"If I am thinking about Santa Claus, then there is something I am thinking about.
But Santa Claus does not exist, so I am thinking about nothing."


Bertrand Russell(1) 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 Frege(2) 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.  Although Frege clearly did maintain that empty names like "Santa Claus" can have sense:

"Although the tale of William Tell is a legend and not history and the name 'William Tell' is a mock proper name, we cannot deny it a sense."(3)

Russell's theory of descriptions proposes that the meaning of a proper name is more like that proposed by John Stuart Mill(4) - directly that which we pick out from the world.  And we pick out the referent of the name because, according to Russell, a proper name can be construed as a definite description in disguise(5).  "Santa Claus" means 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.  This means, on this theory, that when I am thinking about "Santa Claus", I am actually thinking about "the white bearded jolly old elf that brings presents to good little boys and girls at Christmas". 

Unfortunately, "descriptivist" theories of meaning like Russell's suffer from one fatal flaw.  This was pointed out by Saul Kripke in his Naming and Necessity(6).  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.  Different cultures associate different images with the name "Santa Claus".  The modern western advertising image is not universal.  It is also 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 of a different culture in this actual world might associate with the name "Santa Claus" is 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 what it is we are thinking about when we are thinking about "Santa Claus".  So we have to look elsewhere for a satisfactory account of what it is to think about something that does not exist.

A much better approach is offered by John Searle's cluster theory(7) 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 word) acquisition.  On this basis, then, what I am thinking about, when thinking of "Santa Claus", is a uniquely personal cluster of descriptions rather than some referent picked out of the world.  So I am no longer thinking of nothing when the referent of the cluster of descriptions does not exist.  Whether the referent exists or not, what I am thinking about when I am thinking about a proper name (or any other name, for that matter) is the cluster of descriptions by which I pick out the referent from the world (when there is a referent to pick out).

In lecture II of his Naming and Necessity, Kripke offers a critique of Searle's 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.  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.  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.(8)]

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'.  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". 

4) If the vote yields no unique object, 'X' does not refer.  Kripke presents 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 (2).  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. 

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

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

(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.

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 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 -- if there is one (the weights being provided by the subject).  Moreover, for Searle, such content can vary widely from speaker to speaker.  What matters for the purposes of successful conversation is that two conversing speakers actually pick out the same referent.  How they do so is (mostly) irrelevant.  It does not matter, in most cases, how congruent are our respective clusters of descriptions fitting "Santa Claus".  Since, in this case, there is no existent referent, only the roles assumed by the description matter.  And it is sufficient that the respective roles we are thinking about are roughly the same, to ensure that we are thinking about the same "thing".  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, when it has a referent.  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 thinker, associated with "Santa Claus" will be a description like "the person/thing whom others in my conversation call 'Santa Claus'".  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 "Santa Claus" 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(9).  But one can easily come up with more common "mistakes" -- if I tell you to "put the bread in the boot", are you going to put the baked goods in the foot wear, or the money in the trunk of the car?

Therefore, we can summarize the Intentional Cluster Theory of Names as holding that Mill was correct in maintaining an essential part of the meaning of a name is what the name denotes in the world -- if it does denote anything in the world.  Mill 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, however, 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 and what it is that we are thinking about when thinking about what is named, 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 unique 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 the name.  Which means that if I am thinking about Santa Claus, then there is something that I am thinking about -- my own personal cluster of descriptions that I have learned to associate with that name.  The fact that there is no actual referent for that name -- assuming Santa Claus does not exist -- does not entail that I am thinking about nothing.


Notes & References

(1)  Irvine, A. D.;  "Bertrand Russell" in The Stanford Encyclopedia of Philosophy (Winter 2012 Edition), Edward N. Zalta (ed.), URL=<http://plato.stanford.edu/archives/win2012/entries/russell/>.

(2)  Zalta, Edward N.;  "Gottlob Frege" in The Stanford Encyclopedia of Philosophy (Winter 2012 Edition), Edward N. Zalta (ed.), URL=<http://plato.stanford.edu/archives/win2012/entries/frege/>.

(3)  Frege, Gottlob;  "Logic", in Posthumous Writings, H. Hermes, F. Kambartel, and F. Kaulbach (eds.), Basil Blackwell, Oxford, England. 1897/1979. Pg 130.

(4)  Wilson, Fred;  "John Stuart Mill" in The Stanford Encyclopedia of Philosophy (Spring 2012 Edition), Edward N. Zalta (ed.), URL=<http://plato.stanford.edu/archives/spr2012/entries/mill/>.

(5)  Ludlow, Peter;  "Descriptions", The Stanford Encyclopedia of Philosophy (Fall 2008 Edition), Edward N. Zalta (ed.), forthcoming URL = .

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

(7)  Searle, J. R.;  Speech Acts: An Essay in the Philosophy of Language. Cambridge University Press. Cambridge, England. 1969.

"Proper Names", Mind, New Series, Vol 67, No 226, (Apr 1958), pp 166-173

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

(8)  Wikipedia contributors; "Richard Feynman" in Wikipedia, The Free Encyclopedia. URL=<http://en.wikipedia.org/w/index.php?title=Richard_Feynman&oldid=528399191>.

(9)  Reimer, Marga;  "Reference", The Stanford Encyclopedia of Philosophy (Winter 2007 Edition), Edward N. Zalta (ed.), URL = .


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

Fitch, Greg and Nelson, Michael;  "Singular Propositions" in The Stanford Encyclopedia of Philosophy (Spring 2009 Edition), Edward N. Zalta (ed.), URL=<http://plato.stanford.edu/archives/spr2009/entries/propositions-singular/>.

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

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

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;  "On Denoting", in Mind 14. 1905. pg 479-493.

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.

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

Wikipedia contributors;  "Empty Name" in Wikipedia, The Free Encyclopedia. URL=<http://en.wikipedia.org/w/index.php?title=Empty_name&oldid=492619880>.

Wikipedia contributors;  "Sense and Reference" in Wikipedia, The Free Encyclopedia. URL=<http://en.wikipedia.org/w/index.php?title=Sense_and_reference&oldid=525543095>.


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