two beings. Of which does the principle hold? In other words, does the principle of non-contradiction extend to all beings because (1) no being can belong and not belong to a substrate, or because (2) no attribute can belong or not belong to any being? To allay any suspicions that the problem arises from the abuse of the idea of the extension of the

principle let me pose the question in still a different way: is the principle of non-contradiction falsified by (1) an attribute that belongs and does not belong or by (2) the substrate to which it belongs and does not belong?

It is easy to see that these formulations are equivalent and that neither alternative is adequate. If, though, (1) the principle refers to the being that belongs to the substrate or if the principle is falsified by the attribute, then it cannot extend to substances because they are not predicated of all beings. If, on the other hand, (2) the principle extends to the being that is qualified by attributes or if the principle is falsified by a substrate, then the principle extends only to substances; for attributes are not qual ified by attributes (1007b2-3). Neither alternative is satisfactory.

In fact, though, this dichotomy is bogus. The principle is about both substances and attributes, and any falsification must involve both: the

principle would be false if some substance were qualified by an attribute and its negation in the same respects. Apparently, non-contradiction extends to both substances and attributes but in different ways. Sub stances fall under the principle because they cannot be qualified in con

tradictory ways; attributes fall under the principle because they cannot

qualify in contradictory ways.

Can this be the way that the principle of non-contradiction belongs to all beings? Probably not. This interpretation makes the principle ambigu ous; the principle would say different things about substances and attri butes. Further, this interpretation places the force of the principle on

substances; for it is the character of substances that does not allow of

contrary qualification, and thus enables the principle to extend to all

beings. This interpretation begins to resemble alternative (2). While Aris totle does assert that philosophers who deny non-contradiction do away with substance and essence (1007a20-21), he also speaks of attributes


ARISTOTLE ON NON-CONTRADICTION 371

such as "sweet" as if they had essences (1010b23-28), and his argument that non-contradiction extends to such attributes does not refer to the substances in which they inhere. In short, non-contradiction extends to attributes in a more significant way than this interpretation admits.

Some commentators have in fact construed the extension of the principle along the lines I have just rejected and limited their discussions to sub stance.2 However, Aristotle is quite clear about the universal extension of the principle.

It is possible to develop the formulation of the principle that I gave earlier in a way to explain how attributes fall under it: Aristotle accepts attributes as having essences and as thereby capable of having their own attributes (in a secondary sense). This will be clearer later. For the present the easiest way to understand the universal extension of the principle is to focus on another of Aristotle's formulations of the principle: "it is not

possible for the same (being) to be and not be at the same time" (B2, 996b30; also 1006bl8-19). Unlike the other formulations, this one involves

only a single being. There is no longer any difficulty in understanding how it can extend to attributes: it is impossible for sweet to be and not to be at the same time in the same respect, etc. And the formulation

applies in the same way to substances.

The reason that the importance of this formulation has been overlooked may be that commentators have been distracted by a distinction between an objective principle of non-contradiction that applies to things and a

subjective or psychological principle that is a "law of thought."3 (1) "It is

impossible for the same to be and not to be" instances the former while (2) "it is impossible for someone to believe the same to be and not to be at the same time" is an instance of the latter. This second appears in the initial discussion of non-contradiction (r3, 1005b29-30); (1) appears else

where in T4-8. Since the two are distinguished and (2) placed among psychological principles, the significance of the formulation in T has been

missed.

Aristotle does maintain that neither things nor thoughts can contradict each other, but it is a mistake to divide this view into two distinct prin ciples. The reason that non-contradiction is a principle of thought is that

things cannot both be and not be if we are to know them. Non-contradiction is at once a claim about the nature of things and about our capacity to know them. Accordingly, when Aristotle prefaces the principle with, "it is impossible for someone to believe...," he is not expressing a psychological principle. The reason he mentions belief here is clear later when he

acknowledges that, though people verbally deny non-contradiction, they do not really believe what they say (1009al6-22; cf. 1005b35-1006a2).

Thus, the statement of the principle that includes belief is not different from the one that omits it. With this conclusion we can see the formulation that I have claimed allows us to most easily understand the universal extension of the principle present with Aristotle's other statements of



the principle in T3 (1006b26-27). Since there is ample evidence of it

throughout T4-8 (e.g. 1006a3-4; 1006bl8-19), there is no reason to suppose that it is not Aristotle's central formulation.

II

That non-contradiction extends to all beings is now clear. What, though, is the basis for this universal extension? Philip Merlan has argued that

Hintikka's analysis of the Greek view of knowledge answers this ques tion.4 According to Hintikka, the objects of knowledge must be unchanging for the Greeks because their knowledge claims are temporally indefinite; i.e., they include no references to time. Claims about an object that could

change would be falsified if the object did change. Lacking any reference to time, a knowledge claim must be about something that does not change if it is to be eternally true.

Now Aristotle maintains that the principle of non-contradiction is clearest in regard to supersensibles and that those who deny the principle do so because they fail to recognize a realm beyond the sensible (1009a36 38; 1010al-3; 1010a25-35; 1012b30-31). According to Merlan, the prin ciple obviously applies to supersensibles because, as unchanging, they can be the object of knowledge claims that cannot be contradicted. Aris totle extends the principle to sensible substances by recognizing that they too are "permanent and exempt from the flux of time."5

This analysis has the advantage of explaining Aristotle's otherwise puzzling remarks about supersensibles in T4-8. However, it contains three serious defects. First, the principle of non-contradiction is not temporally indefinite. It is Plato who probably sees a contradiction in Socrates' sitting and not sitting. Aristotle denies a contradiction here by noting that the sitting and the not sitting are not at the same time Octroi). While 'ct|xa

may be rendered "together" here, the temporal qualification is surely included in the principle (see 1005b27-28).

Even if the principle were temporally indefinite, there would be other

problems with Merlan's interpretation. The least of these is that it extends the principle only to substances. It is quite clear that Aristotle regards the principle as extending to all beings. Can accidents too be "permanent and exempt from the flux of time"?

A more important difficulty is that Merlan does not really explain why the principle extends to sensible substances. On what ground does he claim that they are unchanging? Quite the contrary, instead of justifying the extension of non-contradiction, the Merlan-Hintikka analysis rather

explains why Aristotle's philosophical predecessors would have asserted that there are contradictions in the sensible world: temporally indefinite claims about changing things will be contradictory. Plato in particular supplies a similar analysis in the Timaeus in order to reject the possibility of knowledge of sensibles. Only the unchanging forms can be objects of



knowledge. Sensibles are objects of belief (28a); they may not possess an account (Xcryos) that is "at all points entirely consistent with itself and exact" (29c, Cornford; cf. 51e). In short, Plato is claiming that sensibles admit of contradictions,6 and the Merlan-Hintikka analysis seems to lie behind this conclusion. If, though, this is the case, and if Aristotle and Plato express knowledge claims in temporally indefinite sentences, then both of them are in much the same position in regard to non-contradiction. In sum, if Merlan's analysis is correct, it is hard to see how Aristotle has any basis for going beyond Plato in extending non-contradiction to sensi bles. We must look elsewhere if we are to find a justification for extending the principle universally.

Ill

The preceding analysis has not adequately explained the basis for Aris totle's extension of non-contradiction to all beings, but one point at least is clear: the question of the extension of non-contradiction is effectively equivalent to the Platonic problem of the possibility of knowledge of sensibles. There can be no doubt that non-contradiction holds of Plato's forms and Aristotle's supersensibles. The crucial question is whether it also extends to sensibles. If not, they cannot be known. If, though, the

principle does extend to sensibles, there is no reason to doubt that they are knowable. In this light the assertion of the universal applicability of the principle is a significant metaphysical claim.

There is no doubt that Aristotle is aware of the metaphysical issue. In T3 he asserts that non-contradiction is a principle that "it is necessary to know for anyone who knows anything" (1005bl6-17). If non-contradic tion is a necessary prerequisite of knowledge, it must extend just as far as knowledge does.

The question remains, however, on what basis does Aristotle maintain that non-contradiction, and thus knowability, extend to sensibles? Rather than addressing this question, T4-8 seem to concentrate on establishing the principle of non-contradiction by means of a series of "elenchic argu

ments" that refute denials of the principle (cf. 1006all-13). Yet there are, I maintain, reasons for doubting this traditional picture. I am going to maintain that Aristotle's primary concern lies not so much with estab

lishing non-contradiction as with the twin issues of the principle's uni versal extension and the possibility of knowing sensibles.

As a first step, let us consider the assumption that Aristotle

acknowledges as the first step in all of his elenchic arguments:

The starting point of all such arguments is not for our opponent to say that

something is or is not?this might seem to beg the question?but to signify

(cnqixatveiv) something to himself and to another (1006al8-20).

Further if "man" signifies (something) one, let this be the "two-footed ani

mal." And I mean by "signifying (something) one" thus: if "man" is some



thing which is a man, then this (something) is the being of man (to avftpom


only to show the close connection of definability, essences, significant speech, and non-contradiction?it does do this?but Aristotle's constant

method is to point out how the assumption of another character allows us to refute denials of non-contradiction. He seems to be assuming that non-contradiction holds and using this to support the assumptions of definability and essences.

The conclusion that emerges from this discussion is that the real import of T 4-8 is not in establishing non-contradiction but in asserting the metaphysical claims contained in what is presented as an assumption. The apparent conclusion, non-contradiction, is functioning as a premise that supports the apparent premise but real conclusion, definability. In short, as I see Aristotle's analysis, ?on-contradiction is clear from the start. The issue is, what is it necessary to assume in order to refute denials of non-contradiction? or, what are things to be like if non-con tradiction is to hold? Aristotle's answer is that they must have essential definitions. We know that things have essences because this assumption allows us to infer non-contradiction. Of course, this argument provides only probable support for the existence of essences.

The necessity of justifying what Aristotle calls the starting point of the argument, definability, supports my claim that it is definability or the existence of essences that is at issue in T4-8. Aristotle does mention

philosophers who seem to deny non-contradiction, but he never entertains serious doubts about it. Instead, the text emphasizes the definability assumption. In addition to the long passage that I partially quoted above, Aristotle carefully points out three more times that his arguments rest on the "assumption" of definability (1006bll-13; 1012a21-24; b5-8). Why does Aristotle emphasize a controversial "assumption" that he does not

justify? The only plausible answer is that he intends the fact that the

assumption allows us to infer non-contradiction as a kind of justification for the assumption.

Additional support for my interpretation lies in T 3's claim, to which I earlier referred, that non-contradiction is presupposed by all knowledge. A being must be subject to non-contradiction if it is to be knowable. However, the arguments of T4-8 all begin from definability in order to arrive at non-contradiction. Now if a being is definable, it possesses an

essence, and it is surely knowable. Hence, in assuming definability, Aris totle is assuming knowability?exactly what T3 claims requires non-con tradiction. On the surface, Aristotle is going in a circle: he is assuming knowability (definability) in order to show knowability. However, once we recognize that the real starting point is non-contradiction the difficulty vanishes. Artistotle is using a non-contradiction to support definability, and thereby showing knowability. In sum, Aristotle's claim in T3 that non-contradiction is presupposed by all knowledge suggests that Aristotle is using non-contradiction to support definability and thereby knowabil

ity.

If the foregoing analysis is correct, the force of T 4-8 does not lie in



establishing non-contradiction but in supporting definability, the claim that beings have essential definitions.

IV

The interpretation of T 4-8 that I have been expounding puts us in a

position to tackle the central question of this paper, on what basis does Aristotle extend the principle of non-contradiction universally? The answer, stated simply, is that all beings possess essential definitions. However, Aristotle cannot support the universal extension by referring to essences. As I see it, he uses non-contradiction to support his claim that sensibles have essences.

In the remainder of this paper, I am going to reconstruct the outlines of what I take to be Aristotle's analysis in T4-8. As I have mentioned, Aristotle begins with a part of the assumption of definability, that terms such as "man" signify something one, and then uses this along with non-contradiction to delimit the rest of the definability claim.

Why must Aristotle assume that a term signifies a "one"? Consider the variety of formulations of the principle: "It is impossible for the same to be and not be at the same time" (1005b29-30). "The same cannot be

qualified by contraries at the same time" (1005b26-27). "The same cannot belong and not belong to the same at the same time" (1005bl9-20). Common to all of these formulations is the assumption that what is subject to the principle is the "same." This latter term signifies oneness of substance (1012all, 1018a4-9). The assumption that "man" signifies something that is one allows us to speak of "man" as "one and the same" and thereby to substitute it into the statement of the principle of non-con tradiction.

Obviously, it is no contradiction to assert "something is" and also "some

thing is not" unless the "something" in each case is one and the same. That a term signifies a "one" is a precondition for even expressing it in the formulation of the principle. Clearly, only things that are one can be subject to non-contradiction.

This claim seems thoroughly trivial, but its consequences for Greek philosophy are profound. It shows immediately why Plato would restrict the principle of non-contradiction to forms. In the Phaedo he distinguishes the forms as "always the same" (ctei (ixroarrcos Taina exovTa) from the

sensibles which are "never the same" (80b). Lacking all sameness and oneness, the sensibles are not in themselves subject to the principle of non-contradiction. It is not that Plato is claiming that they are necesarily contradictory. They simply fall outside of the scope of the principle. It is not clear how the principle could apply to them.

The same insight lies behind Cratylus' correction of Heraclitus. The reason that it is impossible to step into the same river even once is that, in perpetual flux, the river is never properly the "same" (1010al2-15).



That a term signifies something one and the same is a minimum pre condition for even considering whether what the term signifies is subject to the principle. Clearly, then, for a thing to be subject to non-contradiction it is necessary that it be "one" and the "same". Furthermore, it is obvious that it is sufficient for it to possess the eternal unchanging unity and sameness of the Platonic form to be subject to the principle. Thus Aristo tle's references to the principle's being obvious for supersensibles. Aristo tle's insight is that possessing a weaker kind of unity is also sufficient for a thing to be subject to the principle. In particular, he claims that we need only assume that a term signifies some one nature in order to infer non-contradiction. The term or the nature is one in that it possesses an essential definition (cf. T 6, 1016a32-35). His analysis has two parts. The first, comprising T4, uses this assumption to deduce non-contradiction. In the second, beginning in T 5, Aristotle is maintaining that arguments advanced to dispute the applicability of the principle to sensibles are not

compelling. Although Aristotle's analysis is quite lengthy, a brief sketch will suffice for the present purposes.

Aristotle begins, as I have noted, with the assumption that a term such as "man" signifies one thing. Then, the negation of this term must signify something else. Were this not the case, then there would be no difference in asserting "man" and "not-man." It follows that to claim that "man" is "not-man" is to make two things one, an absurdity. Hence, this denial of non-contradiction must be false (cf. 1006bl8-32).

Pursuing these considerations, Aristotle maintains that to completely deny non-contradiction is to make all things one and all names to signify one thing. The question of whether non-contradiction obtains then comes down to the question whether a name signifies a particular essential nature or whether all names signify one and the same thing. In the latter Heraclitean world (cf. Phys. 185bl9-25) there can be no significant speech. Thus, anyone who tries to assert the Heraclitean position necessarily contradicts himself.

Of course, anyone who seriously maintains that there are contradictions is unlikely to be bothered by a demonstration that he too is contradicting himself. However, Aristotle's analysis shows that anyone who maintains the Heraclitean position must also surrender significant speech.

T 4 goes on to argue that someone denying non-contradiction also gives up "substances and essences" (1007a20ff.). The analysis is similar to what we have seen. If there is an essence of man, then this essence will be different from the essence of not-man. To claim that man is not-man is to make two things one.

In this way Aristotle uses the "assumption" that a term signifies some

thing one to dismiss denials of non-contradiction. Whatever has a single essential nature is subject to the principle. But the question remains, which terms signify such a nature? For the refutation of Heraclitus' claim



that non-contradiction never obtains, it suffices to prove that it holds in at least a single instance. However, Aristotle's position is much stronger. He maintains that the principle always obtains. Thus, each name involved in significant discourse must signify one essential nature.

Unable to argue directly for this position, Aristotle confines his atten tion to dismissing arguments that have supported contrary conclusions. There are two sorts. First, physicists such as Anaxagoras point to the fact that sensibles change and take on contrary characters (1009a22-38; 1010a7-9). Aristotle's response is that sensible substances possess these characters potentially but not actually; they are potentially two but actu

ally one (1009a32-36). Further, despite these changes the form of the sensible substance does not alter (1010a22-25). Hence, these arguments are not grounds for denying non-contradiction of sensible substances.

The second kind of argument advanced to deny non-contradiction stems from Protagoras' interpretation of sensation. From the fact that different

people sense the same thing as both sweet and non-sweet, Protagoras seems to conclude that the same thing has these contrary characters. Nonsense, says Aristotle, we are simply mistaken in ascribing one of these qualities to the thing. In any case, though, the sweet itself of neces

sity has its own nature, and we are always right about it. "Sweet" cannot be and not be (1010bl9-26). Thus, to avoid Protagorean denials of non-con tradiction Aristotle assumes that sensible characters have their own essential nature. "Sweet" and other accidents must also signify one thing. Hence, Protagoras' argument also fails to be a ground for denying non-con tradiction of sensibles.

Both of these arguments address the question of the extension of non

contradicton, and both posit the existence of essences in order to dismiss denials of non-contradiction. The only way to make sense of these argu ments is to acknowledge that they are assuming that non-contradiction does hold. Only if Aristotle is convinced that non-contradiction holds can he advance the existence of essences of sensible substances and of acci dents as a way of avoiding contradictions. Again, the force of this argu ment lies not in asserting that non-contradiction holds but in justifying the existence of essences on the ground that they allow us to dismiss

arguments against non-contradiction.

From Aristotle's perspective there is no doubt that what is subject to non-contradiction must be "one" in some way. While Plato insists that

only the forms are one, Aristotle distinguishes a variety of things said to be "one" in A 6. In T4-8 he maintains that something that is "one" in virtue of possessing an indivisible essential formula (cf. 1016b32-35) is

subject to the principle of non-contradiction. Aristotle disputes Plato by showing that a weaker "one" suffices to dismiss denials of the principle and that if we assume that all beings are "one" in this way we can dismiss all arguments against non-contradiction. Since all beings will be one in the pertinent way only if they all possess essences, Aristotle is assuming



that all beings possess essences in order to refute arguments against non-contradiction. Because non-contradiction must hold, we ought to

accept the claim that all beings possess essences. The reasoning is induc tive but anyone challenging Aristotle bears the burden of finding an alternative way of rejecting arguments against non-contradiction.

Several loose ends remain. First, if my analysis is correct, Aristotle is

using the discussion of non-contradiction to assert that all beings possess essences. Essence (to tl i\v elvai), however, is often thought to belong exclusively to substances. Though this view is widespread, it is a mistake. Essence in its primary and strict sense does belong to substance alone; but Aristotle also recognizes a secondary sense in which all beings possess an essence and a definition (Z 4, 1030a29-32, 17-23). It is this secondary essence to which Aristotle refers when he claims that deniers of non-con tradiction destroy essences (1007a20-21).7

Second, what are we now to say about the multiplicity of formulations of non-contradiction? The problem we encountered earlier was how to

apply them to accidents. However, once we recognize that accidents have some sort of essence, this difficulty vanishes. If an accident possesses any essence, it can also be said to have accidental attributes. To be sure, Aristotle insists that an accident can only qualify another accident if both belong to the same (proper) substrate (1007b2-5). Nevertheless, non contradiction can still be asserted of the attribute: it is impossible for a white (thing) to be musical and not-musical at the same time in the same

respect, etc. This statement is equivalent to asserting that it is impossible for the musical to be and not be at the same time. It follows, then, that all of the formulations apply equivalently to all beings. This conclusion

depends on my analysis and stands in support of it.

Finally, I earlier promised to put T 4-8 in the context of Aristotle's

larger concerns in the Metaphysics. This task is now nearly complete. Let me only add that these chapters are an appropriate sequel to ri-2. After arguing that there is a single science that knows all beings insofar as they are beings, Aristotle is faced with the spectre of a Heraclitean universe. In accordance with the Aristotelian notion of a science, to claim that there is one science of all beings is to claim that there is one formula of all beings. Thus, the result of ri-2 looks very much like the Heraclitean universe where everything has a single formula (Aristotle even insists that non-beings are-1003bl0).8

The question Aristotle then faces is, is the only knowledge that we have of all beings the knowledge of them as beings? No, Aristotle answers, for then all would be one; there would be contradictions; and there would be no significant speech. Consequently, each being must be known not

merely as a being but also through its own essential formula; it must be one nature. That this is the case is the real result of T4-8. It remains to Z-H and especially to Z 4-5 for Aristotle to explain how each being can have its own formula.



To conclude, in T 4-8 Aristotle is considering a logical principle, non-con

tradicton, in order to arrive at the metaphysical claim that each being possesses some sort of essence. Although this conclusion will surely be

disputed, many modern philosophers should feel sympathy with Aristo tle's procedure.

University of Georgia Received August 1, 1983

NOTES

1. See, e.g., Christopher Kirwan, Aristotle's Metaphysics: Books T, A and E (Oxford: Clarendon Press, 1971), pp. 85-121; R. M. Dancy, Sense and Contradiction: A Study in

Aristotle (Dordrecht, Holland: D. Reidel, 1975). The "law of the excluded middle" (Tl) is

also one of the "firmest principles;" but Aristotle devotes more attention to non-contradic

tion, and I shall focus on it exclusively here.

2. E.g., Philip Merlan, "Hintikka and a Strange Aristotelian Doctrine," Phronesis, vol.

15 (1970), p. 98.

3. W. D. Ross, Aristotle's Metaphysics, I (Oxford: Clarendon Press, 1924), p. 264. Jonathan

Barnes, "The Law of Contradiction," Philosophical Quarterly, vol. 10 (1969), pp. 302-309.

Jan Lukasiewicz, "On the Principle of Contradiction in Aristotle," tr. Vernon Wedin, Review of Metaphysics, vol. 24 (1970-71), p. 487.

4. "Hintikka and a Strange Aristotelian Doctrine." J. Hintikka, "Time, Truth, and Knowl

edge in Ancient Greek Philosophy," American Philosophical Quarterly, vol. 4 (1967), pp. 1-14.

5. Merlan, p. 98.

6. At Republic 436b-3, Plato does apply the principle of non-contradiction to sensibles

like a top. However, the application of the principle here presupposes the existence of

forms, a point that is brought out more fully later in the discussion of three fingers at

523b-e. In themselves the sensibles would not be subject to the principle. I will return to

this shortly.

7. So too Dancy, pp. 95-98.

8. Cf. G.E.M. Anscombe and P.T. Geach, Three Philosophers (Ithaca, Cornell University

Press, 1976), pp. 42-43.


Article Contentsp. 369p. 370p. 371p. 372p. 373p. 374p. 375p. 376p. 377p. 378p. 379p. 380

Issue Table of ContentsHistory of Philosophy Quarterly, Vol. 1, No. 4 (Oct., 1984), pp. 355-468Volume InformationFront MatterThe Conclusion of the Theaetetus [pp. 355-367]Aristotle on the Extension of Non-Contradiction [pp. 369-380]Adam Wodeham's Anti-Aristotelian Anti-Atomism [pp. 381-398]Descartes Knows Nothing [pp. 399-411]Knowledge of Substance and Knowledge of Science in Locke's Essay [pp. 413-428]Civility and Society [pp. 429-443]The Thesis of the Second Antinomy [pp. 445-452]Mill and Censorship [pp. 453-463]Back Matter

Documents

Halper-Aristotle on the Extension of Non-Contradiction