Can I surmise that each of these same propositions is about the same states of affairs? — creativesoul

<shrug>

I believe that I am shorter than the Eiffel Tower. Do you want to call that one state of affairs? Two? Three? How would you decide?

I believe that I am shorter than the Eiffel Tower. Do you want to call that one state of affairs? Two? Three? How would you decide?

Point taken. I would only note that the conversation focused upon what it would take in order for justification to be preserved from p to (p v q).

Do you still hold that every proposition has it's own unique truth conditions such that no two propositions have the same truth conditions?

Do you still hold that every proposition has it's own unique truth conditions such that no two propositions have the same truth conditions? — creativesoul

Yes.

If one believes that either this(p) or that(q) is true, then one believes that both cannot be. That is not the case with Smith.

What would change if, say, Jones still owned a Ford?

It would still be the case that Smith has validly inferred (p v q).

Both p and q would be true.

Smith would still believe that (p v q) is true if either p or q is. Smith would be correct in following the rules, but the rules would be wrong.

Would his belief that (p v q) still be true?

You see what's happening here regarding the clear distinction being drawn between believing that a proposition(p v q) is validly inferred, and believing that a proposition(p v q) is true?

You see what's happening here regarding the clear distinction being drawn between believing that a proposition(p v q) is validly inferred, and believing that a proposition(p v q) is true? — creativesoul

Yes, I've already explained the difference.

1. I am a woman
2. I am a woman or London is the capital city of France

I believe that p ∨ q is validly inferred, but that p ∨ q is false.

3. I am a woman
4. I am a woman or London is the capital city of England

I believe that p ∨ q is validly inferred, and that p ∨ q is true.

In Smith's case,

5. Jones owns a Ford
6. Jones owns a Ford or Brown is in Barcelona

Smith believes that p ∨ q is validly inferred, and that p ∨ q is true.

You're the one conflating, arguing that Smith believing that p ∨ q is true is just believing that p ∨ q is validly inferred. That's just not the case.

Interesting mischaracterization...

If one believes that either this(p) or that(q) is true, then one believes that both cannot be.

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), and to believe that both cannot be.

Believing that "Either 'Jones owns a Ford' or 'Brown is in Barcelona'" is true, if based upon belief that Jones owns a Ford, and accepting the rules of correct inference is to know that if either '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'", and to believe that both 'Jones owns a Ford' and 'Brown is in Barcelona' cannot be.

...You're the one conflating...

Didn't you earlier claim that g, h, and i were all true?

:(

I don't think so. If I did, I misspoke. g, h, and i are all believed to be true, and could all be true (if Jones owns a Ford). But in Gettier's example, only one of them is true.

Interesting mischaracterization... — creativesoul

How so? What part of my post do you disagree with?

If one believes that either this(p) or that(q) is true, then one believes that both cannot be.

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), and to believe that both cannot be.

Believing that "Either 'Jones owns a Ford' or 'Brown is in Barcelona'" is true, if based upon belief that Jones owns a Ford, and accepting the rules of correct inference is to know that if either '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'", and to believe that both 'Jones owns a Ford' and 'Brown is in Barcelona' cannot be. — creativesoul

Gettier is using the inclusive or, not the exclusive or, as the exclusive or doesn't follow from p.

It's p ∨ q, not p ⊻ q.

You're the one conflating, arguing that Smith believing that p ∨ q is true is just believing that p ∨ q is validly inferred.

That's an oversimplification. See my last post above that sums up my notion of what Smith's belief that (p v q) is true consists in.

That's an oversimplification. See my last post. I think that that sums up my notion of what Smith's belief that (p v q) is true consists in. — creativesoul

And it's wrong. Again:

1. I am a woman
2. I am a woman or London is the capital city of England

My belief that 2 is true isn't just a belief that 2 is validly inferred. Else you would have to say that I believe that 4 is true:

3. I am a woman
4. I am a woman or London is the capital city of France

Except I don't. I believe that 4 is false, even though it's validly inferred. There is a very clear difference between believing that p ∨ q is entailed by p and believing that p ∨ q is true. Smith believes that p ∨ q is true (and that it is entailed by p).

Smith cannot believe that both p and q could be true.

Yes he can. Take, for example:

1. My name is Michael or my girlfriend is having a shower (p ∨ q)
2. My name is Michael or my girlfriend is having a bath (p ∨ r)

I believe that my name is Michael. If my name is Michael then both of 1 and 2 are true. Therefore, I believe that both 1 and 2 are true. Furthermore, I believe that my girlfriend could be having a shower, and so believe that both p and q could be true. And I believe that my girlfriend could be having a bath, and so believe that both p and r could be true.

Granted, I can't believe that p, q, and r are all true, as I can't believe that both q and r are true, but that's irrelevant to Gettier's argument.

I'm not even sure what you're talking about when you say it's wrong... again.

Quote me and argue against the parts you say are wrong.

Your claim that Smith's belief that p ∨ q is true is just the belief that p ∨ q is validly inferred from p. It isn't. As you make clear here, there's a "clear distinction being drawn between believing that a proposition(p v q) is validly inferred, and believing that a proposition(p v q) is true".

And again:

1. I am a woman
2. I am a woman or London is the capital city of France

I believe that p ∨ q is validly inferred, but that p ∨ q is false.

3. I am a woman
4. I am a woman or London is the capital city of England

I believe that p ∨ q is validly inferred, and that p ∨ q is true.

Smith's belief is of the latter kind. A valid inference with a true conclusion.

I wrote:

Smith cannot believe that both p and q could be true.

You objected:

Yes he can. Take, for example:

1. My name is Michael or my girlfriend is having a shower (p ∨ q)
2. My name is Michael or my girlfriend is having a bath (p ∨ r)

I believe that my name is Michael. If my name is Michael then both of 1 and 2 are true. Therefore, I believe that both 1 and 2 are true. Furthermore, I believe that my girlfriend could be having a shower, and so believe that both p and q could be true. And I believe that my girlfriend could be having a bath, and so believe that both p and r could be true.

Granted, I can't believe that p, q, and r are all true, as I can't believe that both q and r are true, but that's irrelevant to Gettier's argument.

No, he cannot.

Gettier claims that Smith is totally ignorant about Brown's location. That is a problem for the inclusive notion. Smith does not believe any of the Q's. In order for Smith to believe that both p and q could be true, Smith must believe q. Gettier also claims that Smith believes all three. If Smith believes all three and believes that p and q can both be true, then he either holds contradictory belief about Brown's location or he holds belief about Brown's location. Neither is acceptable given that Smith is totally ignorant regarding Brown's whereabouts.

No, he cannot.

Gettier claims that Smith is totally ignorant about Brown's location. That is a problem for the inclusive notion. Smith does not believe any of the Q's. In order for Smith to believe that both p and q could be true, Smith must believe q. — creativesoul

Smith doesn't need to believe that both are true. It's a disjunction, not a conjunction.

Your arguments are making less and less sense.

He needs to believe that both could be. Smith cannot believe that both p and q could be true, for the reasons I've been giving.

He needs to believe that both could be. He cannot for the reasons I've been giving. — creativesoul

You mean this reason?

In order for Smith to believe that both p and q could be true, Smith must believe q. — creativesoul

That's simply false.

Let's say that q is "creativesoul is over 40 years old". You're saying that I can only believe that q could be true if I believe that q is true? That is obviously wrong.

He needs to believe that both could be.

Also, he doesn't. He can believe that q is false and that p is true. The following is a disjunction that I believe to be true:

My name is Michael or pigs can fly.

And it's true. And I'm justified in believing that it's true.

Point taken.

We're getting back into your territory... My case cannot be made in those terms. I've removed the bit regarding inclusive/exclusive...

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).

Believing that "Either 'Jones owns a Ford' or 'Brown is in Barcelona'" is true, if based upon belief that Jones owns a Ford, and accepting the rules of correct inference is to know that if either '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'".

What's your criticism here? Please use Gettier's case as a counter...

I want to set out the argument in long form, I suppose. Particularly, I want to see the missing premisses from belief that p to belief that (p v q).

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). — creativesoul

You're conflating again. Believing that p ∨ q is true is not the same thing as believing that p ∨ q is entailed by p. I can believe that p ∨ q is entailed by p but believe that p ∨ q is false (as with the example of "I am a woman or London is the capital city of France" being entailed by "I am a woman").

So that's where you think I'm conflating. I agree with what you've said here, aside from the charge...

I'm setting out what is required in order to even be able to arrive at "Either 'Jones owns a Ford' or 'Brown is in Barcelona'" is true, if based upon belief that Jones owns a Ford.

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).

I've changed the bit I think you took issue with.

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'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

So Smith believe that p ∨ q is true. And Smith is justified in believing that p ∨ q is true. And p ∨ q is true. Therefore, Smith has a justified true belief.

Nothing you've said refutes Gettier's argument.

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

Smith is wrong.

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