You are correct that is what Smith believes. But why does that mean the Gettier case is wrong? Smith does not need to believe q or use q as a point of inference to arrive at (p v q). The propostion q can be anything that is not ~p. It can even be something Smith does not really have any opinion on. All Smith needs to be justified in believing (p v q). And if Smith is justified in believing p is true, then, by extension, he is justified believing (p v q) is true, as only one of the propositions in a disjunction is required for it to be true.

In this case, Smith is justified in p and believes p. By extension, he is justified in believing (p v q) is true, though Smith is indifferent to q's truth value or thinks q is false (he might even be justified in believing q). Therefore, Smith is justified in believing (p v q).

Smith has justified belief in (p v q). He is two thirds the way there.

It turns out (p v q) is true, but not because p; p is false and q is true. Smith has a justified false belief that p, so he is still justified in (p v q). It's just that his grounds for justification are false. However, q is true. Therefore, Smith believes a true proposition (p v q) and is justified in believing (p v q). Therefore, Smith has knowledge under the traditional account of knowledge: he has justified, true belief. But this seems wrong. Smith does not have knowledge of (p v q). Therefore, the traditional account fails.

Gettier wrote:

Imagine that Smith a)realizes the entailment of each of these propositions he has constructed and b)proceeds to accept (g), (h), and (i) on the basis of (f)...

p1. ((p) is true)
p2. ((p v q) follows from (p))(from a)
p3. ((p v q) is true if either (p) or (q) is true)(from a,b)
C1. ((q) is not true)(from p1,p3)
C2. ((p v q) is true)(from p3,C1)

Smith's belief that: ((p v q) is true because (p) is true) is inferred from his belief that: ((p) is true), ((p v q) follows from p), ((p v q) is true if either (p) or (q) is true), and ((q) is not true).

"This immediately reminded me of Gettier 'problems' with the JTB account."
— creativesoul

There is a kind of connection to the argument here. Gettier cases are examples of epistemic luck -- you have a belief, it's true, it's got something that counts as justification, but the proposition believed to be true is true under a different interpretation than the one you intended, and our intuition that these are not examples of knowledge is because the justification you had fit the interpretation under which your sentence was false, not the one under which your sentence was true. (That's probably not all cases -- if it were, I would have just solved the Gettier problem.)

There's another sort of luck that's even easier to get at because there's no question of knowledge at all: that's when you're asked a question on an exam (or a game show, whatever) and you guess -- and your guess is right! If you're asked when the Battle of Hastings was, "1066" is the right answer whether you've ever even heard of the Battle of Hastings or not, because truth is not the same thing as knowledge.

(Not getting into the disjunction thing yet, as I have an argument that uses disjunction still under litigation.) — Srap Tasmaner

That was a couple months ago in the "'True' and 'Truth'"" thread, and might be worth revisiting now.

P ∨ Q has four possible models:
(1) P=0, Q=0
(2) P=1, Q=0
(3) P=0, Q=1
(4) P=1, Q=1

The gist of the above remarks was that, to take Case II as the example, Smith's justification relates to the models in which P is true (2 or 4), but it turns out P ∨ Q is in fact true under the third model, in which only Q is true.

@creativesoul is arguing that because all of Smith's beliefs are formed under one of the interpretations in which P is true, that his belief does not include or encompass the interpretations in which P is false.

Michael Dummett makes a distinction (when talking about assertion, as usual -- here it is Smith's acceptance that is at issue) that may be helpful here: there are the grounds upon which you make an assertion (which he calls its "justification"), and then there is what you are committed to by making the assertion. It is clear that Smith's belief that P is the grounds upon which he accepts that P ∨ Q, but by accepting that P ∨ Q he is committed to accepting all four possible models.

The commitment part is what we rely on when we judge lucky guesses to be correct. If, on the basis of nothing more than a hunch, you were to wager that the Battle of Hastings was fought in 1066, your bet would pay off. It is also possible to get the right answer for the wrong reasons, rather than for no reason.

This distinction shows up in our language use in many ways. If you believe you will be off work in time to meet me for a 7:00 movie, and you promise to, you have committed to being there and that commitment doesn't change because you end up working late and standing me up. You have broken your promise. Misunderstandings too often arise because a person might have one thing in mind, but the plain language of what they say admits of another interpretation, and if they misspoke, perhaps only an interpretation they did not intend. "That's not what I meant!" "But that's what you said!"

We do not, in general, take the grounds upon which an assertion is made as constraining the commitment made by that assertion. If we did, much about our language use would be different, but one thing in particular. To assert, or in Smith's case to accept, that a proposition is true is generally to accept that it may be false. That's usually the point of making an assertion. You provide information to your audience by telling them something is the case that might not be. (I tell you I stopped at the store and got milk, because I might not have.)

The exception, of course, is statements that are necessarily true. To make an assertion in which you admit as possible only the models in which the statement is true is take the statement as true necessarily. (If this were generally the case, we would all of us believe whatever we believed to necessarily be the case.)

In this case, if Smith were to accept that "Jones owns a Ford or Brown is in Barcelona" only insofar as Jones owns a Ford, then he would be allowing no possibility that Jones does not own a Ford. He would be taking "Jones owns a Ford" to be a necessary truth.

Obviously, there is no support for this claim in the text.

C1. ((q) is not true)(from p1,p3) — creativesoul

Once again, that is correct only if "or" is taken exclusively.

Gettier wrote:

Imagine that Smith realizes the entailment of each of these propositions he has constructed and proceeds to accept (g), (h), and (i) on the basis of (f)...

...Smith is therefore completely justified in believing each of these three propositions. Smith, of course, has no idea where Brown is.

I just showed how that works...

The exclusive/inclusive distinction is irrelevant here. Smith, given what he believes, posits all three q's as a means to create a proposition, not as a means to state belief. Gettier says as much.

Another example would arise if you are allowed multiple answers. You may strongly believe that the Battle of Hastings was fought in 1166, but if you are allowed to answer "1166 or 1066," then you'll be right.

The exclusive/inclusive distinction is irrelevant here. Smith, given what he believes, posits all three q's as a means to create a proposition, not as a means to state belief. Gettier says as much. — creativesoul

It is relevant. Smith accepts all three.

All for the same reasons, as the argument clearly shows, and Gettier clearly states...

Gettier wrote:

Imagine that Smith a)realizes the entailment of each of these propositions he has constructed and b)proceeds to accept (g), (h), and (i) on the basis of (f)...

p1. ((p) is true)
p2. ((p v q) follows from (p))(from a)
p3. ((p v q) is true if either (p) or (q) is true)(from a,b)
C1. ((q) is not true)(from p1,p3)
C2. ((p v q) is true)(from p3,C1)

Smith's belief that:((p v q) is true because (p) is true) is inferred from his beliefs that:((p) is true), ((p v q) follows from p), ((p v q) is true if either (p) or (q) is true), and ((q) is not true).

You're on the wrong track, in my view. I have explained why as best I can.

The idea I sketched a couple months ago, that justification cannot cross the boundary between one interpretation and another, is essentially the mainstream response to Gettier, that something is needed to guarantee the relevance of the belief's justification to its truth for that belief to count as knowledge. You must get the right answer for the right (sort of) reasons.

...It is clear that Smith's belief that P is the grounds upon which he accepts that P ∨ Q, but by accepting that P ∨ Q he is committed to accepting all four possible models...

Nothing Gettier states warrants such talk about Smith's belief.

You wrote:

You're on the wrong track, in my view. I have explained why as best I can.

The idea I sketched a couple months ago, that justification cannot cross the boundary between one interpretation and another, is essentially the mainstream response to Gettier, that something is needed to guarantee the relevance of the belief's justification to its truth for that belief to count as knowledge. You must get the right answer for the right (sort of) reasons.

The last comment here reminds me of Davidson...

I understand that the mainstream view focuses upon justification. Smith's belief, as I've just set it out, is not true. For Smith(given his strong belief that p), arriving at a complex thought/belief such as belief that:((p v q) is true) requires knowing what (p v q) means, what it takes for (p v q) to be true, and inferring what I've set out...

Gettier wrote:

Imagine that Smith a)realizes the entailment of each of these propositions he has constructed and b)proceeds to accept (g), (h), and (i) on the basis of (f)...

p1. ((p) is true)
p2. ((p v q) follows from (p))(from a)
p3. ((p v q) is true if either (p) or (q) is true)(from a,b)
C1. ((p v q) is true because (p) is true)(from p1,p3)

That's better. The "because (p) is true" in C1 is equivalent to and/or satisfies Gettier's own criterion of "on the basis of (f)..."

Gettier continues:

...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.

C2. ((p v q) is true)(from p3,C1)

Gettier wants to get to the above without going through C1, even though he explicitly states acceptance on the basis of (f). C2 doesn't adequately represent Smith's thought/belief, as Gettier himself sets out. It is only C1 that exhausts Smith's thought/belief, as Gettier himself sets out.

Smith's belief that:((p v q) is true because (p) is true) is not equivalent to belief that:((p v q) is true)

Salva veritate

Smith's acceptance of all three on the basis of (f) is...

Belief that:((g) is true because (f))
Belief that:((h) is true because (f))
Belief that:((i) is true because (f))

...and belief that:((p v q) is true) is inadequate. It is found to be sorely lacking.

creative wrote:

This immediately reminded me of Gettier 'problems' with the JTB account.

Srap replied:

There is a kind of connection to the argument here. Gettier cases are examples of epistemic luck -- you have a belief, it's true, it's got something that counts as justification, but the proposition believed to be true is true under a different interpretation than the one you intended, and our intuition that these are not examples of knowledge is because the justification you had fit the interpretation under which your sentence was false, not the one under which your sentence was true. (That's probably not all cases -- if it were, I would have just solved the Gettier problem.)

There's another sort of luck that's even easier to get at because there's no question of knowledge at all: that's when you're asked a question on an exam (or a game show, whatever) and you guess -- and your guess is right! If you're asked when the Battle of Hastings was, "1066" is the right answer whether you've ever even heard of the Battle of Hastings or not, because truth is not the same thing as knowledge.

(Not getting into the disjunction thing yet, as I have an argument that uses disjunction still under litigation.)

Srap continued:

That was a couple months ago in the "'True' and 'Truth'"" thread, and might be worth revisiting now.

P ∨ Q has four possible models:
(1) P=0, Q=0
(2) P=1, Q=0
(3) P=0, Q=1
(4) P=1, Q=1

The gist of the above remarks was that, to take Case II as the example, Smith's justification relates to the models in which P is true (2 or 4), but it turns out P ∨ Q is in fact true under the third model, in which only Q is true.

Alright. I know that this is a common approach to the Gettier problem. I reject it as irrelevant. That claim carries with it a justificatory burden. I'll honor that.

The Gettier problem has as it's target Smith's beliefs. That is crucial to keep in mind. Gettier quite clearly sets out the thought/belief process that Smith goes through. Smith believes Jones owns a Ford. Smith isolates his own thought/belief by virtue of putting it in the following statement form:'Jones owns a Ford' or (f). He then constructs 3 propositions, (g), (h), and (i). The propositions all follow the rules of entailment. Smith realizes this much. Smith believes that (g), (h), and (i) follow from (f) because he believes that all three follow the rules of correct inference. So, Smith's belief that:((g), (h), and (i) are valid inferences) is correct, as Gettier says below.

Gettier set out Smith's thought/belief:

...Imagine that a)Smith realizes the entailment of each of these propositions he has constructed and b)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...

Now, with regard to what Srap is talking about above, Smith's belief renders interpretations of "or" irrelevant because Smith's belief is explicit. Gettier claims that Smith accepts (g), (h), and (i) on the basis of (f). The argument provided below adds clarity to the understanding here. It sets out Smith's thought/belief process as Gettier sets out...

Smith believes that:

p1. ((p) is true)
p2. ((p v q) follows from (p))(from a)
p3. ((p v q) is true if either (p) or (q) is true)(from a,b)
C1. ((p v q) is true because (p) is true)(from p1,p3)

Smith has false belief. There is no issue with JTB.

Smith has false belief. There is no issue with JTB. — creativesoul

Yes, he does. But he also has a true belief, and that is an issue.

You can keep repeating that Smith believes that p ∨ q is true because p is true, but this does nothing to address the fact that Smith believes that p ∨ q is true.

That's not a fact. Belief that:((p v q) is true) is utterly inadequate. I've already argued for this without subsequent refutation...


Smith's belief that:((p v q) is true because (p) is true) is not equivalent to belief that:((p v q) is true)

Salva veritate

Smith's acceptance of all three on the basis of (f) is...

Belief that:((g) is true because (f))
Belief that:((h) is true because (f))
Belief that:((i) is true because (f))

...and belief that:((p v q) is true) is inadequate. It is found to be sorely lacking in it's ability to meet Gettier's own criterion regarding the thought/belief process that Smith goes through; and it is quite the metacognitive process...

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

I know they're not equivalent. They're two different things that Smith believes, just as "Donald Trump is the President" and "Donald Trump is the President because he won the popular vote" are two different things that I believe.

In each of these cases there is a false belief and a true belief. You're ignoring the true belief, but it's the true belief that is relevant to the topic at hand.

No, it's not two different things that Smith believes.

I've already said that that objection is irrelevant. I suppose that charge carries a burden with it...

"Donald Trump is the President" is not existentially contingent upon "Donald Trump is the President because he won the popular vote." You can arrive at the former without going through the latter. That is not the case with Smith's thought/belief process.

Gettier wrote:

Imagine that Smith a)realizes the entailment of each of these propositions he has constructed and b)proceeds to accept (g), (h), and (i) on the basis of (f)...

p1. ((p) is true)
p2. ((p v q) follows from (p))(from a)
p3. ((p v q) is true if either (p) or (q) is true)(from a,b)
C1. ((p v q) is true because (p) is true)(from p1,p3)
C2. ((p v q) is true)(from p3,C1)

Now, as the above argument clearly shows, Smith cannot arrive at C2 without going through C1. That is according to Gettier's own descriptions of Smith's thought/belief processes.

False analogy.

"Donald Trump is the President" is not existentially contingent upon "Donald Trump is the President because he won the popular vote." You can arrive at the former without going through the latter. That is not the case with Smith's thought/belief process. — creativesoul

And Smith can arrive at "p ∨ q" without going through "p". He could have believed "q", just as I could have believed "Donald Trump won the most electoral college votes".

So I don't understand your distinction. We both arrived at our belief from a false reason but could have arrived at our belief from a true reason. Regardless, my belief that Donald Trump is the President is true and Smith's belief that p ∨ q is true is true.

That doesn't follow from Gettier's description of Smith's thought/belief processes Michael.

Given exactly what Gettier sets out, I have constructed an argument which is meant to represent Smith's thought/belief process.

That doesn't follow from Gettier's description of Smith's thought/belief processes Michael. — creativesoul

But when I described my thought/belief processes that led me to believe that Donald Trump is the President you said it didn't matter. You're moving the goalposts.

Do I or do I not have a true belief that Donald Trump is the President, despite arriving at this belief from a false reason?

Gettier set the goal posts. You're moving them. I set them out in painstaking detail.

You've put forth a process that does not follow Gettier's description of Smith's.

How is it different? I believe that X entails Y, I believe that X is true, and so I believe that Y is true. But X isn't true. This is the same as in Smith's case.

But let's do a different example that is similar to your argument:

p1. ((p) is true)
p2. ((p v q) follows from (p))(from a)
p3. ((p v q) is true if either (p) or (q) is true)(from a,b)
C1. ((p v q) is true because (p) is true)(from p1,p3)
C2. ((p v q) is true)(from p3,C1)

p1. "John is a widower" is true
p2. "John was married" follows from "John is a widower"
p3. "John was married" is true if either "John is a widower" or "John is a divorcee" is true
C1 "John was married" is true because "John is a widower" is true
C2. "John was married" is true

But John isn't a widower; he's a divorcee. According to you, if I believe that John is a widower then I cannot have a true belief that John was married, because what I really have is the false belief that John was married because he is a widower.

This is clearly wrong. It doesn't matter why I believe that John was married. I do, and he was. People can have true beliefs arrived at from false reasons.

I believe that X entails Y, I believe that X is true, and so I believe that Y is true. But X isn't true. This is the same as in Smith's case.

No, it's not the same as Gettier's case. First of all, it does not follow from the fact that Y follows from X that Y is true.

That's not what Gettier sets out.

You wrote:

p1. ((p) is true)
p2. ((p v q) follows from (p))(from a)
p3. ((p v q) is true if either (p) or (q) is true)(from a,b)
C1. ((p v q) is true because (p) is true)(from p1,p3)
C2. ((p v q) is true)(from p3,C1)

p1. "John is a widower" is true
p2. "John was married" follows from "John is a widower"
p3. "John was married" is true if either "John is a widower" or "John is a divorcee" is true
C1 "John was married" is true because "John is a widower" is true
C2. "John was married" is true

Two completely different kinds of description Michael. The former argument represent Smith's thought/belief process as Gettier sets it out. The latter does not. The first premiss is the only thing close to being a parallel.

You wrote the following:

p1. "John is a widower" is true
p2. "John was married" follows from "John is a widower"
p3. "John was married" is true if either "John is a widower" or "John is a divorcee" is true
C1 "John was married" is true because "John is a widower" is true
C2. "John was married" is true

That was supposed to adequately represent my argument below. It doesn't.

p1. ((p) is true)
p2. ((p v q) follows from (p))(from a)
p3. ((p v q) is true if either (p) or (q) is true)(from a,b)
C1. ((p v q) is true because (p) is true)(from p1,p3)
C2. ((p v q) is true)(from p3,C1)

You wrote:

..But John isn't a widower; he's a divorcee. According to you, if I believe that John is a widower then I cannot have a true belief that John was married, because what I really have is the false belief that John was married because he is a widower.

Alright. So we have three separate propositions at work here. John is a widower. John was married. John is a divorcee. They need to be put into the appropriate form. 'John is a divorcee' is a parallel to q. You would need to be totally ignorant regarding John's marital status, otherwise there is no parallel to Gettier's description of Smith's thought/belief process. So, with that in mind, we arrive at the following parallels...

A. "Either John is a widower or John is a divorcee" could parallel (p v q)
B. "Either John was married or John was a divorcee" could parallel (p v q)

B makes no sense at all, for if you're totally ignorant about John's marital status, then you could not hold strong justified belief about it. Since that is the case, B is rejected. That leaves us with A. Let's work through it...

p1. ((p) is true)
p2. ((p v q) follows from (p))(from a)
p3. ((p v q) is true if either (p) or (q) is true)(from a,b)
C1. ((p v q) is true because (p) is true)(from p1,p3)
C2. ((p v q) is true)(from p3,C1)


p1. ((John is a widower) is true)
p2. ((Either John is a widower or John is a divorcee) follows from (John is a widower))
p3. ((Either John is a widower or John is a divorcee) is true if either (John is a widower) or (John is a divorcee) is true)
C1. ((Either John is a widower or John is a divorcee) is true because (John is a widower) is true)
C2. ((Either John is a widower or John is a divorcee) is true)

That's what it would look like, and it suffers the same fate as Smith's belief.

Srap I'm working on a response to all sorts of other stuff you've mentioned here. Now seems a good time to get into that stuff. I mean, since I've finally come to acceptable terms with exactly what I'm trying to set out. Thanks to an old friend of mine who gave me the appropriate tools...

;)

I'm not ignoring your last post. Much of it has been addressed. None-the-less, I plan on attending to it...

;)

I believe that A is true. I believe that B is true if A is true. Therefore, I believe that B is true. B is true. Therefore, I have a true belief, even if A is false. This is the form that all of these arguments follow.

I believe that John was married because he is a widower. John isn't a widower, but my belief that John was married is still a true belief.

I believe that Trump is the President because he won the popular vote. Trump didn't win the popular vote, but my belief that Trump is the President is still a true belief.

I believe that p ∨ q is true because p is true. p isn't true, but my belief that p ∨ q is true is still a true belief.

You can keep insisting that these aren't comparable, but they are. I can't put it any simpler for you. Smith has a true belief.