Thursday, August 24, 2006
Monday, August 21, 2006
Constructing a Gettier-style Example
I wrote the following last year for one of Tony Brueckner’s classes. Since it was long time ago, some portions of it (footnotes 2 and 3) are not very clear even to myself. Anyway, I post it here for fun.
Consider the following case:
It is widely known to the people who work in philosophy and logic that the Incompleteness Theorem is proved by the person who has been called ‘Gödel.’ Suppose, however, that his real name was not ‘Gödel,’ but ‘Schmidt.’ Suppose also that he did not really prove the theorem. The real author of the theorem was someone who is totally unknown to contemporary philosophers and logicians, whose name was ‘Gödel.’ What happened was the following: Gödel, the real Gödel, proved the theorem and died. His death was not known to anyone except Schmidt. Schmidt somehow had gotten hold of the theorem and pretended that he was the author, secretly changing his name into ‘Gödel.’ The truth of this thriller-type story has not been revealed to any contemporary philosophers and logicians. As a result, Schmidt, known as ‘Gödel,’ has been regarded as the author of the theorem in the contemporary philosophy scene. Now, Jones, a philosophy major at UCSB, has formed the following belief while taking Salmon’s logic class:
P: Gödel proved the Incompleteness Theorem.
It seems that Jones is justified in believing P. First of all, there is no doubt that P is true, since Gödel is the person who proved the theorem, as already assumed in the description of the case. It is also assumed that Jones believes P. Finally, Jones seems to be justified in believing P. Let us say that, adding to the fact that Salmon mentioned the name ‘Gödel’ many times in the class, Jones borrowed several books from the library and they all attribute the authorship of the theorem to the person named ‘Gödel.’ These are very good evidences for him to accept P.
The considerations so far strongly suggest that knowledge is not equal to justified true belief, since although P seems to be a justified true belief of Jones, it is hard to say that he knows P. However, an advocate of the causal analysis of knowledge would argue that Jones is not justified in believing P. According to the causal analysis, in order for one to be justified in believing some proposition, his belief must be caused by some fact in the world that makes that proposition true. Jones’s belief was not caused by the fact that makes P true – i.e. the fact that Gödel proved the Incompleteness Theorem, since this fact was not known to anybody in the contemporary philosophy scene. Rather, his belief was caused by the fact that Salmon attributed the authorship of the theorem to the name ‘Gödel,’ and the fact that the books he borrowed from the library ascribed the authorship to the person named ‘Gödel,’ etc. Obviously, these are not the facts that make P true. Thus, Jones was in fact not justified in believing P. This explains why Jones does not know P.
 Someone might point out that the person whom Jones had in mind in this belief is different from the one who is referred by ‘Gödel’ in P. That is correct. However, it does not follow from this that Jones does not believe P. At least, if we follow Gettier’s reasoning, we should say that Jones believes P. In the example Gettier provided, Smith is granted to believe that the man who will get the job has ten coins in his pocket although the person whom Smith had in mind in that belief, i.e. Jones, is different from the man who will get the job, i.e. Smith himself.
 According to the stronger version of causal analysis, one’s belief must be caused by some fact in order for it to be knowledge. If we take this interpretation, we should say that Jones is justified in believing P, but since his belief was not caused by the fact that makes P true, it is not strange that he does not know P.
 What (counterfactually) can be made true by these facts is the following proposition: “Schmidt proved the Incompleteness Theorem.”
Thursday, August 17, 2006
I'm a Giraffe
"I know who I am. No one else knows who I am. If I was a giraffe, and someone said I was a snake, I'd think, no, actually I'm a giraffe."
- Richard Gere
What is this supposed to mean? It's funny. And it may have some philosophical import. Any comments?