To: Atilio G.
From: Geoffrey Klempner
Subject: Truth value of 'Santa Claus does not exist'
Date: 30th December 2010 14:01
Thank you for your email of 14 December, with your essay for the University of London BA Logic module, in response to the question, 'Is there a satisfactory account of the truth of the sentence 'Santa Claus does not exist'?'
This is a good essay. It doesn't matter too much that it took you longer than an hour to write. That time has been well spent. The chances are if you came across a suitable question in the actual exam, your writing would be more fluent. (One must always be aware, however, that the nuances of the question in the actual exam might be different so you can't simply rely on memorizing an essay that you've written for practice.)
I would qualify what you say about Parmenides, with the observation that the view amongst scholars seems to be that his question about 'What is not' is not solely confined to 'what does not exist'. For Parmenides, the very notion of negation is problematic. It is equally problematic in the statement, 'x is not F' for some predicate F, or x is not y, where the 'is' in question signifies identity.
I am trying to recall where -- or whether -- Frege claims that in the case of a name lacking a referent, such as 'Santa Claus', we can make the true statement, 'Santa Claus does not exist.' Surely not. The statement, 'Santa Claus does not exist' is *not* the same statement as, ''Santa Claus' lacks a referent.' The first statement is purportedly about an object, while the second statement is about a referring term. The first is about the world, while the second is about language. Whereas in the example, 'Tom believes that Santa Claus came down the chimney last night', the term 'Santa Claus' refers to the sense of the term 'Santa Claus', which is different from the (alleged) reference of 'Santa Claus' and different again from the linguistic term 'Santa Claus'.
Frege viewed the possibility that purportedly referring terms lack a referent as a defect of natural language. His view is generally associated with the idea of 'truth value gaps'. If I say 'Santa Claus came down the chimney', the reference of my statement is neither to 'the True', nor 'the False' because the reference of a statement is a function of the references of its constituent parts, and, by hypothesis, the term 'Santa Claus' lacks a reference. However, this can easily be patched up if we stipulate that the reference of purportedly referring terms which lack a reference is to be some arbitrary abstract object, e.g. the null set. Then the statement, 'Santa Claus came down the chimney' is false because it is false that the null set came down the chimney.
Frankly, I think this is quite an elegant solution, and a lot more economical than Russell's theory of descriptions.
Your objection to Russell's analysis is be that it is 'not correct' to say that 'x is Santa Claus' is always false, i.e. in terms of first-order predicate logic, Not-(Ex)(x is Santa Claus). Or, if we are being more specific, Not-(Ex)(x wears a red coat and x lives at the North Pole and x brings presents to children at Christmas and...). On the contrary, we say and believe lots of things about 'Santa Claus'.
In defence of Russell, however, there is no inconsistency in claiming that a statement like, 'Santa Claus wears a red coat and lives at the North Pole' is false. However, what is not false is that this statement is often made or believed, in which case we have a true statement where the belief or claim about Santa Claus occurs in an indirect context, as in the case of little Tom. It is true that Tom believes that Santa Claus came down the chimney and also true that Santa Claus did not come down the chimney. Of course, that still leaves us with the challenge of analysing indirect contexts, but that is different from the challenge of accounting for the truth conditions for 'Santa Claus does not exist'.
There is, however, a problem which you do not mention, namely that is no clear consensus about which predicates are such that their joint satisfaction would entail the existence of Santa Claus. In other words, there seems to be an unacceptable arbitrariness about the definition of the predicate, 'x is Santa Claus'.
With regard to Gareth Evans' resourceful analysis. It is important to remember that if I state, 'Santa Claus does not exist', meaning, 'Santa Claus does not really exist' in Evans' sense, then I am making a statement about the things that exist (i.e. really exist), to the effect that none of them satisfy the predicates taken to be jointly definitive of the predicate, 'x is Santa Claus'. I am not making a statement about the fictional or mythical object 'Santa Claus'. (I'm not saying that you imply this.) If I were, then this would imply the possibility that the fictional 'Santa Claus' could acquire the extra property of 'real existence'. Or, correlatively, that some object in the actual world could lose the property of 'real existence'. And that is not (on my understanding) what Evans is claiming. If 'real existence' is a property which some Meinongian 'object' can either have or lack, then we are back with the old problem which Frege's analysis was designed to solve.
All the best for 2011!