Kripke's so-called puzzle about beliefs actually presents a quandary only if one ascribes, like Kripke, to a Millian theory of names. To any variation of a Fregean theory of names, it is no puzzle at all, and presents us non-Millians no quandary at all about ascriptions of belief.
According to Mill, a name is simply a name. The meaning of a name is simply its bearer.(1) The referent of a name exhausts its semantic contribution. Mill accepts Hobbes's definition: "a word taken at pleasure to serve for a mark which may raise in our mind a thought like to some thought we had before, and which being pronounced to others, may be to them a sign of what thought the speaker had before in his mind."(2) For a Millian theory of names, co-referring names should be everywhere intersubstitutable not only salva veritate but even salva significatione.
Since "Cicero" and "Tully" are names for the same metaphysical object (namely, Marcus Tullius Cicero, the Roman philosopher, statesman, lawyer, orator, political theorist.(3)), then a Millian theory of names will argue that "Ann believes that Cicero was a philosopher" and "Ann believes that Tully was not a philosopher" represent contradictory beliefs, and if Ann consciously holds these two contradictory beliefs she is behaving irrationally. But clearly, this is not necessarily the case. If Ann does not know that both names refer to Marcus Tullius Cicero, she could consciously and rationally believe both contradictory beliefs.
In his "A Puzzle About Belief", Saul Kripke(4) presents his famous "puzzle" as part of a defense of a Millian conception of names. He starts off by claiming that the standard criticism of Millianism, based on the fact that co-referring names are not interchangeable in belief ascriptions salva veritate, is based on a logical fallacy. He claims that the criticism is based on the principle of substitution, and that it is improper to convict Millianism on the basis of a problem with the principle of substitution. He argues that the same reductio ad absurdum conclusion can be reached without using the principle of substitution. He demonstrates that the problem of apparently conflicting beliefs can be arrived at using the principles of disquotation and translation, or just the principle of disquotation. He suggests that the problem of apparently conflicting beliefs must be due to these principles that are employed in the arugments, and not necessarily to the nature of Millianism. And then he suggests that because it is not obvious why these various "intuitively obvious" principles should lead to the contradictory beliefs, it represents a real puzzle that must be solved.
However, as pointed out by a number of authors, most notably David Sosa(5), Kripke's reasoning is still based on a thoroughly Millian conception of names. As Sosa lays out in his "The Import of the Puzzle About Belief", Kripke's arguments depend on the Millian concept that a given name has only one semantic contribution. Kripke relies on the premise that if an argument finds itself using two instances of some name, then the semantic import of both instances must be the same. This is most easily seen in Kripke's Paderewski Puzzle. Here is how Sosa analyzes Kripke's argument:-
|(1) Peter is rational.||
(2) Peter, on reflection, assents to "Paderewski has musical talent".
|(3) Peter, on reflection, assents to "Paderewski does not have musical talent".||Assumption.|
|(4) Peter believes that Paderewski has musical talent.||From 2 & Disquotation.|
|(5) Peter believes that Paderewski does not have musical talent.||From 3 & Disquotation.|
|(6) Peter believes that Paderewski has musical talent and Peter believes that Paderewski does not have musical talent.||From 4, 5 & Conjunction.|
|(7) If Peter believes that Paderewski has musical talent and Peter believes that Paderewski does not have musical talent, then Peter has contradictory beliefs.||Definition.|
|(8) Peter has contradictory beliefs.||From 6, 7 & Modus Ponens.|
|(9) If Peter has contradictory beliefs, then Peter is not rational.||Definition.|
|(10) Peter is not rational.||From 8, 9 & Modus Ponens.|
Kripke, of course, claims that because this reductio ad absurdum conclusion is not reached by using the principle of substitution, as used in the traditional criticism of Millianism, it cannot be used to criticize the Millain theory of names. At most, he claims, it can be used to criticize the principle of disquotation that he uses here, because it is the only logical principle used that is not universally accepted as part of standard logic.
However, it is fairly obvious that step (6) is only acceptable if the word "Paderewski" has a common semantic role in both (4) and (5). And this, argues Sosa, is the Millian conception of names. Intuitively, it is not an acceptable step if Peter does not know that the two people he calls "Padewerski" are one and the same person.
That Kripke has in mind a Millian theory of names is clear from two separate lines of evidence. The first is his quick dismissal of the "Frege-Russellian tradition" of a descriptive theory of names. He mentions, but does not elaborate on, a number of criticisms of a strict Frege-Russellian approach to names. Significantly, he assumes that a descriptive theory of names would necessarily involve a "defining description" of the name. And he argues that because this particular concept of a descriptive theory of names does not work in the case of Feynman (a name Kripke suggests has a defining description of "a physicist") and Gell-Mann (a name Kripke suggests also has a defining description of "a physicist"), no sort of descriptive theory of names will work. Kripke also quickly dismisses the cluster theory of names, probably because he is sometimes thought to have provided a definitive refutation of that theory in his Naming and Necessity(6) -- even though Searle(7) has provided a clear demonstration that Kripke's critique was quite off the mark.
The second clear evidence that Kripke is thinking in terms of a Millian theory of names throughout his article, is his asking "Does Pierre, or does he not, believe that London is pretty?" He is thinking that by using the name "London" he can be referring to a unique physical object in the world. But if a Millian theory of names is the not proper way to understand names, this question is illegitimate.
Sosa goes on to analyze all of the examples that Kripke presents, and shows that the same common Millian step is used to generate the "puzzle" that Kripke finds in the results. So, contra Kripke's conclusions, his argument strengthens rather than weakens the reductio ad absurdum conclusion that the Millian conception of names is untenable.
The solution to Kripke's "puzzle" is therefore quite obvious. It is to adopt a non-Millian theory of names that gives a name some form of Fregean "sense", in addition to its role of denoting a referent. If the "sense" of the name Padewerski in (4) and (5) above is different, then the conjunction operation in (6) would be invalid, and the "puzzling" conclusion impossible to reach.
To describe one possible approach to a Fregean-style theory of names, consider a theory that maintains that the semantic role of a name (proper name, ordinary name, name of a kind, or whatever) is to label a large cluster of descriptions -- a cluster that is unique to any one mind; which contains all of the relevant information that mind has available to it; and which may or may not pick out a unique referent in the world. Then as long as Pierre does not encounter any information that would cause him to recognize his error, he can quite rationally believe that Londres is not the same city as London, and that one can be pretty while the other is not. And Kripke cannot ask whether Pierre thinks that London (without qualifying it with a mode of presentation or identification) is pretty or not. Similarly, as long as Peter does not discover his error, he can rationally believe that Padewerski (under the mode of identification as a violinist) is not the same person as Padewerski (under the mode of identification as a politician). Ann can rationally believe that the jolly fat man in a red suit shown in Coca-Cola commercials, known as Santa Claus, is not the same person as the magical elf, also known as Santa Claus, who brings good little girls nice gifts at Christmas. And both Oscar(8) and Twin-Oscar can (before 1750) rationally believe that what runs out of their taps is water.
As I said at the beginning, Kripke's so-called puzzle about beliefs presents a quandary only to a Millian theory of names. To any variation of a Fregean theory of names, it presents no quandary at all for ascriptions of belief.
(1) Reimer, Marga; "Reference" in The Stanford Encyclopedia of Philosophy (Spring 2010 Edition), Edward N. Zalta (ed.), URL=<http://plato.stanford.edu/archives/spr2010/entries/reference/>.
(2) Mill, John Stuart; The Collected Works of John Stuart Mill, Volume VII - A System of Logic Ratiocinative and Inductive, Chapter II -- Of Names, URL=<http://oll.libertyfund.org/index.php?option=com_staticxt&staticfile=show.php%3Ftitle=246&layout=html#chapter_39785>.
(3) Wikipedia contributors; "Cicero" in Wikipedia, The Free Encyclopedia. URL=<http://en.wikipedia.org/w/index.php?title=Cicero&oldid=537083207>.
(4) Kripke, Saul A; "A Puzzle About Belief" in Meaning and Use (Studies in Linguistics and Philosophy), A. Margalit (ed.), D. Reidel Publishing Company, Dordrecht, Holland, 1976. Pgs 239-283.
(5) Sosa, David; "The Import of the Puzzle About Belief" in The Philosophical Review, Vol. 105, No. 3 (Jul., 1996), pp. 373-402, URL=<http://www.jstor.org/stable/2185705>.
(6) Kripke, Saul A; Naming and Necessity. Harvard University Press. Cambridge, Massachusetts. 1980. ISBN 0-674-59845-8.
(7) Searle, J. R.; "Proper Names", Mind, New Series, Vol 67, No 226, (Apr 1958), pp 166-173.
Speech Acts: An Essay in the Philosophy of Langauge. Cambridge: Cambridge University Press. 1969.
Intentionality: An Essay in the Philosophy of Mind. Cambridge: Cambridge University Press. 1983.
(8) Putnam, Hilary; "Meaning and Reference" in Meaning and Reference, A.W.Moore (ed.), Oxford University Press, 1993. Pg150-160
Feit, Neil; "Rationality and Puzzling Beliefs" in Philosophy and Phenomenological Research, Vol 63, No 1 (Jul 2001), pp 29-55, URL=<http://www.jstor.org/stable/3071088>.
Fitch, Gregory; "On the Logic of Belief" in Nous, Vol 19, No 2 (Jun 1985), pp 205-228, URL=<http://www.jstor.org/stable/2214930>.
Garrett, Richard; "Putnam on Kripke's Puzzle" in Erkenntnis, Vol 34, No 3 (May 1991), pp 271-286, URL=<http://www.jstor.org/stable/20012345>.
Laurier, Daniel; "Names and Beliefs: A Puzzle Lost" in The Philosophical Quarterly, Vol 36, No 142 (Jan 1986), pp 37-49, URL=<http://www.jstor.org/stable/2219308>.
Noonan, Harold; "Names and belief" in Prodeedings of the Aristotelian Society, New Series, Vol 81 (1980-1981), pp 93-108, URL=<http://www.jstor.org/stable/4544967>.
Over, D.E.; "On Kripke's Puzzle" in Mind, New Series, Vol 92, No 366 (Apr 1983), pp 253-256. URL=<http://www.jstor.org/stable/2253785>.
Strawson, P.F.; "On Referring" in Meaning and Reference, A.W.Moore (ed.), Oxford University Press, 1993. Pg 56-78
Wikipedia contributors; "Descriptivist Theory of Names" in Wikipedia, The Free Encyclopedia. URL=<http://en.wikipedia.org/w/index.php?title=Descriptivist_theory_of_names&oldid=532084624>.
Wikipedia contributors: "Direct Reference Theory" in Wikipedia, The Free Encyclopedia. URL=<http://en.wikipedia.org/w/index.php?title=Direct_reference_theory&oldid=531199283>.
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