I recently reread Leibniz's "Monodology." Most people don't know much about Leibniz - even philosophy majors like me. Leibniz was always taught as a sort of bridge getting from Descartes to Hume and ultimately to Kant. At least in my courses he wasn't considered someone to take seriously. I knew him most through the parody deployed by Voltaire in Candide. Leibniz once said that this must be the best of all possible worlds because if God could have made it better, he would have made it better. Voltaire basically said "Then God fucked up" but with more and different words. Leibniz also argues that God must exist because it's possible that God does exist and since it is a God that grants possibilities in the first place God must be the cause of his own possibility. That sounds crazy, but it's also kind of awesome. And here's why.
As a philosophy major, you read for truth. You establish truth by creating a systematic study of what a thinker says. You do this by invoking a language with words like "necessary" and "sufficient" and "a priori" and " a posteriori," "subjective" and "objective," and so forth. You invoke logical fallacies and ultimately you prove things. And well, approached this way, Liebniz is caught in what is called "circular reasoning" (Since God is possible, he must exist and he must have caused himself.) After you establish this, you can dismiss a thinker and move on to the next. To do this there's one thing you actually never need to do: Read Leibniz. All of these critiques can be accomplished quickly and simply in an Intro to Philosophy Book, taking up about a page and a half.
So let's do something radical and actually look at the text. Here's a sentence that gets me excited, "But he (M. Bayle in an attempt to critique Liebniz's belief in a 'universal harmony.') was unable to bring forward any reason why this universal harmony, which means that every substance exactly expresses every other through the relationships it has with them, was impossible." How does a substance have a relationship with all other substances. Leibniz is one of two people that invented Calculus (Newton). They both made their breakthroughs independently - which seems like such a calculusy thing to do. So Leibniz sees objects as a kind of bounded infinity.
Okay - let's try for an example. When I look at my guitar, I see not only my guitar, but I can also see the effects of the craftsman that worked on it. Now of course he brings with him another multiplicity of connections to other things and so on. I can also see my guitar and notice how it is different from a bass, for example. If I look long enough the history of music seems caught up in this one piece of wood and string. For Leibniz the world folds itself back into objects in a multiplicity of ways. The trick, of course, is to not think one "reading" of the guitar is the final reading. However - and this is what is so difficult to truly grasp - it does not follow that the guitar means whatever you think it means. It's not absolutely infinite - it's a bounded infinity. It is the infinity of calculus.
Of course there's also the butterfly effect argument that everything, no matter how small, has effects on everything else. In this way too all things are folded back into other things. All becomes cause and effect.
What I most admire about Leibniz is the audacity of the project: I'm going to create a cosmology that is 90 propositions long and takes about an hour to read?! There's something to be said about brevity. I mean it takes a long time to read most people's history of everything (Bible, quantum theory). Leibniz does it in an afternoon.
The trick - well that's not the right word exactly - is to learn to actually read instead of falling into a categorical judgment: this is wrong because God doesn't exist, for example. That reading dismisses the beauty of the rest of Leibniz's thought. I mean everything is folded into everything - everything is pregnant with a bounded infinity. That's some seriously poetic shit: we are all progenitors of the muck of the world - that we are simultaneously caught up in and constituted by.
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