Sunday, November 05, 2006

How to Keep Humpty Dumpty from Falling

In class was raised this objection to Millianism:

Humpty Dumpty says:
a)"I believe ODB is a rapper"
b)"I believe RJ is not a rapper"

-now, no matter how much Humpty Dumpty asserts these properties, the Millian must claim that Humpty Dumpty is wrong: that he ACTUALLY, deep down, believes that RJ is a rapper. The Millian must say this because he holds that "the content of a linguistically simple singluar term is its referent". Of course, ODB and RJ refer to the same being, so it is bizarre to both believe and disbelieve that somebody is a rapper.

Now, the Millian holds that when somebody believes something, they have a BEL relation to that thing.

i.e. (BEL) A believes P iff There is some x such that(A takes P in way x & BEL (A,P,x).

Now, my solution is controversial and may not be easily incorperated into the Millian schema. What I will do is to call the amplified version of Millianism "Millianism'".

Millianism' shall incorperate one thing - that instead of Belief being a simple Yes/No relation, it is instead a probability relation. That is, A has 75% belief in P. This could be taken as a confidence level in one's belief.

There is precedent for this move in the philosophical literature. See Wesley Salmon's “Rationality and Objectivity in Science or Tom Kuhn Meets Tom Bayes.” (Scientific Theories. C. Wade Savage (ed.) Minneapolis: University of Minnesota Press (1990), 175-204.), and Harold Brown's “Reason, Judgement and Bayes’s Law” (Philosophy of Science 61 (1994), 351-369.), to name a few.

If we take the Millian BEL relation in this probibalistic way, we can approach a solution to the Humpty problem.

Let us look at the claims again, and I will attach probabilities to them...
a)"I believe ODB is a rapper" - 90% BEL. Humpty has seen the ODB in some of his more popular music videos, and one Halloween (back in '93) he saw some friends dressed up as the Wu-Tang Clan. I will not give him 100% BEL because it has been a while since ODB passed away, and Humpty doesn't want to confuse him for a used car salesman down the street.

b)"I believe Russell Jones is not a rapper" - Humpty is not a huge rap fan, but knows all of the big name rappers. Russell Jones is not one of these names. This is what he bases his belief off of - 55% BEL.

Now, Humpty will say he believes both of these claims, and he has reasons for believing both of them. However, the probability of belief hypothesis (Millianism') gives room for error in each of these beliefs. We often assert things that we believe, but are not totally sure of. In this case Humpty was just wrong about one of his beliefs.

The Millian was previously put in an unfavorable position where he had to claim he knew what a person's beliefs were better than that person themself. In Millian', the Millian acknowledges that the person knows what he believes, but also knows that when a person says they believe something, they accept that they could be wrong.


Blogger Dan said...

so, this strategy essentially adds something like a conviction factor, let's call that C. So belief would be defined thusly:
(BEL*) A believes P to degree d iff There is some C(A,x)=d such that CBEL = (C(A,x),P) and x is a mode of presentation of P.

Here, C is a function that takes an Agent and a mode of presentation as arguments and returns a real number between 0 and 1. This can be seen as A's conviction that P relative to mode of presentation x. Here CBEL is simply an ordered pair of C and the proposition P (representing how strongly one believes P).
This merely makes the problem one of probabilities. Now Humpty believes P with 90% conviction, and also believes p to 55% conviction. We can still say to Humpty "you believe RJ is a rapper with 90% conviction" and we'd be right and he'd be wrong in his denial of that. In a way this seems almost worse, not only do we know his beliefs better than he does, we know how strongly he holds those beliefs better than he does. The fact that Humpty accepts error about the proposition doesn't seem to be relevant when confronted with his supposed error about his own belief.

3:20 PM  
Blogger Adam said...

You said: "In a way this seems almost worse, not only do we know his beliefs better than he does, we know how strongly he holds those beliefs better than he does."

- I disagree. The merits of this approach would be that Humpty would agree with us in our assessments of his convictions. He would say, yes... I do feel 90% confident in this, and 55% in that. I do suppose it is possible that somebody could feel overconfident in their knowledge - say he felt 100% sure that RJ was not a rapper. Though this looks troublesome, it is not - if this were the case we would say Humpty is simply irrational. This is the case because 100% confidence should rely on a)knowing how ODB and RJ look (should be the same), b)knowing all psuedonyms of RJ, c)knowing about his history, etc... If one knew all these facts and was 100% confident ODB was a rapper and RJ was not, we'd call them crazy!

7:30 PM  
Blogger Chris Tillman said...

There was a recent discussion of a not unrelated proposal in the Online Philosophy Conference. The paper is by David Chalmers. The reply is by David Braun. Interested parties are encouraged hereby to check it out:

11:09 PM  
Blogger Chris Tillman said...

The link's not working. I'm posting it on the main site.

11:10 PM  
Blogger Dan said...

Humpty would agree with us if we said "You believe ODB is a rapper to a degree of 90%" but he would disagree if we told him "You believe RJ is a rapper to 90%". These (under the millian approach) express the same proposition; so we would be correct in both cases. Thus, we would know better than him about the strength of his own convictions. Humpty does believe RJ is a rapper with 90% assurance, he merely doesn't accept that sentence with 90% assurance.

this is essentially the original objection

8:56 PM  

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