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Peter highlights one of the more intriguing findings of the Tractatus Logico-Philosophicus’ fourth proposition, regarding the slipperiness of trying to describe or prove logic itself. Logic is the underlying framework of the universe; you can’t construct a proof to demonstrate the validity of logic, or precisely describe logic itself, because doing so would require stepping outside of logic. That’s not something we’re capable of. Peter has a good analogy:
Sort of how I can’t really tell you what it’s like to be alive, because both you and I would have to be dead first to actually comprehend the contrast.
I first encountered the problem of how to demonstrate that logic or reason were useful tools for understanding the universe in Descartes’ Meditations. Early on in the Meditations, Descartes decides that if he can’t be certain of the validity of his perception, then reason is all he has to rely on. But then he starts asking himself why he has any reason to think that reason itself is reliable, and the result is the painfully contorted piece of reasoning we call the Cartesian Circle.
It goes like this:
- Whatever I clearly and distinctly perceive (meaning, essentially, can hold in my mind and understand wholly from a mental picture) is true.
- I know that my clear and distinct perceptions are accurate because they are given to me by God, and God is not a deceiver.
- I know God exists because I can clearly and distinctly perceive Him. I just imagine a perfect, infinite being, and understand that it is more perfect for something to exist than to not exist.
I don’t think I need to spell out the problems here. And it shouldn’t be hard to see why I prefer Wittgenstein’s far more elegant answer to the question: “How do we know reason itself is valid?”