One can understand the claim, "The baby has been sick all day",
without supposing there is one and only one baby in the world.
So Russell's theory of definite descriptions is wrong.'
Discuss.

A definite description is a phrase in the form of "The X" where X is a noun-phrase or a singular common noun(1).   In this case, "The X" is the noun phrase "The baby".   A definite description is called "proper" if the noun phrase applies to (or picks out from the world) a unique individual or object.   For example "The Prime Minister of Canada on January 1st, 2009" applies to, or picks out, or denotes the particular individual existent known as "Stephen Harper".   A definite description where the noun phrase applies to more than one thing, like "The baby", is called "improper".   (And just to complete the picture, a definite description that applies to nothing - like "The first man on Mars" or "The largest prime number" - is also called "improper".)

In his 1905 seminal work "On Denoting"(2), Bertrand Russell presented what has become recognized as the benchmark analysis of proper definite descriptions.   His analysis of the definite description "The baby has been sick all day" would break down the phrase as the logical conjunction of three separate assertions: -

(i)                                   there is at least one x such that x is a baby; and

(ii)                               there is at most one x such that x is baby; and

(iii)                             whatever is x has been sick all day.

In the symbology of classical quantified predicate logic, this would be translated as -

(∃x)(Bx & (∀y)(By ⊃ y=x) & Sx)   -  
                      where "B" is the predicate "is a baby"
                      and "S" is the predicate "has been sick all day".

Now clearly, by Russell's theory of definite descriptions, the truth-status of this description turns out false, since there is obviously more than one baby in the world.   (The conjunct (∀y)(By ⊃ y=x) is false, therefore the conjunction of the three conjuncts is false.)   Hence, on a superficial analysis, Russell's theory of definite descriptions is quite inadequate in providing a meaning for this statement.   Thus the suggestion that Russell's theory of definite descriptions is wrong.

However, following the suggestions of many post-Russellian philosophers (particularly Neale(3)), the superficial difficulties with Russell's approach to understanding improper definite descriptions can be easily corrected.  

First, we have to recognize a distinction between a statement or sentence containing a definite description - like the statement in the essay title - and an utterance of that statement or sentence.   Recognizing the distinction allows us to acknowledge that no definite description is uttered (written, spoken, or thought) without being uttered at some specific time, in some specific place, by some specific speaker, in some specific context of discourse.   The naïve interpretation of the Russellian theory of definite descriptions, when applied to utterances rather than statements or sentences, can then be expanded to take into consideration these additional contextual factors.

We can add to the naïve Russellian interpretation of "The baby" an additional element that provides for those contextual factors that distinguish an utterance from just a string of symbols on the page.   The contextually delineated conditions narrow the field of relevance so that the description, as actually used, does pick out a single individual baby - as Russell's theory requires.   Such an extension of Russell's original theory is intuitively acceptable since it is eminently reasonable to suppose that no one would actually employ the statement "The baby has been sick all day" without having some specific baby in mind.   The additional contextual element that is added to the theory simply takes into consideration the contextual elements that allow us to identify which baby the utterer has in mind.   With this contextualizing addition to the classical Russellian interpretation of the description, the uniqueness clause of the conjunction becomes true.   The symbolic formulation is expanded into -

(∃x)((Bx & Cx) & (∀y)((By & Cy) ⊃ y=x) & Sx)   -  
  where -                   "B" is the predicate "is a baby", and
                                              "C" is some contextual factor that narrows the field of discourse, and
                                              "S" is the is the predicate "has been sick all day".

In the case of some specific utterance of the particular statement of the essay title, say by me at the time of this writing, the additional contextual factors might be "That I have been hearing crying next door."   Hence, when the definite description is contextualized by the context of utterance, we have a proper definite description that picks out one and only one unique existent in the world.   Russell's theory of definite descriptions is rehabilitated.   The "improper" definite description "The baby" is understood to denote one unique existent - in the case of this utterance, the individual of the baby that I have been hearing all day next door.

There remains one potential difficulty with a contextualization of Russell's Theory of Descriptions.   That difficulty arises from the fact that the contextual factors are not explicit.   Russell's theory was an attempt to provide an objective meaning for definite descriptions - a way in which we could objectively determine what a definite description actually means.   However, if one has to rely on non-explicit contextual factors in order to correctly understand the meaning of an improper definite description, then Russell's theory of descriptions is turned into a subjective theory.   Each interpreter of some improper definite description might apply a different set of contextualizing factors.   Rather than rendering a single objective interpretation, therefore, an utterance of an improper definite description (like that in the title statement), might generate multiple competing subjective interpretations.   If I were to assert to you that "The baby has been sick all day", I might mean "The baby (that I have been hearing crying next door) has been sick all day".   And you might understand me to mean "The baby (that I can see over there) has been sick all day".

This would be a serious, perhaps fatal, problem for anyone who maintains that the meanings of language utterances are (at least to some degree) fixed and objective.   For example, anyone who follows Putnam's "meanings ain't just in the head"(4) meaning-externalism would have serious difficulties with a contextualized Russellian theory of definite descriptions.   On the other hand, for those of us who follow Searle(5), the subjectiveness of a contextualized Russellian theory of definite descriptions would be the expected result.   A detailed analysis of Putnam's meaning externalism versus Searle's meaning internalism is beyond the scope of this essay.   However, actual experience with the confusions that have arisen in conversation would seem to support a Searlean position of meaning internalism, and a subjective contextualization of Russell's Theory of Definite Descriptions.  

So one can indeed understand the claim, "The baby has been sick all day", without supposing there is one and only one baby in the world - simply by acknowledging that whenever that claim is actually made the utterer (under normal circumstances) has some specific baby in mind.   So a contextualized extension of Russell's theory of definite descriptions is not thereby wrong.

Notes and References

(1)   Wikipedia contributors;   Definite Description. Wikipedia, The Free Encyclopedia. February 5, 2009, 20:16 UTC. Accessed February 24, 2009.   Available at URL=<http://en.wikipedia.org/w/index.php?title=Definite_description&oldid=268755946>.

(2)   Russell, Bertrand;   On Denoting, in Mind, New Series, Vol 14 (1905) pgs 479â"493.

(3)   Neale, Stephen;   Descriptions. The MIT Press. Cambridge, Massachusetts. 1990.

(4)   Putnam, Hilary;   The meaning of 'meaning'. Minnesota Studies in the Philosophy of Science, Vol 7 (1975). Pgs:131-193.

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

 

Donnellan, Keith; Reference and Definite Description. The Philosophical Review Vol 75 (1966), pgs 281-304.

Evans, G.;   The Varieties of Reference, Oxford University Press. Oxford, England, 1982.

Grice, H.P.;   Logic and Conversation (William James Lectures) in Syntax and Semantics, Vol. 3, Speech Acts, ed. by Peter Cole and Jerry L. Morgan. New York: Academic Press 1975, 41-58.

Ludlow, Peter, "Descriptions", The Stanford Encyclopedia of Philosophy (Spring 2009 Edition), Edward N. Zalta (ed.), forthcoming URL=<http://plato.stanford.edu/archives/spr2009/entries/descriptions/>.

Kripke, Saul;   Naming and Necessity. Harvard University Press. Cambridge, Massachusetts. 1980.

Kripke, Saul;   Identity and Necessity, in Meaning and Reference, A.W.Moore (ed.), Oxford University Press, 1993.   Pg162-190.

McKay, Thomas and Michael Nelson, "Propositional Attitude Reports", The Stanford Encyclopedia of Philosophy (Fall 2008 Edition), Edward N. Zalta (ed.), URL = <http://plato.stanford.edu/archives/fall2008/entries/prop-attitude-reports/>.

Russell, Bertrand;   Descriptions, in Meaning and Reference, A.W.Moore (ed.), Oxford University Press, 1993.   Pg 46-54

Putnam, Hilary;   Meaning and Reference, in Meaning and Reference, A.W.Moore (ed.), Oxford University Press, 1993.   Pg150-160

Sainsbury, R.M.;   Russell, Routledge & Kegan Paul. Boston, Massachusetts. 1979

Schiffer, Stephen;   Russell's Theory of Definite Descriptions, in Mind, New Series 2005 114(456):1135-1183

Strawson, P.F.; On Referring, in Meaning and Reference, A.W.Moore (ed.), Oxford University Press, 1993.   Pg 56-78

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