Believing that (g), (h), and (i) are entailed by (f) is not equivalent to believing the disjunctions. — creativesoul

It is if you believe that f is true. For example, if I believe that it is Sunday and if I believe that it being Sunday entails that the Post Office isn't open then I must believe that the Post Office isn't open.

So if g, h, and i follow from f and if I believe that f is true then I must believe that g, h, and i are true.

I'm not so sure about that, Michael. I would have to hold inconsistent beliefs but I reckon that is not too unusual a condition to be in.

What inconsistent beliefs?

Belief can be wrong....is the cup in the cupboard?. Reality and logic are not joined at the hip but they are generally pretty friendly.

Michael: I can believe that the post office is open, that it's Sunday and that the post office is always closed on Sundays. So I'm confused and irrational, as people sometimes are. "I must believe the post office isn't open" - this "must" means "should, ought to, rationally would" believe. Even if a proposition follows necessarily from another, my believing anything does not follow necessarily from my believing anything else. If beliefs were like that then we would never hold irrational or inconsistent beliefs - but we occasionally do.

True, but I think that the Gettier example assumes that the person is rational. Smith believes f, Smith recognises that g, h, and i follow from f, and so Smith believes g, h, and i. If his belief in f is justified then his belief in g, h, and i are also justified. If g is true then Smith has a justified true belief in g, and so according to the traditional definition, knowledge of g.

Yes, I think you're right. The Opening Post criticism of Gettier is that he conflates entailment of propositions with entailment of beliefs about propositions. But I don't think Gettier does that. His characters happen not to be confused or irrational AND they have justified true beliefs AND they do not have knowledge.

Personally I don't think Gettier counter-examples knock down JTB, although they do make us analyse the 'J' part rather more closely.

And in both of Gettier's original cases he is explicit that his mark sees the entailment and makes the deduction, precisely because you can't assume that he did, even if it's the rational thing to do.

The real problem with any theory that tries to be precise with a definition of knowledge is that there are just too many uses of the word, i.e., we will never capture every possible use in a definition or theory. There are just family resemblances. Wittgenstein kept trying to make this point over and over again. However, people keep trying to do what's impossible. It's like trying to come up with a definition of the word game that covers every possible use. It can't be done, at least with many words.

I think we can generally say that most uses of the word knowledge do incorporate the idea of being justified in some way, but keep in mind there are many ways of justifying a belief besides inductive and deductive arguments.

Accepting (f) isn't equivalent to believing that (f) is true. I've argued for this without subsequent refutation. Gettier starts with "accepts" and finishes with "believes". The two are not the same. I agree that if one believes that (f) is true, then one believes (f).

Accepting (f) only requires accepting that (f) follows the rules of correct inference, and as such it doesn't require and/or entail belief that (f) is true. Gettier's argument requires one to neglect that much.

Edited at a later date to add:

Jeesh! I have no idea wtf I was talking about here. I must've been waaaay tired. Replace (f) with (g), (h), and (i)... I think that's what I was talking about...

:-#

Accepting (f) only requires accepting that (f) follows the rules of correct inference, and as such it doesn't require and/or entail belief that (f) is true. — creativesoul

If you mean as this as a matter of psychology, then yeah, people have inconsistent beliefs. But they shouldn't.

"Years of Academy training wasted!"

No. You're missing the point.

Smith - himself - would not form belief about Brown's location. One cannot know they are ignorant about Brown's location and simultaneously form and/or hold a belief about where Brown is located.

The mistake here is conflating knowledge of the rules of entailment/disjunction with belief. Believing that (g), (h), and (i) are entailed by (f) is not equivalent to believing the disjunctions. Following established rules counts as being justified in putting those rules to use. Smith is justified in believing that he has followed the rules of correct inference to correctly/sensibly arrive at disjunction.

Moreover, it is humanly impossible to believe that (g), (h), and (i) are true. Gettier's case neglects this brute fact.

It's not inconsistent to believe that the rules of correct inference allow (g), (h), and (i), while not believing anything at all about Brown's whereabouts.

One cannot know they are ignorant about Brown's location and simultaneously form and/or hold a belief about where Brown is located. — creativesoul

Sure you can. Anyone who said that I'm at home or at work or driving from one to the other would almost always be right. (I lead an exciting life.)

They would always be wrong, unless you were in every place at once.

You are skirting around the issue with disjunction though.

...people have inconsistent beliefs. But they shouldn't.

There's a bit of irony here.

Gettier's case requires that.

g) Either Jones owns a Ford, or Brown is in Boston.
(h) Either Jones owns a Ford, or Brown is in Barcelona.
(i) Either Jones owns a Ford, or Brown is in Brest-Litovsk.

One cannot believe that any of the three random locations are where Brown is if s/he is aware that they have no clue of Brown's whereabouts.

One can however, be aware that they have no clue where Brown is and accept that the rules of correct inference allow all three of these conjunctions.

Brown is in Boston.
Brown is in Barcelona.
Brown is in Brest-Litovsk.

One cannot believe that all three of these are true. One can believe that one of them is. One cannot believe that they are totally ignorant of Brown's location and also believe any of the three.

And yet...

One can believe that they are totally ignorant of Brown's location and accept that the rules of correct inference allow all and/or any of the three to be attached to another belief with the terms "either/or", and be properly called a "disjunction".

You wrote:

Smith believes f, Smith recognises that g, h, and i follow from f, and so Smith believes g, h, and i.

Recognizing that g, h, and i follow from f does not require belief that g, h, and i are true. One cannot believe that Brown is in three places at once, thus it cannot be the case that Smith believes g, h, and i. Believing all three follow from f is not the same as believing that any of the three say something true about Brown's location.

I can believe all three to some degree:
Boston: 10%
Barcelona: 20%
Brest-Litovsk: 70%
and I can believe 100% that he's in one of those three.

But I can't do this:
Boston: 50%
Barcelona: 50%
Brest-Litovsk: 50%
or I'm vulnerable to a Dutch Book.

You can't arrive at those percentages based upon the rules of disjunction.

But I can arrive at disjunction based on those percentages.

That's not a Gettier case.

Consider these:

1. London is the capital city of England
2. Either London is the capital city of England or I am in London
3. Either London is the capital city of England or I am in Exeter
4. Either London is the capital city of England or I am in Ipswich

Do you accept that 2, 3, and 4 follow from 1? Do you believe that 1 is true? Do you believe that 2, 3, and 4 are all true?

Because they do follow, and they are all true. Being the rational person that I am, I believe that they are all true.

Your mistake is in thinking that I have to believe that I am in London or Exeter or Ipswich to believe that 2, 3, and 4 are true. I don't. I only need to believe that London is the capital city of England. Which is exactly why I believe the following to be true (and why they are both true):

5. Either London is the capital city of England or pigs can fly
6. Either London is the capital city of England or pigs can't fly

I'm not sure what those percentages have to do with the Gettier case. As I explained above, it has nothing to do with what you believe about Brown's location and everything to do with what you believe about Jones owning a Ford.

I'm not sure what those percentages have to do with the Gettier case. — Michael

Agreed, but we seem to have drifted into the issue of what natural language disjunctions are. There are old arguments about their interpretation.

1. London is the capital city of England
2. Either London is the capital city of England or I am in London
3. Either London is the capital city of England or I am in Exeter
4. Either London is the capital city of England or I am in Ipswich

Do you accept that 2, 3, and 4 follow from 1? Do you believe that 1 is true? Do you believe that 2, 3, and 4 are all true?

Because they do follow, and they are all true. Being the rational person that I am, I believe that they are all true.

Your mistake is in thinking that I have to believe that I am in London or Exeter or Ipswich to believe that 2, 3, and 4 are true. I don't. I only need to believe that London is the capital city of England. Which is exactly why I believe the following to be true (and why they are both true):

5. Either London is the capital city of England or pigs can fly
6. Either London is the capital city of England or pigs can't fly

Interesting charge. Am I the only one here using common sense?

Gettier's case requires Smith to hold belief about Brown's location, for that is precisely the purported belief that is true. If believing that g, h, and i follow from f does not necessarily require belief about Brown's location then the whole thing is a sham... which it is.

Bewitchment.

Note that it is statements of thought/belief that are true in these cases. Disjunction combines a speaker's one belief with another statement that the speaker does not believe and then holds it all as belief. Gettier cases put this error on display.

There is also an equivocation of "true" at work... I think. During the set up, "true" means consistent with the rules of correct inference(coherence), but at the conclusion of the argument, when we get to Brown's actual location, "true" means corresponding to the way things are.

Gettier's argument is this:

(1) If you are justified in believing p, then you are justified in believing p v q.
(2) You can have a justified true belief that p v q even if p if false, so long as q is true.

Nobody cares whether you actually form this belief. The issue is that if you did, you would have a justified true belief we are not inclined to count as knowledge.

(1) claims that entailment preserves justification, which is hardly objectionable. The natural approach, in light of (2), is to conclude that (1) is too simple, that we need an extra condition governing how entailment preserves justification.

I understand the historical approach...

Gettier's case requires Smith to hold belief about Brown's location, for that is precisely the purported belief that is true.

Are you denying this?