Friday, March 13, 2009

The Work of the Symbolic (5)

In 1922 everything may have been simpler. In his introduction to Wittgenstein's Tractatus Logico-Philosophicus, Bertrand Russell was able to write this kind of thing:

There is the question: what relation must one fact (such as a sentence) have to another in order to be capable of being a symbol for that other? [This] is a logical question ... [Wittgenstein] is concerned with the conditions for accurate Symbolism, i.e. for Symbolism in which a sentence 'means' something quite definite. In practice, language is always more or less vague ... [but] the whole function of language is to have meaning, and it only fulfils this function in proportion as it approaches to the ideal language which we postulate.

The next sentence is one of my favourites: "The essential business of language is to assert or deny facts." Today, this statement seems simple-minded, reductionist and just plain wrong. And we could even invoke (the later) Wittgenstein if we wanted to argue against it. But we have to keep Russell's qualification in mind: in practice, he grants, language is vague. He might also have granted that it is involved in many other kinds of business. He (and the early Wittgenstein) is here, in 1922, interested in the workings of a "logically perfect language".

I emphasize this passage because the interest in strictly logical problems allows us, it seems, to write simple, direct sentences. Consider, by contrast, the sentence I have been looking at over the last few posts:

Qualitative-constructivist methodology has a unique advantage for exploring the work of the symbolic in institutional processes as it stresses the embodiment of experience in shared sociolinguistic meanings and practices.

Because "the work of the symbolic" is not a simple business "in practice", it seems, we tend not to write simple sentences about it.

I thought I was going to be done with this sentence today, but I'm going to have to say a bit more on Monday.


Presskorn said...

My point about ”sociolinguistic” - which may be good or bad, I don't really know – might also be expressed as a purely logical problem.

Grammar, Wittgenstein tells us at one point, is a Russellian theory of logical types. And one task pertaining to a theory of types would be specifying the range of objects that particular adjectives can be sensibly attached to. Say, specifying what types of objects that can sensibly be called ”sociologistic”. A theory of logical types would delimit the cases in which an adjective has determinate sense from the cases in which it doesn't.
(Or more logically expressed: it would define what sort of objects that might be reached by the quantifier in a specific type of propositional function.)

Thomas Basbøll said...

Remind me: where does Wittgenstein say this? I thought he said logic can do without Russell's theory of types.

Did you mean "sociolinguistic"? Or is there a problem of self-reference that I'm not grasping here.

Presskorn said...

[I wrote this tract of a response rather quickly, so I apologize for slips & spelling in advance – just I as I apologize for the unintended occurrence of “sociologistic”. Unfortunately, when I write such things they are generally just mistakes and not outbursts of logical brilliance.]

Yes, according to TLP, there is no *need* for Russell's theory of types.

Russell's theory of types was developed in order to avoid certain set-theoretical paradoxes that could be derived from Cantor's work. In specific, Russell wanted to set up rules that would forbid statements of the following type:

”The set of all sets is itself a set”.

Russell avoided or forbade such sorts of statements by setting up rules restricting the domain of quantification associated with predicates such as ”x is a set”. The Wittgenstein of TLP saw no need for setting up up such rules, since he argued that once you've understood such predicates as 'x is a set' you will see that the paradoxes are nonsense (and not the sort thing that threatens the foundations of mathematics etc.). Once you've understood, the nonsense is in plain view. It's just as obviously nonsensical as, say:

”The class of lions is a lion.”

So, in this sense there was no *need* for Russell's theory of types. Within the metaphysical framework of TLP, Russell's formulation of the theory of types also misconstrues the metaphysical relation between logic/language and the world – so there is another sense in which it is also mistaken (which I will return to).

But this doesn't mean that what the theory of types tries to *indicate* is wrong, i.e. that the domain of quantification of such predicates as ”is a set” or ”is a lion” is not restricted. In fact, TLP makes very harsh restrictions on the certain domains of quantification. These restrictions are mirrored in what TLP calls 'formal concepts' (TLP §4.126 - §4.1274), e.g. concepts which express that some name is the name of a 'function', of a 'number', of a 'sound' or of a 'colour'. Once we see that 'red' is a name that falls under the formal concept of a 'colour', we can immediately see that, say,

”Red is a loud sound”

is nonsensical. However, according to the metaphysical and logical framework of TLP, we cannot assert that formal concepts exist, since specifying that ”Red is not a sound” is not part of the fact-stating discourse that alone is meaningful to TLP. Rather the existence of formal concepts *shows* itself. Or better : a formal concept is a just an abstraction gathered from the concrete logico-syntactic behaviour of specific names. Russell's mistake consists in wanting to assert that there are such things as formal concepts; as it were, he is wrong to say them out loud. That is to say, in the strict Tractarian sense, Russellian type-restrictions such as:

”The class of lions is *not* a lion.”

are also, strictly speaking, nonsense.

However, once Wittgenstein left the metaphysical framework of TLP, he could freely speak of what was right in the idea of a theory of types – without fearing his own former criteria of nonsense. So to answer your question: Wittgenstein remarks that ”Grammar is a 'theory of logical types'.” in Philosophical Remarks, §7, and the immediate context of this remark is PR, §6-9.

I suspect that the single scare-quotes are suppose to indicate that fact that Wittgenstein does not mean a 'theory of logical types' in the sense of a very intricate set-theoretical theory, but in the more simply sense, which I exemplified by my remarks on adjectives.

The examples which occur in PR§6-9 are, at least, of this kind:

§6: ”X is ill” is a predicate which only defined for human & other living creatures.

§8: No variable can both taken the property of being a sound & of being a colour. E.g. it makes no sense to say: ”No, wait, that wasn't a sound after all, it's a was color.”

§9: ”Identical” is not defined as a scaling adjective, i.e. ”Identical” is not defined for uses such as ”This table is as identical as this lamb.”

Later, of course, Wittgenstein's notion of grammar modified in ways extending beyond what is contained in the idea of a 'theory of logical types'. But, as you know, that's another very long story. Enough for now and I hope this response was not long enough to bore you.