BBC Radio on Wittgenstein

Here is audio of Ray Monk, Marie McGinn and Barry Smith discussing Wittgenstein on BBC radio's "In Our Time."

30th Annual Wittgenstein Symposium

Some pictures and recap here.

Another Wittgenstein Conference

The conference, Wittgenstein: Philosophy & Science, is in Leipzig, September 26-30. The program is here.

Here are the presenters and their papers:

James Conant, Mild Mono-Wittgensteinianism
Sebastian Rödl, The Idea of Practice
Oliver R. Scholz, Philosophie, Wissenschaft und Common Sense – Überlegungen im Anschluss an Wittgenstein
Hans Julius Schneider,„Nur erscheint dadurch der Unterschied der Bedeutungen zu gering." (PU 339) Wittgensteins philosophischer Blick auf die Sprache
Jesús Padilla-Gálvez,Wittgensteins kritische Einwände in der Metalogik
Juliet Floyd, Wittgenstein and Turing
Felix Mühlhölzer, Wittgenstein and Metamathematics
Warren Goldfarb, Wittgenstein and Logicism
William Tait, Wittgenstein and the Problem of Objectivity in Mathematics
Thomas Ricketts, Logical Segmentation in Wittgenstein's Tractatus
Peter Hacker, The Relevance of Wittgenstein’s Philosophy of Psychology to the Psychological Sciences
John W. Powell, Are arguments based on Wittgenstein's remarks about pictures psychological or philosophical?
Joachim Schulte, Wittgenstein's Late Remarks on the Philosophy of Psychology: A Critique of a "Young Science"?
Wolfgang Kienzler, Philosophische Klarheit und wissenschaftliche Exaktheit in der „Logisch-Philosophischen Abhandlung"
Carl Friedrich Gethmann, Wittgensteins angeblicher Sprachspielrelativismus und das Problem trans-kontextueller Geltungsansprüche
John McDowell, Wittgenstein and the Inner

'~', 'φ', and 'ξ'

In the notes that Wittgenstein dictated to Moore in April of 1914, there occurs the following passage.

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. (Notebooks, 116)

I have been unable to make sense of this. Take the third sentence, for example—φx and φp are of different types because to give ~x a meaning there has to be a property ~ξ. What? From the next sentence it seems that ξ concerns subjects, not properties. How, then, does ξ differ from the variable x? And what do ~x and ~ξ have to do with φx and φp?

[Update: In an earlier passage Wittgenstein writes, Take φa and φA: and ask what is meant by saying, "There is a thing in φa, and a complex in φA"?
(1) means: (∃x). φx.x = a
(2) (∃x,ψξ). φA = ψx.φx.
Concerning this passage, Anscombe notes "ξ is Frege's mark of an Argumentstelle [argument-place], to show that ψ is a Funktionsbuchstabe [function-letter]."

Sign, Symbol, and Syntax

In "The Method of the Tractatus" (online here), Conant argues that the "standard interpretation" (exemplified by Baker and Hacker) of Early Wittgenstein on logical syntax is Carnapian, not Wittgensteinian. Conant published a revision of the relevant sections of "The Method of the Tractatus" as "Two Conceptions of Die Überwindung der Metaphysik: Carnap and Early Wittgenstein" (in Wittgenstein in America). Peter Hacker responded to the latter in "Wittgenstein, Carnap, and the New American Wittgensteinians" (online here). And Cora Diamond responded to Hacker in "Logical Syntax in Wittgenstein’s Tractatus" (Philosophical Quarterly).

According to Conant,

Logical syntax, in the Tractatus, is concerned neither with what Carnap calls
"logical syntax" nor with what Russell calls "a theory of types." To express the
same point in the idiom of the Tractatus: logical syntax is concerned neither
with the proscription of combinations of signs nor with the proscription of
combinations of symbols. It is not concerned with the proscription of
combinations of signs, because Tractarian logical syntax does not treat of
(mere) signs; it treats of symbols—and a symbol only has life in the context of
a proposition. It is not concerned with the proscription of combinations of
symbols, because there is nothing to proscribe—"Every possible proposition is
legitimately constructed" (§5.4733). Tractarian logical syntax treats of the
categorically distinct kinds of logically significant components into which
sinnvolle Sätze can be segmented—such components being the sort of components
they are only in virtue of their participation in a possible proposition. (UM,
42)

Conant claims that signs do not have logical syntax. This conflicts with Tractatus 3.33: "In logical syntax the meaning of a sign [Zeichens] ought never to play a role; it must admit of being established without mention being thereby made of the meaning of a sign; it ought to presuppose only the description of the expressions." What does the "it" after the semicolon refer to? To the logical syntax of … what? It appears that Wittgenstein is talking about the logical syntax of the sign. Conant’s response to 3.33 is unsatisfying:

Wittgenstein’s remark in the Tractatus that "in logical syntax the Bedeutung of
a sign ought never to play a role" (§3.33) sounds just like Carnap’s remark that
logical syntax "should have no reference to the Bedeutung of signs." But
Wittgenstein is not saying what Carnap is saying. Mere marks on paper have no
Tractarian logical syntax. Only symbols—"the parts of a proposition which
characterize its Sinn"—have logical syntax. (UM, 43)

In other words, 3.33 doesn’t mean what it says. Only symbols have logical syntax. This, apparently, is supposed to follow from the quotation (an excerpt from 3.31).

Hacker disagrees with Conant:

Conant’s claim that according to Wittgenstein logical syntax concerns only
symbols and not signs is similarly false. It is a confused statement of the
correct point that, according to the Tractatus, there can be nonsensical signs,
but no nonsensical symbols, since a symbol just is a sign used according to the
rules for its correct use. ‘Syntax’, Wittgenstein dictated, ‘is the totality of
rules that specify in what combinations a sign has meaning. It describes
nothing, it sets limits to what is describable. A symbol is what can be
perceived of a sign plus the rules for its use, of its syntax. An understanding
of language presupposes knowledge of the meaning and syntax of signs’ (WWK, p.
220). Accordingly, the logical syntax of a sign is partly constitutive of the
resultant symbol…. (WC, 13)

The passage that Hacker quotes is from 1929-30. Wittgenstein continues,

The form of a proposition is obtained by turning its words into variables
while leaving their meaning out of consideration. A subject-predicate
proposition has a different form from a relational proposition; a symmetrical
relational proposition has a different form from an asymmetrical one. A state of
affairs is a combination of things. The signs of a proposition go proxy for
things, not for the form of a state of affairs, which is exhibited by the form
of a proposition.

Clearly, these are Tractarian doctrines. Thus, we may reasonably conclude that the preceding definitions of syntax and symbol are also Tractarian. Syntax is the totality of rules that specify in what combinations a sign has meaning. And a symbol is a sign used according to those rules.

This is confirmed by Waismann’s Theses. The aim of the Theses was "to present the results of TLP in an easily comprehensible form" (LWVC, 22). Wittgenstein dictated the original Theses to Waismann in the Summer of 1930. Waismann made revisions in 1930-31, but the differences between the versions are minor. According to McGuinness, Waismann was merely "experimenting with different arrangements of the same material" (Ibid.) Given the nature of Wittgenstein’s collaboration with Waismann, it is probable that Wittgenstein supervised the revisions.

Section two of the Theses concerns syntax:

Syntax consists of rules which specify the combinations such that in them alone
a word makes sense. It is by syntax that the construction of nonsensical
combinations of words is excluded.
Our ordinary languages have a syntax. Maps, musical notation, temperature curves also depict reality; they, however, make do without syntax. How is this difference to be explained?
A map can depict reality truly or falsely, but never in a nonsensical fashion. Everything a map represents is possible. A description by means of verbal language, on the other hand, can be nonsensical. I can say, for instance, ‘A is to the north of B, and B is to the north of A’. Such a proposition does not tell us anything, as it does not have the form of the fact it is supposed to represent.
Syntax is hence connected with the possibility of nonsense. (‘Nonsense’ is not the
opposite of ‘sense’. You can indeed say, ‘This proposition expresses a sense,’ but not, ‘This proposition expresses a nonsense.’ It is the use of signs that is nonsensical.)
Syntax hence becomes requisite where the nature of signs is not yet adjusted to the nature of things, where there are more combinations of signs than possible situations. This excessive multiplicity of language must be confined by artificial rules; and these rules are the syntax of language.
The rules of syntax assign to combinations of signs the exact multiplicity they must
possess in order to be pictures of reality.
You could say that a system of signs which is perfectly suited to its purpose renders syntax superfluous. And conversely—syntax renders such a system of signs superfluous. Each of them deputizes for the other. The fact that the form of a system of signs can deputize for syntax is important, for it shows us that the rules of syntax
describe nothing.
You need not first invent an ‘ideal language’ in order to depict reality. Our ordinary language already is a logical picture as soon as you know how each word signifies. The point is only to make the rules of syntax into a system.
The rules of syntax are rules dealing with signs.

Section seven of the Theses discusses symbols:

A symbol is an applied, rule-governed sign.
A sign is what can be perceived of a symbol. (So one and the same sign can be common to two symbols. The sign will then symbolize differently in those two cases.)

This is further confirmed by Wittgenstein’s explanation of Tractatus 3.326, "In order to recognize the symbol in the sign we must consider the significant use":

I think "significant" is al[l]right here. The meaning of the prop[osition]
is: that in order to recognize the symbol in a sign we must look at how this
sign is used significantly in propositions. I.e. we must observe how the sign is
used in accordance with the laws of logical syntax. Thus "significant" here
means as much as "syntactically correct." (Letters to Ogden, 59)

Thus, it is the sign that is used in accordance with the laws of logical syntax. These passages suffice to refute Conant’s claim that signs do not have logical syntax.

Where does this leave Conant? Conant proposes to distinguish mere nonsense from illuminating nonsense (what he calls "substantial nonsense") as follows. Mere nonsense is "a string composed of signs in which no symbol can be perceived, and which hence has no discernible logical syntax." Substantial nonsense, on the other hand, is "a proposition composed of signs that symbolize, but which has a logically flawed syntax due to a clash in the logical category of its symbols" (MT, 400). If these are the alternatives, then there is only mere nonsense. However, once it is admitted that signs have logical syntax, Conant’s argument against "substantial nonsense" becomes irrelevant.

The distinction between mere nonsense and illuminating nonsense is as follows. Mere nonsense is a string of signs that do not have logical syntax, e.g., "lkdjg lsdfkd adsfasd." Illuminating nonsense, on the other hand, is a string of signs that have logical syntax, but are not being used according to those rules, e.g., "Caesar is a prime number." The latter does not involve symbols because a symbol is a sign used according to the rules of logical syntax.

I have written several more pages on the relation between everyday language and Begriffschrift, the 3.31s, and Diamond’s response to Hacker, but this is already long for a single post, so I think I’ll make those comments into separate posts. I’ve also got a criticism of Conant’s interpretation of Wittgenstein’s context principle in the queue, but that will have to wait.