Friday, February 17, 2012

Contingent and necessary identity

Anthony asks what happens if we attach the sentence "Someone called Shakespeare wrote Macbeth" to a text containing a fragment such as

(*) There was [also] a man called ‘Shakespeare’ who lived in Stratford. Shakespeare was a shareholder of the Globe company

I argued in my previous post that indefinite terms act as ‘referential isolators’. They prevent back-reference to any term in an earlier sentence. What Anthony seems to be getting at here is that ‘wrote Macbeth’ seems to be a description that applies to the Shakespeare who was a shareholder of the Globe, and so we might infer an identity, and hence a reference, that is ruled out by the ‘isolator’ theory.

I don’t agree. Consider

(**) Someone called ‘Shakespeare’ wrote Macbeth. There was [also] a man called ‘Shakespeare’ who lived in Stratford. Shakespeare was a shareholder of the Globe company.

I say that the identity between the Stratford man and the Globe man follows from the truth of the second and third sentence, because we cannot understand the ‘Shakespeare’ of the third sentence without understanding that it refers back to the indefinite ‘a man called Shakespeare’. Hence the identity statement ‘The Stratford man was the shareholder of the Globe company’ is true in virtue of the meaning of the terms.

By contrast, the identity of the author of Macbeth and the Globe shareholder cannot be inferred as a logical consequence of the truth of discourse (**) above. It makes the identity highly probable, admittedly, but probability, even if almost absolutely certain, is not the same as logical certainty. This is because of the referential isolator of the second sentence. By contrast, if we change this to

(***) Someone called ‘Shakespeare’ wrote Macbeth. Shakespeare lived in Stratford. Shakespeare was a shareholder of the Globe company.

i.e. if we turn the isolator into a back-referring term, the statement ‘the author of Macbeth was the Globe shareholder' is now true in virtue of the meaning of the terms.

This resolves Wittgenstein's complaint about identity, Tractatus 5.5303 - "Roughly speaking, to say of two things that they are identical is nonsense, and to say of one thing that it is identical with itself is to say nothing at all.  To say that "X is identical with itself" is trivial, because 'itself' refers back to the subject of the sentence. Because of the grammar, we cannot place an isolator between 'itself' and 'X'.  When there is an isolator, as with (**) above, the identity ceases to be trivial. The identity sign therefore is an essential constituent of our language.

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7 Comments:

Blogger Anthony said...

Okay, if the world consisted merely of perfectly ordered texts, this might work.

I'm looking forward to reading how you're going to move this into the real world, however, where everyone has read and/or perceived and/or otherwise come to know different facts in a different order, but yet we still are able to communicate.

12:52 am  
Blogger Anthony said...

"In addition to being worth more than 99.9% of Americans, if elected president, Romney would also be wealthier than any president except one."

1:44 am  
Blogger David Brightly said...

Ed,

On reading your final paragraph my initial reaction was 'Of course! How neat!' but on further reflection I am not so sure.  Your suggestion seems to be that Wittgenstein's complaint arises through a quirk of grammar---the way language is forced to distinguish between and serialize synchronic information on disparate objects.  I think it goes deeper than this.  Consider an arithmetic statement like 3*4=5+7.  Aren't we forced into saying something like 'the number calculated by the formula on the left is the same number as the number calculated by the formula on the right?   We are back with Wittgenstein:  How can two things be sensibly said to be identical?  And I don't see this being resolved by looking at the syntax of the expression.  I'm more inclined to suggest that the logic of identity is a 'shorthand' for something more complicated.  We are not (being realist about numbers for sake of argument) saying that two external objects are one.  Rather we are saying that two singular concepts are co-instantiated.  3*4 is one way of thinking about 12 and 5+7 is another way.  The two ways are distinct but a single number instantiates both ways and we only discover this by doing the arithmetic.  Likewise we may discover that the distinct concepts author of Hamlet and Stratfordian called Shakespeare are co-instantiated.  This is not to say that your analysis in terms of referential isolators is wrong.   It looks to me a good account of how we parse stories into concepts.  I just don't think it resolves Wittgenstein's complaint. 

1:59 pm  
Blogger David Brightly said...

One further thought.  A couple of times you say some statement is true by virtue of the meaning of the terms.  For example, given the story

(**) Someone called ‘Shakespeare’ wrote Macbeth. There was [also] a man called ‘Shakespeare’ who lived in Stratford. Shakespeare was a shareholder of the Globe company.

you say that

Hence the identity statement ‘The Stratford man was the shareholder of the Globe company’ is true in virtue of the meaning of the terms.  

The phrase the meaning of the terms  suggests an a priori character to the necessity of this identity.  Do you really intend this?   I'd be happy to say that the identity is an inference from the structure of the sentences---a species of logical necessity---but not from the meanings of the terms.   After all, we could substitute alternative names and predicates into the story and obtain a corresponding inference.   It seems to be the form of the story that counts in this---the shape of the tree, not the details of its leaves.

1:37 pm  
Blogger Edward Ockham said...

I did spot that there may be a mistake there but hoped no one would notice. If we say

A is an F
That F = A

is that true in virtue of meaning or not?

1:45 pm  
Blogger Edward Ockham said...

By contrast, in

John is running.
He = John

The identity is clearly true in virtue of &c.

1:47 pm  
Blogger David Brightly said...

I'm not sure I appreciate the contrast. I'd say that

A is an F
That F is a G
Ergo, A is a G

is an inference schema which critically depends on how 'that F' ties back to the preceding 'an F'. 'An' and 'that' are somewhat like logical constants, perhaps. They clearly make some contribution to the meaning of the story.

5:39 pm  

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