Is there a satisfactory account of the truth of the sentence
'Santa Claus does not exist'?

The title question inquires about an account of the truth of the quoted sentence "Santa Claus does not exist", so it appears to invite a discussion of how the quoted sentence can be true (or not).   An exploration of how the sentence would be interpreted as true (or not) according to various theories of Truth might therefore be in order.   On the other hand, the sentence quoted is a classic example from discussions of the meaning of proper names.   So the question may be interpreted as inviting an exploration of various theories of the meaning of proper names.   On the whole, it would seem that Russell's descriptive theory of proper names is the hidden assumption behind the question.   Unlike other theories of the meaning of proper names, Russell's theory (if valid) can be interpreted as providing both an account of the meaning of "Santa Claus", and via that account, an account of how the quoted sentence can be true (or not).

Bertrand Russell (1872 1970) approached the problem of the meaning of names from a primary interest in quantificational classical logic.   He proposed that the meaning of a proper name is not, as Friedrich Ludwig Gottlob Frege (1848 1925) proposed, a combination of that which we pick out from the world (the "referent") and the mode of presentation of the referent (the "Sense") by which we pick out the referent.   Russell's theory of descriptions proposes that the meaning of a proper name is more like that proposed by John Stuart Mill (1806 1873) - directly that which we pick out from the world.   And we pick out the referent of the name because a proper name is but a short hand abbreviation for a definite description something like "The white bearded jolly old elf that brings presents to good little boys and girls at Christmas".   This theory has a nice intuitive feel to it.   If asked what some name means, we tend to provide a description of who or what it is we are talking about.   For Russell, then, the meaning of a proper name is the definite description that in turn picks out some referent from the world.

In addition to its intuitive feel, and the great advantage that this approach had for his treatment of names using quantified classical logic (it is relatively easy to translate a definite description), Russell's theory of definite descriptions also has the advantage that one does not require any referent to make sense of the description.   The statement "Santa Claus does not exist" becomes, according to Russell, {it is not the case that (there exists an object "x" such that "x" is "The white bearded jolly old elf that brings presents to good little boys and girls at Christmas")}.   Or,more formally -

~∃x(x=s)

Since there exists no x such that x=s, the negation of the existential sentence comes out nicely true.   And this can be contrasted with the theories of Mill and Kripke (and possible Frege, depending on how one interprets his "Sense").   These alternative theories would maintain that because there is no referent for "Santa Claus", the quoted negative existential statement is actually meaningless.

Unfortunately, "descriptivist" theories of meaning like Russell's suffer from one fatal flaw.   This was pointed out by Saul Aaron Kripke (1940 "¦.) in his Naming and Necessity.   As Kripke noted, no matter what description one might offer as the meaning of "Santa Claus" it is possible, in modal and counterfactual scenarios, that the thing being picked out by the description is not in fact what the user of the name had in mind.   It is quite conceivable that in some possible world, Santa Claus exists yet is neither white bearded, nor jolly, nor old, nor an elf.   Or, alternatively, it is quite conceivable that the description that someone in this actual world might associate with the name "Santa Claus" has him as neither white bearded, nor jolly, nor old, nor an elf.   So given some counterfactual or non-standard (to Western advertising executives) description of "Santa Claus", would we still be talking about the same Santa Claus?   Russell and Frege would argue that we would not different descriptions results in different meanings, and pick out different referents (if any).   Kripke argues that the common intuition is that in such counterfactual or non-standard scenarios, we are indeed talking about the same thing.   Hence, he concludes, Russell's descriptivist approach to the meaning of "Santa Claus" is wrong.   If Russell's descriptive theory of the meaning of "Santa Claus" cannot properly pick out what is being talked about, then Russell's theory also cannot properly provide an acceptable account of the truth of the sentence "Santa Claus does not exist".   So we have to look elsewhere for a satisfactory account of the truth of that sentence.

A much better approach is offered by John Rogers Searle's (1932 - "¦) cluster theory of identifying descriptions.   Searle proposed that what picks out the referent of a proper name is not a single description, as proposed by Russell, but a whole collection of descriptions and other contextually relevant information.   In addition, he argued that this cluster of descriptions is not something that grants an objective sense of meaning to the name, as was argued by Frege and Kripke.   Rather, the cluster of descriptions is internal to the mind that does the referring.   What ensures that we both pick out the same referent (if and when we do) is the conventional nature of language (and proper name) acquisition.  

In lecture II of his Naming and Necessity, Kripke offers a critique of the cluster theory that has generally been considered to have refuted the theory.   But in his response to Kripke in Intentionality: An Essay in the Philosophy of Mind, Searle argues that Kripke has misunderstood the theory.   Kripke starts his critique of Searle's theory by summarizing it 6 theses (p.71).   Searle does not dispute Kripke's summarization, merely Kripke's interpretation of the summary.   So I"ll borrow here Kripke's summary as a starting point:

1) to every name or designation expression "X", there corresponds a cluster of properties, namely the family of those properties φ such that A believes "φX".

2) One of the properties, or some conjointly, are believed by A to pick out some individual uniquely.

3) If most, or a weighted most, of the φ's are satisfied by one unique object Y, then Y is the referent of "X".

4) If the vote yields no unique object, 'X' does not refer.

5) The statement, "If X exists, then X has most of the φ's" is known a priori by the speaker.

6) The statement, "If X exists, then X has most of the φ's" expresses a necessary truth (in the idiolect of the speaker).

(C) For any successful theory, the account must not be circular. The properties which are used in the vote must not themselves involve the notion of reference in such a way that it is ultimately impossible to eliminate.

Against Thesis 2, Kripke argues that even though their cluster of descriptions does not uniquely pick out a unique "Feynman", the average person still refers with that name to the one and only Feynman [Richard Phillips Feynman (May 11, 1918 February 15, 1988), American physicist known for the path integral formulation of quantum mechanics.]   Against Thesis 3, Kripke provides the counter-example of Godel and Schmidt.   If the only description one has for the proper name "Godel" is "The man who first proved the incompleteness of arithmetic" and it turns out that, contrary to popular belief, Schmidt is this man, then Schmidt would then be the referent of "Godel".   This, as Kripke argues, is contrary to the normal understanding of the referent of the name "Godel".   Against Thesis 4 is the obvious fact that some names are meaningful even though the description associated with it does not pick out a unique individual as was shown in response to Thesis Two. Also, the name can refer even if no one meets the description, as for example the name "Godel" would still refer to the same man, even if counter-factually the proof of the incompleteness of arithmetic turned out to be flawed in some fashion.   Against Thesis 6 Kripke presents the argument that even if we assume that the referent of a name like "Hitler" is in actual fact uniquely picked out by a cluster of descriptions, it does not follow that Hitler must have any of the features given by those descriptions.   Against Thesis 5, Kripke argues that since it is not necessary that Hitler have any of the properties that are used to pick him out uniquely, it is not possible that A know that Hitler has any of these properties a priori.

Searle's response argues that a plausible version of his theory can nullify each of Kripke's objections.   Searle formulates his cluster theory in the context of his theory of intentionality.   To grasp Searle's notion of intentional content it is essential to recognize that the content of a given mental act is not (normally) covered by what the subject might say about it.   Hence, Kripke's notion that the relevant cluster of descriptions can be found by questioning a suitable population is fatally flawed.   The relevant cluster of descriptions involved in the meaning of any proper name is significantly broader than Kripke thinks.   Rather, the reference-fixing cluster consists of the totality of "intentional content" that the subject associates with the name in question.   The referent will be whatever entity actually fits a weighted bulk of this content.   Moreover, for Searle, such content can vary widely from speaker to speaker.   What matters is that two conversing speakers actually pick out the same referent.   How they do so is (mostly) irrelevant.   Thus the cluster of descriptions is not to be regarded as giving the meaning of the proper name, where the "meaning" of a name is construed as something like a definition.

In response to the problem of unwanted necessity (Thesis 6), Searle's argument is that it is indeed necessary that Aristotle has a significant portion of the properties that the speaker associates with the name "Aristotle".   But the associated descriptive content is not in any way "Synonymous" with the name.   It merely fixes its reference.   In response to the "rigid designator" problem (Thesis 3), Searle points out that one normally assumes that a description is rigidified, unless it is specifically altered by the counter-factual presumption at issue.   Hence, "Aristotle" refers, in all possible worlds, to the individual who actually has such-and-such properties.   In response to the problem of ignorance and error (Thesis 2), Searle argues that given the larger cluster dictated by his intentionality theory, the problem of ignorance and error simply does not arise.   For any subject, associated with "Feynman" will be the description "The individual whom others in my conversation call "Feynman" ".   This normal member of every cluster of descriptions explains why Kripke's causal-history theory appears to work so well.   It is not because of any external causal chain that a subject's use of "Einstein" refers to who it does, but because of the intention of the user to refer to the same individual as others in his/her conversational community.   This chain of intention can be traced back to the initial Kripkian baptism just as easily as can Kripke's causal-history chain.   But it also explains some of the examples that Kripke's theory has difficulty with.   Mistakes in the intention to refer to the same referent as one's conversational partners can result in actual changes in referent.   The example of the changed referent for "Madagascar" is cited by Gareth Evans.

Therefore, we can summarize the Intentional Cluster Theory of Proper Names as maintaining that Mill was correct in maintaining an essential part of the meaning of a proper name is what the name denotes in the world.   He was wrong, as Frege pointed out, in thinking that this was all there was to the meaning of a name.   Kripke's notion of a description "fixing the referent" also shows that Mill was wrong to think that a name directly denotes its referent.   The referent for a name is picked out from the world (if it is) by way of descriptions as argued by Frege, Russell, and Kripke.

Russell was correct in interpreting the Fregian "Sense" as a definite description.   He was wrong in thinking of the sense as just one particular description.   Even while allowing that a referent might be picked out by multiple differing descriptions, Russell treated the meaning of a name in any one use as being determined by only one particular definite description.   (Otherwise, his quantificational logic would not have worked.)   Searle recognized that for any one user of the name, the meaning of the name is a related bundle of descriptions - a bundle consisting of all the propositions that the user is aware of (true and false), relating to that particular thing that is intended to be referred to.

Kripke is correct in his argument that a name is a rigid designator.   However, this is of less significance for the meaning of the name, than it is for understanding how names function across possible worlds in modal and counterfactual scenarios.   The bundle of descriptions which a person associates with a name picks out the referent (when it does) in the actual world.   The referent then becomes part of the meaning of that name such that it becomes the intentional referent of the name when modal and counterfactual scenarios are pursued across possible worlds.

Frege was correct in thinking that a good part of the meaning of a name is the "Sense" the manner in which the referent is "presented" to the user of the name.   But he was wrong to think that this "Sense" was an objective property of the name.   As Searle points out, it is entirely subjective.   If our respective bundle of descriptions is sufficiently disjoint, then nothing but confusion will result from any attempt to use the name when talking to each other.   In general, learning the meaning of new names is learning to associate with the name a bundle of descriptions sufficiently similar to other users of the name that confusion is reduced to a tolerable level.

The significance of Searle's intentional cluster theory of names for an "empty" proper name like "Santa Claus" is that the meaning of the name, for any particular user of the name, is the bundle of descriptions that each has learned to associate with the name.   And, assuming that our respective bundles of descriptions are even remotely similar, since that bundle of descriptions picks out no actual referent in the world, there is no referent for name.

So, what the sentence "Santa Claus does not exist" actually asserts is that there is no referent in the actual world picked out by the bundle of descriptions that is commonly associated with the label "Santa Claus".   And, given some relatively benign assumptions about what descriptions are commonly associated with the label "Santa Claus", that assertion is in fact true.   Hence we have a satisfactory account of the meaning of "Santa Claus", and a satisfactory account of the truth of the assertion that "Santa Claus does not exist".

References

Campbell, Richard;   "Proper Names", Mind, New Series, Vol 77, No 307, (Jul 1968) pp 326-350

D'Cruz, Mark;   "A Theory of Ordinary Proper Names", Mind, New Series, Vol 109, No 436, Oct. 2000, pp 721-756

Frege, Friedrich Ludwig Gottlob;   "Über Sinn und Bedeutung", in Zeitschrift für Philosophie und Philosophische Kritik 100: 25-50; English translation reprinted as "On Sense and Meaning" in Collected Papers on Mathematics, Logic and Philosophy, trans. by M. Black, V. Dudman: Geach, H. Kaal, E.-H. W. Kluge, B. McGuinness, and R. H. Stoothoff, New York: Basil Blackwell. 1984. ISBN: 0-6311-2728-3. Pg 157-177

Kripke, Saul Aaron;   Naming and Necessity. Harvard University Press. Cambridge, Massachusetts. 1980. ISBN 0-674-59845-8.

Ludlow, Peter;   "Descriptions", The Stanford Encyclopedia of Philosophy (Fall 2008 Edition), Edward N. Zalta (ed.), forthcoming URL = <http://plato.stanford.edu/archives/fall2008/entries/descriptions/>.

Mill, John Stuart;   A System of Logic, University Press of the Pacific, Honolulu, 2002, ISBN 1-4102-0252-6

Reimer, Marga;   "Reference", The Stanford Encyclopedia of Philosophy (Winter 2007 Edition), Edward N. Zalta (ed.), URL=<http://plato.stanford.edu/archives/win2007/entries/reference/>.

Russell, Bertrand Arthur William;   "On Denoting", in Mind 14. 1905. pg 479-493.

Russell, Bertrand Arthur William;   "Knowledge by Acquaintance and Knowledge by Description", in Mysticism and Logic. Doubleday, New York, New York.. 1957

Russell, Bertrand Arthur William;   Introduction to Mathematical Philosophy. Allen and Unwin. London. 1919.

Russell, Bertrand Arthur William;   The Problems of Philosophy.   Oxford University Press, Oxford, 1997.   ISBN 0-19-511552-x.

Searle, John R.;   "Proper Names", Mind, New Series, Vol 67, No 226, (Apr 1958), pp 166-173

Searle, John R.;   Intentionality : An Essay in the Philosophy of Mind, Cambridge University Press, Cambridge, England. 1983.

Wettstein, Howard;   "Turning the Tables on Frege or How is it that "Hesperus is Hesperus" is Trivial", Philosophical Perspectives, Vol 3, Philosophy of Mind and Action Theory, 1989. pp 317-339

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