Priest (1.2) Doubt Truth To Be a Liar, ‘The Law of Non-Contradiction (5b 18-22)’, summary

by Corry Shores

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[The following is summary. My commentary is in brackets. Boldface in quotations is mine unless otherwise indicated. Proofreading is incomplete, so please excuse the typos.]

Graham Priest

Doubt Truth To Be a Liar

Part 1 Truth

Ch.1 Aristotle on the Law of Non-Contradiction

1.2 The Law of Non-Contradiction (5^b 18-22)

Brief summary:

In his Metaphysics, Aristotle says that for an entity to have being (that is to say, to be a being) it must conform to the Law of Non-Contradiction (LNC) and to the Law of Excluded Middle (LEM). The general formulation of the LNC is: it is not possible for there to be a proposition, α, such that α ∧ ¬α. (“opposite {i.e. contradictory} assertions are not simultaneously true” Metaphysics Γ, 1011^b 14, curly brace insertion is Priest’s). Aristotle also gives another sort of formulation: it is not possible that there is an object, a and a property, F, such that Fa ∧ ¬Fa. (“For the same thing to hold good and not hold good simultaneously of the same thing and in the same respect is impossible” Metaphysics Γ, 1005^b 18-22). Certain potential counter-examples are not valid, because they do not fulfull the qualification that the contradictory properties hold “of the same thing and in the same respect.” An example of contradictory properties holding in the same respect but not of the same thing: In the same respect, the Channel Tunnel is both in England and not in England (since half of it is on the French side and is thus not in England). But this does not ascribe the contradictory properties to the same thing. Its being in England is ascribed to the part on the English side, and its being not in England is ascribed to the part on the French side. But as one whole thing, we cannot say that the Channel Tunnel is not in England, because part of it is. And an example of contradictory properties holding for the same thing but not in the same respect: The same thing, a spinning top, with one respect of motion is moving with angular velocity (it is rotating), but with another respect of motion, it is not moving with linear velocity (it spins in one place). But we cannot say that it is both moving and not moving with the same respect of motion. However, there are in fact very strong counter-examples to the LNC, like the Liar Paradox, but Aristotle does not explain how the LNC can be defended in light of them.

Summary

1.2.1

[Aristotle claims in his Metaphysics that for an entity to have being, to be a being, it must conform to the Laws of Non-Contradiction (LNC) and Excluded Middle (LEM).]

We are examining Aristotle’s Metaphysics Γ, 1003^a21-1012^b34. Priest will begin with a quick look of the book before we focus on the fourth chapter, which interests us here especially. Up to chapter four, Aristotle “explains that there is a study whose job is to investigate the most fundamental features of ‘being qua being’, i.e. the properties that all entities have merely in virtue of being entities.” There are two features that an entity must have in order to have being, that is, to be a being. All beings must conform to {1} the Law of Non-Contradiction (LNC), and to {2} the Law of Excluded Middle (LEM). Priest then summarizes the rest of the book: “Chapter 4 contains arguments against those who would violate the LNC. Chapters 5 and 6 attack the arguments that were supposedly given by various Presocratics for violating the Law. Chapter 7 defends the LEM; and chapter 8 deals with both laws, but adds essentially no new arguments concerning the LNC” (8).

1.2.2

[The general formulation of the LNC is ‘it is not possible for there to be a proposition, α, such that α ∧ ¬α’. In chapter 3 of Metaphysics, Aristotle gives another form that the general form can be reduced to, namely, (reworded) ‘it is not possible that there is an object, a and a property, F, such that  Fa ∧ ¬Fa’]

In chapter 3, Aristotle states the LNC in the following way (1005^b18-22):

For the same thing to hold good and not hold good simultaneously of the same thing and in the same respect is impossible (given any further specifications which might be added against dialectical difficulties).

(8)

Priest then offers two comments. {1} The way it is worded here is not the most general form for the law. The most general form would be something like: “it is not possible for there to be a proposition, α, such that α ∧ ¬α.” But the way it is worded in this passage, it is more like: “it is not possible that there is an object, a and a property, F, such that Fa ∧ ¬Fa” (8). In fact, later Aristotle will formulate the more general form: “‘opposite {i.e. contradictory} assertions are not simultaneously true’ (11^b 14)” (8, note, in footnote 5, Priest explains that his own insertions are between curly braces. Also, he abbreviates the Aristotle pagination. This for example is 1011^b 14). Priest interprets this less general formulation in the following way: “Aristotle is simply assuming that the general case can be reduced, in some way or other, to this one” (8).

1.2.3

[This formulation emphasizes that contradiction is impossible when we think of the object in its unity and of same properties as holding in the same respect. An example of the unity confusion: if we think of the Channel Tunnel as having two parts, then we can say that the part on the English side is in England and the part on the French side is not in England. But we cannot say that the Channel Tunnel as a whole is both in England and not in England. An example of the respect confusion: A spinning top, in one respect of movement, is moving with angular velocity (it is rotating), and in another respect of movement, it is not moving with linear velocity (it spins in place). But we cannot say that it is both moving and not moving in the same respect.]

[Priest’s second point notes the qualifications in the Aristotle passage. One is that it is impossible for something to both hold and not hold in the same respect (for one single thing). There are many cases where one thing can have opposing states of a property, when those states are understood in different respects. A top both moves and does not move. It moves with respect to its rotational motion, but it does not move with respect to its linear motion. Also, we might ascribe opposite properties, if we consider an object as having distinct parts. In other words, the property does not hold for the same thing, even if that property is understood in the same respect. So the Channel Tunnel is both in England and not in England, if we think of it as two things, the part on the English side and the part on the French side. But if we think of it as a unified object, then we cannot say it is not in England, because part of it is.]

Secondly, Aristotle realizes that there are many apparent violations of the LNC: a top is moving (has angular velocity) and not moving (has no linear velocity); the Channel Tunnel is in England (at one end), but also in France, and so not in England (at the other); capitalism is private production (in that the means of production are privately owned), but public production (in that the means are worked communally). But these apparent violations are due to the fact that we have not spelled out the object or the property finely enough: once we say which part of the object we are referring to, and in what respect the property is claimed to apply, the apparent violations disappear.

(8)

1.2.4

[There are obvious counter-examples to the LNC, like the Liar Paradox, but Aristotle does not explain how the LNC can be defended in light of them.]

[I may not summarize the next ideas effectively, so please consult the quotation to follow. They might be the following. There are certain counter-examples to the LNC, for example, the Liar Paradox. Here it seems we have one thing which can be said to be true and not true, with being true here being understood in the same respect in each case. But Aristotle does not explain how to defend the LNC in the face of such counter-examples. Priest notes some ways that the the LNC has been defended while solving the Liar Paradox. He says that some have argued it is “true in one context, false in another, or true in one tokening and false in another”. Priest then might be saying that these solutions can assume the LNC (there is no guarantee that they do not assume it), but if that is what is meant, I am not sure why. Maybe the idea is you can show the sentence is true in context 1, and false in context 2, but not be able to show that it is also false in context 1 and true in context 2. Yet that is likely wrong, so please read the quotation below.]

Aristotle is rather vague about what qualifications may be made to save the Law from apparent counter-examples. And given a putative counter-example, it is always possible for a defender of the Law to try to disarm it with suitable qualifications. For example, some have tried to solve the Liar Paradox by arguing that the relevant sentence is true in one context, false in another, or true in one tokening and false in another. These suggestions have to be taken on their individual merits (and demerits). Note, however, that there is no reason to suppose that such a device will always work, unless, in advance, one assumes the LNC. That this device is sometimes available does not, therefore, constitute a defence of the LNC. Aristotle pursues the matter no further.

(9)

Graham Priest. Doubt Truth To Be a Liar. Oxford: Oxford University, 2006.

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