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Dissolving Philosophy By Logical Atomism, December 15, 2005
Since most of the reviews of the Tractatus here contain either fawning praise or vituperation without much expository content, it may perhaps be useful to give an account, in reasonably clear terms, of what this book is actually about. Granted that my account is somewhat simplified, it will still be better than quasi-mystical gushing praise or bitter unargued criticism. The central idea of the Tractatus is expressed very clearly at proposition 4.01 and certain comments following it:
"A proposition is a picture of reality.
A proposition is a model of reality as we imagine it." [4.01]
"At first sight a proposition--one set out on the printed page, for example--does not seem to be a picture of the reality with which it is concerned. But neither do written notes seem at first sight to be a picture of a piece of music . . . And yet these sign-languages prove to be pictures, even in the ordinary sense, of what they represent." [4.011]
"A gramophone record, the musical idea, the written notes, and the sound-waves, all stand to one another in the same internal relation of depicting that holds between language and the world.
They are all construed according to a common logical pattern." [4.014]
So, Wittgenstein's basic view in the Tractatus is simple: statements ("propositions") are pictures or models of the situations they are about. The sequence of words "The cat is on the mat" would be taken by him to picture the situation that consists in one object (the cat) standing in a certain relation (being on) to another object (the mat). Or rather, this would be the way to understand this proposition if the cat and mat themselves were indivisible atoms, without any smaller parts. Since, actually, the cat is made up of a great many smaller parts, as is the mat, the full analysis of "The cat is on the mat" would be much more complicated. But basically, a proposition is a picture of the situation it describes just as the notes on a sheet of music depict a melody, and just as the written letters "pop" depict a certain sound. In breaking down the cat and the mat, we must eventually come to a point where things can't be broken down any further, with objects that are the basic constituents of reality. The relationships between these basic objects, which Wittgenstein just calls "objects", but which others have called "logical atoms", constitute the most elementary situations. These situations are described by what he calls "elementary propositions". Given a bunch of elementary propositions, we can combine and re-combine them by certain basic operations, called truth-functional operations, which are explained in any textbook of elementary formal logic. Two such operations are conjunction and negation. So, given three atoms, a, b, and c, and a relation R (R might be the relation "being on", as with the cat and the mat), we have, as elementary propositions, for instance:
aRb ("a is on b")
bRc ("b is on c")
aRc ("a is on c")
Then we can make new, compound propositions like
(aRb & bRc)
~aRc
(aRb & bRc) & ~aRc
Where "&" just means "and", as in "The cat is on the mat and the cherry is on the tree", and "~" means "It is not the case that", as in "It is not the case that the cat is on the mat". So the first of the above three compounds means "a is on b and b is on c", and the second means "It is not the case that a is on c", that is, a is not on c. You can easily work out the third one for yourself.
By means of operations like this (actually, Wittgenstein uses a different, but equivalent operation), one can build up an enormous stock of compound propositions. In fact, according to Wittgenstein, anything that can be said at all can be said by taking elementary propositions and applying operations like this repeatedly (albeit you might have to apply such operations infinitely, or to an infinite collection of propositions). Basically, then, given the simplest pictures of the world, we can stitch them together into more and more complicated pictures, and these yield all the statements and thoughts we can make, or at least all the ones that make any sense. Every meaningful statement ultimately breaks down to elementary propositions, propositions entirely in terms of simple signs or names (like "a" and "b") that stand for logical atoms. Everything that can be said meaningfully can, in principle, be broken down like this. This is the basic idea of logical atomism. Most of the technical work in this book consists of machinery for reducing all propositions of science and mathematics to combinations of elementary propositions. In the process, Wittgenstein shows you, he thinks, how to reduce claims with notions like "all" and "some" (like "All whales are mammals", "Some lawyers are crooks") and numerical claims ("There are four books on the shelf") to combinations of elementary propositions. If Wittgenstein succeeds in this, he considers himself to have shown that his "picture theory" of language is correct.
Okay, now you want to know, what's the *philosophical* point of all this? Well, for one thing, it means that anything you *can't* picture cannot be expressed by a meaningful proposition. If you try to speak of things that can't be pictured in Wittgenstein's way, you end up talking nonsense, in that what you are saying won't be true or false. Such utterances may express how you feel, or they may serve some other function (besides saying something) but they won't *say* anything that can be true (or false), and so there won't be any point in *arguing* about it. And what "things" are these, that you can't meaningfully talk about? The short answer is, all of traditional philosophy. Take ethics, for instance: "things" like right and wrong, or good and bad, can't be pictured, and so ethical "propositions" like "Murder is wrong" don't say anything. Maybe they express your feelings, or reflect some psychological fact, but they are not true or false. Likewise for religious claims that defy picturing, like "God is love" or "Brahman manifests itself in all things". Likewise for metaphysical claims about God or substance or causation or any underlying non-empirical reality. Likewise for epistemological worries about justification or rationality; these cannot be pictured in the requisite way either (hence Wittgenstein dismisses skepticism as nonsense). Wittgenstein's views of language are *so* restrictive that most of what philosophers have wanted to talk about turn out to fall into the category of the unspeakable, what he calls "the mystical". The mystical is what cannot be pictured, what is therefore beyond the realm of logic, reasoning, and articulate speech. About it, Wittgenstein claims, we cannot speak, and therefore we should be silent.
Oddly enough, Wittgenstein's own book turns out to be an attempt to talk about the mystical. For one of the things that cannot be pictured, is the very fact, as Wittgenstein takes it to be, that propositions are pictures of reality. (Think about it: how can you make a picture that says that propositions are pictures of reality? There's no way to do it along the lines of "The cat is on the mat", is there?) In fact, every attempt to talk about the relation between language and reality is itself an attempt to speak of the unspeakable, to attempt to characterize what can't be pictured. Wittgenstein recognizes this and responds thus:
"My propositions serve as elucidations in the following way: anyone who understands me eventually recognizes them as nonsensical, when he has used them--as steps--to climb up beyond them. (He must, so to speak, throw away the ladder after he has climbed up it.)
He must transcend these propositions, and then he will see the world aright." [6.54]
Wittgenstein's Tractatus itself, then, is a violation of his commandment to be silent in the face of the mystical. And once it is *recognized* as a violation, Wittgenstein hopes you will throw the book away and return to the ordinary, empirical world, free of any further desire to do philosophy, having gotten a clear vision of language and the world that makes it obvious to you that philosophy is a mistaken attempt to speak of the unspeakable. (You can now see why this book provokes bitter hostility in those who cherish traditional philosophy--after all, it says they're wasting their time!) But if so, how can Wittgenstein himself be right in writing the book? Isn't *it* a mistaken attempt to speak about the unspeakable? Yes and no. Yes, it *is* an attempt to say what can't be said--hence, once you understand it, paradoxically, you see that it's nonsense! But it is not a *mistaken* attempt, rather it is a self-conscious attempt, made necessary by our confusion and unclarity about the world while we are still enmeshed in the tangles of traditional philosophy. While that nonsense imprisons us, we cannot recognize it *as* nonsense, and as such, like mentally deranged people, we have to be approached *with* nonsense if we are to be cured--nonsense is all we respond to. So this book is a kind of curative "nonsense", like a purgative for the soul; it is meant to cleanse the mind of philosophical confusion (that is, of philosophy itself) and, at the end, to remove itself as the final piece of "confusion". To use a computer metaphor, the Tractatus is a program that wipes your whole philosophical "hard drive", and erases itself as its final operation. And after that final erasure, we return to the ordinary world, free of philosophy, in the deafening silence that is our acknowledgement of "das Mystiche"--the mystical in, and above, the ordinary.
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