It's a hypothetical. He asks us to assume that Smith forms this belief. Your argument is that he doesn't, or can't, or shouldn't. What's not clear is your grounds for denying the premise.

This is a really important and constantly overlooked point, but making it is often like "speaking in parables to the blind", unfortunately.

Gettier's case requires Smith to hold belief about Brown's location — creativesoul

No it doesn't. It only requires that you believe that Jones owns a Ford. That's the whole point. Given that "Either Jones owns a Ford or Smith is in Barcelona" follows from "Jones owns a Ford" then if you are justified in believing that "Jones owns a Ford" is true then you are justified in believing that "Either Jones owns a Ford or Smith is in Barcelona" is true. And if Smith is in Barcelona then "Either Jones owns a Ford or Smith is in Barcelona" is true, even if Jones doesn't own a Ford.

So you have a justified true belief if one operand of a disjunction is false but justifiably believed to be true and if the other is true but not justifiably believed to be true (or even justifiably believed to be false).

I don't need to believe that "pigs can fly" is true to believe that "either London is the capital city of England or pigs can fly" is true.

I wrote:

Gettier's case requires Smith to hold belief about Brown's location.

You replied:

No it doesn't. It only requires that you believe that Jones owns a Ford. That's the whole point.

Then Smith does not believe that Brown is in Barcelona. If Smith does not believe that Brown in is Barcelona, then Smith does not have JTB, and that's the whole point. Believing that g, h, and i follow from f doesn't require belief about Brown's location. And yet, that is the only purported belief that is true here. It's not a belief of Smith's at all. It's a random statement about Brown's location.

Bewitchment.

Leave out knowledge and belief for a moment. If I am justified in asserting p, am I justified in asserting p v q?

It's all about belief. I mean, that is precisely what grounds my objections here srap. Smith does not hold/have belief about Brown's whereabouts.

To answer your question...

An either/or claim is a claim that one or the other is true. The problem with Gettier's case is that both could be. That is because they have nothing to do with one another. A proper either/or claim posits mutually exclusive propositions. The two cannot both be true. Thus, to put the two statements that Gettier has into an either/or form is ill-conceived.

It's all about belief. I mean, that is precisely what grounds my objections here srap. Smith does not hold/have belief about Brown's whereabouts. — creativesoul

I get that. But I wanted to clarify your views on the logical constants and standard inference rules.

An either/or claim is a claim that one or the other is true. The problem with Gettier's case is that both could be. That is because they have nothing to do with one another. A proper either/or claim posits mutually exclusive propositions. The two cannot both be true. Thus, to put the two statements that Gettier has into an either/or form is ill-conceived. — creativesoul

And, as it turns out, you have a non-standard view of "or".

It's entirely possible that in everyday English usage, the exclusive "or" predominates. That's an empirical question. By "proper" do you mean "conforming to everyday usage"?

And would you, in general, reject inferring "p ∨ q" from "p"?

Can you answer a question for me Srap?

When one says either X or Y, do you think that it makes any sense at all to put it like that if both X and Y are true or could be so?

Put p v q in meaningful terms. I mean, give them value.

When one says either X or Y, do you think that it makes any sense at all to put it like that if both X and Y are true or could be so? — creativesoul

That's a linguistics question. In some cases, exclusive or is more natural, and in some cases inclusive.

There are reasons classical logic settled on the inclusive or. For instance, by De Morgan's law,
¬(A & B) ↔ ¬A ∨ ¬B
because it seems most natural to say that "A & B" can be false by either or both of A and B being false.

Certainly people use the exclusive or sometimes, but it's so well known that "or" is ambiguous that we have "but not both" to make it clear when the exclusive interpretation is intended.

Then Smith does not believe that Brown is in Barcelona. If Smith does not believe that Brown in is Barcelona, then Smith does not have JTB, and that's the whole point. — creativesoul

I'll spell it out more clearly for you.

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

I do not see how setting out how A&B can be false is relevant to the case at hand. For one, it's not a counterexample of either/or. It may, however, shed some much needed light upon how combining two propositions/assertions/statements into one monolith is a mistake. It could offer enough evidence to show the equivocation of "true". It could also lead to a more productive direction by virtue of helping us to recognize how Gettier conflates propositions/assertions/statements with belief.

You wrote:

I'll spell it out more clearly for you.

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

I understand the historical approach. I've seen the above 'proof' or something similar before, although 6 looks out of place. It should say I know that q if my belief that q is justified and true. The problem is, of course, that there is no belief that q. Never-the-less...

Smith does not hold/have belief about Brown's whereabouts. That's a given. As I've already spelled out for you, if Smith does not hold belief about Brown's whereabouts, then Smith cannot believe that Brown is in Barcelona. The statement that is true is the one about Brown's whereabouts. That is not a statement of Smith's belief.

The conflation is at 2. Belief that p v q does not require belief that q. Belief that q is precisely what the case requires in order to be a case of belief, regardless of whether or not it's justified or true.

although 6 looks out of place. It should say I know that q if my belief that q is justified and true. — creativesoul

r is just a placeholder, like p and q. It's the justified true belief definition of knowledge. In this case, r is p ∨ q, which is shown to be a justified true belief in 5.

The conflation is at 2. Belief that p v q does not require belief that q. Belief that q is precisely what the case requires in order to be a case of belief, regardless of whether or not it's justified or true.

I'm not saying that there's a belief that q. I'm saying that there's a belief that p ∨ q. So, no, there's no conflation at 2.

It just looks to me like you don't accept any of Gettier's premises, including the use of classical logic to analyse natural language.

Is there common ground for you and Gettier that I'm missing?

(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.

That is the problem.

If Smith can believe each of those three propositions, and those three propositions include contradictory statements about Brown's whereabouts, then either Smith believes Brown is in three places at once or believing each of those three propositions does not require belief about Brown's whereabouts. Since all three propositions include statements about Brown's whereabouts, and Smith has no idea where Brown is, it is clear that what Gettier counts as being justified in 'believing' each of those three propositions does not require belief that the statements about Brown's whereabouts are true.

So, then what does it mean to believe each of these three propositions if not believing that inferring p v q from p is justified?

Fair enough.




I suspect that there is much common ground.

That is the problem.

If Smith can believe each of those three propositions, and those three propositions include contradictory statements about Brown's whereabouts, then either Smith believes Brown is in three places at once or believing each of those three propositions does not require belief about Brown's whereabouts. Since all three propositions include statements about Brown's whereabouts, and Smith has no idea where Brown is, it is clear that what Gettier counts as being justified in 'believing' each of those three propositions does not require belief that the statements about Brown's whereabouts are true.

So, then what does it mean to believe each of these three propositions if not believing that inferring p v q from p is justified? — creativesoul

He doesn't need to believe anything about Brown's location. He only needs to believe that Jones owns a Ford. That's just a fact about disjunctions.

Again, the following are both true, I believe both to be true, and I am justified in believing both to be true:

1. London is the capital city of England and/or pigs can fly
2. London is the capital city of England and/or pigs can't fly

I know both of these to be true. And by the same token, I know that the following are both true, even though I have no opinion on where you are:

3. London is the capital city of England and/or creativesoul is in London
4. London is the capital city of England and/or creativesoul is in Barcelona

I suspect that there is much common ground. — creativesoul

Such as?

I understand all of that Michael.

I'd like you to answer the question...

What does it mean to believe each of these three propositions if not believing that inferring p v q from p is justified?

What does it mean to believe each of these three propositions if not believing that inferring p v q from p is justified? — creativesoul

You believe that p v q is true if you believe that one or both of the operands is true.

That looks like an equivocation of "is true".

Believing that p is true or believing that q is true is to believe that p or q corresponds to fact/reality. Note that these are two separate statements. Believing that p v q is true if you believe that p or q corresponds to fact/reality is to believe that calling p v q "true" is consistent with the rules of correct inference.

I note also that your examples have a p that is true. Gettier's p is false. Not sure what the ramifications of that are, aside from whether or not one is justified in deriving p v q from a false p? Of course, all of this recent stuff is aside from my original objection(s). It's always interesting to look at Gettier cases none-the-less.

I think our differences involve the different conceptions/notions regarding what counts as belief.

I don't understand your distinction. If p is true then doesn't p v q correspond to fact/reality? Surely the statement "London is the capital city of England and/or pigs can fly" describes some state-of-affairs in the world?

I note also that your examples have a p that is true. Gettier's p is false. Not sure what the ramifications of that are — creativesoul

In terms of the logic, nothing. In terms of our intuition regarding what counts as knowledge, everything. It shows that the JTB definition of knowledge isn't correct (or at least, isn't sufficient).

I asked:

What does it mean to believe each of these three propositions if not believing that inferring p v q from p is justified?

You answered:

You believe that the disjunction p v q is true if you believe that p is true or if you believe that q is true.

Is that different than believing that inferring p v q from p is justified?

You see, I know what it takes for p to be true. I know what it takes for q to be true. However, I do not understand how "is true" could mean the same thing when talking about what it takes for p v q to be true. It seems like the only criterion for p v q being true is either p or q being believed.

Is that different than believing that inferring p v q from p is justified? — creativesoul

It has nothing to do with believing that p v q is a justified inference from p, so I don't understand why you're bringing it up. Gettier is simply saying that because p v q is entailed by p then if a belief that p is justified then ipso facto a belief that p v q is justified.

It seems like the only criterion for p v q being true is either p or q being believed.

It's not. It's very basic logic, as shown in this truth table. p v q is true if one or both of p and q are true.

It's worth mentioning that you can believe and assert "p v q" when you believe one of them is true but you don't know which one.

It has nothing to do with believing that p v q is a justified inference from p, so I don't understand why you're bringing it up. Gettier is simply saying that because p v q is entailed by p then if a belief that p is justified then ipso facto a belief that p v q is justified.

I'm bringing it up because believing that p v q is a justified inference from p has everything to do with the self-imposed bewitchment. I understand the historical approach. I understand that if one accepts all of Gettier's premisses, then the only substantive argument against his cases needs to involve justification.

I've no skin in the game either way as far as the justification aspect goes. My approach criticizes the belief aspect. So, set the preconceptions aside for a moment and follow along. That is the only way for you to understand how what I'm bringing up is relevant.

Whether or not p v q is entailed by p is determined solely by the rules of correct inference. As you, yourself, have said - that's just a fact about disjunction. I'm not denying that. I'm granting it. Gettier is saying that because Smith knows the rules(realizes the entailment), he proceeds to accept (g), (h), and (i) on the basis of (f). That much is clearly seen below...

..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).

Here is where the bewitchment begins. The key word here is "accept". Accepting (g), (h), and (i) on the basis of (f) requires only realizing and accepting(believing) that the rules of correct inference allow such a thing. That much is indisputable..

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.

Notice that Gettier changes "accepts" to "believes". Smith is completely justified in believing that each of these three propositions follow the rules of correct inference, thus he believes that all three are valid. Believing that each of the three propositions are valid allows one to place 'is true' at the end, again based upon the rules.

Don't let that bewitch you.

Believing that each of the three is valid is remarkably different than believing each of the three correspond to fact/reality. They cannot all be true, even though - as a result of the rules - the terms "is true" can be affixed to each. Smith knows that. Believing all three requires believing that all three are true(as compared/contrasted to valid). Smith knows that. One cannot form and hold three contradictory beliefs simultaneously, although one can believe that three contradictory propositions are all valid. Smith does not believe all three propositions, even though he accepts that they are all valid inferences.

What I'm pointing out here is the equivocation of "is true" that is at hand. It bears witness to the fact that Gettier is conflating Smith's belief that each disjunction follows the rules of correct inference with Smith's believing that each one is true. One can believe that three contradictory propositions all follow from the same p. This allows one to affix each disjunction with 'is true', because in this situation 'is true' signifies valid inference, and all of this follows the rules of correct inference.

So, 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?