Book review: Tractatus Logico-Philosophicus

Tractatus Logico-Philosophicus
by Ludwig Wittegnstein, 1922

This book is not easy to understand.  I have consulted several secondary sources during my reading and found The Philosophy of Wittegnstein by George Pitcher particularly helpful.  My interpretation of “early” Wittgenstein’s thought does not precisely match any of my sources.  However, there is such a diversity of opinion among scholars on every aspect of the Tractatus that whatever error I can be accused of will be found in more extreme form among some or other of these learned men.

Facts and objects

1.1 The world is the totality of facts, not of things.

This appears to announce a novel metaphysics.  Russell accused substance ontology of not capturing all the facts of the world because it can’t handle relations.  Well, you know what definitely captures all the facts?  All the facts.  True, facts themselves have structure, but this is not necessarily a problem.  After all, substances have accidents, and events have prehensions.  Facts are objects and their logical arrangement.  But if facts are fundamental, what makes the same object in two facts to be the same object?  (Compare:  the same attribute inhering in two substances is not numerically identical.)  In fact, the Tractatus quickly slips into treating objects as its fundamental entities.

Wittgenstein’s “objects” are not everyday objects (the latter being composite beings).  His objects are absolutely simple and eternal.  The latter surprising property follows from Wittgenstein’s doctrine that the “sense” of an object’s name is the object itself, so we could not even talk about an object that has ceased to exist.  (Linux users might be reminded of soft links, which don’t work when the original file is deleted.)  Of course, we talk about past things all the time, so those must actually refer to configurations of objects.  Pitcher argues that objects are also propertyless, because Wittgenstein’s characterization of facts as objects and their arrangements seems to preclude proposition functions of one variable.  Thus reality would be entirely combinatoric, a remarkable claim that I would have expected Wittgenstein to have made explicit.

What are the “objects” of the Tractatus?  There is no consensus among scholars.  Are they elementary particles?  But how could a theory of physics plausibly be extracted from an analysis of human propositions?  Are they sense data (e.g. such-and-such point in my field of vision)?  But surely all my propositions can’t reduce to just that?  We’ll return to this issue later.

Propositions and logic

Most facts are composite.  They can be factored into elementary units called “atomic facts”.  In the formulation of the Tractatus, facts are all independent:  each may be true or false without affecting the others.  It is not implausible to me that logic space could be “orthogonalized” like this.  One might wonder about a fact such as “the photon’s energy is 13.6eV” which is not independent of it being some other number.  One would have to rephrase this or any other quantitative statement, say, by expressing the asserted number in binary and reinterpreting the digits as an infinite sequence of Boolean variables, so that such-and-such digit of the binary expression is a true/false assertion independent of all others.

In addition to objects, there are propositional functions that map tuples of objects to atomic facts.  (Wittgenstein gives a lot of attention to the distinction between facts and their representation in propositions, but since his point is to establish an isomorphism between them in an ideal language, I will ignore all such subtleties in this review.)  “The world” in this construction is naturally a map from propositions to truth values.  All compound propositions are constructed from atomic propositions and logical functions (e.g. “and”) which take them as inputs.  Wittgenstein represents these logical functions via truth tables.  Their meaning is exhausted by their output to all possible combinations of inputs.  A function which returns “true” for all inputs is a tautology; one that returns “false” for all inputs is a contradiction.

The discussion of logic in proposition sections 4 and 5 are the most compelling part of the book.  Wittgenstein points out how odd it is to think that we might identify laws or axioms of logic.  To state such a law is to make it seem like a contingent fact, but logic must govern everything meaningful we could possibly say.  To state a real law of logic, one would have to be able to step outside logic, outside the world as we are able to conceive it, into some more general space of possibilities, of which a logical world would be a definable subset.  If we regard logical rules as tautologies in Wittgenstein’s sense, then the mystery disappears.  For example, p or ~p is true for any input p, as can be seen from its truth table.  That table in turn is derived from the truth tables of the functions “and” and “not”, which are simply chosen by us; they are matters of definition.  They say nothing about the world.

The world is my world, and I am my world

Wittgenstein at the time of the Tractatus is a positivist.  He insists that the only articulable knowledge is that provided by the natural sciences.  His objects and their arrangements accommodate nothing else.  Atomic facts combine only by logic operators.  He concludes that there is no causality, since his framework has no place for it.  It seems, though, that this is all assumed rather than argued, a matter of materialist, positivist prejudice.  From the little the Tractatus tells us, we have no way of knowing that its objects couldn’t include Platonic Forms, angels, or other such things, and we are given no reason to deny that propositions can be related by causal or neo-Platonic emanationist links.  In fact, one can think of many counter-examples where the truth of a proposition seems to depend on something other than the truth of its inputs, the only thing that Wittgenstein’s propositional functions allow.  He deals with one such case.

5.541 At first sight it appears as if there were also a different way in which one proposition could occur in another.
Especially in certain propositional forms of psychology like “A thinks that p is the case”, or “A thinks p”, etc.
Here it appears superficially as if the proposition p stood to the object A in a kind of relation.
(And in modern epistemology (Russell, Moore, etc.) those propositions have been conceived in this way.)

5.542 But it is clear that “A believes that p”, “A thinks p”, “A says p”, are of the form “‘p’ says p”:  and here we have no coordination of a fact and an object, but a coordination of facts by means of a coordination of their objects.

5.5421 This shows that there is no such thing as the soul–the subject, etc.–as it is conceived in contemporary superficial psychology.

…

5.62 …
In fact what solipsism means is quite correct, only it cannot be said but shows itself.
That the world is my world shows itself in the fact that the limits of the language (the language in which I understand) mean the limits of my world.

5.63 I am my world.  (The microcosm.)

5.632 The subject does not belong to the world but it is a limit of the world.

I quoted this above because Wittgenstein has a sort of cult of admirers, and when I say that this is terrible reasoning I do not wish to be accused of misrepresenting.  First of all, “‘p’ says p” is not a viable replacement for “A says p”, because nothing in the former refers to A in particular.  The situation would not even be helped if the denial of an enduring metaphysical self were used as a premiss rather than a conclusion, because we must still single out the instantaneous neural state of a particular glob of molecules.  In any case, “‘p’ says p” still doesn’t fix the problem (if it is a problem); it’s still a proposition whose truth doesn’t depend on the truth of p.  And from the fact that we have changed the subject to not talk about the conscious subject A, we are to conclude that there are no subjects.  Of course, one could prove the nonexistence of anything this way.

Having registered my disagreement, I will now claim that the discourse on solipsism is the key to the Tractatus.  We see that when Wittgenstein talks about “the world” he is not speaking of something entirely objective with no reference to a subject; nor is he speaking merely of the sum of a subject’s sensory input (2D visual field, etc).  Things become clearer if we regard “the world” as “the subject’s (e.g. my) conceptualization of the world”.  Your consciousness, for instance, is not directly accessible to my experience, but it is part of my mental map of the world, hence part of “my world.”  The expendability of a subject comes from noticing that, once one has the idea of “a subject’s conceptualization of the world”, nothing is lost by just calling it “a conceptualization of the world”.  I am my world.  And the truth of solipsism is that my world in this sense is necessarily the only world I can talk or think about.

What, then, are the objects of my world?  I can only provide possibilities given my reading of the book as a whole.  One might imagine, for instance, that despite whatever physics might find, my mental world uses Newton-style absolute space, and points in this space might be plausible objects.  Suppose I say “this morning the dog was at region X”.  If subsequently region X is somehow deleted from this space, I can no longer make sense of this proposition, which is only meaningful if I know in principle how to get back to X.

But then that my world is made of facts not objects is hardly radical after all–I already knew that!  What I want to know is what the world is like outside my head–not my world, the world.  But here Wittgenstein could reply that what I’m asking for is incoherent.  I want to bring the world into my head while keeping it out of my head.  To escape my world, I would have to escape me.

Nonsense and silence

Wittgenstein is famously restrictive about what one is allowed to say.  Metaphysics, religion, and ethics are out, as you would imagine.  Even a number of seemingly benign statements such as “2 is a number” are declared senseless as well.  For instance, one cannot say that such-and-such is an object, because “object”, when “properly” rendered in symbolic logic, appears not as a function (as a property would) but as a variable name.  E.g. “ such that …”; the objects are the domain of our quantifier.  Wittgenstein will not allow that one can say anything about the number of objects; such statements cannot be put into proper logical form.  Russell was reputedly incredulous on this point, drew three dots with a pen on a piece of paper, and claimed that there are at least three objects in the universe.  Wittgenstein was adamant.  That there are at least three objects had been shown, but it cannot be said.

The distinction between what can be said and what can be shown recurs in the Tractatus.  We have seen that the solipsist is supposedly not able to say what he means, but he apparently gets his point across anyway.  I tend to think that the claim that some obvious proposition is senseless, nonsense, or unsayable is often more of an indictment of Wittgenstein’s inadequate model of language than of the proposition itself.  The later Wittgenstein would in some ways agree.  However, even within the system of the Tractatus, if we seem to be able to get our point across–showing when we cannot say in a way that would withstand full logical scrutiny–why should we not continue to do so?  The book famously concludes by turning its apparatus against itself, declaring its own statements nonsense.

6.52 We feel that even if all possible scientific questions be answered, the problems of life have still not been touched at all.  Of course, there is then no question left, and just this is the answer.

6.521 The solution of the problem of life is seen in the vanishing of this problem.
(Is not this the reason why men to whom, after long doubting, the sense of life became clear, could not then say wherein this sense consisted?)

6.522 There is indeed the inexpressible.  This shows itself; it is the mystical.

6.54 My propositions are elucidatory in this way:  he who understands me finally recognizes them as senseless, when he has climbed out through them, on them, over them.  (He must so to speak throw away the ladder after he has climbed up on it.)  He must surmount these propositions; then he sees the world rightly.

7 Whereof one cannot speak, thereof one must be silent.

As Russell wryly comments in his introduction, “Mr. Wittgenstein manages to say a good deal about what cannot be said, thus suggesting to the skeptical reader that possibly there may be some loophole…”