A: So, how do you understand the principle of contradiction?
B: That we cannot affirm and deny the same thing.
A: But we affirm and deny the same thing whenever we change our mind.
B: But I meant that we cannot affirm and deny the same thing at the same time.
A: But this doesn’t have anything to do with affirming or denying
– we can’t do any two actions simultaneously (changed b/c/ of critique by Eli Horowitz). We can’t affirm something twice at the same time either. So by adding a necessary qualification you have made the statement have nothing in particular to do with the thing you wanted to talk about.
B: When I say “at the same time” I don’t mean that you say two things at once actually, but that when you say anything is true or false, you are necessarily committed to thinking something else. As long as you are committed to thinking something about SP, you are committed to thinking something about S not-P.
A: So it seems that, if this is right, the principle of contradiction is based on a deeper idea of claims being connected together, that is, we see that there are necessary consequences of committing ourselves to the truth or falsity of something. It’s as though our primary vision or awareness is that every claim or commitment can only be a part of a larger body of commitments.
B: I don’t know. I would guess that this is a consequence of the principle of contradiction and not something prior to it.
A: It might be logically, I don’t know, but it seems like there is an ontological basis from the principle: sc. that no one truth we know exhausts the mind completely, but always occurs in the context of a principle that says “this commits you to something else”. Our mind has a sort of necessary motion. If any mind held a truth that was completely adequate to it, it wouldn’t need the principle of contradiction to know.
B: And so a completely satisfied intelligence, even if would have to be aware of contradictions, would not find its knowing falling under the principle of contradiction.
A: That seems right: I think the principle of contradiction follows upon a peculiar condition of an intellect – sc. when nothing it knows, and no multiplication of the things it knows is adequate to it.
B: But this raises the question whether the inadequacy of an object is necessary to being an intellect – doesn’t an intellect have to transcend the things it knows? If it did not, what sense would there be to saying that it can both affirm and deny?
A: Well, if it were simply true that intellect had to transcend its object, I don’t see what sense we could make of saying that an intellect can know itself.
B: So in this sense, self-Knowledge is the first hint we have of an object that would be perfectly adequate to intellect.
A: It can’t be more than a hint- on the one hand, it makes us aware that some known thing is a broad as the intellect that knows it; but on the other hand, the soul immediately sees itself as empty and receptive.