When he was no longer in France. Obviously. And you ceased to know he was in Paris when he was no longer in Paris. I don't see the problem.

Consider the similarity between this and the Gettier example.

A1. Smith believes that the man who will get the job has 10 coins in his pocket.
A2. He is justified in believing that that man is Jones, not Smith.
A3. It is true that that man is Smith, not Jones.
Therefore:
A4. He does not know that the man who will get the job has 10 coins in his pocket.
(A4 seems to be generally agreed.)

B1. I believe that my friend is in France.
B2. I am justified in believing that he is in Paris, not Lyon.
B3. It is true that he is in Lyon, not Paris.
B4. (by analogy with A4) I do not know that he is in France.

But you claim that, so long as he is in France, I know he is in France. Can you please explain why the belief at A1 is not knowledge but the belief at B1 is.

... suppose, however, we put ACB's friend on a Eurorail train in France ... in which case, it is not logically impossible to be on a Eurorail train but not in France ...

I don't understand that. Has Eurorail some special political status?

... no, it doesn't - and that is precisely the point ... Eurorail trains travel all over Europe such that it cannot be inferred from "ACB's friend is on a Eurorail train" that "ACB's friend is in France" ... so even though ACB's friend is on a Eurorail train, you cannot use this as an alternative means to infer that ACB's friend is in France (in contrast to what you were able to infer from the statement "ACB's friend is in Lyon") ... at any rate, it still seems rather counter-intuitive to say that someone knows a generalized belief that was derived from a specific justified belief simply because the same generalized belief can be inferred by way of an alternative (but not believed) truth ...

But you can infer from A's friend in in a Eurorail train in France that he is in France. Just as you can infer from the statement that he is in Lyon, and Lyon is in France, that he is in France.

the difference is that since Lyon is in France, then it necessarily follows that anyone in Lyon is in France, so it is impossible for anyone who knows that A is in Lyon, and that Lyon is in France, not to know that A is in France. Whereas, on the other hand, it does not necessarily follow from the fact that someone has 10 coins in his pocket, that he will get some particular job.

Consider the similarity between this and the Gettier example.

A1. Smith believes that the man who will get the job has 10 coins in his pocket.
A2. He is justified in believing that that man is Jones, not Smith.
A3. It is true that that man is Smith, not Jones.
Therefore:
A4. He does not know that the man who will get the job has 10 coins in his pocket.
(A4 seems to be generally agreed.)

B1. I believe that my friend is in France.
B2. I am justified in believing that he is in Paris, not Lyon.
B3. It is true that he is in Lyon, not Paris.
B4. (by analogy with A4) I do not know that he is in France.

But you claim that, so long as he is in France, I know he is in France. Can you please explain why the belief at A1 is not knowledge but the belief at B1 is.

That is an interesting example, and I am not sure what the answer is. But I am inclined now (I might change my mind later) to say that the difference is that since Lyon is in France, then it necessarily follows that anyone in Lyon is in France, so it is impossible for anyone who knows that A is in Lyon, and that Lyon is in France, not to know that A is in France. Whereas, on the other hand, it does not necessarily follow from the fact that someone has 10 coins in his pocket, that he will get some particular job. It is a peculiarity of the Gettier problem, that there can be no Gettier problem when the justificatory inference is deductive rather than inductive, and the Lyon case contains deductive rather than inductive justification. That is, it is logically impossible to be in Lyon, but not in France, but it is not logically impossible to have 10 coins in one's pocket and not be give some particular job.

The difference between deductive and inductive justification in Gettier examples has not (to my knowledge) been worked out. All of Gettier's examples (and all Gettier examples I have seen) have contained inductive, not deductive justification. And your counter-example contains deductive justification. I am very vague about this, I know, because I am not, myself clear about all of the implications. But that is what I now have to say about it. I would be interested to hear more comments about the matter.

I do not think that is a correct analogy. Firstly, it is not a case of "anyone who knows that A is in Lyon....", because I do not know he is in Lyon. Secondly, if you look at my example again, you will see that the deductive pair of conditions ("in Lyon" and "in France") are drawn from my B3 and B1 respectively, whereas the inductive pair ("has 10 coins in his pocket" and "will get some particular job") are both drawn from A1.


I think the two cases have the same reasoning structure, as follows:

• A1 describes a belief in a contingent state of affairs; so does B1.
  
• Given the truth at A3 (the man who will get the job has 10 coins in his pocket and is Smith), the belief at A1 (the man who will get the job has 10 coins in his pocket) is necessarily true. Likewise, given the truth at B3 (my friend is in Lyon), the belief at B1 (my friend is in France) is necessarily true.
  

So I would argue that if one case contains inductive justification, so does the other.

First I note that (A4) does not seem to me to follow from (A1) through (A3). It does not seem to me to be an inference at all. You did not write that (B4) is an inference either. If (A4) is inferred, then the cases are not analogous. Or maybe you did with the "by analogy with A4". Clarify please.

Second technically it is never the case that a belief is knowledge. "is knowledge" is not a predicate of beliefs. Perhaps you can reword your request to "Can you please explain why the person in case A does not know but the person in case B does.".

Third it seems to me that the best way to show that they are analogous is to formalize them.

Interpretation keys
Domain x ≡ persons
Bx(P) ≡ x knows that P
Jx(P) ≡ x P is e-justified for x
Kx(P) ≡ x knows that P
Sx ≡ x is Smith
Jx ≡ x is Jones
m ≡ the man who will get the job
s ≡ Smith

A1. Bs(Hm)
A2. Js(Jm)∧?Js(Sm)
A3. Sm∧?Jm
A4. ?Ks(Hm)


Interpretation keys
Domain x ≡ persons
Bx(P) ≡ x knows that P
Jx(P) ≡ x P is e-justified for x
Kx(P) ≡ x knows that P
Lx ≡ x is in Lyon
Px ≡ x is in Paris
m ≡ my friend
i ≡ I/me

B1. Bi(Ff)
B2. Ji(Pf)∧?Ji(Lf)
B3. Lf∧?Pf
B4. ?Ki(Ff)


The next thing to do is to make sure that the predicates are analogous. I think that they correspond in this way:
Jx, Px
Sx, Lx
m, m
s, i

The rest are identical.

The cases definitely seem analogous to me based on this analysis. However the analysis may be too superficial to reveal the reason why there is no knowledge in the first case and so an analogy will not show that there is no knowledge in the analogous case. I'm not sure it is sufficiently deep to reveal the reason why there is no knowledge in the first case.

---------- Post added 11-23-2009 at 11:43 AM ----------



It seems to me that the justification in deductive in both cases but the relevant conditional is not necessarily true (i.e. contingently true) in the Gettier example but it is necessarily true in your example. That is a difference. It may be relevant. I don't know. Obviously there are differences between two analogous cases, the question is whether they are relevant or not to the analogy.

---------- Post added 11-23-2009 at 11:51 AM ----------



Careful with the predicate "is necessarily true". What you write here is technically ambiguous. But I think you mean:

(A3) logically implies (A1), and (B3) logically implies (B1).

First I note that (A4) does not seem to me to follow from (A1) through (A3). It does not seem to me to be an inference at all. You did not write that (B4) is an inference either. If (A4) is inferred, then the cases are not analogous. Or maybe you did with the "by analogy with A4". Clarify please.

Second technically it is never the case that a belief is knowledge. "is knowledge" is not a predicate of beliefs. Perhaps you can reword your request to "Can you please explain why the person in case A does not know but the person in case B does.".

Careful with the predicate "is necessarily true". What you write here is technically ambiguous. But I think you mean:

(A3) logically implies (A1), and (B3) logically implies (B1).

Interpretation keys
Domain x ≡ persons
Bx(P) ≡ x knows that P
Jx(P) ≡ x P is e-justified for x
Kx(P) ≡ x knows that P
Sx ≡ x is Smith
Jx ≡ x is Jones
m ≡ the man who will get the job
s ≡ Smith

A1. Bs(Hm)
A2. Js(Jm)∧?Js(Sm)
A3. Sm∧?Jm
A4. ?Ks(Hm)

... does it add anything to show the (generalizing) implications that are being made? E.g. (pardon my use of a forward E to represent the existential qualifier):

Interpretation keys
Domain x ≡ persons
Bx(P) ≡ x believes that P
Jx(P) ≡ P is e-justified for x
Kx(P) ≡ x knows that P
Sx ≡ x is Smith
Jx ≡ x is Jones
m ≡ the man who will get the job
c ≡ a man who has ten coins in his pocket
s ≡ Smith

A1. Bs(Jm∧Jc)->Bs(Ex:xm∧xc)
A2. Js(Jm∧Jc)->Js(Ex:xm∧xc)
A3. Sm∧Sc∧?Jm∧Jc
A4. ?Ks(Jm∧Jc)->?Ks(Ex:xm∧xc) ∧ Ks(Sm∧Sc)->Ks(Ex:xm∧xc)

... the problem here seems to be due to the fact that ?Ks(Jm∧Jc)->?Ks(Ex:xm∧xc) looks to be invalid according to traditional logic but is intuitively valid, whereas Ks(Sm∧Sc)->Ks(Ex:xm∧xc) looks to be valid according to traditional logic but is intuitively invalid in this situation ... the implication being that the concept of knowledge cannot be modeled using traditional logic? ...

You can find the symbols here.

As for your post. I have no clue. I don't understand it. To be honest I have given up understanding anything you write. Your points don't come across. What's your native language?

... thanks!



One point is that to truly capture what is going on from A1 to A4 it may require additional logical detail. E.g., rather than simply stating Bs(Hm), explicitly show that Bs(Hm) has been inferred from Bs(Jm). In addition, including the detail that what is actually believed is Bs(Hm∧Hc) [and perhaps even going to the level of detail of Bs(∃!xm∧xc)] may help to illuminate any formal differences between the Gettier problem and the problem of ACB's friend [which it appears cannot be decomposed any further than Bi(Ff)]. Lastly, in any formalization of a concept the question arises as to whether or not the formalization is isomorphic with the concept. Thus far, it seems that we are missing the target. This could be due to inaccuracies in our formalization, or it could be due to the inexpressibility of the JTB concept of knowledge using traditional logical operators. The latter could perhaps be remedied by introducing new logical operators that allow the JTB concept of knowledge to be formally expressed (assuming, of course, that the JTB concept of knowledge is coherent).

So that although JTB is necessary for knowing, it is not sufficient for knowing. This is completely clear. What is not clear is that JTB is insufficieint for knowing. And that is the Gettier issue.

... unless I'm mistaken, you've just contradicted yourself ... that is, you have just said that it is both completely clear that JTB is insufficient for knowing but that at the same time it is not clear that JTB is insufficient for knowing ... in that last bit did you mean to say "What is not clear is why JTB is insufficieint for knowing."? ... anyhoo, I think I've got a pretty good handle on the Gettier problem - one thing I'm trying to resolve is why the intuitive notions of knowledge are different for the Gettier problem and ACB's problem ... up to this point, the consensus seems to be that the two problems are of the same logical form, so the mystery is why the two are intuited differently ... I am merely suggesting that if you express the two problems in a little more logical detail, it may turn out to be the case that the two problems are not precisely of the same logical form ... the other thing is the Gettier problem itself ... again, if that problem is expressed in a little more logical detail will things start falling into place? - or will we have to invent a new "logic of knowledge"? ...

And that is Gettier's point, only Gettier claims that it is clear that JTB is not sufficient for knowing, since a person can have JTB and not know.

... which is precisely why both ACB and myself have been throwing out ideas to extend JTB to be both necessary and sufficient ... and if we can understand exactly why Gettier's problem and ACB's problem are intuited differently (despite their superficial similarities), perhaps we would stand a better chance of refining those ideas into an extended JTB theory that aligns with intuition ...