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Enduring Aristotle’s Dialectic

The Discipline of Non-Contradiction

Jamie Mellway

Forum: Enlightenment's First Annual Meeting.
This paper will be defended at the June Meeting. Participants are invited to draft written commentaries of this work for inclusion in the published Proceedings of the Meeting.
Now, since philosophy is merely the rational cognition according to concepts, there will be no principle to be found in it that deserves the name of an axiom. --Immanuel Kant, The Critique of Pure Reason [A732/B760]


In this paper, I will be looking at the selection of Aristotle’s Metaphysics Book Gamma (1005b35-1007b18) analyzed by R. M. Dancy in his Sense and Contradiction. In order to prove the Principle of Non-Contradiction (PNC), by way of refutation, Aristotle is trying to drive us either to concede that the PNC is true and towards his own views on signification and ontology or to adopt a radical view that appears inconsistent. However, this way of proving is not impervious, since one could develop a theory that adopts a consistent version of the radical view. While it seems doubtful that one could come up with a "consistent" theory that denies the PNC, it may be possible if a weaker principle is accepted in its place.

In order to deny the PNC, Aristotle’s interlocutor needs to adopt a view that, at the very least, denies that terms have a definite meaning and denies substance ontology. These two denials are necessary, but not sufficient, conditions to deny the PNC. While it is possible to adopt such a view without also denying the PNC, one will have to maintain the PNC with respect to meaning and ontology if meaning is definite or ontology is substantive. In order to extend Dancy’s analysis of Aristotle’s interlocutor, to whom Dancy has given the name Antiphasis, I want to claim that holding these two required opinions is a credible position to take. While this does not refute the PNC, it will hopefully add plausibility to a view that denies its validity. Section one deals with the issue of meaning, section two with ontology, and section three summarizes what propositions one can deny in order to grant the radical view Aristotle is pushing us to accept.

In section four I discuss how someone who denies definite meaning and substance ontology can nevertheless accept a weaker principle: the Discipline of Non-Contradiction (DNC). The term ‘discipline’ is being use in a Kantian sense of being a formal condition that is applied to our understanding in order to make our concepts distinct. The discipline of pure reason is distinguished, in Kant, from the formal condition of canon and architectonic of pure reason that are conditions of thoroughness and systematic ordering, respectively, instead of a condition of distinctness. The DNC would have us temporarily assume a, more or less, definite and precise meaning to a term for personal thought or communication with others. The DNC will also allow us to temporarily assume that an object is intrinsically distinct, such that we can talk about its properties, without actually conceding to substance ontology. The weaker DNC allows us to utilize the power of the PNC without also making bolder concessions to theories of meaning and ontology. The DNC can be contrasted from the PNC as the DNC is a formal condition and the PNC is material condition, as the DNC is only applied to our concepts and the PNC appears to be saying something about the noumenal.

Part One: Meaning

Aristotle’s first refutation (1006a11-b34) attempts to get his interlocutor to say a term that has a definite meaning, presumably a Natural Kind term, so that Aristotle can force him to accept that the PNC applies with respect to the signification of that term. By getting the interlocutor to agree that the meaning is what the term signifies, Aristotle can dialectically get them to accept that it is impossible for what is what the term signifies and not what the term signifies. For example, if the meaning of ‘man’ is biped animal, then it is impossible for anything that is a man not to be a biped animal. Which brings us to that it is impossible for anything that is a man not to be a man. The force of Aristotle’s dialectic appears to be that definite signification, that terms have a definite meaning, relies on the PNC with respect to the signified terms. However, there are several ways that Antiphasis might try to get out of conceding to Aristotle’s conclusion.

One possible objection that Dancy raises [see Dancy, pp. 38-43] as one that Antiphasis could have taken, but did not, is that people use terms meaningfully without having "anything available that we would want to defend as a definition." Furthermore, we cannot, even in principle, have it possible that we can give a definition to fill in the meaning of the term. The move Dancy appears to be trying to avoid is the move from

‘Man’ signifies something


‘Man’ signifies biped animal.

In other words, simply saying that the term ‘man’ signifies something does not, even in principle, imply that it signifies something in particular and it does not imply that we can say something like:

($ x) ‘Man’ signifies x.

I think this is a valid objection that Antiphasis could take and one that I find intuitive. I do, however, want to extend this idea a bit further.

It is unclear from Dancy’s analysis if he wants to say that a speaker might not agree to a definite definition in principle or if he wants to say that the term does not necessarily have a definite sense. In both cases we seem to be primarily concerned with the intentional meaning (i.e., speaker-meaning) of the term, but it is unclear if the term has an associated intensional meaning (i.e., Fregean sense) as well.

If we were to maintain that terms have an intensional meaning, but that we cannot in principle come to know it, then it seems that Aristotle can get us to accept the PNC. A term with an intensional meaning would imply that it has a definite meaning and there will, for example, be a definite yes-or-no answer to the question, "Is Frankenstein’s monster a man?", although two people can legitimately disagree on what the answer is. Frankenstein’s monster either is a man or not-man—but not both. Our indefinite intentional meaning might be off from what the definite intensional meaning really is, so we might attribute to the subject contrary properties, but this is an error on our part as we are off the real meaning. We cannot believe that the real (i.e., intensional) meaning will let us violate the PNC. [This is the cognitive priority of the PNC. See 1005b29.] This problem would not occur if we reject that there is a definite intensional meaning, and state, instead, that meaning is intentional.

In either case, both are different from what Antiphasis argument would have been. It seems that Antiphasis would claim that the term has infinite number of definite intensional meanings and that we cannot pick which it has. Antiphasis’ position appears to "say that the word has an infinite number of meanings" [1006b6], but it is not clear what could mean. It might be an obscure way of trying to say that it does not have a definite meaning. Alternatively, it might be assuming that the meaning is in flux, in which it might have a definite sense at one time although it is changing in time. This is similar to an alternative we have Heraclitus’ river: either we cannot step in the same river twice or we cannot even step in it once. If we can step in the same river once or if a term as a definite sense at any one time, then the PNC holds. If we cannot step in the same river even once, then the river has no identity and the PNC might not hold. Similarly, if the term does not have a definite meaning, then we do not have strict signification and the PNC might not hold. I do not think that an infinite number of definite intension meanings gives Antiphasis the theoretical objection he would need to counter Aristotle. I think the more charitable reading of Antiphasis' objection is that he would reject that terms have one definite intensional sense.

Dancy makes this objection, instead of what he thinks is Antiphasis actual position, since the actual position "would lead to subjectivism". It is not clear how it would do this. First of all, a subjectivist with respect to meaning would not necessarily claim that terms do not have a definite sense. The extreme example of a subjectivist regarding meaning is usually given as Lewis Carrol’s Humpty Dumpty, but even that character’s terms have a definite meaning and a name must mean something particular even though "it means just what I choose it to mean -- neither more nor less" [Through the Looking Glass, Chapter 6.]. The source of the meaning, whether intrinsic or nominalistic, is a different issue than whether a term has a definite meaning. Second, as Dancy mentions [p. 43], there are also positions that are alternative to intrinsic and subjectivistic theories of meaning and thus, it is not clear that how we are led to subjectivism by either denying definite sense or by claiming that there are an infinite number of definite senses. One alternative position is the conceptualist position. Roughly, this position states that general terms are grouped by intentional similarity and it rejects the idea that the similarities are somehow linked to an intrinsic natural kind. While conceptualism does not entail indefinite meaning, it is compatible with it, as meaning will ultimately depend on intentionality. It will get us too far afield to get into a positive account of conceptualist position, so I will leave conceptualism here as the position that 1) rejects natural kinds and 2) is compatible with indefinite intentional meaning.

To give some plausibility to denying that terms need to have a definite meaning, let’s return to the example of Frankenstein’s monster. It seems that I can use the term ‘man’ in day to day conversation without specifying the status of borderline cases like whether Frankenstein’s monster is a man or not. This seems at least true for cases that do not involve Frankenstein’s monster directly. It seems extremely rigid to require that a term have a definite meaning to this degree. However, this intuition is not in favour of indefinite meaning, but rather simply allows for our use of terms that are intentionally left vague.

Nevertheless, I believe this is sufficient in the interlocutor’s role in the dialectic. If pressed, all they have to say is that they do not grant that we should be talking about a "real" definite meaning opposed to meaning with respect to our intentional use of terms. If the questioner wants to press even further by moving the discussion to the metaphysical basis of meaning, then he is free to do so. This is what Aristotle does in the second refutation.

Part Two: Ontology.

The second refutation can be divided into two parts. The first part (1007a20-32) argues that someone who denies the PNC must claim that all properties must be accidents, since essential properties requires the PNC. The second part (100a32-b18] argues that accidents must have an particular substance they are attached to and also that there must be something that can denote the substance.

If one is to deny the PNC, then one will also have to deny essential properties. If being a man is an essential property of Socrates, then he cannot be a non-man as well. Essentialism has the PNC falling out of that view. To be an essential property, requires that it, and not its opposite, be a property to be what it is. Furthermore, since Aristotle’s theory of definition depends on essences, they to must denied, or given a different theoretical justification then intrinsic essences. This almost seems like too much to give up.

If we have been dialectically pushed, from the first refutation, to reject that words have a definite meaning, then the jump to denying that there are not definite definitions should be quite a small leap. Definite definitions appear to be our identification of the definite meaning of a term. Once we lose definite meaning, then there is not a meaning out there to identify with our definition. Let us call the identification of a definite sense the "real definition". This must be denied by Antiphasis to avoid conceding the PNC.

We can further deny that there are metaphysical essences as they are the metaphysical basis of definitions and definite senses. If we are willing to reject real definitions and definite senses, then it is not clear why we need to postulate that there are metaphysical essences. It seems clear that if metaphysical essences do not exist, then we lose the metaphysical basis and justification for real definitions and definite senses. However, it may be possible to believe that they exist, but there is an epistemological barrier such that we lose any access to real definitions and definite senses. Nevertheless, I will take Antiphasis view to be rejecting that there are metaphysical essences--as well as rejecting real definitions and definite senses.

The second part continues off the first. Once Aristotle tries to get us to assert that all properties are accidents, he argues that that the properties must be attached to some substance. If he can get Antiphasis to concede to that, then Aristotle leads him to accept the PNC. Dancy calls the position that all properties are accidents associated to a substance the ultra-essentialist [p. 107]. We might also call this view haecceitas-essentialism (i.e., thisness-essentialism). This view is still a species of essentialism as we are assuming that there is a substance there that we can denote and "denoting the substance of a thing means that the essence of the thing is nothing else" [100726-7]. On this view, we cannot, for example, say that Socrates is a this and non-this as being a this is essential to Socrates—even though he could be a man and a not-man.

Alternatively, the proponent of ultra-essentialism might be claiming that we can make identity assertions (e.g., A is A) de re, rather then asserting anything about substance. However, it is not clear to me how one can claim that some object can have the property of self-identity without also postulating a substance-ontology that has the property of "being a this" as an essential property. Hence, if claiming that an object has mind-independent identity is not the same as claiming that the object is a this, then it seems to be a stronger claim to say that an object has an identity, they to say that it is a this. However, it still might be possible to somehow talk about identity de re without postulate a substance ontology.

If Antiphasis still wants to deny the PNC, he needs to be pushed to the more extreme view of ultra-accidentalism. This view is that there are only accidents. Aristotle rejects such a view as "there will be nothing primary about which [the subjects] are made" [1007a34-5] and we are left if an infinite regress of accidents said of other accidents.

One way of getting out of the problem is to go to the radical view that there are no intrinsically distinct objects and that an entity is a part of noumenal reality that has been intentionally isolated [Cf. Ray and Radcliffe 2000 and Radcliffe 1999]. I will not elaborate this view here [See Ray and Radcliffe 2000], but instead dialectically secure a proposition denying that there are intrinsically distinct objects in order to avoid the line of argument that Aristotle is taking. I will leave it open for the questioner to pick up the disputation at this point if they so desire.

Part Three: Summary

Although there may be several ways to endure Aristotle’s dialectical attacks in the first and second refutation, one of these ways is to reject four related theses. These theses are:

    1. Terms have definite meaning
    2. Terms have a real definition
    3. Objects have essential properties
    4. There are intrinsically distinct objects

While a view that denies all of these theses would be radical, I want to maintain that it is plausible. While it is not possible to give an adequate justification of such a view in an essay of this size and scope, I believe such an elaboration is not required for the interlocutor denying the PNC. My purpose here is to boldly assert a view that is being forced on the denier of the PNC. Since Aristotle has pushed me to secure propositions, such as ‘I deny that terms have definite meaning", the dialectic can start anew attacking those propositions.

Denying these four theses does not entail the denial of the PNC. All one seems to need to do is postulate that something exists as something definite, and the PNC should follow. Furthermore, since we still want to talk about meaning and objects, we need to appeal to something like the PNC in order to communicate and think with any precision. In the next part of this essay, I want to concede a weaker version of the PNC that I can apply to meaning and objects that still allows me to deny the four theses. I am calling this weaker principle, the Discipline of Non-Contradiction (DNC).

Part Four: The Discipline of Non-Contradiction

Even if terms do not have definite meaning, we still want to impose a distinct meaning to the term. This imposition will be a formal condition, opposed to a material condition, as we are concerned with constraining our terms/concepts and not with describing the noumenal. The formal condition here is to make the meanings of out concepts distinct, i.e., have a discipline of pure reason. For example, when we are wondering if Frankenstein’s monster is a man we make sure that our concept of man is distinct such that there is a definite answer. We could add another formal condition that we make sure that the concept is exhaustive, i.e., a canon of pure reason, such that the concept of man is distinct enough that we can answer any question of whether an instance is included.

The distinctness we are imposing is not only on general terms, but is imposed on specific terms as well. We might intentionally hold that Frankenstein’s monster, for instance, has a personal identity that it is distinct from whoever’s brain was used. We might intentionally hold, for example, that a valley is an entity in order to talk about a geographical region. We might also talk a mob of people as if it were a single object in order to discuss a riot. In each of cases, we are asserting that there is some thing, and not a not-thing, without relying on a specific ontology.

Weakening the PNC such that it is only a formal condition, instead of a material condition, allows us the utility of the PNC without buying into any specific ontological view. Furthermore, since it is merely an imposed formal condition, it might be possible to deny it as well.


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