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Monday, August 21, 2006

Constructing a Gettier-style Example

Dear Friends

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.

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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.[1] 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.[2] 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.[3] Thus, Jones was in fact not justified in believing P. This explains why Jones does not know P.

[1] 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.

[2] 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.

[3] What (counterfactually) can be made true by these facts is the following proposition: “Schmidt proved the Incompleteness Theorem.”

3 Comments:

  • At 8:33 PM, Blogger Huiyuhl Yi said…

    There are something that I want to add about footnotes 2 and 3.

    Concerning footnote 2: I think it should be revised as the following:

    According to the weaker version of causal analysis, one’s belief must be caused by some fact(s) that make(s) that belief true 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.

    Concerning footnote 3: More clearly, what I meant in the footnote 3 was the following:

    What is made true by the facts that Salmon attributed the authorship of the theorem to the name ‘Gödel,’ and the books Jones borrowed from the library ascribed the authorship to the person named ‘Gödel,’ etc is the following proposition (rather than P): Schmidt proved the Incompleteness Theorem.

    I am still sympathetic with this view, but somemone might object. I'd like to hear what everyone thinks.

     
  • At 11:40 AM, Blogger Josh said…

    That's an interesting case. It seems like some of the difficulties arise from issues in the philosophy of language and mind rather than epistemology. Footnote one talks about this a bit. It's difficult to assess whether Jones believes that P. He certainly assents to the sentence that is P. However, does he believe the proposition expressed by the sentence? What is the proposition expressed by the sentence? That depends on one's views on reference and what a name contributes to a proposition (whether "Godel", in the sentence P, refers to Schmidt or the real Godel or even whether it's some descriptive thing) and one's views on the content of mental states (whether the content of Jones's belief that P has Schmidt or the real Godel or some descriptivey sense thing in it).

    I, for one, don't pretend to have any firm views on this, as I am still trying to figure it out. But, this case does bring out these issues. So, it seems like you have to make a judgement about the issues I mentioned in order to decide (the epistemology of) this case.

    -Josh "If I was a giraffe, and someone said I was a snake, I'd think, no, actually I'm a giraffe" May

     
  • At 7:33 PM, Blogger Jim said…

    IMO This doesn't qualify as a legitimate "Gettier-style" problem. It trades on an ambiguity of the 'sentence.' The 'proposition' believed is not the 'proposition' that is true. The 'proposition' believed is false.

     

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