Smith's belief is that Jones owns a Ford, and that each of the three propositions derived from that follow the rules of logic.

That takes the steam out of it all, does it not?

Smith's belief is that Jones owns a Ford, and that each of the three propositions derived from that follow the rules of logic? — creativesoul

And that each of those propositions are true.

He believes that p v q is true because he believes that p, and he believes that the rules of correct inference allow him to derive p v q based upon p. — creativesoul

Yes. And he's justified in believing that p ∨ q. And p ∨ q is true. He has a justified true belief.

That takes the steam out of it all, does it not?

No, because he has a justified true belief that intuitively shouldn't be considered knowledge. Therefore, the JTB account of knowledge is lacking.

See post 759

There's nothing more to believing that (p v q) aside from believing that p, knowing that p v q follows from p, and knowing that if p is true, then so too is (p v q).

I have been at pains to show that belief that (p v q) is nothing more than believing that the rules of correct inference say that (p v q) follows from p.

Believing that (p v q) is true, if based upon belief that p, is to believe that if p is true then so too is (p v q).

That may do it.

Yep. I think that that does it. Let me know what you think Michael...

1. My belief that p is justified
2. From 1, my belief that p ∨ q is justified
3. p is false and q is true
4. From 3, p ∨ q is true
5. From 2 and 4, my belief that p ∨ q is justified and true
6. I know that r if my belief that r is justified and true
7. From 5 and 6, I know that p ∨ q

The entire argument neglects what belief that p v q requires. As such it works from an ill-conceived criterion for what counts as belief.

Believing that (p v q) is true, if based upon belief that p, is to believe that if p is true then so too is (p v q). That bit of knowledge effectively dissolves this particular Gettier problem.

Applying the above bit of knowledge we arrive at...

1. My belief that p is justified
2. From 1, my belief that if p is true then so too is (p v q) is justified
3. p is false and q is true
4. From 3, p ∨ q is true
5. From 2 and 4 my belief that if p is true then soo too is (p v q) is justified and true
6. I know that r if my belief that r is justified and true
7. From 5 and 6, I know that if p is true then so too is (p v q).

No problem.

Yep. I think that that does it. QED

2. From 1, my belief that if p is true then so too is (p v q) is justified — creativesoul

This isn't in conflict with what I had for 2:

2. From 1, my belief that p ∨ q is justified.

You haven't shown this to be false.

Take, for example, the following claim:

1. It is wrong to steal.

From this, we can infer:

2. It is wrong for me to steal

Using your logic, all I'm doing is inferring that one statement follows from another. But that's not all I'm doing. I'm also stating that 2 is true. And if we bring in belief:

1. I believe that it is wrong to steal
2. Therefore, I believe that it is wrong for me to steal

My belief isn't just that 1 is true and that 2 follows. It's also that 2 is true. There's nothing wrong with the argument I provided here. Smith has a justified true belief that shouldn't be considered knowledge. The Gettier case stands. Nothing you've said refutes this.

I don't know what an "entailment" is, and what a "disjunction" is. I can't form an opinion while these two concepts are involved in the question, proposition, or offered solution. Many others participating in the thread, I assert, but don't claim, also have no clue what these two words mean, but they say something anyway.

Well, I don't say things "anyway".

This isn't in conflict with what I had for 2:

And yet you object? Upon what grounds? I've exhausted the notion of belief that (p v q) being used in this particular Gettier case. I've done so without conflicting what you claimed. What I had for 2 has much stronger justificatory ground as a result of all this. A rational person steps back and recognizes the relevance of this novel approach, then sees it through.

I used your logic by the way. If you want to argue you'll have to argue against this, for it's the only thing different between our arguments.

Believing that (p v q) is true, if based upon belief that p, is to believe that if p is true then so too is (p v q).

Believing that (p v q) is true, if based upon belief that p, is to believe that if p is true then so too is (p v q). That bit of knowledge effectively dissolves this particular Gettier problem.

Applying the above bit of knowledge we arrive at...

1. My belief that p is justified
2. From 1, my belief that if p is true then so too is (p v q) is justified
3. p is false and q is true
4. From 3, p ∨ q is true
5. From 2 and 4 my belief that if p is true then soo too is (p v q) is justified and true
6. I know that r if my belief that r is justified and true
7. From 5 and 6, I know that if p is true then so too is (p v q).

No problem. Smith has JTB.

Hmmm... 5 is a problem. May need to change something in the bit of knowledge.

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

That should do it.

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

It's also to believe that p ∨ q is true. Why is this so hard for you to understand?

Smith believes that the proposition "Jones owns a Ford or Brown is in Barcelona" describes some fact about the world, just as I believe that the proposition "either she's having a shower or she's having a bath" describes some fact about the world.

Your argument might be valid, but so is mine (or, rather, Gettier's). And my (Gettier's) argument shows that the JTB definition of knowledge is lacking.

Smith doesn't just believe that the inference is valid. He also believes that the inferred propositions are true. And, as I keep saying, nothing you're saying refutes this. You've just ignored it.

I wrote:

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

You replied:

It's also to believe that p ∨ q is true. Why is this so hard for you to understand?

I'm tempted to be a smartass.

Re-read the quote you are addressing and pay close attention to how it begins.

I'm tired tonight. I appreciate your input Michael. Tomorrow, I'll show how that bit of knowledge regarding what belief that (p v q) consist in/of exactly follows from how Gettier sets up. You could compare yourself if you like... in the meantime.

I've not ignored that Smith believes that (p v q). To quite the contrary, I unpacked that notion using Gettier's set up and a bit of much needed critical thinking.

I see how it begins. I'm addressing your reductionist account of it. You say that to believe that p ∨ q is true is just to believe that if p is true (or q is true) then p ∨ q is true.

That's like saying that to believe that "it is wrong for me to steal" is true is just to believe that if "it is wrong to steal" is true then "it is wrong for me to steal" is true.

You're setting up the belief just as:

B(p → r).

I'm saying that the belief is:

B(r).

Where r is "it is wrong for me to steal" or "either she's in the shower or she's in the bath" or "Jones owns a Ford and/or Brown is in Barcelona".

As before, I've no skin in the game to speak of.

How and/or if classical logic can account for what belief that (p v q) takes is of no concern of mine. I think that the issue is one that I struggled with. Your point is well taken though. Here's the fix...

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

Gettier attempts to take an account of thinking about thought/belief as though it were the same as thought/belief. It's not.

Does Smith also know that p v q would be true if q is, even though he has no opinion on the truth or falsehood of q?

Of course. He must in order to believe that (p v q) based upon belief that p and the rules of correct inference. Otherwise, he doesn't derive the disjunctions.

to know that if p or q is true then so too is (p v q). — creativesoul

It's worth looking at the scope of "know":

(1) I know that: p or q is true.
(2) I know that: p is true or q is true.
(3) I know that p is true or I know that q is true.

(1) and (2) are actually the same thing -- it's just the definition of "or".

(3) is a reason for (1) -- and thus (2) -- but the converse does not hold.

I'm not following you Srap.

Remember Gettier???

Imagine that Smith realizes the entailment of each of these propositions he has constructed by (0, and proceeds to accept (g), (h), and (i) on the basis of (f). Smith has correctly inferred (g), (h), and (i) from a proposition for which he has strong evidence. Smith is therefore completely justified in believing each of these three propositions.

It's really rather simple when you think about it. Lose the logic talk for a moment, for that is precisely what bewitches people...

If Smith believes that p, and then derives (p v q) from p, and realizes the entailment, then he knows the rules of disjunction. If he knows the rules of disjunction then he knows that (p v q) is true if either p or q is.

Gettier, and evidently everyone since doesn't take this brute fact into consideration.

That bit of knowledge regarding what belief that (p v q) takes dissolves this purported Gettier problem. It works from an utterly inadequate notion of belief that (p v q). That is of no surprise to me, because it is a consequence of the whole of philosophy having gotten thought/belief wrong, by virtue of not drawing and maintaining the crucial distinction between thought/belief and thinking about thought/belief. Belief that (p v q) requires the latter. Belief that p does not. Gettier's notion of belief that (p v q) doesn't take this into proper account, and cannot as a result of neglecting the aforementioned distinction.

You're forgetting that we are treated to a buffet of reasons for Smith to believe that p.

The reasons that p is justified are irrelevant to the the case I'm making.

The issue is what belief that (p v q) requires in order for it to even form and/or be held.

My apologies to all the participants for a reply of mine on the first page... I mean, upon re-reading the thread as a means to follow my own train of thought, I realized that I posted something(my first reply after the OP) that made no sense whatsoever as it was written. Be that as it may, I commented upon it...

No one called me out. However, the replies to that particular post now have a bit of different meaning to me than at the time. Here I was wondering what on earth some of you were thinking, when it would've been much more appropriate the other way around. Thanks for the charitable reading!

:D