Dance with the Rhino

Ludwig WittgensteinI picked up Wittgenstein in 90 Minutes and wanted to see if I could read it in 90 minutes. But I got stuck on page 14 for well over 90 minutes. It was a logic problem. In Principles of Mathematics, Bertrand Russell argued that the foundation of mathematics was logic. But he ran into a nice little paradox. Some classes are members of themselves and some are not. For example, the class of humans is not a member of itself because a class is a not a kind of human. But the class of non-humans is a member of itself because the class of non-humans is in fact non-human. Okay, we’re all fine. But then in a Godel-like move (although this was three years before Godel was even born), he asks, “What about the class of all classes that are not members of themselves?”

Paradox alert! Danger Will Robinson!

If this class is a member of itself, then the class would not be a class that is not a member of itself. The class is defined as a collection of classes that are not members of themselves. Thus: it cannot be a member of itself. But if the class is not a member of itself, then it is a class that is not a member of itself. Thus it must be a member of itself, or more accurately: the class is not the class of all classes that are not members of themselves.

This is effectively Godel. Either (1) the set contradicts itself or (2) the set is incomplete. Regardless, there is a problem with logic here. Wittgenstein’s solution to this problem is just to say that there is no problem: it is improper to formalize mathematics in this way. As always with him, it comes down to semantics: we are trapped by our language.

Here’s the thing about Wittgenstein: I find his work aggravatingly trivial. That probably speaks to how profoundly he has influenced thought that most of my own personal philosophical thought (which seems original) is just what he thought. But he seems to go an awfully long way out of his way to come to an intuitive understanding of existence. As a result, it strikes me as full of sound and fury but in the end signifying nothing.

I will admit, I am a very people centered person. I find it hard to love the thinking of a man who was a monster, or in Wittgenstein’s case, an arrogant and narcissistic bully. And I think this is largely why he has been so important in the history of philosophy. There is no question that he was unimaginably (for me) brilliant. When combined with his aggressive personality, it is not surprising that lesser thinkers would cow to him. After all, Schopenhauer was the first to introduce eastern thought in a serious way into western philosophy. Wittgenstein just continues that trend, effectively making mystical arguments against philosophy.

But I should be clear. I have found my little efforts at reading the great man himself frustrating: I find he lacks clarity in the way that, say, Kant did not. And there is another fundamental problem to it: logic itself is composed of large stretches of dark matter. So logical arguments against logic or at least our ability to discuss it strike me as contradictions themselves. And I’m fine with that. Wittgenstein had mystical tendencies. I am a mystic.

One big argument that Wittgenstein had with Russell was how one can know there is no rhino in the room. Wittgenstein claimed that we couldn’t know. Russell argued that we could know because: “Look: no rhino!” The only way I can accept Wittgenstein’s argument is on solipsist grounds: we cannot know anything but what is going on in our minds. And that is an interesting idea that I find compelling, but from a philosophical standpoint, it is also a trivial observation. By that observation, how could he say he was even having that conversation with Russell?

Existence is a paradox. But at least we can dance. And if you want to, dance with the rhino. He’s in the room. Really.

Leave a Reply

Your email address will not be published. Required fields are marked *