Tractatus 5.473, Take II

Upon further review, I am skeptical of the interpretation sketched in my previous post on 5.473. It seems to me that I misread the following passage from the Notes dictated to Moore:

φ cannot possibly stand to the left of (or in any other relation to) the symbol of a property. For the symbol of a property, e.g., ψx is that ψ stands to the left of a name form, and another symbol φ cannot possibly stand to the left of such a fact: If it could, we should have an illogical language, which is impossible.

Wittgenstein does not say that φ, understood as the symbol of a property, cannot stand to the left of another symbol of a property. Rather, he says that no symbol can stand to the left of the symbol of a property. Perhaps this still poses a difficulty for resolute readings, but as I don’t know what to make of it, I’m not in a position to say.

I’d like to back up then, and pursue another line of thought. I pointed out in the previous post that the Notebooks version of 5.473 contains a sentence that is missing from the Tractatus. Here it is again:

Logic must take care of itself.
φx. If syntactical rules for functions can be set up at all, then the whole theory of things, properties, etc., is superfluous. It is also all too obvious that this theory isn’t what is in question either in the Grundgesetze, or in Principia Mathematica. Once more: logic must take care of itself. A possible sign must also be capable of signifying. Everything that is possible at all, is also legitimate. Let us remember the explanation why "Socrates is Plato" is nonsense. That is, because we have not made an arbitrary specification, NOT because a sign is, shall we say, illegitimate in itself!

Clearly, "the whole theory of things, properties, etc." is the theory of types. Wittgenstein is claiming that theories of types are superfluous given syntactical rules for functions. This is reminiscent of a comment he makes to Russell in a letter from January of 1913:

I have changed my views on "atomic" complexes: I now think that qualities, relations (like love) etc. are all copulae! That means I for instance analyse a subject-predicate proposition, say, "Socrates is human" into "Socrates" and "something is human", (which I think is not complex). The reason for this is a very fundamental one: I think that there cannot be different Types of things! In other words whatever can be symbolized by a simple proper name must belong to one type. And further: every theory of types must be rendered superfluous by a proper theory of symbolism: For instance if I analyse the proposition Socrates is mortal into Socrates, mortality and (∃x,y) ε 1 (x,y) I want a theory of types to tell me that "mortality is Socrates" is nonsensical, because if I treat "mortality" as a proper name (as I did) there is nothing to prevent me to make the substitution the wrong way round. But if I analyse (as I do now) into Socrates and (∃x).x is mortal or generally into x and (∃x)fx it becomes impossible to substitute the wrong way round because the two symbols are now of a different kind themselves. What I am most certain of is not however the correctness of my present way of analysis, but of the fact that all theory of types must be done away with by a theory of symbolism showing that what seem to be different kinds of things are symbolized by different kinds of symbols which cannot possibly be substituted in one another’s places. (Notebooks, 121-2)

This, I think, is a very interesting and important passage. For present purposes, what interests me is Wittgenstein’s claim that, if "Socrates is human" is analyzed into "Socrates" and "something is human," "it becomes impossible to substitute the wrong way round because the two symbols are now of a different kind themselves." In other words, it is impossible to substitute incorrectly because the syntax is built into the signs.

Commenting on this passage, Brian McGuinness writes,

The thought here is clearly derived from Frege. In a properly constructed language the names of objects and the signs for concepts are such that you cannot construct the nonsensical statement ‘mortality is Socrates’. ‘Socrates’ fits into ‘something is human’, but something is human’ does not fit into ‘Socrates’. And in this respect the properly constructed signs (and our own signs when properly understood) exactly match that for which they stand.

Signs go proxy for objects precisely because when properly constructed – or, what comes to the same thing, properly understood – they cannot be combined in ways which are impossible for the objects. This guarantees that every possible proposition is well-constructed; that no nonsensical proposition can be formulated; and consequently that no theory of types is necessary. ("The Grundgedanke of the Tractatus," 56)

Notice that, according to McGuinness, what is impossible in a Begriffsschrift is also impossible in "our own signs," i.e., in natural language, when those signs are properly understood.

It seems to follow from McGuinness's reading that "Socrates is Plato" is an impossible sign when its parts are properly understood. Of course, that is exactly what standard readers want to say. However, I'm having a difficult time reconciling that view with Wittgenstein's claim that the sign is not illegitimate in itself.

Linked Webpages

There are links to the webpages of Peter Hacker (Oxford), James Conant (Chicago), Peter Sullivan (Stirling), and Ian Proops (Michigan) in the "Wittgenstein Links" section. These philosophers have posted several of their papers on Wittgenstein.

Tractatus 5.473

A key passage (perhaps the key passage) for the resolute reading of the Tractatus is 5.473:

Logic must take care of itself.
A possible sign must also be able to signify. Everything which is possible in logic is also permitted. ("Socrates is identical" means nothing because there is no property which is called "identical". The proposition is senseless because we have not made some arbitrary determination, not because the symbol is in itself unpermissible.)
In a certain sense we cannot make mistakes in logic.

In the Prototractatus version of 5.473, instead of "Socrates is identical" Wittgenstein uses "Socrates is Plato."

5.473 is the descendent of an early notebook entry:

Logic must take care of itself.
φx. If syntactical rules for functions can be set up at all, then the whole theory of things, properties, etc., is superfluous. It is also all too obvious that this theory isn’t what is in question either in the Grundgesetze, or in Principia Mathematica. Once more: logic must take care of itself. A possible sign must also be capable of signifying. Everything that is possible at all, is also legitimate. Let us remember the explanation why "Socrates is Plato" is nonsense. That is, because we have not made an arbitrary specification, NOT because a sign is, shall we say, illegitimate in itself! [August 22, 1914]

(Though I won’t discuss it here, I want to draw attention to a noticeable difference between this passage and 5.473. In the Notebooks, Wittgenstein follows "Logic must take care of itself" with a remark about "rules for functions," i.e., logical syntax.)

When Wittgenstein says "Let us remember the explanation why ‘Socrates is Plato’ is nonsense," he is recalling his earlier account of "Socrates is Plato" in the notes he dictated to Moore:

The reason why, e.g., it seems as if "Plato Socrates" might have a meaning, while "Abracadabra Socrates" will never be suspected to have one, is because we know that "Plato" has one, and do not observe that in order that the whole phrase should have one, what is necessary is not that "Plato" should have one, but that the fact that "Plato" is to the left of a name should. [April, 1914]

This passage occurs in the following context.

The reason why ~x is meaningless, is simply that we have given no meaning to the symbol ~x. I.e. whereas—φx and φp look as if they were of the same type, they are not so because in order to give a meaning to ~x you would have to have some property ~ξ. What symbolizes in φξ is that φ stands to the left of a proper name and obviously this is not so in ~p. What is common to all propositions in which the name of a property (to speak loosely) occurs is that this name stands to the left of a name-form.

The reason why, e.g., it seems as if "Plato Socrates" might have a meaning, while "Abracadabra Socrates" will never be suspected to have one, is because we know that "Plato" has one, and do not observe that in order that the whole phrase should have one, what is necessary is not that "Plato" should have one, but that the fact that "Plato" is to the left of a name should.

The reason why "The property of not being green is not green" is nonsense, is because we have only given meaning to the fact that "green" stands to the right of a name; and "the property of not being green" is obviously not that.

φ cannot possibly stand to the left of (or in any other relation to) the symbol of a property. For the symbol of a property, e.g., ψx is that ψ stands to the left of a name form, and another symbol φ cannot possibly stand to the left of such a fact: If it could, we should have an illogical language, which is impossible.

In these passages we have Wittgenstein’s first thoughts on the issues discussed in Tractatus 5.473. Therefore, this seems like a good place to start in search of the correct interpretation of 5.473 (I don’t mean to imply that the resolute reading is incorrect; obviously, I think it is, or rather, I would like it to be; but I want to leave the question open).

These four paragraphs present a mixed bag. The first paragraph seems to provide unequivocal support for the resolute reading. Given that x is a variable name, it makes no sense to place ‘~’ to the left of it because any sign placed to the left of a name must be the sign of a property, and we have given no meaning to ‘~’ as the sign of a property. Of course we could give meaning to ‘~’ as the sign of a property, in which case ~x would attribute that property to the arguments of x. Thus, Wittgenstein does not say (as perhaps a standard reader would expect him to) that the established use of ‘~’ (as a sign of negation) clashes with that of x. He does not say that the sign ‘~’ cannot stand to the left of a name, but only that we have not yet given any sense to such an arrangement.

The second paragraph could be read either way. We "know" that Plato has a meaning (presumably as a proper name). And "Socrates" is also understood as a name. "Plato Socrates" is nonsense. But is it nonsense because the meaning that we know "Plato" to have clashes with that of "Socrates" (i.e., does the meaning of "Plato" follow it into this context), or is it nonsense because we have not given "Plato" a meaning as the sign of a property? Obviously, if we are to take our cue from the previous paragraph, the latter alternative is better supported. But there are still two other paragraphs to consider.

The third paragraph is the most interesting (to me) in that it suggests (again, to me) a possible way of assimilating 5.473 to the standard reading. But before taking a look at it, let’s move on to the fourth paragraph. There Wittgenstein says that it is impossible for ‘φ’ to stand to the left of ‘ψ.’ The reason is that ‘φ’ and ‘ψ’ are both property-symbols (predicates). A symbol for a property stands to the left of a name. Therefore, ‘φ’ cannot stand to the left of a symbol for a property. If it could, we should have an illogical language, which is impossible. Notice that Wittgenstein does not say that φψ is nonsense because we have given no meaning to ‘φ’s standing to the left of a name. Instead, he says that ‘φ’ understood as a predicate cannot stand to the left of another predicate. Otherwise, we would have an illogical language. This passage seems to favor the standard reading.

Returning to the third paragraph, let’s rephrase the example "The property of not being green is not green" as "Green is not green." Wittgenstein says this is nonsense because "we have only given meaning to the fact that ‘green’ stands to the right of a name" (this gets a bit tricky because Wittgenstein switches between the syntactical rules for function-argument notation in which a predicate stands to the left of a name and the syntactical rules for English in which a predicate stands to the right of a name). That is, we have only given meaning to "green" as the name of a property. This positive way of phrasing things is in marked contrast to the previous negative way of putting it. The negative expression would be "‘Green is not green’ is nonsense because we have not given any meaning to ‘green’ as a proper name." This brings to mind a comment of Cora Diamonds:

For Wittgenstein there is no kind of nonsense which is nonsense on account of what the terms composing it mean—there is as it were no ‘positive’ nonsense. Anything that is nonsense is so merely because some determination of meaning has not been made; it is not nonsense as a logical result of determinations that have been made. ["What Might Nonsense Be," 15]

It seems possible to read the third paragraph as contradicting Diamond. "Green is not green" is nonsense because we have given the sign "green" a meaning as a predicate, and the first "green" is not that, i.e., it is out of place for a predicate.

How might this lead to an assimilation of the negative way of putting it to the standard reading? I’m not sure, but perhaps something like this could be said: The sign "green" has the meaning we have given it. It is a color predicate. As such, it belongs in a certain place, viz., to the right of a name (or, if it is phrased in function-argument notation, to the left of a name). However, if the sign is misplaced (i.e., misused), it’s "connection" with its meaning is severed so that it now has no meaning. We could give it a new meaning as a proper name, thereby giving sense to "Green is not green." Nevertheless, the sign landed in the predicament of not having a meaning by being misplaced, i.e., by violating the rules for its use. (David Pears gives a similar account of the context principle in chapter five of The False Prison.)

Thus, the positive and negative way of phrasing things are different sides of the same coin. That would account for the apparent inconsistency between these passages. I have not thought this through, and it may not hold water. But I want to throw it against the wall and see if anything sticks.

Two New Blogs

(1) SOH-Dan. It's run by Daniel, who is a first-year law student at UT, and likes to "play around with" Davidson, Wittgenstein, McDowell, Hegel and Kant "in his spare time."

(2) Brain Scam. The blog is "a rampart against naive materialist views of consciousness." It's run by Anton Alterman, a computer professional with a PhD in philosophy from CUNY (his dissertation was on Wittgenstein's phenomenology).

Check them out.

Yet Another Wittgenstein Conference

The International Wittgenstein Symposium: Transcendental Phenomenology versus Grammatical Phenomenology. Found out about this one a bit late. It's this week, the 5th-7th, in Toledo, Spain. Conference page is here.

Here are the presenters and their papers:

Arkadiusz Chrudzimski (University of Salzburg), Brentanos Deskriptive Psychologie versus Husserls Trranszendentale Phänomenologie
Alejandro Tomasini Bassols (Universidad Nacional Autónoma de México), Phenomenology of Religion and the Grammar of 'God'
José Ruiz Fernández (Bergische Universität Wuppertal), La crítica filosófica del lenguaje como momento fenomenológico
Sabine Knabenschuh de Porta (Universidad del Zulia), Phänomenologie versus phänomenologische Probleme: die parallaktische Lösung Wittgensteins
Andreas Roser (Universität Passau), Die Grammatik der Bilder (Multimedia-Präsentation)
Pirmin Stekeler-Weithofer (Universität Leipzig) “Nicht ich sage, dass, p”, sondern “p” sagt dass p.”
Miguel García-Baró López (Universidad de Comillas), Revisión de la diferencia ontológica
Jocelyn Benoist (Université de Paris-I), 'Fulfilment'
John Hyman (University of Oxford), ‘This extraordinary use of the word “believe”'
Michel Le Du (Université Marc Bloch. Strasbourg 2), Aspect perception and conceptual perception: Wittgenstein on seeing and understanding
João Vergílio Gallerani Cuter (Universidade de São Paulo), The logical roots of Wittgensteins phenomenology
Azelarabe Lahkim Bennani ( Université Sidi Mohamed Ben Abdellah), Religion und tanszendentale Ontologie bei Wittgenstein
Agustín Serrano de Haro (Consejo Superior de Investigaciones Científicas), Defensa de la perspectiva fenomenológica en el análisis del dolor
Jesús Padilla Gálvez (Universidad de Castilla-La Mancha), Variationen über den Satzt: “Diese Augen die dich sehen sind keinen Augen weil du sie siehst sondern weil sie dich sehen”
Norberto Abreu e Silva Neto (Universidad de Brasilia), La crítica de los usos del lenguaje: Wittgenstein y Kart Marx
Eric Lemaire (Université Denis Diderot-Paris 7/Archives Poincaré-Nancy), Did the whistling really stop?
Miguel Ángel Pérez Jiménez (Universidad Javeriana de Bogotá), Segundas y terceras personas en la aparición del pensamiento
Hans-Johann Glock (Universität Zürich), Wittgenstein in America: description, argument and therapy