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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Wittgenblogging: Proposition 3.5
November 2, 2010

Peter’s all caught up on the Wittgenblogging, and pretty close to outstripping me. I’ll admit I haven’t started on the fourth proposition yet; the third sort of took the air out of my tires, and besides that I’ve got a list of philosophy texts I want to read that’s thiiiiis big. But I will get to it soon; this week, hopefully.

Anyway, Peter raised some issues with my last post on the subject that I think I should address.

For example:

First, I would hesitate use “mental pictures,” as the litmus test for the logicality of a statement. There are plenty of statements that I can not picture, but that are almost certainly true. Examples of these include, “People with synesthesia can taste music,” “Bees can see ultraviolet light,” “When in a state of dreamless sleep, you experience nothingness,” and “The universe is infinite.” I can also picture things that, while I guess they don’t contradict logic, are physically impossible*. For example, I can imagine ashes burning.

Peter may be right here, but I think he’s actually being a little over-literal when it comes to the idea of “mental pictures.” While you might not be able to take a literal snapshot of how a synesthesiac (that’s a word, right?) perceive music, you can certainly imagine what it would be like to experience a certain coppery taste when one hears a high C-sharp. I think that when Wittgenstein talks about mental pictures, he just means imagined sets of data that it is within our capability to perceive.

As for the ashes burning thing, I think Peter’s right there. “The ashes are burning” is a phrase that obeys a certain logical form, and you can imagine how one might perceive it. As a result it has some truth value (likely negative). 

Peter also writes:

Second, Wittgenstein directly says, “It is as impossible to represent in language anything that ‘contradicts logic’.” Language is inherently logical. A statement may be meaningless, but it can never be illogical. Therefore, when somebody says “We are all one, because spirit is everything,” they are speaking a logical statement. I think that Ned is confusing the colloquial idea of “logic” with the philosophy of language idea of “logic.”

Right. The “spirit is everything” example clearly obeys the form of a logical statement. When I suggested that it doesn’t express anything, I meant that I have no idea how one would form a mental picture corresponding to that sentence. I think the spiritualist would tend to agree, arguing that these things are beyond our perception — but I think the Tractatus Logic-Philosophicus goes a pretty long way towards establishing that if there’s no faculty we can use to perceive something (even with artificial enhancements to our perception), then it’s unlikely that we can legitimately call it a part of the world.

Nietzsche Blogging: Truth, Reason, and Moral Weakness
August 24, 2010

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I’m starting to get a better sense of Nietzsche’s style, and although I’m still a novice, I know this much: he would have made a damn good blogger. It’s not just his whole books full of pithy aphorisms—like The Gay Science and Human, All-Too-Human—that make me think this. It’s the fact that Kaufmann has seen fit to include a lot of his hastily scribbled notes, and with good reason. You could even excerpt a lot of his longer essays and turn those snippets into self-contained reflections.

But like posts from the best blogs, all of these little scraps are best viewed in the context of his greater project. If you’ll forgive the cliché, the whole is greater than the sum of its parts.

That being said, the whole is frequently bewildering, even in the early stages. (Maybe especially in the early stages? Hopefully.) Nietzsche often seems to contradict himself from one passage to the next, and I can’t decide whether it’s because of the inherent difficulty in translating all the nuances of meaning (which translator Kaufmann acknowledges in the introduction), or because apparent self-contradiction is simply a part of Nietzsche’s inimitable style. I’m leaning towards it being some combination of the two, especially because so far I’ve always managed to parse out some reading in which he’s not actually contradicting himself.

Take the odd juxtaposition Kaufmann creates (presumably intentionally) between the essay “On Truth and Lie in an Extra-Moral Sense,” some of Nietzsche’s 1874-1875 notes to himself and selected passages from Human, All-Too-Human. In “On Truth and Lie,” Nietzsche convincingly argues that very little of what we consider to be “true” is little more than a “lie according to a fixed convention.” He does this by pointing out the inadequacy of words to truly express what they represent, something that I’m already well familiar with from my recent reading of Sartre’s Nausea. (Here, as in the focus on projects, struggle and competition I noted in “Homer’s Contest,” we can see Nietzsche’s influence on the development of existentialism.) Because words have no real fixed attachment to the objects they represent, to use words to describe the outside world at all is to lie in some sense. The example he uses here is the use of the word “leaf” to describe an individual leaf. There is no true, default form of The Leaf as the Greeks might have suggested, and to imply that there is by classifying an individual leaf as being a descendant of that form is inherently dishonest.

So if “truth” is itself a lie, what to make of Nietzsche’s claim in his notes on the very next page that only “friends of the truth” can help determine the proper use of the German state’s power? Is there anything truly true behind this consensus?

Two pages later, we get the answer. If Nietzsche believes in anything, it’s reason. Our ability to describe the real world may be profoundly limited, but the thing that makes us human—or, as I would put it, persons—is that we have some capacity for a priori reasoning, and to, as Nietzsche later points out, “draw correct inferences.”

But then we stumble into another apparent contradiction. If the “highest” reason lies within “the work of the artist, and he may experience it as such,” then what to make of the assertion that, “regarding truths, the artist has a weaker morality than the thinker?”

Here, I think Nietzsche means to draw a distinction between truth in, as he puts it in the title of his essay on the subject, “the extra-moral sense,” and moral truth. The artist may be an enemy of moral truth, a destructive, nihilist force, but he challenges it in the service of truth overall. The artist is a vaccine, and it’s no coincidence that Nietzsche refers repeatedly to “inoculation” of society in Human, All-Too-Human. In his view, society could always use a bracing jolt of destructive nihilism in order to defend, reassess, and thereby strengthen, its convictions. I don’t think it’s a coincidence that this is also what Nietzsche does for his individual readers.

“To educate educators!” he writes in his notes. “But the first ones must educate themselves! And for these I write.”

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