Suppose young Timmy mistakenly takes 'prime number' to be roughly synonymous with 'cool number'. So he goes around saying things like '666 is a prime number'. Does he believe that 666 is a prime number? Presumably not. He certainly doesn't have a de dicto belief involving the concept prime number, since he lacks this concept (he associates the words, 'prime number', with a different concept entirely). Nor does he have any de re beliefs about primes, i.e. beliefs which talk about this property under a different guise: he does not believe, for example, that 666 is divisible only by itself and 1. What Timmy believes is that 666 is a cool number (or, more likely yet, that '666' is a cool numeral), and he mistakenly takes the sentence '666 is a prime number' to express this belief.
What of Timmy's meta-beliefs? He might not have any, if he's very young, but let's suppose that he's aware of himself as a believing agent. What does he think he believes? Jack suggests to me the following: Timmy believes that he believes that 666 is a prime number. But this attribution seems mistaken for exactly the same reasons. Timmy lacks the concept prime number, so he can't have any (even meta-) beliefs involving it. And nor can he have any de re beliefs about primeness (under whatever guise), because he lacks any alternative grasp of the property in question. He's not capable of having primeness feature in his mental content at all.
Instead, I would suggest that Timmy has entirely accurate meta-beliefs. (We have no reason to doubt his introspective abilities.) He believes, truly, that he believes that 666 is a cool number. That's all. It's only his linguistic beliefs that are false. For example, he falsely believes that he can express his above (true) meta-belief by asserting, 'I believe that 666 is a prime number.' He can't; this assertion means something different from what Timmy thought. It means something that happens to be false, whereas all Timmy's non-linguistic beliefs are true.
The upshot of this is that sincere assertions do not always succeed in expressing your beliefs. Linguistic errors may mean that what you end up saying actually means something different from what you believe (i.e. what you meant to say).
This seems to me the tidiest way to make sense of what's going on in these cases. Is there any residual problem that the above analysis fails to deal with?
Saturday, February 16, 2008
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You here assume that words have an intrinsic meaning to them. While the truth is words have conventional meaning. So Timmy has a different meaning for "prime numbers" that the commonly agreed to meaning for this two-words combination.
ReplyDeleteSo I would say: "Timmy believes that 666 is a prime number." And this would be true relativist belief. If someone is confused we can elaborate by saying: "Timmy believes that 666 is a prime number. He also believes that prime numbers mean cool numbers."
We cannot judge the second proposition that "Timmy believes that prime numbers mean cool numbers" as a false belief, because the meaning of 'prime numbers' as the divisibility by 1 and itself only is strictly applicable to those who agree to this definition of this two-words combination.
DM, I think we need to be more careful about the use/mention distinction. 'Prime number' is a two word phrase that could have meant something else entirely. But a prime number (here I am using language, not mentioning it, to get at objects in the world) is a number divisible only by 1 and itself. This latter fact is non-contingent and non-conventional: we can't change the mathematical truths just by changing how we speak! Using the numeral '3' to denote the number 4 will not make 2+2=3. It will instead make the sentence '2+2=3' express the truth that 2+2=4.
ReplyDeleteNow, the reason we can't say that "Timmy believes that 666 is a prime number" is that when we speak, we are using the words in our language, and so 'prime number' there means prime number rather than cool number. (Which, as my original post explains, cannot possibly be what Timmy believes.)
You might think the underlying problem of (1) and (2)--the being surprised if you're right problem--strike down (3) as well, though not as dramatically.
ReplyDelete(1) Timmy believes that 666 is a prime number.
(2) Timmy believes that he believes that 666 is a prime number.
(3) Timmy believes that 'prime number' means cool number.
Describe a world in which 'prime number' means cool number. It would be very different from the actual world, qualitatively speaking. Depending on Timmy background story, it might well be that the most similar world to the actual world in which 'prime number' means cool number is not a world that Timmy thinks is actual at all. (His textbooks would be qualitatively different than they actually are, his teacher would have said things that she actually didn't...)
As a second comment, I find it very hard to deny the following de re ascription:
(4) Some prime number are such that Timmy believes they are numbers.
For (4) to be true, Timmy need only believe that 2 and 3 are numbers. He does not need to possess the concept of a prime number to believe of some prime numbers that they are numbers. Nor, does he need to possess the concept of a prime number to believe of prime numbers in general, that they are numbers/integers,...
Ok, bear with me... Your argument is convincing, but I still have few subtle issues that I am not sure we are getting correctly.
ReplyDeleteYou say: "It will instead make the sentence '2+2=3' express the truth that 2+2=4."
Here you refer to '2+2=3' as an expression of the mathematical truth that 2+2=4. The problem is '2+2=4' itself is NOT a mathematical truth, but only just like '2+2=3' is also an expression of a mathematical truth. So neither '2+2=3' nor '2+2=4' are mathematical truths, both are expressions of that truth.
You say in the post: "It's only his linguistic beliefs that are false." - I don't think that any linguistic beliefs can be false. While certain truths like mathematical truths can be considered as objective truths, language is by its nature relativist.... No expression is wrong for an idea.
So if someone says: '2+2=3' and he means by that expression what we mean, we can say that he is objectively wrong from a mathematical perspective. But if '2+2=3' refers to what we mean '2+2=4', then he is objectively correct... But we cannot judge the expression '2+2=3' to be symbolically\linguistically wrong! Or can we?
You are right: When we make a proposition, we make it in our own language. So I agree that when we say, "Timmy believes that 666 is a prime number" is a false statement. But I don't agree that he has wrong linguistic beliefs. He only has different linguistic beliefs...
DM - '2+2=4' (the string of symbols) is an expression of the mathematical truth that 2+2=4. [For another example of the use/mention distinction: 'this sentence' is two words, but this sentence contains nineteen words.]
ReplyDeleteAs for linguistic beliefs, I partly agree with you. I should have stipulated that Timmy intended to use his words in the same way as the rest of his speech community does (so when we tell him what the rest of us mean by 'prime number', he will respond, 'oops, my mistake'). But we can imagine a case where Timmy has no false beliefs at all. He may just be stubborn and uncooperative, intentionally using the term 'prime number' in a different way from the rest of us. He would then not be speaking English, but Timmy-ish. That's possible. But it's not the case I meant to describe; we are to suppose that Timmy is speaking English.
Jack - I agree with your second point. Timmy can have de re beliefs about (the objects that are) prime numbers. But my point was that he can't have de re beliefs about (the property that is) primeness.
ReplyDeleteI think your first point misapplies the No-Surprise principle. To test whether Timmy believes that p, we do not ask how surprised he would be if the p-world closest to the actual world were actual. Instead, we look to the p-world where most of his other beliefs remain true.
This is what separates (2) from (3). There is no possible world where Timmy has all the qualitative states he takes himself to have and yet also has the belief that 666 is a prime number. Any world where his meta-belief is true (i.e. where he has the first-order belief) is radically different from how Timmy takes things to be. Not so for (3). There is a world where 'prime number' means cool number, and school textbooks still report that '2 is the smallest prime number', etc.
I can't see how the mention/use situation overrides the distinction between proposition and statement. The linguistic error Timmy is making forces him to misuse (relative to common understanding) the concept of "prime number," so that it represents a different proposition for Timmy than it does for others.
ReplyDeleteTimmy believes "666 is a prime number" because that represents the proposition "666 is a cool number" to him. He also legitimately believes that he believes that--he has no reason to doubt it until he's corrected. The fact that the statement "666 is a prime number" represents the proposition "666 is a number divisible only by 1 and itself" to the rest of us doesn't interfere with his belief generally, just his knowledge.
If Timmy believed that the statement "Chickens are pink" expressed the proposition "666 is a prime number," it would likewise be a legitimate belief until someone taught him the conventional meanings of the words he used.
Jason - right, I was talking about propositions before, but everything you say about statements there is also correct (and compatible with my earlier claims).
ReplyDeleteIt's standard practice to take propositions, not statements, as being the objects of belief. But we can accommodate both by saying, e.g., that Timmy believes [the statement] "666 is a prime number" == Timmy believes [the proposition] that the statement '666 is a prime number' is true.