I see it as knowing the what makes (p v q) true. — creativesoul

We're not actually disagreeing. :-)

"p ∨ q" has three semantic components: p, q, and ∨. You have to know what they all mean to know what "p ∨ q" means; you have to know whether p and q are true to know whether "p ∨ q" is true.

knowing that if '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'. — creativesoul

You've mentioned this several times. I see this as knowing the definition of "or".

If A or B, then A-or-B.

It seems interesting if you throw in "is true", but it's really not.

If A is true or B is true, then A-or-B is true.

But again that's just the definition.

Natural language isn't shorthand for logical notation. — creativesoul

I presented it in natural language.

Show me where that argument for 4 goes wrong — creativesoul

As I said before, I think "A because B" is just shorthand for a modus ponens:
If B then A;
B;
therefore A.
As it happens, you had included the conditional in your premises (1 I think), but p was nowhere to be found.

If we have the conditional explicitly, that means p is presupposed by 4, and there's no need for that, because we've been told in so many words that Smith believes that p.

2 is what matters. It's the whole point of Case II.

We already have, as a premise, a justified false belief for Smith, namely p, which for some reason you don't like to talk about.

4 annoys me, but I'm not even sure it matters, unless the idea is to pretend that Smith doesn't believe that p.

2 is the justified true belief.

What are you denying? — creativesoul

What point are you making?

I've said I object to 4 because it runs two premises together and obscures the main issue. I don't know if it's false, but it's not helpful.

What do you get if I grant 4?

The justification is irrelevant. Smith's belief is false. (p v q) is not true because p is. — creativesoul

Justification is the whole point of the exercise.

Smith has loads of false beliefs, starting with p. What does that get you?

I'm not talking about his belief that p. — creativesoul

But you should be. I think you're trying to block the justification of p v q by hiding p, which is the only justified belief on the table.

Smith believes that p v q because p is true. — creativesoul

I heard you the first time. ;-)

Let me put it this way: your statement is just shorthand for this one

p & p→(p v q).

It's not like you can believe "p v q because p" without believing that p. You're just pushing the two premises together.

So, it's justified false belief? — creativesoul

His belief that p is a justified false belief, yes. At least that's the premise, which hasn't been challenged here.

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

"Because" is a slippery word though.

We can talk loosely about this, and it usually does no harm. I could say something like "p's being true makes p v q true." Mathematicians talk this way, but again this is to speak loosely. That's not a good idea here.

(If we really want to say something like this, we should probably say that whatever makes p true also makes p v q true -- but this is just the sort of truth theorizing I don't think we need to do here.)

As I've said, I think the right thing to say is that Smith believes, correctly, that p entails p v q, and he believes, incorrectly, that p. With those two beliefs in hand, he applies modus ponens. This is exactly what Gettier describes, I think.

Look at your 4 the other way round: what makes 4 a false belief is precisely that p is false. That's another reason to split out p, which you have not done here, although Gettier does. Smith has lots of false beliefs, and they all flow from his false belief that p.

And because Smith believes that p, it makes sense to present 4 giving "believe" smaller scope:

4. Smith believes that p v q because Smith believes that p.

That's the other sense of "because" -- not the vaguely causal sense we had above, but the sense in which p is a reason for Smith to believe that p v q, and a good one. By burying p inside a more complex belief, you've left out the reasoning process Gettier attributes to Smith. And it's that reasoning process that carries justification.

At least we're getting closer now to confronting the actual problem.

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

As I said, Smith thinks he's applying modus ponens but he isn't, because p is false.* So yes there is also the false belief that modus ponens is applicable -- but we don't want to go too far down this road because at some point you have to actually make an inference, which is an action not a belief.

Just remember that, for all Smith knows, Brown is in Barcelona. He may not believe that Brown is in Barcelona, but he doesn't believe that he isn't either.

So this is not a case of (p & ~q)→(p v q).

* We're saying m.p. is used here because that's basically what Gettier does. You could also call deriving p v q from p (or from q) a "v introduction rule" as it would be in a natural deduction system.

ADDED: Keep in mind too that Smith thinks m.p. is applicable because he thinks p is true. And that is what he should think. He just happens to be wrong.

Smith believes that (p v q) is true because p is true. Smith holds false belief. — creativesoul

Yeah, the false belief that p.

I thought we'd been over this, for instance here.

It's still true that p entails 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? — creativesoul

Yes.

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?

nothing at all to do with his belief except his belief that (p v q) follows from p. — creativesoul

... and is therefore true. That Smith believes (g), (h), and (i) -- i.e., believes all of them to be true -- is a premise of the argument.

What exactly are your grounds for rejecting this premise? That it is impossible for Smith to believe the conclusion of a valid argument from premises he believes? That it is not rational to do so? That as a matter of fact people do not do this?

Believing (f) and properly inferring (g), (h), and (i) from (f), why on earth should he not believe any of his own conclusions?

In this context: beliefs have propositional content. If that's what you mean, yes.

"I believe that ...", "I know that ...", "I suspect that ...", "I hope that ...", "I doubt that ..." -- these are all propositional attitudes. All of these words have other uses, none of which are relevant here.

You think/believe that every proposition has it's own unique set of truth conditions? — creativesoul

I think that's a pretty reasonable way to define propositions, yeah. You can express the same proposition in multiple ways, in multiple languages, and there will be all sorts of differences that logic just doesn't care about. Insofar as they have the same truth conditions they are different ways of expressing the same proposition.

I do not accept Gettier's notion of belief. — creativesoul

Why not?

Disjunctions are unique. — creativesoul

No they're not, not if we're talking about the logical constants. Are we talking about that, or are we talking about linguistics?

(g), (h), and (i) all consist of (f) and different statements about Brown's location. None of those statements (Q's) are believed by Smith. Smith derives them all by virtue of knowing the rules. — creativesoul

And you've not shown why this matters. At no point does Gettier attribute to Smith a belief in any of the "Q's".

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

Nope.

Disjunctions are unique. — creativesoul

That's not going to work out. I can define all the logical constants in terms of disjunction and negation.

It feels like we're wandering around here. I'm having trouble keeping track of what you accept and what you don't.

I would say that that would be the case if, and only if, P and Q have the same truth conditions. — creativesoul

That would make them the same proposition.

However, I am teasing out the differences between statements that are called 'true' by virtue of being a valid inference, and those that are true. — creativesoul

"Called 'true'"? So you still don't accept that the conclusion is true?

I strongly suspect that there is conflation between the two at work. — creativesoul

There might be if you persist in thinking that being the conclusion of a valid inference makes a proposition true. It doesn't. If you don't think that, then you don't need two different kinds of truth. Or three. Or twelve. Truth is truth.

What makes the following claims true? — creativesoul

What kind of answer are you expecting here?

Because it looks like you are asking, in so many words, for a theory of truth.

Smith's justification for (f) is all relevant to (f). Smith's inferring (g), (h), and (i) from (f) has nothing to do with the justification for (f). This is obvious because Smith could have correctly inferred (g), (h), and (i) even if it were the case that (f) was unfounded. — creativesoul

Well, yes and no. He doesn't make the inference because his belief that (f) is justified, but Gettier claims that inference preserves what justification he has for that belief, just as it preserves truth.

Secondly, for any proposition P, if S is justified in believing P, and P entails Q, and S deduces Q from P and accepts Q as a result of this deduction, then S is justified in believing Q. — Gettier

Rather, (g), (h), and (i) are justified by virtue of Smith knowing the rules and applying them accordingly to his belief that (f). — creativesoul

The trouble with this view is that valid inference from unjustified belief would confer justification upon the conclusion of the inference.* Inference isn't supposed to do that. Valid inference doesn't confer truth upon your conclusion, but guarantees that if the premises are true then the conclusion is too. Inference itself is not the source of the conclusion's truth -- that's still the premises.

I would disagree with Gettier's claim. — creativesoul

Yeah, like I've been saying for a while, you disagree with Gettier's premises. So you should be arguing that the quote above, beginning "Secondly, ...", is false.


* Here's an example of that:

I wake up on a Tuesday morning, groggy, remembering that I didn't have to get up yesterday, and thinking it's Monday and I have to be at work at 9. As it happens, Monday was a holiday and I have forgotten. I have a true belief that I need to be at work at 9, but it is not justified, as it is a valid inference from my unjustified belief that it is Monday, not Tuesday.

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. — creativesoul

And if (f) were true, so would (g), (h), and (i) be.

It's rather the point that Smith thinks he is applying modus ponens but he isn't, because (f) is actually false. That's valid, in the sense that it will preserve truth, but there's no truth to preserve.

Gettier's claim is that if an inference is valid, it preserves justification as well as truth, and thus even though there was no truth to preserve, what justification Smith had for his belief that (f), is passed to (g), (h), and (i) by modus ponens.

Since (h) is true entirely by coincidence, Smith now has one justified true belief, (h), but he has increased his store of justified false beliefs:
(f) Jones owns a Ford;
(g) Either Jones owns a Ford, or Brown is in Boston;
(i) Either Jones owns a Ford, or Brown is in Brest-Litovsk.

What will happen if he ever comes to correct his false belief (f)? Will he now have this inconsistent set of beliefs?
(g') Brown is in Boston;
(h') Brown is in Barcelona;
(i') Brown is in Brest-Litovsk.
No, as a matter of fact he won't: he believed he was applying modus ponens; once he knows that (f) is false, he will no longer infer (g), (h), and (i). Modus ponens is no use if (f) is false.

To believe that you have made a valid inference from a true premise is to believe that the conclusion is true. It is the whole point of making valid inferences. We only do this to get truths we do not yet know from truths that we do.

If you presented an argument here on this forum, what would you think of the following response?

I accept that your premises are true, and I accept that your conclusion may be validly inferred from those premises, but that is all; I do not accept that your conclusion is in fact true.

And here you'd gone to all that trouble of establishing your premises and making careful inferences, all for nought ...

ADDED: Where I say "no truth" above, that's technically wrong, of course, because all of the conditionals are fine:
(f)→(g)
(f)→(h)
(f)→(i).

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?

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

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.

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?

when you say "leave traces" what does that mean? — Sam26

Only that the brain is a pretty complex chemical environment. Who knows what the body might do when experiencing that degree of trauma. And then once blood has stopped flowing, various molecular machines stop doing their jobs as they run out of fuel. When you "reboot", I would expect the whole system to be a mess, and certainly not a typical environment for the brain of a living body. The bizarre chemical imbalances are what you wake up in since there's been no cleaning up going on.

The Wikipedia article describes many unusual circumstances -- injection of ketamine, oxygen deprivation, etc., etc. -- that reproduce some of the features of NDEs. It's clear that monkeying with the brain's chemistry can produce all sorts of effects. I'd just assume all sorts of such monkeying takes place in the moments leading up to and in the moments just after death.

consciousness survives the body. — Sam26

This I don't see.

Death is the most extreme trauma one's body can suffer. What you have are reports of living people who experienced this extreme trauma.

What you do not, and presumably cannot, have are reports from disembodied consciousnesses.

I understand that the claim is that, perhaps for several minutes, someone's consciousness persisted during a period when their body met one or another definition of death. But you do not, and presumably cannot, have reports from people made during this period. You can only have the reports of those who were revived.

Those who were revived suffered extreme trauma. Isn't the most natural assumption that such a traumatic experience would leave traces? Wouldn't a neuroscientific explanation be the most natural?

I would expect some way of weighting the reports by the circumstances of the witnessing. At a baseball game, 30,000 fans might think the runner was clearly out at second, but none of them had as good a view as the umpire standing five feet away watching the play. In turn, if the umpire was poorly positioned, a crew of umpires watching video from another angle might be better placed to make the right call.

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.

I just don't want to say that Superman exists one way in fiction and another way outside it. The fiction exists in our world. Superman doesn't, not even "as" something.

If you want to say he exists here "as an idea", then as an idea of what? As an idea of an object, namely himself. So Superman is the idea of Superman, and that's an infinite regress.

We need a nice way to talk about fictional objects, but this is headed in the wrong direction, I'd say.

I suspect that there is much common ground. — creativesoul

Such as?

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?

In brief, something like:

existence is not a logical predicate (∃ is not just another φ)
existence can be used as a linguistic predicate — jorndoe

Yes, absolutely. But this

Say, Superman exists, but just isn't real. — jorndoe

is confusing for everyone.

And what do you mean when you say that the concept is not instantiated, has no instances? (I deliberately emphasized the verb "to be" in these phrases.) Well, it means that there are no such things, that they do not exist. Oh, wait... — SophistiCat

If your point is that this is not an explanation of existence -- the ineffable there-ness of stuff -- I don't think it was intended to be. Neither, really, is "To be is to be the value of a bound variable," which comes to the same thing. Or saying the copula is sortal-hungry, which also comes to the same thing.

But it does clarify the logical form of existence statements and cut off the weirdness of saying "Superman is an object that has the property of not existing." If instead you say, "The concept of Superman has the property of having no instances," at least you haven't tried to predicate of an object that in the same breath you say doesn't exist. (And people get hinky about this and say things like, before it was built the Empire State Building did exist "as an idea".)

(And you don't even need to predicate of concepts: "Nothing has the property of being Superman" is a reasonable natural language equivalent to "¬∃xFx".)

You know all that though, so what was your point?

ADDED: That sounds belligerent, but was meant to sound puzzled.

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.

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"?

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 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.