And to repeat my earlier question yet again, do you believe that this statement is true?

London is the capital city of England and/or I was born in Leeds.

Smith believes Jones owns a Ford. Smith believes that the statement 'Jones owns a Ford' is true. Smith believes the disjunction 'Jones owns a Ford or Brown is in Barcelona' follows from the statement 'Jones owns a Ford'.

Now from here, you and Gettier want to say that Smith believes that the disjunction 'Jones owns a Ford or Brown is in Barcelona' is true.

Is that right?

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)

Elegance

Smith believes that Jones owns a Ford. Smith believes that the statement 'Jones owns a Ford' is true. Smith believes the disjunction 'Jones owns a Ford or Brown is in Barcelona' follows from the statement 'Jones owns a Ford'.

Now from here, you and Gettier want to say that Smith believes that the disjunction 'Jones owns a Ford or Brown is in Barcelona' is true.

Is that right? — creativesoul

Yes. But Gettier doesn't just want to say it. He does say it. It's one of those premises that it doesn't make sense to refute, like "Jones was renting a Ford".

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)

Elegance — creativesoul

C2. p ∨ q is true (from C1)

Rational people do not believe statements unless they know what they mean. Knowing what a disjunction means is to know what makes them true. You and Gettier leave that part of Smith's thought/belief process sorely neglected.

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)

C2. p ∨ q is true (from C1)

Your report of Smith's thought/belief process is utterly inadequate.

Rational people do not believe statements unless they know what they mean. Knowing what a disjunction means is to know what makes them true. You and Gettier leave that part of Smith's thought/belief process sorely neglected.

Belief that:((p v q) is true) is not equivalent to belief that:((p v q) is true because (p))

Salva veritate

Belief that:((p v q) is true) is not equivalent to belief that:((p v q) is true because (p)) — creativesoul

How many times am I going to explain this? I'm not saying that they're equivalent. This is just a strawman.

I'm saying that the latter entails the former.

Salva veritate

Why do you keep saying this? It has no bearing on our discussion.

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)

There are no problems with this formula. Imagine any disjunction arrived at by virtue of deducing it from believing P. Fill it out.

Your logic and/or some of the rules are wrong. Brace yourself. I've dissolved disjunction problems...

There are no problems with this formula. Imagine any disjunction arrived at by virtue of deducing it from believing P. Fill it out. — creativesoul

I'm not saying that there are problems. I'm saying that it's incomplete, which is why I am filling it out:

C2. p ∨ q is true (from C1)

Your logic and/or some of the rules are wrong. — creativesoul

No, yours are. You've said "False premisses and valid form cannot yield true conclusions". And of the following you've said "Can't get to 3 from 1 and 2. Can't get to 6 from 4 and 5":

1. p
2. p ⊨ p ∨ q
3. p ∨ q

4. Socrates is a man
5. If Socrates is a man then Socrates is mortal
6. Therefore, Socrates is mortal

You're just wrong on all accounts.

Salva veritate

Why do you keep saying this? It has no bearing on our discussion.

It bears on the discussion by virtue of pointing out that the two are not equivalent.

Belief that:((p v q) is true) is not equivalent to belief that:((p v q) is true because (p))

The former neglects the other deduction. The latter exhausts the former, but not the other way around. The latter is utterly inadequate for representing the necessary thought/belief process required for believing Q when Q is a disjunction arrived at from believing P.

There you go again using simple beliefs and statements thereof...

Irrelevant.

Use a disjunction. Apply my formula. Show a problem with the result.

It bears on the discussion by virtue of pointing out that the two are not equivalent.

Belief that:((p v q) is true) is not equivalent to belief that:((p v q) is true because (p))

The former neglects the other deduction. The latter exhausts the former, but not the other way around. The latter is utterly inadequate for representing the necessary thought/belief process required for believing Q when Q is a disjunction arrived at from believing P. — creativesoul

But I'm not saying that they're equivalent. I'm saying that the latter entails the former.

If I believe that Donald Trump is the President because he won the popular vote then I believe that Donald Trump is the President.

So if I believe that Jones owns a Ford or Brown is in Barcelona because Jones owns a Ford then I believe that Jones owns a Ford or Brown is in Barcelona.

I did use a disjunction:

1. p
2. p ⊨ p ∨ q
3. p ∨ q

I swear you're just being wilfully ignorant now. But then you've repeatedly shown that you don't understand basic logic, so perhaps it isn't wilful.

1. p
2. p ⊨ p ∨ q
3. p ∨ q

4. Socrates is a man
5. If Socrates is a man then Socrates is mortal
6. Therefore, Socrates is mortal

There's something missing. Do you not notice?

"All men are mortal" is missing from the latter. p v q is true because p is missing from the former.

Use a disjunction and put the argument in English terms... long form.

There's something missing. Do you not notice? — creativesoul

There isn't. They're valid. It's modus ponens.

:-O

I've little to no reason to continue this discussion. You deny a clearly missing premiss, and are attempting to brow beat me with man-made rules that do not take proper account of actual thought/belief processes...

I did use a disjunction:

1. p
2. p ⊨ p ∨ q
3. p ∨ q

And in English

1. London is the capital city of England
2. If London is the capital city of England then by entailment London is the capital city of England and/or I was born in Leeds
3. Therefore, London is the capital city of England and/or I was born in Leeds

I've little to no reason to continue this discussion. You deny a clearly missing premiss — creativesoul

Because there isn't one. Just look up modus ponens:

If something is F, it is G.
a is F.
Therefore, a is G.

If Socrates is a man then he is mortal
Socrates is a man
Therefore, Socrates is mortal

Rational people do not believe statements unless they know what they mean. Knowing what a disjunction means is to know what makes them true. You and Gettier leave that part of Smith's thought/belief process sorely neglected.

Smith knows what "Jones owns a Ford or Brown is in Barcelona" means. That's how he knows that it follows from "Jones owns a Ford". Your arguments just don't make any sense.

I believe that London is the capital city of England, and so I believe that "London is the capital city of England or pigs can fly" is true.

Smith believes that Jones owns a Ford, and so he believes that "Jones owns a Ford or Brown is in Barcelona" is true.

I agree that Smith knows what the disjunction means.

Knowing what a disjunction means requires knowing what makes it true.

I agree Smith knows what the disjunction means.

Knowing what a disjunction means requires knowing what makes it true. — creativesoul

Yes, and he believes it to be true. And it's true. So he has a true belief.