The thing about doubt is that it never stands alone. Doubt of one thing inevitably involves affirmation of something else. Often the doubter doesn't acknowledge the implied affirmation or is simply unaware of it.
Take solipsism for example. I can doubt that there is an external world and that I am the only thing in existence. No one can prove that I'm wrong because any evidence submitted might simply be a creation of my own mind.
Instead of trying to prove the solipsist wrong, let's see what is implied in his view if taken seriously. I now know calculus, but there was a time when I didn't. I remember being a freshman in high school and looking through my elder brother's calculus book. It contained a lot of funny symbols and complicated math I didn't understand. A few years later, I took calculus myself and the symbols and math became clear.
If solipsism is true, then everything in this history is a creation of my own mind. The book with the symbols I didn't understand as a freshman was a creation of my mind. So were my later calculus teacher, my calculus homework, and my calculus tests. Indeed, calculus itself is a creation of my own mind.
So at one point my mind created a book with funny symbols that I didn't understand, which I only later understood through calculus class. Yet the symbols only make sense in light of calculus, which I didn't understand at the time my mind (supposedly) created the calculus book. Was calculus then a creation of my subconscious mind, and calculus class but a devious way my mind tricks itself into thinking it learned something which it really knew all along? We have to believe something like this if we are to take solipsism seriously.
Beyond the bizarre stories implied concerning personal history, there is the simple fact that solipsism implies that I was the creator of calculus. Calculus is among the greatest mathematical achievements in history and is generally credited to the geniuses Newton and Leibniz. But on the solipsistic hypothesis these gentlemen are fictions of my mind, and in fact I am the inventor of calculus.
And it's not just his calculus that I'm claiming from Newton. I've got his physics as well. Also the electrodynamics of Maxwell, the relativity of Einstein, and the quantum mechanics of Heisenberg - even though I barely made it through QM in college. They are all creations of my mind.
We don't need to stop with science, either. I also wrote the plays of Shakespeare, the symphonies of Bach and Beethoven, and painted the Sistine Chapel. Not really, of course, only in my mind, but it seems all the more impressive to execute a classical painting purely in the imagination.
So what are we left with? Solipsism implies doubt of the external world, which means the external world is a creation of my mind, which means my mind is greater than the sum of all the geniuses in history.
Is that possible? Perhaps. Is it something we can doubt? I would hope so; in fact, any sane person should doubt it.
Solipsism is doubt of the external world coupled with a titanic affirmation of the self.
All doubt operates like this. So when we consider doubting something, we should bring into consideration the affirmations implied in the doubt.
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