It seems clear to me that Smith is e-justified in believing (0).

And also that (O) is true. Let's not forget that.

Yes.

(It is (0) with a zero not (O) with a capital O letter.)

And Smith is e-justified in believing (0). I don't understand why you think that he is not.

I will come back to this point, but first I would appreciate your view on a problem I am having about what constitutes knowledge.

Imagine I have a friend who lives in Paris. I believe, with strong justification, that he is currently in Paris (he has told me that he has important business there today). But, unknown to me, he has actually left Paris and gone on a visit to Switzerland. The question is this:

At what point did I cease to know he was in France?

Was it immediately he left Paris? Was it when he was approaching the Swiss border? Or was it not until he actually crossed the border? Would it make any difference if he did not plan to cross the border at all, but only decided to do so at the last moment? And if he then came back to Paris, would I know once more that he was in France (and Paris)? Would it make any difference how long he had stayed in Switzerland, and how long he had been back?

The more I think about it, the more it strikes me that "knowledge" is a vague term.

And Smith is e-justified in believing (0). I don't understand why you think that he is not.

... but if a theory of knowledge is to be consistent (i.e., avoid the Gettier counter-example), can any proposition that can fall prey to the counter-example be said to be e-justified? ...

... to rephrase: if you want a theory of knowledge that cannot classify the Gettier counter-example as knowledge, do you need to incorporate into e-justification a check for a proposition's susceptibility to the Gettier counter-example? ... in which case Smith would not be e-justified in believing (0) due to the fact that his generalization from (1) to (0) opens the possibility of (0) being incorrectly classified as knowledge ... (unfortunately, such a move might render the phrase "scientific knowledge" an oxymoron, as the scientific method is all about making generalizations!) ...

I have no clue what you are asking of me. And what's with the "..."'s?

... it seems to me that a theory of knowledge based upon JTB has been shown to be inconsistent by Gettier ... that is, Gettier demonstrates that according to the JTB theory of knowledge (0) can be classified both as knowledge and not knowledge ... it is knowledge because applying the JTB criteria to (0) succeeds; and it is not knowledge because applying the JTB criteria to (1) (from which (0) is derived) fails ... the question is with respect to turning a theory of knowledge based upon JTB into a consistent theory ... the ellipses simply reflect the way this stuff pops into my head ...

What do you think about the following as a definition of knowledge to avoid the Gettier problem?

Knowledge is JTB, provided that:
No state of affairs that is (a) consistent with the belief and (b) is J or T or B
excludes the possibility of any other such state of affairs.

Applying this to the Smith/Jones example:

0. "The man who will get the job has 10 coins in his pocket" is JTB [I'll admit it's "believed" for the purpose of this argument]

1. "The man who will get the job, Jones, has 10 coins in his pocket" is consistent with (0) and is J and B

2. "The man who will get the job, Smith, has 10 coins in his pocket" is consistent with (0) and is T

(1) excludes (2), and vice versa.

Hence Smith does not know (0).

You have misunderstood the Gettier objections to JTB. They show that the analysis is false, not inconsistent. There is no contradiction with JTB theory AFAIK but it is widely agreed to be false by epistemologists, I'd say. Ken can perhaps confirm this.

The moderators are not doing a good job of separating different information threads (i.e. conversations) in a forum thread.

What do you think about the following as a definition of knowledge to avoid the Gettier problem?

Knowledge is JTB, provided that:
No state of affairs that is (a) consistent with the belief and (b) is J or T or B
excludes the possibility of any other such state of affairs.

Applying this to the Smith/Jones example:

0. "The man who will get the job has 10 coins in his pocket" is JTB [I'll admit it's "believed" for the purpose of this argument]

1. "The man who will get the job, Jones, has 10 coins in his pocket" is consistent with (0) and is J and B

2. "The man who will get the job, Smith, has 10 coins in his pocket" is consistent with (0) and is T

(1) excludes (2), and vice versa.

Hence Smith does not know (0).

... ah - if no epistemologists actually buy into the JTB theory, then the point is moot ... so what are the accepted criteria for knowledge these days? ...

EDIT: or maybe I misunderstood and you're just reiterating that "it is widely agreed to be false by epistemologists" that the Gettier analysis is false ... in which case, is it false due to some flaw in Gettier's logic, or false simply because the JTB criteria produce a false positive?

Often times it's not best to separate discussions, especially if a tangential discussion is helping to clarify important points, points which may not be understood without going a tad off-topic. I find this to be especially true in many of these logic and epistemology threads, as not everyone has that the same understanding of formal logic as people like you do. The discussion in this thread, as you can see, has taken many turns, but I don't consider this a bad thing; it seems to be helping most of us here. If you disagree, let me know. And if it's agreed upon that some tangential discussion is intruding, I'll remove or move to another thread.

Thanks for your understanding,

Z

OK, I'll revise my wording:

Belief in a proposition X constitutes knowledge if it is a justified true belief, provided that:
No proposition Y that (a) implies X and (b) is justified or true or believed
contradicts any proposition Z that (a) implies X and (b) is justified or true or believed.

Applying this to the Smith/Jones example:

X. "The man who will get the job has 10 coins in his pocket" is a JTB [I'll admit it's "believed" for the purpose of this argument]

Y. "The man who will get the job, Jones, has 10 coins in his pocket" implies X and is J and B

Z. "The man who will get the job, Smith, has 10 coins in his pocket" implies X and is T

Y contradicts Z.

Hence Smith does not know X.

The above argument may need some fine-tuning, but basically what I am saying is that (if it is accepted that he believes X) the detail that Smith specifically believes and is justified (i.e. that Jones will get the job) contradicts the detail that is specifically true (i.e. that Smith will get the job). Such a contradiction should be incorporated as a caveat in any definition of knowledge.

OK, I'll revise my wording:

Belief in a proposition X constitutes knowledge if it is a justified true belief, provided that:
No proposition Y that (a) implies X and (b) is justified or true or believed
contradicts any proposition Z that (a) implies X and (b) is justified or true or believed.

Applying this to the Smith/Jones example:

X. "The man who will get the job has 10 coins in his pocket" is a JTB [I'll admit it's "believed" for the purpose of this argument]

Y. "The man who will get the job, Jones, has 10 coins in his pocket" implies X and is J and B

Z. "The man who will get the job, Smith, has 10 coins in his pocket" implies X and is T

Y contradicts Z.

Hence Smith does not know X.

The above argument may need some fine-tuning, but basically what I am saying is that (if it is accepted that he believes X) the detail that Smith specifically believes and is justified (i.e. that Jones will get the job) contradicts the detail that is specifically true (i.e. that Smith will get the job). Such a contradiction should be incorporated as a caveat in any definition of knowledge.

I will come back to this point, but first I would appreciate your view on a problem I am having about what constitutes knowledge.

Imagine I have a friend who lives in Paris. I believe, with strong justification, that he is currently in Paris (he has told me that he has important business there today). But, unknown to me, he has actually left Paris and gone on a visit to Switzerland. The question is this:

At what point did I cease to know he was in France?

Was it immediately he left Paris? Was it when he was approaching the Swiss border? Or was it not until he actually crossed the border? Would it make any difference if he did not plan to cross the border at all, but only decided to do so at the last moment? And if he then came back to Paris, would I know once more that he was in France (and Paris)? Would it make any difference how long he had stayed in Switzerland, and how long he had been back?

The more I think about it, the more it strikes me that "knowledge" is a vague term.