Monday, May 07, 2012

Wittgenstein on negation

Plato suggests the following problem in the Theaetetus:
In judging one judges something; in judging something, one judges something real; so in judging something unreal, one judges nothing; but judging nothing, one is not judging at all.
According to Anscombe* Wittgenstein returned to this problem again and again throughout his life. It presents a formidable challenge to his picture theory of language. He thought, in his early work, that in a proposition we supposedly put together a picture of the world just as in the law-courts of Paris of the early twentieth century, a car accident is represented by means of dolls. So how do we get a picture of negation?

What any picture, of whatever form, must have in common with reality, in order to be able to depict it - correctly or incorrectly - in any way at all, is logical form, i.e. the form of reality. So what reality does a negative proposition represent? What is the reality represented by 'snow is not black'? According to Wittgenstein, the negation operator 'not' does not make a picture at all, but simply performs a truth functional operation on the picture given by the corresponding affirmation. The picture he drew in his early Notebooks (above) shows this clearly**. And in the Tractatus he writes (my emphasis)
4.0621 But it is important that the signs 'p' and '-p' can say the same thing. For it shows that nothing in reality corresponds to the sign '-'.
Determinatio negatio est. Determination is negation. By drawing a circle in the sand we delimit all the sand on the beach outside the circle as well as all which is inside.

Does this help us to understand how the concept of negation is learned?  Is negation a concept at all?

*G.E.M. Anscombe, An Introduction to Wittgenstein's Tractatus (London 1971) p.13
**Taken from a nice paper by Robert Pippin here about this subject.


Anthony said...

"Does this help us to understand how the concept of negation is learned? Is negation a concept at all?"

Is that a typo? Certainly negation is a concept. I don't think Ockham would have said that "negation" is a syncategorematic term. But is negation, in the context of the word "not", a non-linguistic concept?

You suggest earlier that we might be able to learn the meaning of the word "not", but not be able to learn "the mental term itself".

I think it's worth questioning whether or not there is a "mental term itself".

Can someone who does not have access to any form of language grasp "A is not not-A"? Before we can grasp "A is not not-A", we must have a symbol, A. And assigning symbols to concepts is language (whether the language is spoken, written, felt a la deaf-blind sign language, etc.).

khadimir said...

I am willing to venture that negation is not a determinate, singular concept. It is a general or abstract concept (generalized or abstracted from particulars) that becomes determinate when paired with what it is to negate. That is, it is a 1-place operator requiring a domain and codomain to be well-defined (understood algebraically). Hence, barring a Platonistic or some such view, “negation” would appear not to be univocal. But if that is true, have I not already given into a nominalism? Moreover, my thought might crash on the rocks of “determination is negation,” since we classically say that a thing is determinate if it both is this and not that, etc.

If I follow the strict definition of a “syncategorematic” term, it is not obvious that what I propose is one. It would require some explanation about reference and meaning.

Of course, I suspect EO knows far more on this issue that I do, and I provide perspective rather than specialized knowledge. I think that I have not sufficiently separated the metaphysical and epistemic dimensions in my thoughts, in part because the question of learning seems to be the latter ratehr than the former.

Yes, in answer to Anythony, I do believe that a person or non-human species can grasp determinate negation without language. Language is more than assigning symbols to concepts, and that more would matter if looked at from a developmental account, which is lurking in my mind.

Anthony said...

"Language is more than assigning symbols to concepts"

What is the more?

Certainly modern languages have more. Modern languages are used for communication as well as cognition. But what is the sine qua non of language, if not the assignation of symbols to concepts?

khadimir said...

Communication through social action, which need not be so cognitive as you imply. I'm coming from a symbolic interactionism viewpoint if you're familiar with it. If not, then let's just say that you describe language only at its higher functions, which are not necessarily its bases.

Anthony said...

But what about the inner voice? Is that not a role outside of communication where language plays an integral part?

Anyway, besides whether or not this assignation of symbols to concepts is language, the more substantive point is that explicitly grasping "A is not not-A" requires the use of symbols to represent concepts.

Edward Ockham said...

>>Certainly negation is a concept. I don't think Ockham would have said that "negation" is a syncategorematic term.

A very good point. He would have said that it is an abstract noun. But what is the corresponding concrete? He says the abstract noun 'whiteness' stands for all white things. But what does 'negation' stand for?

Anthony said...

"He says the abstract noun 'whiteness' stands for all white things. But what does 'negation' stand for?"

It stands for all acts of negating.

Maybe I'm wrong about this, but I'm suggesting that these, at least within the context of the word "not", are linguistic acts. Negation, in the context of the word "not", is adding the word "not" to a sentence.

How did Ockham handle the word "nothing"? What is the corresponding concrete for "nothing"?

khadimir said...


Then what does "not" mean? Does it refer to anything? If it does refer, does it refer to a singular? Probably not, since it has already been named an abstract noun, and I suspect that Neo-EO is not going to affirm the existence of abstract objects.

EO is, if you are not aware, engaging in a classical discussion not unlike when I brought up the Meno. I don't think it was ever satisfactorily laid to rest, but I am not the person to ask for details.

Anthony said...

The word "not" is not an abstract noun. It's not even a noun. It's an adverb.

khadimir said...

Clearly I need more coffee. Whiteness, nouns, notness, it's all good.

Edward Ockham said...

I said the word 'negation' is an abstract noun. I did not say the word 'not' is an abstract noun.

Anthony said...

Ed, Jason is the one who said that it was an abstract noun. See the comment above mine. "Then what does "not" mean?" " has already been named an abstract noun".

khadimir said...

And I was mistaken, but that is beside the point as we can just talk about the noun form of the word.

Anthony said...

I'm pretty sure there is no noun form of "not".

khadimir said...

Quoth the Raven,

"I said the word 'negation' is an abstract noun. I did not say the word 'not' is an abstract noun."

Anthony, did you miss that? We can also say "notness," "negativity," "nullity," etc. You are starting to sound like a contrarian.

Anthony said...

"Notness" is not a word.

I'm not trying to be contrarian. I just think that being accurate is important when you get into these types of discussions. If you let these seemingly innocuous inaccuracies get too far you wind up with nonsense like "Das Nichts nichtet".

khadimir said...

I do not believe that to be nonsense. I do think we might disagree on semantics and more, but it is of no consequence to this discussion, because I do not intend to bring up those issues as it is not productive to EO's posts.