Could the statement, "The present Prime Minister might not have been
the present Prime Minister" be true?
Explain your answer.

Can the statement be true?   Yes!

But to explain why, I will need to explore the nature of "definite descriptions", and the nature of "modal assertions".   In other words, to understand why the question can be definitely answered with a "Yes!" we need to understand just what the statement means - just what it is that the statement is asserting.

Definite Descriptions

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 present Prime Minister".   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 present Prime Minister", 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 present Prime Minister" would break down the phrase as the logical conjunction of two separate assertions: -

(i)     there is at least one x such that x is the present Prime Minister; and

(ii)   there is at most one x such that x is the present Prime Minister.

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

(∃x)(Px & (∀y)(Py ⊃ y=x))   -   where "P" is the predicate "is the present Prime Minister"

Now clearly, by Russell's theory of definite descriptions, the truth-status of this description turns out false, since there is more than one instance of a present Prime Minister in the world, and the temporal indexical "present" is unresolved.   Hence, on a superficial analysis, Russell's theory of definite descriptions is quite inadequate in providing a meaning for this phrase

However, following the suggestions of many 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 superficial 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 insert into the Russellian interpretation of "The present Prime Minister" an additional element that provides for those contextual factors.   The contextually delineated conditions narrow the field of relevance so that the description, as actually used, does pick out a single individual - as Russell's theory requires.   Further, since the word "present" in the description is an indexical pointer to some specific temporal instant - namely the instant of the utterance of the statement - rather than leaving the temporal factor imbedded within the contextual term, we can explicitly add into the formula a term for the absolute temporal translation of that indexical.     With these additions to the classical Russellian interpretation of the description, the uniqueness half of the bi-conditional becomes true.   The symbolic formulation is expanded into -

(∃x)((Px & Cx & Tx) & (∀y)((Py &Cy & Tx) ⊃ y=x))
  where -                   "P" is the predicate "is the Prime Minister", and
                                              "C" is some contextual factors that narrow the field of discourse, and
                                              "T" is the absolute temporal translation of the indexical "present".

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 would be "of Canada."   And the temporal factor would be "on February 15th, 2009 at 1325 hrs CST."   Now, with these simple additions, 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 restored to utility.   The "improper" definite description "The present Prime Minister" is understood to denote one unique existent - in the case of this utterance, the individual of Stephen Harper.

Modal Assertions

But now we need to notice that the title statement in question contains the same definite description twice.   In order to clarify this, I will use the symbol "[H]" to signify the individual denoted by both the contextualized definite description and the proper name "Stephen Harper".   I will use this symbol rather than the proper name to avoid any confusion that might arise from the interpretation of the meaning of proper names.   Hence, if we insert the Russellian denoted individual into the title statement we get

"[H] might not have been [H]."

To see how impossible this assertion is, let's put it in "possible worlds" language (without worrying about the potential difficulties that the notion of "possible worlds" adds to modal concepts) -

'there is a possible world wherein [H] is not [H]."

Clearly, on this interpretation of the title statement, it is not at all possible that the present Prime Minister might not have been the present Prime Minister.   In terms of Kripkean(4) "rigid designation", once the Russellian understanding of the definite description has been expanded with the contextual factors to denote a single unique existent, it has become something of a rigid designator.   This is not to suggest that the definite description itself should be considered a rigid designator, because it might not pick out the person of Stephen Harper in every possible world.   But in any given possible world, the unique individual that it does pick out - "[H]" - will be the same one it picks out whenever employed to things in that world.   (We'll ignore, for simplicity, those possible worlds wherein the definite description does not pick out anything.)   So in any given possible world, even if the individual denoted is not Stephen Harper, it is not possible that the individual denoted - "[H]" - is not "[H]".   Whoever the definite description denotes, (on the expanded Russellian interpretation) it denotes one single unique particular existent.   And it is not possible - in that particular possible world - for that particular existent to not have been that particular existent.   So on this interpretation of the title question, the answer would have to be "No!" the statement could not be true.

Referential versus Attributive

But this is not the end of the story.   We now have to fold into our explanation the distinction that Donnellan(5) draws between the referential use and the attributive use of a definite description.   Donnellan's famous illustrative example is the case of Smith's murderer.   Suppose I see Jones on trial for Smith's murder.   During the trial, I observe that Jones is sitting at the defence table talking to himself.   I assert to you "Smith's murderer is insane."   I employ the definite description "Smith's murderer" (equivalently "The murderer of Smith") to draw to your attention the individual sitting at the defence table, on trial for murdering Smith.   I employ the definite description to refer to Jones, and to assert of Jones that he is insane.   I do this even if Jones is not in fact Smith's murderer.   In other words, I successfully employ the definite description in a referential manner, even though the description is in fact false about the individual to whom I am referring.   And, arguably, my statement is true if Jones is insane, not if some person x, who actually murdered Smith, is insane.   (We'll assume that you understand that I was referring to Jones, and not to the actual murderer of Smith.   For simplicity of exposition, in this essay I will ignore the complications of Gricean(6) implicature.)

On the other hand, Dr. Barnes, having heard the testimony about the dramatically brutal and irrational nature of the murder, asserts to the court "Smith's murderer is insane."   He thereby is not referring to Jones, who happens to be on trial for the crime.   He asserts the property of being insane of whoever fits the description of "The murderer of Smith".   The doctor employs the definite description in an attributive manner, irrespective of whatever unique existent the description picks out from the world.

The difference between the two uses of the definite description is one of intent.   In the case of referential usage, the intent is to use the description to denote a specific individual - whether or not the description is accurate.   In the case of attributive usage, the intent is to use the description to pick out from the world whoever matches the description.   Referential usage is "object dependent" in that successful referential usage is dependent on the object intended to be picked out from the world.   Attributive usage is "object independent" in that attributive usage is successful if any object is picked out from the world by "fitting" the description.

If we apply Donnellan's distinction to the title statement, we can see that there are four different ways in which the statement's two definite descriptions might be in intended -

(a)         "[referential] might not have been [referential]."

(b)       "[attributive] might not have been [referential]."

(c)         "[referential] might not have been [attributive]."

(d)       "[attributive] might not have been [attributive]."

In the case of (a) if the description "The present prime minister" is understood to pick out some particular individual existent in the world, then it is not possible that the individual I intend to pick out with that description might not have been the individual I intended to pick out.   This is the interpretation we examined above.

In the case of (d) the statement says of whoever fits the description "The present Prime Minister" (with or without the contextual elements) that he or she might not have fit the description "The present Prime Minister".   Obviously this is also a scenario that cannot possibly be true.   It is trivially true that whoever is the present Prime Minister necessarily is the present Prime Minister - independently of whatever object fits that description.   It is difficult to keep one's mind focussed on this scenario, since the natural tendency is to translate one of the two object-independent descriptions into a referential object-dependent one.   But that is to slip into either scenario (b) or (c).   In this scenario, one has to keep in mind that both descriptions are being employed to establish a class of objects (admittedly, a class with a membership of one), without picking out any particular object.   And one must understand the statement as asserting that "Class A might not have been class A".   And this is as obviously as impossible as scenario (a) above.   (This statement must not be understood as asserting that the contents of Class A might not have been the contents of Class A.   Instead, we must understand the statement as asserting that the definition of Class A might not have been the definition of Class A.   And this is clearly false.)

In the case of (b) we have the statement saying of whoever is picked out of the world by the description "The present Prime Minister" (with or without the contextual elements), that he or she might not be the particular individual I intend to refer to - "[H]" in this case.   Or, to borrow from the previous paragraph - "Class A might not have contained "[H]".   Obviously, this is true.   Given any variation in the contextual elements discussed above, it is entirely possible that my use of the description "The present Prime Minister" might not pick out of the world the individual existent "[H]".   Also, given the variability of possible worlds, and the intended rigid designator function of "[H]", it is entirely possible that in some possible world, "[H]" is not the present Prime Minister.   It wouldn't take much of a variation in recent Canadian politics to have resulted in the fact that "[H]" is not the present Prime Minister.

In the case of (c) we have the statement saying that the individual I intend to refer to - again "[H]" - might not have had the property of being "The present Prime Minister".   It suggests of some particular individual to whom I intend to refer, that the property of being the present Prime Minister is non essential.   In other words, there are many other possible worlds wherein "[H]" happens not to be the present Prime Minister.   So this interpretation is also quite obviously true.

Thus, on two interpretations (a and d) of what the definite description "The present Prime Minister" means, on two interpretations of the intent of the user of the description, the statement turns out false.   On two other interpretations (b and c), including the usually more common one, the statement turns out to be true.   Since the title question is "Could the statement â be true?", then the answer has to be "Yes!"

Metaphysics

But this still is not the end of the story.   All of the interpretations of the title statement discussed so far have depended on a particular understanding of what it means for a situation to "might not have been".   In particular, interpretations (b) and (c) above are dependent on an understanding of "Things that might not have been as they are" that relies on the "possible worlds" semantics of David Lewis(7).   And possible worlds semantics is all about things that are logically possible.   But that need not be the sense in which an utter of the title statement means "might not have been".   Certainly, it is logically possible that things might not have been as they are, and whoever is the present Prime Minister might not have managed to win that office.   But the sense of "might have been" could also be constrained by one's metaphysical assumptions.   If, for example, one assumes a Deterministic metaphysics, then it is in fact metaphysically not possible that things might have been different from the way that they are (or were).

Return to scenario (b) again.   We reasoned that the title statement could be true in this case since given any variation in the context of usage, it is logically possible that my use of the description "The present Prime Minister" might not pick out of the world the individual existent "[H]".   But if the metaphysical premise is Determinism, then this statement is metaphysically false.   Given the infinite variability of logically possible worlds, it is logically possible that in some possible world, "[H]" is not the present Prime Minister.   But then what, metaphysically, are "possible worlds"?

A possible world might describe a logical possibility, but given metaphysical determinism, it would not describe a metaphysically real possibility.   Given Determinism, only the actual world, with its actual history (and future) is metaphysically possible.   So even though it would not have taken much of a variation in recent Canadian politics to have resulted in the fact that "[H]" is not the present Prime Minister, it is not metaphysically possible for that variation to have happened.   So, given metaphysical Determinism, it is in fact not possible that "Class A might not have contained "[H]" if in the actual world "Class A" does (or did) contain "[H]".   Given a metaphysical premise of Determinism, alternative (b) comes out false, not true.

This leaves us with case (c).   Here we have the statement saying that "[H] might not have had the property of being â˜the present Prime Minister'".   But again we depended on the notion of logically possible worlds to argue that there are many other possible worlds wherein "[H]" happens not to be the present Prime Minister.   But once more, given metaphysical Determinism, this comes out false.   Determinism dictates that there is only one existent four-dimensional world-line for any particle or collection of particles.   Given that "[H] does have the property of being â˜the present Prime Minister'" then it is not metaphysically possible for "[H]" not to have that property.   In other words, given Determinism, the property of being the present Prime Minister is (contextually relativized) metaphysically essential to "[H]".    

In other words, given a metaphysical understanding of "might have been," and a premise of metaphysical Determinism, the statement "The present Prime Minister might not have been the present Prime Minister" comes out false under all interpretations of meaning.   So on a metaphysical understanding of "might", the answer to the title question would have to be "No!".

Conclusion

The end of the story is that the answer to the question "Could the statement, "The present Prime Minister might not have been the present Prime Minister,' be true?" depends firstly on how one intends the meaning of "might" as it relates to one's metaphysical premise.   If one assumes metaphysical Determinism and intends the "might" to mean "metaphysically might", then the answer is "No!"   But if one is willing to entertain any logically possible "might", then the answer to the title question has to be "Yes! The title statement could be true!"   And since it is always possible to consider all logical possibilities, even if one does at the moment only mean to include metaphysical possibilities, then again the answer to the title question has to be "Yes! The title statement could be true!"

Notes and References

(1)   Wikipedia contributors;   Definite Description. Wikipedia, The Free Encyclopedia. February 5, 2009, 20:16 UTC. Accessed February 24, 2009.   Available at: 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)   Kripke, Saul;   Naming and Necessity. Harvard University Press. Cambridge, Massachusetts. 1980.

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

(6)   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.

(7)   Lewis, David; Counterfactuals, Blackwell Publishing, Oxford, England. 1973.

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

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; 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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