Retortion and Non-Contradiction in Aristotle, Metaphysics, Gamma 3, 4

Retortion is the philosophical procedure whereby one seeks to establish a thesis by uncovering a performative inconsistency in anyone who attempts to deny it. It is something like that benign form of ad hominem in which person A points out to person B that some proposition p that B maintains is inconsistent with some other proposition q that B maintains. "How can you maintain that p when your acceptance of p is logically ruled out by your acceptance of q? You are contradicting yourself!" This objection is to the man, or rather, to the man's doxastic system; it has no tendency to show that p is false. It shows merely that not all of B's beliefs can be true. But if the homo in question is Everyman, or every mind, then the objection gains in interest. Suppose there is a proposition that it is impossible for anyone (any rational agent) to deny; the question arises whether the undeniability or ineluctability of this proposition is a reason to consider it to be true. Does undeniability establish objective truth? Consider

1. There are no assertions.

Clearly, (1) cannot be asserted if it is true. For if anyone were to assert (1), his act of asserting it would falsify it. The performance of anyone who asserts (1) 'contradicts' the content of (1). We therefore speak of performative inconsistency. There is a 'contradiction' between the speech act of asserting and the content asserted. (I use sneer quotes here because performative inconsistency is not the same as logical consistency: the former is a relation between a speech act (which is not a proposition) and a proposition whereas the latter is a relation between a proposition and a proposition.) But does this performative inconsistency show that the negation of (1), namely,

~1. There are assertions

is true? (~1) is of course true. But can it be objectively established as true by retortion, i.e., by the 'retort' made to anyone who asserts (1) that the asserting of (1) is inconsistent with (1)'s truth? Does the undeniability of (~1) establish it as objectively true?

Not as far as I can see. If by 'objectively true' we mean true whether or not any subjects exist, then it seems that (~1) is true only if there are subjects who make assertions. In this case, then, undeniability does not entail objective truth. It is also quite clear that undeniability does not entail necessary truth. (~1) is contingently true: true in some, but not all, possible worlds.

Now let's consider a juicier example, the Law of Non-Contradiction which, in its property version, can be put like this:

LNC. (F)(x)~(Fx & ~Fx)

which is to say: for any property F-ness, and any object x, it is not the case that x is F and x is not F. For example, nothing is both red and non-red.

This is subject to the usual three qualifications: an object cannot be F and not F (i) at the same time, (ii) in the same respect, and (iii) in the same sense. Thus a ball could be both red and non-red at different times, or red and non-red in respect of different hemispheres, or in different senses: Jack can be both red and non-red at the same time if 'red' in its first occurrence refers to a color, and in its second occurrence to a political affiliation.

Now Aristotle was quite clear that first principles like (LNC) are non-demonstrable. They are so basic that they cannot be proven. Since a proof cannot be circular, (LNC) cannot be derived from itself or from any logically equivalent proposition. To use (LNC) to prove (LNC) would be to beg the question. It is also clear that no proof can have infinitely many inferential steps. So what justifies (LNC)? Is it perhaps unjustifiable, a dogmatic posit? Is it a groundless assumption?

One might just announce that (LNC) is self-evident, that it is self-justifying, that it 'glows by its own epistemic light.' But then how respond to someone like Heraclitus who sincerely maintains that it is not self-evident?

In Metaphysics Gamma, 3, 4, Aristotle can be read as using retortion, or proof by refutation, to establish (LNC). Since he cannot, on pain of begging the question, resort to a direct proof in the case of this most fundamental of all principles, "the surest principle of all," (1005b10) he must try to show that anyone who denies (LNC) falls into performative inconsistency. As I read Aristotle, the key idea is that (LNC) is " a principle one must have to understand anything whatever. . . ." (1005b15) It is a principle that governs all understanding, all definite and determinate speech.

As such, (LNC) seems to function as a semantic constraint: one cannot mean anything definite or make any definite judgment unless one abides by, and thus presupposes, the principle that no subject of discourse both has and does not have a property at the same time and in the same respect. To counter the (LNC)-denier, Aristotle simply demands that the man say something, that he express the same idea to himself and to another, "for this much is necessary if there is to be any proposition (legein, dicere) at all." (1006a20) If the (LNC)-denier says nothing, then "he is no better than a plant" (1006a15) and one can ignore him. But if he says anything definite at all, then he makes use of (LNC). For suppose he asserts 'The arrow is at rest.' He thereby commits himself to 'It is not the case that the arrow is not at rest.' If he asserts both 'The arrow is at rest' and 'The arrow is not at rest,' then, far from making two assertions, he does not even make one. He expresses no definite thought since he violates a principle observance of which is necessary for making sense.

The idea here is that he who asserts something contradictory asserts nothing at all: a necessary condition of there being a definite thought, a definite proposition, is that (LNC) be satisfied. The retortion might be spelled out as follows. The denier states

2. (LNC) is false.

But in making this definite statement, a statement that opposes what the (LNC)-affirmer states, the (LNC) denier commits himself to

3. It is not the case that (LNC) is not false.

But the commitment to (3) is tantamount to an acceptance of (LNC). So the denier's performance -- his stating of (2) -- 'contradicts' the content of (2).

But what exactly does the retortion show? Does it show that (LNC) is true of reality, or does it show merely that it is true of thought-contents? Is it an ontological principle or is it merely a law of thought, a principle that governs how we must think if we are to make sense to ourselves and others? Is it an ontological principle or merely a transcendental one?

I am not clear about this, or about the value of retortion as a philosophical procedure. Which is why I blog on.

Comments

[Ilíon]

"But then how respond to someone like Heraclitus who sincerely maintains that it is not self-evident?"

Myself, I would say, "But you are being intellectually dishonest in your 'sincere' assertion that the LNC is not self-evident." And when Heraclitus objects to being called a liar, I would ask "On what *grounds* are you objecting to being called a liar? Does your objection have anything more than emotive content to it?"

[ocham]

Just to point out again that Aristotle has a slightly different concern in this chapter. Mostly he is not asking whether 'p and not-p' is false, but whether being-an-A and not-being-an-A mean the same or not. Most of his proofs are that they do not mean the same, and thus that they represent different judgments.

Thus he argues that we cannot have the concept of being-a-man, as differentiated from being anything else i.e. not-being-man, unless we could differentiate between being something and not being something.

Turning to the the argument you are referring to.

"For why does a man walk to Megara and not stay at home, when he thinks he ought to be walking there? Why does he not walk early some morning into a well or over a precipice, if one happens to be in his way? Why do we observe him guarding against this, evidently because he does not think that falling in is alike good and not good? Evidently, then, he judges one thing to be better and another worse. And if this is so, he must also judge one thing to be a man and another to be not-a-man, one thing to be sweet and another to be not-sweet. For he does not aim at and judge all things alike, when, thinking it desirable to drink water or to see a man, he proceeds to aim at these things; yet he ought, if the same thing were alike a man and not-a-man. "

LNC is a principle we must have in order to judge anything at all. You ask

"Is it an ontological principle or is it merely a law of *thought*, a principle that governs how we must think if we are to make sense to ourselves and others? "

Aristotle seems to be arguing that it is a law of *judgment*. I am conscious this does not address your main difficulty with the argument. (Indeed I am sure it was I who originally raised this objection).

On a tangential note. As you probably know I am learning Japanese, which is fascinating language, in that it overturns some philosophical preconceptions derived from language.

(1) There is a tradition in Latin logic of an 'order of signification': written sign signifies spoken sign, spoken sign signifies concept, concept signifies thing. The order of the first two is reversed for Japanese Kanji - these are picture symbols which represent concepts directly, to which spoken symbols correspond, but secondarily so.

(2) Japanese verbs have only past and present tense. Future is indicated by indicating a time. Thus 'I go tomorrow to work'. I have already used this idea to challenge Alan Rhoda's view that a future tense proposition must be in some sense true now.

(3) Relating to the present post, there are three verbs for 'being' in Japanese. There is one for non-moving objects which covers rocks and plants. There is another for living moving objects (animals and persons). There is a third which is used for essential predication only, i.e. only to say what kind of thing something is. The last one corresponds to our use of the copula, except it is not used for non-essential predication. For example, if you want to say the plant is standing on the table, you use the verb type (1). If you say the dog is in the kennel, verb type (2). But if you say this is a plant, or this is a dog, verb type (3).

I mention this because Aristotle's concern (I believe) is with essential predication, and explains his argument that without LNC we could not grasp what kind of thing anything was, for being-that-thing and not-being-that-thing would be the same.