Wittgenblogging: The Sixth Proposition, Part 1
November 24, 2010

I went into the Tractatus Logico-Philosophicus expecting more or less what we’ve got over the last five propositions: a lengthy meditation on epistemology, philosophy of language, logic, and metaphysics (mostly how it doesn’t make any sense). What I didn’t expect: grand, zen-like pronouncements over the riddles of life and death. But in the latter half of the Tractatus, Wittgenstein goes there. Who woulda thunk that a proposition that starts with “The general form of a truth-function is [p, E, N(E)],”* would end with “It is not how things are in the world that is mystical, but that it exists.”?

But we’ll get to that in the next post. The first portion of the sixth proposition is all about the role of logic and its relationship with mathematics and empirical science. Logic, Wittgenstein writes, is what gives everything else structure. There is nothing in the world that is outside logic because it is “the scaffolding of the world.” Elsewhere: “Logic is not a body of doctrine, but a mirror-image of the world. Logic is transcendental.”

As a result, there’s no need to demonstrate logic as a proposition. In fact, trying to do so doesn’t make any sense. “The propositions of logic are tautologies.” Remember when I brought up the Cartesian Circle? Turns out Descartes’ first mistake was trying to construct a proof demonstrating the validity of the only tool one can use to construct sensible proofs. “Clearly the laws of logic cannot in their turn be subject to laws of logic.” Logic is true but unprovable.

So logic is self-demonstrating and self-affirming. “It is the peculiar mark of logical propositions that one can recognize that they are true from the symbol alone,” Wittgenstein writes, “and this fact contains in itself the whole philosophy of logic.”

So what is math? Or physics? Wittgenstein writes that mathematics is “a method of logic.” Physics — mathematics and inductive reasoning applied to the physical world — “imposes a unified form on the description of the world.” Wittgenstein compares Newtonian mechanics to an attempt to measure the size of black blotches on a white surface by placing a grid-patterned mesh over the surface “and then saying of every square whether it is black or white. […] The form is optional, since I could have achieved the same result by using a net with a triangular or hexagonal mesh.”

As for causality and induction themselves, Wittgenstein seems to recognize their necessity while also expressing some skepticism. In Proposition 5, he wrote that there is no causal nexis — no metaphysical property that connects a cause to its effect. Here, he says that there is no “law of causality” (it is “the form of a law,” not a law itself), but that if there were, “it might be put the following way: There are laws of nature. But of course, that cannot be said: it makes itself manifest.” In this sense, it is like logical expressions and mathematical equations. “[W]hat the law of causality is meant to exclude cannot even be described.”

“The procedure of induction,” Wittgenstein writes, “consists in accepting as true the simplest law that can be reconciled with our experiences. […] This procedure, however, has no logical justification, but only a psychological one.” As an example, he adds: “It is an hypothesis that the sun will rise tomorrow: and this means that we do not know whether it will rise.”

Then he takes it a step further: “The whole modern conception of the world is founded on the illusion that the so-called laws of nature are the explanations of natural phenomena.” He compares this to the belief of prior generations about God and Fate. However, there is no necessity that makes these laws as “something inviolable”: “The only necessity that exists is logical necessity.” The laws of nature are the mesh, our rough approximation of what the world is. That we can use it with some reliability to extrapolate what the world will be does not mean that we have stumbled upon eternally unyielding principles.

I’m going to stop here, before Wittgenstein gets into ethics, aesthetics, mysticism, and the other seemingly transcendental vagaries of the human condition. That’s a whole other epistemological clusterfuck, and I will do my best to tackle it soon. Probably after Thanksgiving weekend.

*And no, I don’t really know what that means either. Did I mention that I just barely passed my First-Order Logic class?

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