Charley’s (single) ant

And here is another interesting paper by Greg Frost-Arnold, “Too much reference”. He considers the case in some way opposite to empty singular terms: where a singular term ‘refers to’ more than thing.

He writes:

Suppose a person purchases an ant colony. There are many small ants in the colony, and two big ants, Ant A and Ant B. However, the owner of the ant colony does not realize that there are actually two big ants, because he only sees one big ant at a time. (We assume the ants’ behavior is coordinated to satisfy this condition.) The owner believes that there is one big ant in the colony, and the owner decides to name this ant ‘Charley.’ The philosophical issue such a story raises is this: what is the semantic status of sentences that include the term ‘Charley’?

This is a case I discussed, with reference to a Bunuel film, here and here. There are actually two people (Carole Bouquet and Angela Molina) playing the same character (Conchita). Does the name ‘Conchita’ refer to two people – for once you have realised the trick, it is obvious that there are really two characters – or one? Or (pace Greg) to none at all?

If the theory of reference (the ‘Frodo’-Frodo theory) I have argued for is correct, this sort of multiple reference is impossible. The meaning of a name is exhausted by its function of purporting to signify the same thing. To understand the sentences ‘Fa’ and ‘Ga’ is to understand that if they are both true, then “some F is G” is also true. And, because they do not imply that some Fs are G, they they can only imply that one F is G. To say that there are two F’s is to say that there is an F, and there is another F. The word ‘another’ is the complement of a singular term. It always means a different thing, and for there to be one different thing means there being at least two different things.

What about the ants? Can’t it plausibly said that the proper name ‘Charley’ refers both to Ant 1 and to Ant 2? No, because, as I have argued, reference is not a semantic relation between language and reality. As I have argued, we can regard the two ant images as visual proper names. I see ant 1 walking out of the colony, and entertain the visual proposition ‘Here is an ant’. Ant 1 goes back, and ant 2 now comes out. I entertain the visual proposition ‘Here is the same ant’. Since I cannot understand this visual singular as applying to more than one singular, i.e. because I understand it always as meaning ‘the same …’, I cannot understand it as multiple reference. Thus it cannot be multiple reference. Singular terms always refer to singular things.

Is Atlantis West of London?

I just spotted this excellent post from May 2008, by philosopher Greg Frost-Arnold. He says that, in negative free logic (a variety of which I have argued for here, across too many posts to mention), all atomic sentences containing non-denoting names are false. But this leads to the following problem, he says. Assume, as seems probable, that 'Atlantis' is a non-denoting name.  Then in negative free logic, all three of the following sentences must be false.

(1) Atlantis is West of London.

(2) Atlantis is East of London.

(3) Atlantis and London have the same longitude.

But 'x is west of y' means the same as 'x is not east of y, and x does not have the same longitude as y', and now we have a problem.

If 'Atlantis is west of London' is false (as the free logician says), then at least one of 'Atlantis is east of London' or 'Atlantis and London the same longitude' has to be true -- but that contradicts the earlier assumption (of the negative free logician) that all of (1)-(3) are false.

He asks "Does anyone see a good response to this objection on behalf of the proponent of negative free logic?"  I answer: the objection relies, first, on the perfectly valid assumption that if p is equivalent to "~q and ~r", then ~p is equivalent to "q or r".  Second, it relies on the invalid assumption that "Atlantis is West of London" is equivalent to a conjunction of two negatives.  On the contrary, it is equivalent to the conjunction of two affirmatives. It is equivalent (according to our variety of NFL) to "something which is identical with Atlantis is West of London".  This in turn is equivalent to "something which is identical with Atlantis is neither East of London nor has the same longitude as London".  And the negation of that is

(4) It is not the case that something identical with Atlantis is not East of London, or it is not the case that something identical with Atlantis does not have the same longitude as London.

Now if (1) is false then (4) is true, and if Atlantis exists, it follows that Atlantis is East of London, or that Atlantis and London have the same longitude (I will omit the proof, which is elementary).  But if Atlantis does not exist, both (2) - which is equivalent to "something which is identical with Atlantis is East of London" - and (3) - which is equivalent to "something which is identical with Atlantis has the same longtitude as London" - are false.  For the presumption is that nothing is identical with Atlantis. 

This requires the negative free logician to bite a bullet, but it is not the unpalatable one that Frost-Arnold suggests.  We have to concede that sentences like "Atlantis is large" and "Atlantis is not large" are not true contradictories, but contraries.  The second is not the negation of the first. The true negation of the first is "notthing is Atlantis or Atlantis is not large".  But there cannot be simple solutions in philosophy.  When we have exhausted everything that is wrong, what remains must be right.