The argument I'm presenting isn't my argument per se. Rather, it's an adequate account of what Gettier says that Smith does, as compared/contrasted to Gettier's own formulation in the beginning of the paper. With that in mind, p2 accounts for the single deduction in Gettier's formulation. — creativesoul

So what does Gettier use p2 for?

Not following Srap... — creativesoul

You derive C1 from p1 and p3. What do you use p2 for?

p2 accounts for the single deduction in Gettier's formulation. — creativesoul

It's a premise not used in your deduction anywhere.

p1. ((p) is true)
p2. ((p v q) follows from (p))
p3. ((p v q) is true if either (p) or (q) is true)
C1. ((p v q)) is true because (p))(from p1,p3) — creativesoul

Are you going to use p2 for anything?

Also, p3 is just P∨Q→P∨Q.

It's still not a nice word to use, Mr. Michael. Now mind your manners, there's a good boy. ;-)

You'd have to be an idiot. — Michael

Now, now.

a half-century worth of misunderstanding — creativesoul

No.

1. Your reading of Gettier's original paper is wrong on its face and you're never going to convince anyone.

2. Even if you were right, and there was something faulty in Gettier's original cases, no one would care. Once you've seen the trick, it is child's play to construct new Gettier-type cases. The Gettier problem is this whole family of cases, and its seemingly endless adaptability. There is no broad agreement on any version of the JTB theory that meets our intuition of what counts as knowledge while blocking the creation of a Gettier-type case to undermine that specific approach.

You're on the wrong track, in my view. I have explained why as best I can.

The idea I sketched a couple months ago, that justification cannot cross the boundary between one interpretation and another, is essentially the mainstream response to Gettier, that something is needed to guarantee the relevance of the belief's justification to its truth for that belief to count as knowledge. You must get the right answer for the right (sort of) reasons.

The exclusive/inclusive distinction is irrelevant here. Smith, given what he believes, posits all three q's as a means to create a proposition, not as a means to state belief. Gettier says as much. — creativesoul

It is relevant. Smith accepts all three.

Another example would arise if you are allowed multiple answers. You may strongly believe that the Battle of Hastings was fought in 1166, but if you are allowed to answer "1166 or 1066," then you'll be right.

C1. ((q) is not true)(from p1,p3) — creativesoul

Once again, that is correct only if "or" is taken exclusively.

"This immediately reminded me of Gettier 'problems' with the JTB account."
— creativesoul

There is a kind of connection to the argument here. Gettier cases are examples of epistemic luck -- you have a belief, it's true, it's got something that counts as justification, but the proposition believed to be true is true under a different interpretation than the one you intended, and our intuition that these are not examples of knowledge is because the justification you had fit the interpretation under which your sentence was false, not the one under which your sentence was true. (That's probably not all cases -- if it were, I would have just solved the Gettier problem.)

There's another sort of luck that's even easier to get at because there's no question of knowledge at all: that's when you're asked a question on an exam (or a game show, whatever) and you guess -- and your guess is right! If you're asked when the Battle of Hastings was, "1066" is the right answer whether you've ever even heard of the Battle of Hastings or not, because truth is not the same thing as knowledge.

(Not getting into the disjunction thing yet, as I have an argument that uses disjunction still under litigation.) — Srap Tasmaner

That was a couple months ago in the "'True' and 'Truth'"" thread, and might be worth revisiting now.

P ∨ Q has four possible models:
(1) P=0, Q=0
(2) P=1, Q=0
(3) P=0, Q=1
(4) P=1, Q=1

The gist of the above remarks was that, to take Case II as the example, Smith's justification relates to the models in which P is true (2 or 4), but it turns out P ∨ Q is in fact true under the third model, in which only Q is true.

@creativesoul is arguing that because all of Smith's beliefs are formed under one of the interpretations in which P is true, that his belief does not include or encompass the interpretations in which P is false.

Michael Dummett makes a distinction (when talking about assertion, as usual -- here it is Smith's acceptance that is at issue) that may be helpful here: there are the grounds upon which you make an assertion (which he calls its "justification"), and then there is what you are committed to by making the assertion. It is clear that Smith's belief that P is the grounds upon which he accepts that P ∨ Q, but by accepting that P ∨ Q he is committed to accepting all four possible models.

The commitment part is what we rely on when we judge lucky guesses to be correct. If, on the basis of nothing more than a hunch, you were to wager that the Battle of Hastings was fought in 1066, your bet would pay off. It is also possible to get the right answer for the wrong reasons, rather than for no reason.

This distinction shows up in our language use in many ways. If you believe you will be off work in time to meet me for a 7:00 movie, and you promise to, you have committed to being there and that commitment doesn't change because you end up working late and standing me up. You have broken your promise. Misunderstandings too often arise because a person might have one thing in mind, but the plain language of what they say admits of another interpretation, and if they misspoke, perhaps only an interpretation they did not intend. "That's not what I meant!" "But that's what you said!"

We do not, in general, take the grounds upon which an assertion is made as constraining the commitment made by that assertion. If we did, much about our language use would be different, but one thing in particular. To assert, or in Smith's case to accept, that a proposition is true is generally to accept that it may be false. That's usually the point of making an assertion. You provide information to your audience by telling them something is the case that might not be. (I tell you I stopped at the store and got milk, because I might not have.)

The exception, of course, is statements that are necessarily true. To make an assertion in which you admit as possible only the models in which the statement is true is take the statement as true necessarily. (If this were generally the case, we would all of us believe whatever we believed to necessarily be the case.)

In this case, if Smith were to accept that "Jones owns a Ford or Brown is in Barcelona" only insofar as Jones owns a Ford, then he would be allowing no possibility that Jones does not own a Ford. He would be taking "Jones owns a Ford" to be a necessary truth.

Obviously, there is no support for this claim in the text.

If you choose to submit your solution for publication, the natural choice would be Analysis.

These are not equivalent:
(1) Smith does not believe that Brown is in Barcelona.
(2) Smith believes that Brown is not in Barcelona.

((q) is not true) — creativesoul

That is not a belief of Smith.

Yes, we know. I've said as much. It's right there in the text. So what?

p4. 'Brown is in Barcelona' is not true — creativesoul

Here that means "Brown is not in Barcelona," and we are given no such claim.

No, it really hasn't.

Smith has a false belief that (f). From it he derives, by valid inference, a true belief that (h). I describe this as an application of modus ponens by Smith. I think that's accurate enough and it is roughly how Gettier presents it. You describe the modus ponens step as Smith forming a belief that (h) because (f). It makes no difference to the overall argument. Smith then concludes that (h), which is a justified and true belief that is apparently not knowledge.

As I said, modus ponens does not actually apply here because (f) is false, although the conditional (f)→(h) is true. Smith, however, believes that (f), and thus is entirely consistent in applying modus ponens. His trouble comes not from making an inference he shouldn't -- he should, given his belief that (f); his trouble comes from having that false belief that (f).

I think it would also be fair to say that his trouble comes from believing that the evidence he has for (f) is strong enough to warrant a claim to know that (f). It wasn't. But that's another story.

(1) Smith does not believe that (h).

(2) Smith's inference of (h) from (f) is faulty.

What is your claim?

An example I recall reading was Kurzweil and google were working on ways to circumvent the second law of thermodynamics. — JupiterJess

On a related note, from The Onion.

Granting that the second Gettier case has been effectively dissolved, — creativesoul

As far as I can tell, no.

If Smith believes that (h), and is justified in his belief that (h), then if (h) is true, which it is, then Smith should know that (h), which he clearly doesn't.

For judging Case II, nothing else is relevant.

Do you understand why that sentence is there?

BTW, I've considered arguing that this is simply false:

Smith, of course, has no idea where Brown is.

But that's a whole 'nother thing.

Is that what I said?

If Smith believes that (h), and is justified in his belief that (h), then if (h) is true, which it is, then Smith should know that (h), which he clearly doesn't.

For judging Case II, nothing else is relevant.

It does matter if Smith's belief is false. — creativesoul

Because it all starts with a false belief, (f).

I'll have lots more to say in a little while, but first there's this: if you're still talking about all this as adding a step before Smith gets to (h), it doesn't matter. It doesn't even matter if it's false. You have to block Smith's belief that (h) or block it from being justified.

Are you going back to denying that he ever believes (h)?

To some extent, you're agreeing with Gettier: the reliance on Smith's belief that Jones owns a Ford is the source of Gettier's claim that Smith's belief that Jones owns a Ford or Brown is in Barcelona is justified.

Almost everyone feels something is wrong here. Some accept that it's a refutation of the JTB theory of knowledge, but many don't. So the question is what is going wrong here?

You say that (h) is not an adequate characterization of the belief Smith holds. You want (h) to drag (f) along with it. (BTW, your argument was my very first reaction too, so I sympathize.)

I think now that going down this road eviscerates entailment in a way we don't want. If we have a web of beliefs, connected by various degrees of the relation "is a reason for", we still need to individuate those beliefs, even if they confront reality in groups or as a totality, not singly, because we have to be able to revise them individually.

I think the usual approach to Gettier is probably right: we feel that the justification Smith has for believing (f) turns out to be irrelevant to the truth of (h). It's that irrelevance we want to capture. We need rules about how justification passes from one belief to another, something more precise than Gettier's principle that entailment preserves justification just as it preserves truth.

I see it as knowing the what makes (p v q) true. — creativesoul

We're not actually disagreeing. :-)

"p ∨ q" has three semantic components: p, q, and ∨. You have to know what they all mean to know what "p ∨ q" means; you have to know whether p and q are true to know whether "p ∨ q" is true.

knowing that if 'Jones owns a Ford' or 'Brown is in Barcelona' is true then so too is 'Either Jones owns a Ford or Brown is in Barcelona'. — creativesoul

You've mentioned this several times. I see this as knowing the definition of "or".

If A or B, then A-or-B.

It seems interesting if you throw in "is true", but it's really not.

If A is true or B is true, then A-or-B is true.

But again that's just the definition.

Natural language isn't shorthand for logical notation. — creativesoul

I presented it in natural language.

Show me where that argument for 4 goes wrong — creativesoul

As I said before, I think "A because B" is just shorthand for a modus ponens:
If B then A;
B;
therefore A.
As it happens, you had included the conditional in your premises (1 I think), but p was nowhere to be found.

If we have the conditional explicitly, that means p is presupposed by 4, and there's no need for that, because we've been told in so many words that Smith believes that p.

2 is what matters. It's the whole point of Case II.

We already have, as a premise, a justified false belief for Smith, namely p, which for some reason you don't like to talk about.

4 annoys me, but I'm not even sure it matters, unless the idea is to pretend that Smith doesn't believe that p.

2 is the justified true belief.

What are you denying? — creativesoul

What point are you making?

I've said I object to 4 because it runs two premises together and obscures the main issue. I don't know if it's false, but it's not helpful.

What do you get if I grant 4?

The justification is irrelevant. Smith's belief is false. (p v q) is not true because p is. — creativesoul

Justification is the whole point of the exercise.

Smith has loads of false beliefs, starting with p. What does that get you?

I'm not talking about his belief that p. — creativesoul

But you should be. I think you're trying to block the justification of p v q by hiding p, which is the only justified belief on the table.

Smith believes that p v q because p is true. — creativesoul

I heard you the first time. ;-)

Let me put it this way: your statement is just shorthand for this one

p & p→(p v q).

It's not like you can believe "p v q because p" without believing that p. You're just pushing the two premises together.

So, it's justified false belief? — creativesoul

His belief that p is a justified false belief, yes. At least that's the premise, which hasn't been challenged here.

4.Smith believes that (p v q) is true because p is true. — creativesoul

"Because" is a slippery word though.

We can talk loosely about this, and it usually does no harm. I could say something like "p's being true makes p v q true." Mathematicians talk this way, but again this is to speak loosely. That's not a good idea here.

(If we really want to say something like this, we should probably say that whatever makes p true also makes p v q true -- but this is just the sort of truth theorizing I don't think we need to do here.)

As I've said, I think the right thing to say is that Smith believes, correctly, that p entails p v q, and he believes, incorrectly, that p. With those two beliefs in hand, he applies modus ponens. This is exactly what Gettier describes, I think.

Look at your 4 the other way round: what makes 4 a false belief is precisely that p is false. That's another reason to split out p, which you have not done here, although Gettier does. Smith has lots of false beliefs, and they all flow from his false belief that p.

And because Smith believes that p, it makes sense to present 4 giving "believe" smaller scope:

4. Smith believes that p v q because Smith believes that p.

That's the other sense of "because" -- not the vaguely causal sense we had above, but the sense in which p is a reason for Smith to believe that p v q, and a good one. By burying p inside a more complex belief, you've left out the reasoning process Gettier attributes to Smith. And it's that reasoning process that carries justification.

At least we're getting closer now to confronting the actual problem.

Smith's knowing that if p or q is true, then so too is (p v q) and still believing that (p v q) is true despite not believing any of the Q's, is for Smith to believe that (p v q) is true because p is. — creativesoul

As I said, Smith thinks he's applying modus ponens but he isn't, because p is false.* So yes there is also the false belief that modus ponens is applicable -- but we don't want to go too far down this road because at some point you have to actually make an inference, which is an action not a belief.

Just remember that, for all Smith knows, Brown is in Barcelona. He may not believe that Brown is in Barcelona, but he doesn't believe that he isn't either.

So this is not a case of (p & ~q)→(p v q).

* We're saying m.p. is used here because that's basically what Gettier does. You could also call deriving p v q from p (or from q) a "v introduction rule" as it would be in a natural deduction system.

ADDED: Keep in mind too that Smith thinks m.p. is applicable because he thinks p is true. And that is what he should think. He just happens to be wrong.

Smith believes that (p v q) is true because p is true. Smith holds false belief. — creativesoul

Yeah, the false belief that p.

I thought we'd been over this, for instance here.

It's still true that p entails p v q.