Having finished Graham Priest’s Beyond the Limits of Thought, you might wonder what one of these true contradictions might be. I discussed the basic logical foundation of it a few posts ago, and one of the conversations I had with friends who read it revolved around what contradictions would actually be true. Because when you open the possibility of true contradictions, you also open yourself to straw man arguments from your enemies to make you look ridiculous.
After all, just because there can be true contradictions doesn’t mean that every contradictory sentence is true. There can be true propositions of regular sorts. That doesn’t mean that every proposition is true. The sentence “I am Adam Riggio and a root vegetable” is contradictory, but it isn’t true because I’m just Adam Riggio, no matter what dreams and aspirations I may have to become a turnip. The sentence “Adam Riggio was born in Jakarta” is a sentence with a non-contradictory form, but its form doesn’t make it true, because it’s empirically false. I don’t even think I want to go to Jakarta. The climate would kill me in the face.
The whole book is an exploration of one type of true contradictions, the contradictions which indicate a limit of thought. We reach a point in our conceptual exploration beyond which our powers to think don’t work. The tricky part of this idea, where contradictions appear, is that in order to identify a limit of thought, we have to transcend the limit. That’s why Priest identifies this contradiction in terms of transcendence and closure. A limit concept of thought generalizes over the totality of what can be thought or expressed or iterated, closing the set. But in order to generalize over that totality, we must refer to what can’t be generalized, transcending the set we just closed. In referring to what can’t be encompassed in the totality of what can be thought, we think it. So we both can think it and are unable to think it.
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| Bertrand Russell's most fertile period in philosophy was spent working to overcome what he held to be intolerable contradictions in logic. Personally, he also reminds me of an interesting take on Doctor Who. |
In the history of philosophy, this was often conceived as the thought of the infinite. Finite creatures can’t conceive of the infinite, so goes the idea. Especially since in some periods of philosophy’s history, the infinite was conceived as the uncountable, and mathematical conception only included very simple counting methods. When set theory was developed, we now had a system of rules that could count infinite quantities, or at least quantify over them. Being able to do this helped clarify a confusion, or rather identify that our previous thought had been less transparent than we believed. Set theory was a new standard to think about infinity.
Priest’s book looked through the history of philosophy to find the common thread in all these limit concepts of thought: totalizing self-reference. The perfect example in logic is the set of all sets. Being itself a set, it would have to include itself in its own set. But that would make it subject to the classic Russell paradox, that a set being a member of itself implies that it is not a member of itself. Russell’s generation of logicians spent years obsessed with overcoming this contradiction because they took as an unquestionable premise that consistency was a necessary condition of the true, that a contradiction could never be true because reality was consistent. It’s been an obvious and clear truth since Aristotle declared it to be so in his writing.
Aristotle was also a teleological evolutionist and believed in a geocentric cosmology. Aristotle is no authority.
Self-reference is one species of true contradiction. There are probably others, but I don’t want to talk about them today. Except perhaps for one little moment of jamming, a speculation that I’ve wondered about for years, ever since I started studying the nature of human thought and mind.
The limit of our thought lies in the contradictions of self-reference, reflexive and reflective thought, self-consciousness. We wouldn’t have the personalities we do without self-consciousness, the ability to think beyond immediate needs and immediate perceptions. Self-consciousness is the ability to imagine the future and the past, planning for uncertainties and conceiving of priorities and desires. Self-consciousness is the ability to critique and change ourselves and our behaviour. To do so, we must refer to ourselves, include ourselves in our statements about the world, even as referring to the world implies that we are somehow separate from the world. Sartre, for example, described human consciousness as beyond the world, but embedded in it. Self-conscious creatures like humans may very well be another species of true contradictions walking around all over this planet.
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