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: The Third Proposition
October 17, 2010

Please read Peter’s thoughts on the second proposition. What he writes about the gestalt of knowledge is quite true, and I’ve found myself doing it a bit too. As Wittgenstein delves more into the philosophy of language—a subject I unwisely elected not to take in college, going for philosophy of mind instead—he loses me in a thicket of expressions, symbols, propositions, variable, propositional variables, and so on. But his thoughts on what can be understood and articulated—and therefore, for our purposes, exist—has been extremely helpful. I’m starting to embrace Wittgenstein’s view that what we call “metaphysics” is more a sort of confusion over what language is capable of expressing.

On that note, I found the first few passages in the third proposition a lot more engaging than the rest, which mostly concerned itself with the heavy-duty philosophy of language that is both beyond my ken and not directly relevant to my own philosophical project.

In the early going, Wittgenstein attempts to explain why, when discussing and describing things, we’re limited to discussing and describing them logically. That’s the sort of suggestion that’s bound to make a lot of people bristle; more than once I’ve heard proponents of mystical views about the universe defend these views by insisting that you can’t critique them logically, because they exist outside of logic. To which Wittgenstein says:

3. A logical picture of facts is a thought.

[…]

3.031 It used to be said that God could create anything except what would be contrary to the laws of logic. The truth is that we could not say what an ‘illogical’ world would look like.

3.032 It is as impossible to represent in language anything that ‘contradicts logic’ as it is in geometry to represent by its coordinations a figure that contradicts the laws of space, or to give the coordinates of a point that does not exist.

One obvious objection one might raise: People say illogical things all the time! It’s not very hard. For example, if I say, “Boris Yeltsin is the pineapple of my green space” (surely the first time that has ever been said), that seems, on the face of it, like an illogical proposition. But it also doesn’t really express anything, which is why you can’t form a mental picture of it. Now apply that same reasoning to a sentence like, “We are all one, because spirit is everything.” It sure sounds like that means something. Does it?

I’m curious to hear what Peter thinks about Wittgenstein’s definition of a “thought.” Surely his discipline—cognitive neuroscience—has a thing or two to say on the topic.

Wittgenblogging: The Second Proposition
October 10, 2010

Here we go. Right around halfway through the second proposition—which is a good eight or nine times longer than the first—things start to get complicated.

Here Wittgenstein introduces several new concepts into his list of the constituent parts of the universe. In the last proposition we got facts and things (AKA objects). Now we also have:

  • States of affairs: Arrangements of objects in some definitive relationship to one another. All possible states of affairs are encoded into the relevant objects regardless of whether or not those states occur.
  • Form: ”The possibility of structure.” I think of form as the distinguishing characteristics by which we can organize objects. So for example, color is a form because we can identify commonalities between different objects based on their proximity on the spectrum of color. Time is one because it is one of the major organizing principles of our experience, but doesn’t appear to have any substance to it. Speaking of which:
  • Substance: ”What subsists independently of what is the case.” Also: “Objects make up the substance of the world.” I think substance is that which is empirically observed and not really open to interpretation.
  • Pictures: Models of reality we construct in our heads, be they accurate or inaccurate.
  • Sense: That which a picture represents. “The agreement or disagreement of its sense with reality constitutes its truth or falsity.”

But what strikes me most about the second proposition isn’t what Wittgenstein identifies as constituting reality, but what he  excludes. For example, Wittgenstein writes that, “It is essential to things that they should be possible constituents of states of affairs.” And also: “The sum-total of reality is the world.” This “reality” doesn’t include anything like values, God, or any other sort of metaphysical propositions.

And here’s something else: Wittgenstein argues that pictures, even if they are not intended to correspond with the world as it actually is, most still borrow some form from them. So, as he says in the last line of the second proposition: “There are no pictures that are true a priori.” That leaves me with the question: Does Wittgenstein think all a priori reasoning is impossible? Or just pictures?

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