You wrote:

Nothing you've said refutes Gettier's argument.

Are you sure???

Believing that (p v q) is true, if based upon belief that p, and accepting the rules of correct inference, requires knowing that if p or q is true then so too is (p v q). 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.

Smith has false belief.

(p v q) is true because q is true.

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

Smith is wrong.

(p v q) is true because q is. — creativesoul

You're conflating "Smith believes that 'p ∨ q is true because p is true' is true" with "Smith believes that 'p ∨ q' is true because Smith believes that p is true".

Take this example:

1. I believe that "Donald Trump is the President" is true.
2. I believe that the President is elected by popular vote and that Donald Trump won the popular vote.

According to you, my belief that Donald Trump is the President is false because Donald Trump didn't win the popular vote (and nor is that how the President is elected). That's just wrong. My belief that Donald Trump is the President is a true belief, even though I believe it for a false reason.

Smith has a true belief, even though he has it for a false reason.

Are you claiming that Smith does not believe that (p v q) is true because p is?

Are you claiming that Smith does not believe that (p v q) is true because p is? — creativesoul

No, I'm claiming that Smith believes that p ∨ q is true, that Smith is justified in believing that p ∨ q is true, and that p ∨ q is true. He has a justified true belief.

You're not granting Smith much cognitive ability. I am for it's required in order to arrive at (p v q) is true in the way Gettier sets out...


Believing that (p v q) is true is much different than believing that (p v q) is true because p is. Smith holds the latter, not the former.

I've given the argument for that. Here it is again...

Believing that (p v q) is true, if based upon belief that p, and accepting the rules of correct inference, requires knowing that if p or q is true then so too is (p v q). Smith's knowing that and still believing (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.

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

Believing that (p v q) is true is much different than believing that (p v q) is true because p is. Smith holds the latter, not the former. — creativesoul

Again, you're conflating "Smith believes that 'p ∨ q is true because p is true' is true" with "Smith believes that 'p ∨ q' is true because Smith believes that 'p' is true".

The situation at hand is the latter. I explained this more clearly with my example of Donald Trump being the President. I have a true belief arrived at from a false reason. Smith has a true belief arrived at from a false reason. But a true belief is a true belief nonetheless.

I cannot conflate things that I've not written Michael.

You wrote it in the text I quoted.

I wrote this...

Believing that (p v q) is true is much different than believing that (p v q) is true because p is. Smith holds the latter, not the former.

...not this...

"Smith believes that 'p ∨ q is true because p is true' is true" with "Smith believes that 'p ∨ q' is true because Smith believes that p is true".

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.

It's not that simple Srap

Believing that (p v q) is true, if based upon belief that p, and accepting the rules of correct inference, requires knowing that if p or q is true then so too is (p v q). 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.

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

Smith has false belief.

(p v q) is true because q is true.

Now you're just being pedantic. I was fleshing out your claim.

You said: "[Smith believes] that p v q is true because p is". There are two different ways to interpret this:

1. Smith believes that "p ∨ q is true because p is true" is true, and
2. Smith believes that "p ∨ q" is true because Smith believes that "p" is true

You seem to think that it's just the first. But it isn't. It's also the second. To repeat my earlier example:

1. I believe that "Donald Trump is the President because Donald Trump won the popular vote, and the President is elected by popular vote" is true, and
2. I believe that "Donald Trump is the President" is true because I believe that "Donald Trump won the popular vote, and the President is elected by popular vote" is true

It doesn't matter why I believe that "Donald Trump is the President" is true – even if for a false reason. I do, and my belief is true.

It doesn't matter why Smith believes that "p ∨ q" is true – even if for a false reason. He does, and his belief is true.

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.

I'm not sure what you're trying to flesh out Michael. It's crystal clear. Here it is again in long-form...

Believing that 'either Jones owns a Ford or Brown is in Barcelona' is true, if based upon belief that 'Jones owns a Ford' is true, and accepting the rules of correct inference, requires 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'. Smith's knowing that and still accepting that 'Either Jones own a Ford or Brown is in Barcelona' is true despite not believing that 'Brown is in Barcelona' is true, is for Smith to believe that 'Either Jones owns a Ford or Brown is in Barcelona' is true because 'Jones own a Ford' is true.

Smith believes (p v q) is true because p is true.

Smith has false belief.

(p v q) is true because q is true.

1.Smith knows that (p v q) is true if either p or q is true
2.Smith believes that (p v q) is true.
3.Smith does not believe that q is true.
4.Smith believes that (p v q) is true because p is true.
5.(p v q) is true because q is true
6.Smith holds false belief

What more could you ask for?

X-)

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.

So, it's justified false belief?

My point is that Gettier's notion of Smith's belief is too simplistic.

An old friend of mine who's much more knowledgable with logical notation than I said this...

So the refutation rests on
Smith believes that: ((p v q) is true because p is true)
against
((p v q) is true because q is true)

interesting....

If one knows what Smith knows, then one can believe (p v q) is true for one of only two possible reasons. Either (p v q) is true because p is true or because q is true. Smith doesn't believe that q is true. Thus...

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

That's what Gettier tries to do Srap. It neglects to take the fact that Smith knows the truth conditions of (p v q) and doesn't believe q.

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.

I'm not talking about his belief that p. That should be clear.

1.Smith knows that (p v q) is true if either p or q is true
2.Smith believes that (p v q) is true.
3.Smith does not believe that q is true.
4.Smith believes that (p v q) is true because p is true.
5.(p v q) is true because q is true
6.Smith holds false belief

What are you denying?

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.

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.

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

1.Smith knows that (p v q) is true if either p or q is true
2.Smith believes that (p v q) is true.
3.Smith does not believe that q is true.
4.Smith believes that (p v q) is true because p is true.
5.(p v q) is true because q is true
6.Smith holds false belief

What are you denying?

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?

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?

Smith's belief that (p v q) is true because p is true is false.

Smith does not have a JTB to begin with. One cannot quite make the claim that Gettier shows a problem for JTB if Gettier's example is JFB... now can they?

;)

2 is the justified true belief.