## Thursday, August 18, 2011

### Rigid designation

Is the following argument valid?
The UK Prime Minister is a man
The UK Prime Minister used to be a woman
Some man used to be a woman
You will probably say not.  The first is true because David Cameron (who at the time of writing is Prime Minister) is a man.  The second is true because Margaret Thatcher (who used to be the Prime Minister until the 1990s) is a woman, and always has been.  But the implication is clearly invalid, since the premisses could be true and the conclusion false if no man had ever undergone a sex change.

Kripke's take on this is famous: definite descriptions such as 'The UK Prime Minister' are not rigid. They have different referents in different possible worlds, and so the inference is not valid, because of the non-ridigity of reference.  By contrast, proper names are rigid designators.  Understood in the same sense, they always refer to the same individual.  Thus, if you substitute 'David Cameron' into the inference above, you get something that is valid (although not sound, of course, for the second premiss is false - as far as we know, David Cameron never used to be a woman).

The leader of Cambridge City Council is a woman
The leader of Cambridge City Council used to be a man
Some woman used to be a man
As it happens, the (current) leader of Cambridge City Council is Jenny Bailey, who underwent a sex change operation to become a woman. So Jenny Bailey is now a woman, but used to be a man, and so some woman used to be a man.  The premisses can't be true (assuming "The leader of Cambridge City Council" has the same referent in both premisses) and the conclusion false, so the inference is valid.

How do we explain this?  Are definite descriptions rigid or not?

Ockham has a quite different take on this, distinguishing between 'sense of composition' and 'sense of division'.  He explains it in Book III of his great Summa Logicae here.  In the sense of composition it is signified that a mode (such as 'is possible' or 'was the case that') is predicated of the whole proposition. In the sense of division it is denoted that the predicate is predicated of the subject by a verb determined by such a mode. Thus we must distinguish between 'it was the case that the (then) PM was a woman' and 'it is the case that the (current) PM was a woman'.  Clearly, read in the sense of composition, the subject term may have a different sense in the different premisses.  In 'The UK Prime Minister used to be a woman', the subject term means Margaret Thatcher. In 'The UK Prime Minister is a man' it means David Cameron.  Hence (read in the sense of composition) the inference is not valid because of equivocation, just as any syllogism is invalid because of equivocation.  But read in the sense of division it is valid.  If by 'The UK Prime Minister used to be a woman' I mean that David Cameron used to be a woman, the first inference is valid, just as the second is (where 'The leader of Cambridge City Council' refers in both premisses to Jenny Bailey).

Hence we do not have to accept any fundamental distinction between definite descriptions and proper names.  Rather, it is easier to read definite descriptions in an ambiguous way.  When we say 'The UK Prime Minister used to be a woman', we can read it either as saying that the present PM used to be a woman, or that some former PM used to be a woman.  And this ambiguity is not fundamentally different from the one we find here.

William Pitt was the youngest Prime Minister
William Pitt was not the youngest Prime Minister
the youngest Prime Minister was not the youngest Prime Minister

For there was more than one person called 'William Pitt', just as there was more than one person called 'Prime Minister of the UK'.

David Brightly said...

Can't we subsume much of this under the notion of 'elision of context'? Proper names and definite descriptions are intended to pick out unique individuals from some explicit or more often, implicit, context. Establishing a shared context between speaker and hearer can be tricky. If the name or description fails to deliver any individual it's a clue that the context may be too narrow; if more than one individual too wide. Tense is a significant clue to temporal context.

The UK Prime Minister[now] is a man[now]
The UK Prime Minister[then] used to be a woman[then]
The leader of Cambridge City Council[now] used to be a man[then]
William Pitt[Napoleonic Wars] was the youngest Prime Minister[UK]
William Pitt[first Earls] was not the youngest Prime Minister[UK]

Edward Ockham said...

>>Can't we subsume much of this under the notion of 'elision of context'?

Much but not all, if I am right. I come back to my requirement for a causal relation between the singular term and a specific text, or piece of information. Consider

Two twins walked down the road.
One had blue eyes. So did the other.
The former was exactly 6’ tall. So was the other.
The former was exactly 38 years old. So was the latter. (and so on)

The individuating descriptions here are ‘the former’ and ‘the latter’. But these are not true of the men being ‘referred to’. The reference is to a location in the text – ‘the former’ means ‘the first person referred to in the text’.

Or consider

A soldier came home from the war. The soldier was weary of fighting.

The description used in the second sentence is hardly unique. Millions of soldiers have returned from thousands of wars. Some writers talk about the individual having the feature of ‘being salient’, but that is obscure in the extreme. ‘Salience’ cannot be a property of an individual, any more than ‘being former’. Clearly it is a textual relation that is required.