A Dialogue (or Trialogue) On The Law of Non-Contradiction

Adam Pearson: It is a basic principle of all knowledge that nothing can be both true and false in exactly the same sense at exactly the same time. For instance, I can say that there is no separate self and that all is Self, simultaneously, but here I am using “self” in two senses.

If I were to say there is a self and no self in exactly the same sense, my words would be incoherent; in fact, they wouldn’t express anything possible let alone actual.

Emile Graham: Aristotle: “A cannot be A yet not A” I think he beat you to it Adam!

Adam Pearson: I liked Aristotle’s presentation of this idea, but always felt that it was missing a clause. “In exactly the same sense” is the clause I propose adding. We can say for instance, that a person is both happy and not happy at the same time. In the short-term sense, for example, she may be experiencing happiness, but in the long-term sense, she may be generally unhappy in her life and her present joy may be simply a fleeting diversion.

My complete Law of Non-Contradiction would read something like “a thing cannot be both A and not A in exactly the same sense of A at exactly the same time.”

Emile Graham: I think to say “in the same sense” is not necessarily useful, considering we’re using the same noun, and in philosophy there should be no double meanings (law of identity).

Dave Kovacs: Aristotle most certainly did include your proposed clause about “in the same respect.” In fact, a 20th century logician called Nagel claimed that was the whole weakness: What constitutes “The same respect?” Two things, Nagel claimed, are in the same respect iff they conform to the law of non-contradiction. Thus, he accused Aristotle of circularity.

All that aside, the principle is pretty well established and accepted by nearly all logicians.

Adam Pearson: I disagree with Nagel’s objection on grounds from the philosophy of language. In my formulation, I use the term “sense,” and not “respect” for a precise reason. “In a different sense” just means “in a different sense (or meaning) of the word” or “in a different understanding of the concept” (e.g. .self” or “happiness” in the two examples I provided above).

There is no circularity involved in referring to different senses of a term or concept as not violating the law of non-contradiction because using different senses of words projects different propositions. To say “she is happy (in the short term)” and to say “she is unhappy (in the long term)” involves stating two distinct propositions.

Emile Graham: I’m just saying that the addition of the clause “in the same sense” has no utility.

Dave Kovacs: Sure it does:
Man is a three letter word.
Socrates is a man.
.:. Socrates is a three letter word.

Unless we make sure we are avoiding equivocation then we are, well, equivocating.

Emile Graham: There’s a reason Aristotle used the variable A (greek a i guess) when he stated his law: its because the variable has the same meaning. He didn’t say: A cannot be A and not B.

Dave Kovacs: I don’t even remember Aristotle using the symbol; he simply says that a thing can not both be and not be in the same respect and at the same time. It is, in symbolic logic, represented as ~(A & ~A).

Emile Graham: “It is impossible for the same attribute at once to belong and not to belong to the same thing and in the same relation.”  Hence, he says the same attribute.  So there should be no confusion involved.

Dave Kovacs: You have to keep in mind that what he is trying to do is find something which can make a declarative statement about Being. Without having the Greek in front of me, I am going to venture to say that any translation which incorporates the word attribute is probably a loose translation, since where Aristotle discusses this (Metaphysics IV) he is trying to make a point about being; he is also giving nod to Parmenides: That which is, is, that which is not, is not. But what Parmenides failed to see was that something can be in one sense, namely insofar as it is actual being, and not be in another, namely insofar as it is potential to some other kind of being.

Emile Graham: Then I guess Parmenides was right. The only thing which is common to things in a different sense is their symbol, and a logical system which works shouldn’t have symbols with multiple meanings.

Dave Kovacs:  Yeah, some people would suggest that the benefit of symbolic logic is that it eliminates equivocation; but it only does that if there is enough clarity when assigning the symbols to begin with!

Emile Graham: I mean, to some extent the person needs to know what we’re talking about anyway. I think definition isn’t always that useful considering that if the person doesn’t know what the object or concept is, it might be only showable, not tellable. I think that’s the reason why Wittgenstein wrote his tractatus in a bunch of short propositions without extensive definition. Or only definitions.

Dave Kovacs: Again, recall that for Aristotle plenty of things are in one sense and are not in another; a baby is grammatical in the sense that it is the sort of thing that will naturally develop a sense of grammar; but it won’t work in a scientific demonstration where the major premise is “all grammatical things use verbs.” One could go through the Metaphysics especially and find places where in Aristotle is saying “in one sense.” In one sense, matter is the ultimate subject of predication; but in another (far more important) sense, it is not.

Emile Graham: I think Aristotle was a bit confused. Compare this with 20th century logical positivists.

Dave Kovacs: There are people (including myself) who still subscribe to Aristotle; but after Quine, no one is able to subscribe to logical positivism. After TWO DOGMAS OF EMPIRICISM, logical positivism was dead. Even Ayer had to admit this. You won’t find a single logical positivist, at least none of the pre-Quine variety, in today’s universities.

Adam Pearson:  I do believe we have gotten a little off-track from our original topic.  But that’s alright. I’ve enjoyed the ride.

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