That bit of knowledge regarding what belief that (p v q) takes dissolves this purported Gettier problem — creativesoul

I still have no idea what this is supposed to mean or what point you think you've made. In what way is Case II dissolved?

Fair enough Srap. I'm making quite the claim, aren't I? Extraordinary claims require extraordinary proof. I like that, and ought honor it.

I'm working on that now...

I've dissolved this Gettier case. Let's look, once again, at Gettier's set up...

Let us suppose that Smith has strong evidence for the following proposition:
(f) Jones owns a Ford. Smith's evidence might be that Jones has at all times in the past within Smith's
memory owned a car, and always a Ford, and that Jones has just offered Smith a
ride while driving a Ford.

Let us imagine, now, that Smith has another friend, Brown, of whose whereabouts he is totally ignorant. Smith selects three place names quite at random and constructs the following three propositions:

(g) Either Jones owns a Ford, or Brown is in Boston.
(h) Either Jones owns a Ford, or Brown is in Barcelona.
(i) Either Jones owns a Ford, or Brown is in Brest-Litovsk.

Each of these propositions is entailed by (f). 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. Smith, of course, has no idea where Brown is.

It is here that it would behoove us all to pause a moment and give this very careful attention. Granting all of the above, let us critically examine what Gettier is saying by virtue of assessing what it would actually take in order for one to even be able to do what Gettier says that Smith does.

Smith has justified belief that p. Smith constructs three propositions from his belief that p. Smith realizes the entailment of these three propositions. Smith accepts all three on the basis of his justified belief that p. Smith is therefore justified in believing each (p v q). Gettier stops here though, without putting it all together. Smith has three different beliefs that (p v q).

What does it take in order for Smith to even be able to do all of that?

If Smith believes that p, derives 3 versions of (p v q) from p, and realizes the entailment, then he knows the rules of correct inference. If he knows the rules of correct inference then he knows that (p v q) follows from p; He knows that the rules of correct inference presuppose the truth of the premisses; he knows that a valid inference is called "true" because validity preserves the truth of the premisses, and he also knows that the inference is true(as compared/contrasted to just valid) if, and only if, the premisses are true and the inference valid. Given that Smith knows all of the above...

Smith's 'belief' that (p v q) is not that (p v q) is true. Rather, it is that "(p v q) is true" is valid and that is justified true belief in all three cases. It is nothing less than knowledge that (p v q) follows from p. The truth conditions of p and q are irrelevant to knowing that (p v q) follows from p.

QED.

Smith's 'belief' that (p v q) is not that (p v q) is true. Rather, it is nothing less than knowledge that (p v q) follows from p. That is justified true belief in all three cases. The truth conditions of p and q are irrelevant to knowing that (p v q) follows from p. — creativesoul

It's more than this, as I explained here.

You can believe that r follows from p and believe that r is false, and you can believe that r follows from p and believe that r is true. In Gettier's case, Smith doesn't just believe that r follows from p; he also believes that r is true.

I revisited your explanation Michael. I would prefer using Gettier's case. Your case has significant differences. My claim is that Smith's belief that (p v q) is knowledge that (p v q) follows from p. I've just argued for that without subsequent refutation. I do not see anything in Gettier's case that requires concluding that Smith doesn't know that (p v q) follows from p.

Smith doesn't believe that (p v q) is true. — creativesoul

Yes he does. He believes that r follows from p, that p is true, and so that r is true.

He believes that "(p v q) is true" is valid — creativesoul

This doesn't make any sense. Inferences are valid, not propositions. "(p ∨ q) is true" is a proposition.

The below is an example of a valid inference:

1. p → r
2. p
3. r

These are three separate propositions that can be true and believed in. You might believe 1, 2, and 3. You might believe 1 but not 2 or 3. You might believe 1 and 3 but not 2. You might believe 2 and 3 but not 1. You might believe 2 but not 1 or 3. You might believe 3 but not 1 or 2.

In Gettier's case, r is p ∨ q.

He knows the rules of correct inference. So, he knows that (p v q) follows from p, he believes that p is true, and so he knows that if p is true, then so too is (p v q).

So, he knows that (p v q) follows from p, he believes that p is true, and so he knows that if p is true, then so too is (p v q). — creativesoul

And he also believes that p ∨ q is true.

No. He knows that (p v q) is valid.

No. He knows that (p v q) is valid. — creativesoul

p ∨ q isn't an inference, and so isn't the sort of thing that is valid. It's a proposition that is either true or false.

Smith knows the rules of correct inference. Gettier doesn't take that into account.

Smith knows the rules of correct inference. Gettier doesn't take that into account. — creativesoul

He does take that into account. It's right there in your quoted passage: "Each of these propositions is entailed by (f). Imagine that Smith realizes the entailment of each of these propositions he has constructed"

He doesn't take it into proper account.

He doesn't take it into proper account. — creativesoul

He does take it into proper account. Smith believes that f is true. Smith knows that g, h, and i follow from f as per the rules of inference. Therefore, Smith believes that g, h, and i are true.

Compare with: Smith believes that f is false. Smith knows that g, h, and i follow from f as per the rules of inference. Smith believes that g and h are false and that i is true.

Believing that r follows from p is one thing. Believing that r is true (or false) is something else.

No. Smith believes that f is true. Smith knows that g, h, and i follow from f as per the rules of correct inference. Therefore, Smith knows that g, h, and i are valid.

Only if Smith knows that f is true would he know that g, h, and i are true.

No. Smith believes that f is true. Smith knows that g, h, and i follow from f as per the rules of correct inference. Therefore, Smith knows that g, h, and i are valid — creativesoul

g, h, and i are not the sort of things that can be valid or invalid, as I keep saying. Inferences are valid, not propositions. g, h, and i are propositions. They are either true or false.

Smith believes that f is true. Smith knows that g, h, and i are valid inferences from f. Therefore, Smith believes that g, h, and i are true.

Only if Smith knows that f is true would he know that g, h, and i are true. — creativesoul

And Gettier would agree. The problem is that Smith has a justified true believe in g, h, and i. Therefore, the JTB definition of knowledge is lacking.

So, you're saying that g, h, and i follow from f according to the rules of correct inference but they are not valid?

Hows that work?

So, you're saying that g, h, and i follow from f according to the rules of correct inference but they are not valid?

Hows that work? — creativesoul

Because propositions are not the sort of things that are valid or invalid. Inferences are valid or invalid. Propositions are true or false. g, h, and i are propositions.

This is basic logic.

Smith has a justified true belief that g, h, and i follow from f - not in g, h, and i.

Smith has a justified true belief that g, h, and i follow from f - not in g, h, and i. — creativesoul

This isn't mutually exclusive. He has a justified true belief that g, h, and i follow from f and a justified true belief that g, h, and i are true.

Ah. By definitional fiat. I'll grant it.

So then, propositions are not inferred?

So then, propositions are not inferred? — creativesoul

Propositions are inferred, but they are not inferences. This is an inference:

1. Socrates is a man
2. All men are mortal
3. Therefore, Socrates is mortal

Each of the three propositions is either true or false, with the argument itself being valid or invalid. It doesn't make sense to say that "Socrates is mortal" is valid.

4. London is the capital city of England
5. Therefore, London is the capital city of England or I am a woman

Each of the two propositions is either true or false, with the argument itself being valid or invalid. It doesn't make sense to say that "London is the capital city of England or I am a woman" is valid.

1. Socrates is a man
2. All men are mortal
3. Therefore, Socrates is mortal

Each of the three propositions is either true or false, with the argument itself being valid or invalid. It doesn't make sense to say that "Socrates is mortal" is valid.

So, conclusions aren't valid?

4. London is the capital city of England
5. Therefore, London is the capital city of England or I am a woman

Each of the two propositions is either true or false, with the argument itself being valid or invalid. It doesn't make sense to say that "London is the capital city of England or I am a woman" is valid.

Where's the argument?

Does it make sense to say that "London is the capital city of England or I am a woman" is an invalid conclusion?

Believing that 'Either Jones owns a Ford or Brown is in Barcelona' is true, if based upon belief that 'Jones owns a Ford', is knowledge 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'.

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

It is nothing less than knowledge that (p v q) follows from p. The truth conditions of p and q are irrelevant to knowing that (p v q) follows from p.

Propositions are inferred, but they are not inferences.

That makes no sense at all. Either an inference is not inferred, or being inferred doesn't count as being an inference.

What follows below is self-contradiction...

I wrote:

Smith believes that f is true. Smith knows that g, h, and i follow from f as per the rules of correct inference. Therefore, Smith knows that g, h, and i are valid.

Read this carefully people...

You replied: g, h, and i are not the sort of things that can be valid or invalid, as I keep saying. Inferences are valid, not propositions. g, h, and i are propositions. They are either true or false.

Smith believes that f is true. Smith knows that g, h, and i are valid inferences from f. Therefore, Smith believes that g, h, and i are true.

So then, g, h, and i are only valid inferences when you say so? What sense does this make?

On the one hand, you claim that g, h, and i are propositions not inferences, and because only inferences are valid, g, h, and i cannot be so. On the other hand, you say that Smith knows that g, h, and i are valid inferences from f.

Smith believes that f is true. Smith knows that g, h, and i follow from f as per the rules of correct inference. Therefore, Smith knows that g, h, and i are valid inferences. Because Smith knows that g, h, and i are valid, his belief is not that g, h, and i are all true unless he conflates being valid with being true. Smith is rational and knows the rules, so doesn't do this. Rather Smith knows that g, h, and i are all true if and only if his belief that f is.

The truth conditions of q have no bearing upon either Smith's belief or his knowledge.

So then, let's say that Smith is just a regular joe, and says with unshakable certainty "Well, either Jones owns a Ford or Brown is in Barcelona" even though he knows that he's ignorant regarding Brown's whereabouts.

He would believe that f, but would not know that h followed. Thus, his assertion would be unjustified, and the case ends there.