What Exactly is Kripke's Puzzle About Belief?

I will try to explain it as clearly and succinctly as I can.  I will explain the simplest version of the puzzle, the 'monoglot' version.  We shall cleave to English as to our dear mother.

The puzzle is generated by the collision of two principles, one concerning reference, the other concerning disquotation.  Call them MILL and DISQ.

MILL:  The reference of a proper name is direct: not routed through sense as in Frege.  The meaning of a name is exhausted by its reference.  The semantic value of a name is just the object to which it refers.  (Gareth Evans plausibly recommends 'semantic value' as the best translation of Frege's Bedeutung.)

DISQ:  If a normal English speaker S sincerely assents, upon reflection, to 'p,' and 'p' is a sentence in English free of indexical elements, pronominal devices, and ambiguities, then S believes that p.

The puzzle is interesting, and not easily solved, because there are good reasons for accepting both principles.  The puzzle is puzzling because the collision of the two principles takes the form of a flat-out logical contradiction.

And as we all know, philosophers, while they love paradoxes, hate contradictions.

(DISQ) strikes this philosopher as a principle than which no more luminous can be conceived.  How could one who is competent in English and familiar with current events sincerely and reflectively assent to 'Hillary is a liar' and not believe that Hillary is a liar?  The intellectual luminosity of (MILL), however, leaves something to be desired.  And yet it is plausible, and to many experts, extremely plausible.  Brevity being the soul of blog, I cannot  now trot out the arguments in support of (MILL).

The collision of (MILL) and (DISQ) occurs at the intersection of Mind and World.  It comes about like this.  S may assent to

a. Cicero was a Roman

while failing to assent to

b. Tully was a Roman

even though

c.  Cicero = Tully.

Given (DISQ), S believes that Cicero was a Roman, but may or may not believe that Tully was a Roman.  But how is this possible given the truth of (c)?  Given (c), there is no semantic difference between (a) and (b):  the predicates are the same, and the names are semantically the same under (MILL).  For on the latter principle, the meaning of a name is its referent.  So sameness of referent entails sameness of meaning, which is to say: the semantic content of (a) and (b) is the same given the truth of (c).

How can S believe that Cicero was a Roman while neither believing nor disbelieving that Tully was a Roman when the sentences express the very same proposition?  This is (an instance of) the puzzle.  Here is another form of it.  Suppose S assents to (a) but also assents to

d. Tully was not a Roman.

On (DISQ), S believes that Tully is not a Roman.  So S believes both that Cicero was a Roman and that Tully was not a Roman.  But Cicero = Tully.  Therefore, S believes that Cicero was a Roman and S believes that Cicero was not a Roman.  This certainly looks like a contradiction. 

It seems that our governing principles, (MILL) and (DISQ), when applied to an ordinary example, generate a contradiction, the worst sort of intellectual collision one can have.

The Paderewski case is similar.  On different occasions, Peter assents to 'Paderewski is musical' and 'Paderewski is not musical.'  He has no qualms about assenting to both since he supposes that this is a case of two men with the same name.  But in reality he is referring to one and the same man.  By (DISQ), Peter believes both that Paderewski is musical and that Paderewski is not musical.  Given (MILL), Peter believes contradictory propositions.  How is this possible given that Peter is rational?

Given the luminosity of (DISQ), one might think the solution to Kripke's puzzle about belief is simply to jettison (MILL).

Not so fast.  There are powerful arguments for (MILL).

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Comments

[Ed from London]

>> Given (MILL), Peter believes contradictory propositions.
This proves you have still misunderstood Kripke’s argument, which is that DISQ on its own leads to belief in contradictory propositions. As I commented on your last post, either read through section II of his paper carefully, or refer to my post about this misconception of the Kripke puzzle, or to Ephraim Glick’s explanation of the same misconception (from which mine is largely borrowed).

>> Not so fast. There are powerful arguments for (MILL).
Right, but the ‘powerful argument’ is the Kripke puzzle itself.

>>It seems that our governing principles, (MILL) and (DISQ), when applied to an ordinary example, generate a contradiction, the worst sort of intellectual collision one can have.
Again, no. DISQ on its own leads to the contradictory belief.

[Ed from London]

Note also what Ephraim says.

Kripke doesn’t conclude that Millianism is true. But he does conclude that problems about substitution don’t favour Fregeanism over Millianism. Note: It is absolutely crucial to Kripke’s conclusion that Fregeanism doesn’t provide a plausible way to deny or restrict (D) or (T). If it did, then Kripke’s path to the paradox would be blocked while the path through SUB would still be clear, troubling Millians.

Right. I have been saying this all along.

[Bill Vallicella]

Good discussion, Ed. Thanks for the link to the Glick handout which is very clear and helpful.

>>DISQ on its own leads to belief in contradictory propositions.<<

I don't think so. DISQ allows us to generate

Peter believes that Paderewski is musical and Peter believes that Paderewski is not musical.

But you cannot conclude that Peter has contradictory beliefs about one and the same man since Peter is rational and naturally thinks that there are two men with the same name. There is no contradiction because Peter attaches a different sense to each of the tokens of 'Paderewski.'

To derive a contradiction you need more that DISQ, you need MILL as well. Otherwise you won't be able to block the Fregean way out.

Your move. (I think I know what it will be.)

[Bill Vallicella]

One other thing. You may have Glick on your side, but I have the formidable Ruth Barcan Marcus, that fountainhead of a lot of the ideas that Kripke and Co. developed about ten years after she introduced them.

See her paper, "A Proposed Solution to a Puzzle About Belief," Midwest Studies in Philosophy VI, 1981, 501-510.

Marcus sets up the puzzle as I did.

[Ed from London]

>>There is no contradiction because Peter attaches a different sense to each of the tokens of 'Paderewski.'<<
Which is precisely why I carefully pointed you to the assumptions that Kripke sets out, about the ‘standard meaning’ of proper names. You said I was ‘changing the subject’ but I don’t think so. Kripke constantly affirms that it is not enough to sincerely assent to an utterance containing a proper name. We must also understand the name, i.e. the sense we attach to the name must be its standard or usual sense. Thus we have to modify your DISQ as follows:

(DISQ*) If S sincerely/reflectively assents to and understands ‘p’ then S believes that p.

Now if as you say Peter ‘attaches a different sense’ to each of the tokens of the proper name, it follows he hasn’t understand one of them (or both) in the standard sense, i.e. hasn’t understood the name in its proper or standard sense. So DISQ* fails.

Does DISQ* require that co-referential names have the same sense? No. As I said in the comment linked to above, ‘Kripke never sets up the problem by claiming that Pierre learns that the meaning of ‘London’ is London itself. Only that he learns the name as we all do’. The whole point of his long-winded story about Pierre and Londres and London and Paderewski is to show, purportedly, that Peter acquires the names in the usual way.

>> Marcus sets up the puzzle as I did.
Well possibly, I haven’t looked at her paper. That doesn’t address the puzzle of how Kripke sets the puzzle up. Are we discussing the Kripke puzzle or the Barcan Marcus puzzle? Kripke gives a superficially plausible story of how a person learns the meaning of a name, then assents to contradictory utterances containing tokens of the same name, apparently attaching the same meaning, i.e. the meaning he learned, to each of them.

That is the puzzle you need to address.

[Ed from London]

I looked up the Barcan Marcus paper but it is not on JSTOR, nor does my library have the journal in which it originally appeared.

But a plea here. We can discuss what other people say Kripke’s puzzle is, i.e. whether it is as Barcan Marcus supposedly says it is, or as Glick says it is, or as anyone else says it is, or I say it is. Or we can discuss it as Kripke himself sets it up, and I suggest any careful reading of his paper makes it reasonably clear. He carefully sets out his approach in Section II, then there is the very long section which follows, which gives the translation (‘London’) version of the puzzle, which invokes (D) and (T), and the simpler ‘Paderewski’ version which invokes (D) only. Why would Kripke have gone to the elaborate lengths of showing us how Pierre learns the respective names, if he could have made it much simpler by just stating MILL?

[Ed from London]

>>To derive a contradiction you need more that DISQ, you need MILL as well.
We need LEARN.

(LEARN) Pierre learns the meaning of ‘Pad’ in the usual way.

Probably we need a few more trivial assumptions, such as if we have learned the meaning of a word, then we understand it, and that to learn the meaning of a word is to learn its standard meaning. From this it follows that, if Pierre grasps ‘Pad is musical’ as having the meaning that he learned, and likewise for ‘Pad is not musical’, then we can use DISQ* on its own.

Hence we do not need MILL. MILL is one way of implying that the meaning of the two tokens of the proper name is the same. But LEARN is another. You could argue that perhaps LEARN implicitly requires MILL. But then you have a big problem on your hands, I think you can see what that is.

[Bill Vallicella]

Ed,

Do you have a bibliography of items commenting on Kripke's puzzle? That would be useful. You must if you are writing a paper on this topic.

IMHO, Kripke, though a genius for sure, is not that good a writer. So I think it is wise to consult experts in the phil of lang, especially people of the stature of Marcus.

Another question: Can we or can we not adequately discuss this topic while remaining within the English language by using the Paderewski and similar examples? Or is translation somehow essential to the formulation of the puzzle?

[Bill Vallicella]

I said: "To derive a contradiction you need more that DISQ, you need MILL as well. Otherwise you won't be able to block the Fregean way out."

That may be inaccurate. What is needed in addition to DISQ is

SUB: Proper names are everywhere intersubstitutable salva veritate.

(SUB) licenses the validity of

Tom believes that George Orwell is a novelist
George Orwell = Eric Blair
ergo
Tom believes that Eric Blair is a novelist.

MILL entails SUB, but it is not clear that SUB entails MILL. On MILL proper names are senseless tags. But one could hold that names have senses, but not reference-determining senses.

Accordingly, MILL is sufficient (together with DISQ) to generate the puzzle, but MILL is not necessary.

[Bill Vallicella]

>>Now if as you say Peter ‘attaches a different sense’ to each of the tokens of the proper name, it follows he hasn’t understand one of them (or both) in the standard sense, i.e. hasn’t understood the name in its proper or standard sense. So DISQ* fails.<<

This is the move I expected.

You seem to be saying that the name 'Paderewski' is a name type, and that this type has a standard sense, and that if Peter understands this standard sense then he understands that every token of the type has the same sense. So Peter cannot attach different senses to different tokens of 'Paderewski.'

You speak of a standard sense. Is this a reference-determining sense? If yes, then we are back to a Fregean theory and Kripke's puzzle dissolves. So you must be assuming that names have senses that do not determine reference.

So what is the standard sense of 'Paderewski'? Is it given by 'a famous pianist' or by 'a famous politician'? Suppose the former.

Peter assents to 'Pad is musical' and so believes that Pad is musical. Later on, Peter is presented with 'Pad is not musical' but refuses to assent to it because he understands the standard and proper sense of 'Pad.' So the contradiction cannot be generated.

You may be hoist by your own petard. To block my appeal to different senses of 'Pad' you invoked a "standard and proper sense" but if there is one such sense then the puzzle cannot be generated.

[Ed from London]

>> Do you have a bibliography of items commenting on Kripke's puzzle?
I do indeed. Probably far from comprehensive, let me know of any notable omissions.

>> is not that good a writer
Actually I think he is a masterful writer, but this is subjective.

>> Can we or can we not adequately discuss this topic while remaining within the English language by using the Paderewski and similar examples? Or is translation somehow essential to the formulation of the puzzle?<<
I mentioned the ‘London’ version because it is there he sets out his main assumptions, particularly about how the names are learned. The Paderewsi version is less carefully framed.

>> Accordingly, MILL is sufficient (together with DISQ) to generate the puzzle, but MILL is not necessary.
And that is precisely K’s point.

But pushing on – you see we are in agreement again. The weakest part of K’s argument, in my view, is LEARN. It is essential to setting up the problem that Pierre learns the name twice. In the London example, he first learns the name ‘Londres’. K supposes that Pierre lives in France and has ‘heard of that famous distant city, London, which of course he calls Londres’. He adds that Pierre satisfies all criteria for being a normal French speaker, in particular, that he satisfies whatever criteria we usually use to judge that a Frenchman (correctly) uses Londres – standardly – as a name of London. So that’s the first time Pierre learns the ‘correct’ use of the name Londres. Then he learns the meaning of the name ‘London’ through talking with his neighbours. This allows K to use the translation and disq principles to generate the puzzle. Likewise, Pierre learns the name ‘Paderewski’ ‘with an identification of the person named as a famous pianist’. (Perhaps you are right about his being a bad writer – what does that mean?). Later ‘Peter learns of someone called ‘Paderewski’ who was a Polish nationalist leader and prime minister’.

So it’s essential that he learns each of the puzzle names twice. Therefore, according to Kripke, it is possible to assent to ‘a is F’, where ‘a’ is a token of a name correctly learned one way, and also to assent to ‘a is not F’, where ‘a’ is a token of the same name but correctly learned a second way. Note that we don’t even need DISQ, in my view. It is paradoxical that we should even assent to contradictory utterances when we grasp the subject terms as having the same meaning. And what justifies Kripke’s assumption that it is possible correctly to learn the same name twice, in this way? It is obvious – and here I agree with you – that Pierre attaches different meanings to the tokens of the name as tokened under different learnings.

But there is still a problem. Kripke’s examples convincingly show that we can attach different meanings to tokens of the same name, even though we learn it each time in the way that everyone learns it. So how do we learn names at all?

My take on the problem, as you might have guessed, is that it strongly argues for an alternative theory of proper name learning and use. I shall say no more.

[Ed from London]

Our comments crossed.
>> You speak of a standard sense.
Kripke speaks of a standard sense, throughout his famous paper. It is essential to his puzzle that Pierre correctly learns the name. If he learns it incorrectly, then it’s clear he must attach different meanings or senses to the name. So a ‘standard sense’ is (def) the sense we learn when we learn the name in any of the standard ways.

>>You seem to be saying that the name 'Paderewski' is a name type, and that this type has a standard sense, and that if Peter understands this standard sense then he understands that every token of the type has the same sense. So Peter cannot attach different senses to different tokens of 'Paderewski.' <<
See the post that crossed. It seems possible for S to learn the same name twice, and thus assent to ‘a is F’ and ‘a is not F’, where he understands the first token of ‘a’ with his learning the name one way, and the second token with learning the name the second way. The problem is that in both cases he learns the name in a standard or orthodox way.

>>So what is the standard sense of 'Paderewski'? Is it given by 'a famous pianist' or by 'a famous politician'? Suppose the former. Peter assents to 'Pad is musical' and so believes that Pad is musical. Later on, Peter is presented with 'Pad is not musical' but refuses to assent to it because he understands the standard and proper sense of 'Pad.' So the contradiction cannot be generated.<<
See above. The puzzle is that he learns the same name two ways, but both ways are standard ways of learning a proper name.

>>You may be hoist by your own petard. To block my appeal to different senses of 'Pad' you invoked a "standard and proper sense" but if there is one such sense then the puzzle cannot be generated.<<
A standard mode of learning.

[Bill Vallicella]

Your Igal Kvart reference is wrong in your bibliography. His paper cannot be located in Midwest Studies, 1981. I have a number of those vols but couldn't find his paper.

[Ed from London]

I also note a confusion that has been running through this discussion, about the meaning of ‘contradiction’. I do not mean to appeal to etymology or authority, but it’s important we agree on what we mean by it. On my understanding, a contradiction is not ‘the tallest girl in the class is 18’ and ‘the cleverest girl in the class is not 18’, even when the tallest girl is also the cleverest. Someone could easily believe both, without being irrational. The point of the Kripke puzzle is that Pierre seems to end up with an irrational belief. So it’s essential, as Kripke specifies, that he must correctly understand all the terms in both utterances, and that both utterances are logically contradictory, as in ‘Susan is 18’ and ‘Susan is not 18’.

Do we agree?

>>Your Igal Kvart reference is wrong in your bibliography.
Thanks.

[Ed from London]

>> Therefore, S believes that Cicero was a Roman and S believes that Cicero was not a Roman. This certainly looks like a contradiction.<<
It’s not a contradiction, nor does it look like one to me. It is an instance of someone whose beliefs are contradictory. The existence of contradictory beliefs is not itself contradictory, unless we also assume that contradictory beliefs is impossible.

Note also your ‘therefore’is not a logical therefore unless (for the Cicero-Tully case) you assume the translation principle. This says that we can substitute expressions when they have the same meaning. So the assumptions required are these.

(DISQ) If a normal English speaker S sincerely assents, upon reflection, to 'p,' and 'p' is a sentence in English free of indexical elements, pronominal devices, and ambiguities, [and S correctly understands ‘p’], then S believes that p.
(MILL) Names with the same referent have the same meaning
(TRANS) Expressions with the same meaning can be substituted salva veritate.

Thus from DISQ, we get ‘S believes that Cicero was a Roman’ ‘S believes that Tully was not a Roman’. From MILL, that ‘Cicero’ and ‘Tully’ have the same meaning, because of the same referent. From TRANS, ‘S believes that Tully was not a Roman’ translates to ‘S believes that Cicero was not a Roman’, from which we get the contradictory belief.

Kripke’s insight is that MILL is only required to infer the sameness of meaning. If we can appeal to some other principle, it follows that MILL is not essential. The alternate principle he (implicitly) appeals to is the learning principle: if we learn a name in the standard way, i.e. the way everyone learns it, then we correctly understand it. The whole point of the London and Paderewski examples is to show how a person can acquire the meaning of a name, say ‘Paderewski’ by means of two separate learnings. He assents to an utterance where he interprets the name under the meaning acquired one way, and assents to an utterance where he interprets the name under the meaning acquired the other way. But the two utterances are contradictory.

To my mind there are a number of questions here. To start with, why does it follow that when we learn a name ‘in the usual way’, we have learned it correctly? The history of pedagogy abounds in examples of failed teaching, even when the teaching methods are applied rigorously and following the manual. And there is no manual here, it’s self-teaching. Pierre, by Kripke’s account, is picking up the language (when he moves to London) as he goes along. Isn’t it obvious that he associates one meaning with one method of learning, and a different meaning with the other method? So the assumption that Pierre correctly understands the meaning of the utterances is faulty, IMO.

[David Brightly]

We now seem to be asking what further premise needs to be in place in order that we can infer a contradiction from Peter's belief. This strikes me as hopeless. Peter's belief can be rendered as

∃x,y. names ('Paderewski', x) ∧ musical (x) ∧ names ('Paderewski', y) ∧ ¬musical (y) ∧ x≠y. (P)

Can we infer a contradiction from this if we adjoin some general principle? No, since presumably there is some possible world in which Peter's belief is true. To obtain a contradiction we would need to adjoin some statement specific to x or y or both. If Peter comes to believe more about x and y he may find himself in this position. At which point he will no doubt reconsider some or all of his beliefs.

The puzzle, I suspect, is not so much about belief as about the reporting of belief. Can beliefs about n+1 objects always be accurately reported in terms of n objects? Kripke's examples show that the answer is No. The impossibility manifests itself in the absurd conclusion that Peter has inconsistent beliefs.

So Kripke's examples are reductios ad absurdum of any proposed general principles that allow us to infer from P a statement inconsistent with P. No matter how obviously correct they may seem. The interest shifts to explaining why such principles are faulty.

[David Brightly]

Just to expand on the last. Tom has two predicates to distribute over two objects. He can always do this consistently. In representing Tom's belief we take his two predicates but distribute them over just one object. If the two predicates are mutually exclusive we have a contradiction.