I need not refute that. It's irrelevant — creativesoul

It isn't irrelevant. Smith believes that p ∨ q is true, and p ∨ q is true. Therefore, Smith has a true belief.

Coming to this a bit late....

Isn't Smith's true belief improperly justified? He believes p v q, because he believes p; and yet ~p, but q.

Does Smith have a justified true belief? p v q is justified by q; it is true; and it is believed by Smith; but Smith thinks it is justified by p.

So does Smith know (p v q)? One could go either way, but I'd say that he does not know (p v q), because what he believes justifies knowing (p v q) is false.

If you have a good reason to believe p and if p entails p ∨ q then you have a good reason to believe p ∨ q.

Right, that's part of Gettier's setup. The only belief he attributes the Smith is the belief that p v q; he seems purposefully to avoid attributing p, which will turn out to be false anyway. Gettier only relies on p for justification, not for truth.

So for you two, a justification need not be true.

For Creative, it must.

Which of you is correct?

@creativesoul has nothing to say about justification, as he will tell you himself. His issue is something about the psychology of logic, I think.

So for you two, a justification need not be true.

For Creative, it must.

Which of you is correct? — Banno

creative isn't even talking about justification. He's saying that Smith doesn't believe p ∨ q.

So for you two, a justification need not be true. — Banno

I assume everyone who accepts the JTB account of knowledge feels the same way, else having both justification and truth would be redundant.

Alright, let's find agreement...

Smith believes P, deduces Q from P and accepts Q as a result...

Agreed?

Gettier sets that out himself. So...

What does that consist in/of?

That's the question at hand. I say that it doesn't include believing Q. Gettier seems to agree, because his next line is...

..."therefore S is justified in believing Q".

Seems that Srap and Michael hold otherwise.

By the way, creative does have a position regarding justification. However, I've found good reason to not let the notion get in the way. That's part of the problem...

Believing is obviously different than accepting. Offering Gettier the benefit of the doubt, we must assume that Gettier saw it that way as well, otherwise his description wouldn't put it that way. This is supported by noting not only his formula's language use, but also noting that Case II fills out that formula in the same terms....

Belief is at the beginning and the end...

Now...

Look at the proof.

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)

Gettier only gets to p2 prior to his conclusion that S believes Q. It takes more than that.

The most interesting aspect to me is the fact that that same thought/belief process is necessary and sufficient for believing any and all Q's when Q is a disjunction derived from belief by a rational person. No disjunction is immune. It exhausts them all, without question. Here it is prior to being filled out...

p1. ((p) is true)
p2. ((p v q) follows from (p))
p3. ((p v q) is true if...(insert belief statement(s) regarding what makes this particular disjunction true))
C1. ((p v q) is true because... (insert belief statement(s) corresponding to the prior 'if'))

Fill it out, and you'll never arrive at a problem for JTB. The added benefit, of course, is that it stops an insincere purveyor of disjunction dead in his/her tracks.

I'm gonna be famous.

X-)

The Merrillian Lie-Trap

Here's the underlying issue folks...

Not all Q's are arrived at by virtue of one deduction. The astute reader will note that almost all of Michael's counterexamples were belief of a simple variety. There were no disjunctions that were problematic... and there will not ever be.

Modus Ponens cannot account for disjunction. Believing Q when Q is a disjunction is not that simple... as my solution clearly shows.

The whole of Western philosophy has gotten thought/belief wrong. The typical belief that approach doesn't draw and maintain the crucial distinction between thought/belief and thinking about thought/belief. That approach is of the latter, and as such it is a report upon the former.

That is the real problem and the so-called Gettier 'problem' lands quite squarely in the scope of consequence. Ah, but I digress...

Just for the record. I do hold, and I am arguing that Smith believes Q. C1 exhausts believing Q.

Salva veritate

Srap wrote:

The only belief he attributes the Smith is the belief that p v q; he seems purposefully to avoid attributing p, which will turn out to be false anyway. Gettier only relies on p for justification, not for truth.

This is quite simply not true. We can clearly see for ourselves that Gettier attributes belief that p to Smith. The formula begins with S's believing P, and Case II fills that out by virtue of Smith's believing Jones owns a Ford.

It is worth noting that Michael's position necessarily presupposes that S's believing Q, when Q is a disjunction derived from believing P, not only does not - but cannot - include S's consideration of Q's truth conditions...

In fairness to Michael, he is simply parroting Gettier, who was mistaken to begin with. That is proven by the fact that if Gettier had considered this... openly... he would have noted that another deduction was necessary for believing Q.

C1 exhausts Smith's believing Q.

Salva veritate

Sure about that? The JTB account of course has its origin in the Theaetetus; where it is rejected. Justification is introduced into the dialogue in providing an account that ties a true belief to logos. The account must show how the true belief arrises from perceptions, intuitions and so on.

I am guessing that this is why the account is of interest to Creative, with his odd understanding of thought/belief.

But in any case, it appears to me that justification is the issue.

I assume everyone who accepts the JTB account of knowledge feels the same way, else having both justification and truth would be redundant. — Michael

Having both justification and truth is far from redundant. it is not the case that the justification and the thing justified are the same.

p3. ((p v q) is true if...(insert belief statement(s) regarding what makes this particular disjunction true)) — creativesoul

This should read:
((p v q) is true if...(insert true statement(s) regarding what makes this particular disjunction true)

"Smith believes p, therefore (p v q)" is a non sequitur. It should be "p, therefore (p v q)".

Or alternately,

"Smith believes p, therefore Smith believes (p v q)"

Smith's beliefs about p or q imply nothing about the truth of p or the truth of q.

Sure. But we know that what Smith thinks is a good reason for believing p v q is actually a very bad reason - it is false.

So although Smith thinks he has a justified true belief, and hence knows that p v q, he is wrong because the justification is false.

Sure. But we know that what Smith thinks is a good reason for believing p v q is actually a very bad reason - it is false.

So although Smith thinks he has a justified true belief, and hence knows that p v q, he is wrong because the justification is false. — Banno

What do you mean by the justification being false? In Gettier's example, the justification is "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". These are all facts. So is he justified in believing that Jones owns a Ford? If so then he's justified in believing that Jones owns or Ford or Brown is in Barcelona.

Having both justification and truth is far from redundant. — Banno

I thought you were saying that a belief isn't justified if it's false.

I'll repeat (and add to) my previous explanation here:

1. Smith's belief that p is justified by r
2. p ⊨ p ∨ q
3. From 1 and 2, Smith's belief that p ∨ q is justified by r
4. p is false and q is true
5. q ⊨ p ∨ q
6. From 4 and 5, p ∨ q is true
7. From 3 and 6, Smith has a justified true belief

p is "Jones owns a Ford", q is "Brown is in Barcelona", and r is "Jones has at all times in the past within Smith's memory owned a car, and always a Ford, and Jones has just offered Smith a ride while driving a Ford".

Modus Ponens cannot account for disjunction. — creativesoul

Yes it can. This is valid:

1. p
2. p ⊨ p ∨ q
3. p ∨ q

Modus ponens cannot account for the thought/belief process required for arriving at believing Q when Q is a disjunction deduced from P.

When you have time. Read the following carefully... It is where I'm at in all this. Still honing it. p3 needs left alone. It's not an argument per se, it's a report of the thought/belief process necessary for arriving at believing Q when Q is a disjunction arrived at from believing P following Gettier's formulation...

Gettier states:

I shall begin by noting two points. First, in that sense of "justified" in which S's being justified in believing P is a necessary condition of S's knowing that P, it is possible for a person to be justified in believing a proposition that is in fact false.

I would concur.

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.

This is not always true. To be as precise as ordinary language allows:S must first arrive at a belief before we can say that S is justified in forming/holding that belief. In Gettier Case II, the above formulation is utterly inadequate for S's arriving at belief that:((p v q) is true).

Keeping these two points in mind I shall now present two cases in which the conditions stated in (a) are true for some proposition, though it is at the same time false that the person in question knows that proposition.

This I outright deny.

Gettier's aims at a case that Smith forms/holds a Justified True Belief that:((p v q) is true) by virtue of going through the thought/belief process set out in the above formulation beginning with "Secondly..." Belief that:((p v q) is true) is the only value appropriate for Q in that formulation, for Q is (p v q) and believing Q is nothing less than belief that (p v q) is true. Hence, believing Q is belief that:((p v q) is true).

I will show that Gettier's formulation is inadequate regarding it's ability to take proper account of the thought/belief process required for S's belief that:((p v q) is true). S cannot arrive at that without another step that Gettier leaves out. To be clear, if the astute reader looks carefully at that formulation, s/he will note that only one deduction is purportedly necessary in order to satisfy the formulation. Namely, S's deducing Q from P.

I'm strongly asserting that it takes more than one deduction for S to arrive at belief that:((p v q) is true), and since that is the case, it only follows that Gettier's criterion is inadequate. That will be clearly shown.

To be clear, 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 not necessarily justified in believing Q, for - in this case in particular - believing Q is nothing less than belief that:((p v q) is true) and S cannot arrive at that following Gettier's formulation. Belief that:((p v q) is true) requires yet another deduction that is left sorely unaccounted for in Gettier's formulation. It's been said heretofore, but it now bears repeating...

S must first arrive at a belief before we can say that S is justified in forming/holding that belief. In Gettier Case II, the above formulation is utterly inadequate for S's arriving at belief that:((p v q) is true). The following argument represents the process of thought/belief that is necessary prior to even being able to arrive at believing Q and is an exhaustive account thereof. The term "because" in C1 is the necessary but missing deduction in Gettier's formula.

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)

Gettier wrote:

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 placenames 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...

Note the above stopping point. The quote ends at the precise point where Gettier's next line concludes(by necessary implication) that Smith believes Q. Believing Q is precisely what's at issue here. Q is (p v q). Believing (p v q) is believing that (p v q) is true. Hence, Smith's believing Q is nothing less than Smith's belief that:((p v q) is true). So, using Case II, Gettier has filled out his earlier formulation. Here it is again...

Gettier wrote:

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...

Note here that this quote's stopping point coincides with Case II's, as shown directly above. As Gettier says, Smith believes Jones owns a Ford. Smith constructs (g), (h), and (i); all of which are (p v q). Smith believes p, and deduces (p v q) from p and accepts (p v q) as a result of this deduction. There is nothing about Smith's thought/belief process that the first two premisses below cannot effectively exhaust...

p1. ((p) is true)
p2. ((p v q) follows from (p))

Now, it is well worth mentioning here that nowhere in any of this(the above direct quotes from Gettier) is anything at all about Smith's believing Q. That is of irrevocable significance. It is a crucial point to consider here. Smith has yet to have gotten to the point where he has formed and/or holds belief that:((p v q) is true). Gettier thinks otherwise, as is shown by his saying...

Gettier:

...Smith is therefore completely justified in believing each of these three propositions...

...and...

...S is justified in believing Q.

He lost sight of exactly what believing Q requires. It requires precisely what follows...

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)


Thus, we can clearly see that Gettier's formulation is inadequate to account for the belief that he needs for Smith to hold in order to make his case. Getting to belief that:((p v q) is true) requires both p3. and C1. Further we can also see that Smith's belief is not true, for he does not ever get to belief that:((p v q) is true). Gettier wants us to believe that Smith holds the belief that:((p v q) is true). This post has shown all sorts of problems with Gettier's formulation, and the aforementioned want of Gettier is just yet another.

Belief that:((p v q) is true) is not equivalent to belief that:((p v q) is true because (p)). The former is existentially contingent upon the latter and has a different set of truth conditions. The latter consists in part of the deduction missing in Gettier's account. The missing necessary deduction clearly shows that Smith's belief is false, Gettier's formulation is inadequate, and the 'problem' regarding Case II is non-existent.

Salva veritate

Smith believes Jones owns a Ford. Smith believes that 'Jones owns a Ford' is true. Smith believes that 'Either Jones owns a Ford or Brown is in Barcelona' follows from 'Jones owns a Ford'. Smith believes that 'Either Jones owns a Ford or Brown is in Barcelona' is true if either 'Jones owns a Ford' or 'Brown is in Barcelona' is true. Smith believes that 'Either Jones owns a Ford or Brown is in Barcelona' is true because Jones owns a Ford.

That is Smith's believing Q as the result of another deduction.

QED

Modus ponens cannot account for the thought/belief process required for arriving at believing Q when Q is a disjunction deduced from P. — creativesoul

It does if you accept epistemic closure.

But even if you don't, Gettier states that Smith does believe Q. He's a rational person who believes that this argument is valid and that the premises are true, and so therefore that the conclusion is true:

1. p
2. p ⊨ p ∨ q
3. p ∨ q

To try to argue that Smith doesn't actually believe p ∨ q is completely misplaced. You might as well try to argue that Jones does in fact own a Ford.

So let's put it to you. Do you believe that this statement is true?

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

@creativesoul

Well I just waded through all this, and I have to admit to some skimming. I'll make a few preliminary remarks, and see who wants to swallow them whole and who wants to bite their heads off.

1. (p v q) appears to say more than p, but actually says less. 'The glass contains water or the glass contains vodka' says less than 'The glass contains water'.

2. Nobody in the real world forms arbitrary unrelated disjunctions of things they believe and things they have no belief about, or believe to be false, except for rhetorical purposes, or I'm a monkey's uncle.

3. I'm not a monkey's uncle.

4. Logical implication is a justification.

5. Think of a whole number between 1 and 100. I have justification on the grounds of probability for believing that it is not 92. I have the same justification for thinking it is not any of the other numbers. So I can form the propositions: 1. You did not think of 1, 2. You did not think of 2, and so on. All are equally justified, all but one are correct, all are equally believed.

6. Nevertheless, I have no idea which number you thought of.

4. Logical implication is a justification. — unenlightened

I'm not crazy about this one. (But agree with everything else.) I'd rather say something more like what Gettier says: whatever justification the premises have, the conclusion inherits. As I said earlier, inference is not expected to confer truth, but to preserve it.

I admit that was a bit telegraphic.

inference is not expected to confer truth, but to preserve it. — Srap Tasmaner

Belief, nor justification, nor inference confer truth. Per Gettier, one can have justified false beliefs. Put truth back on the shelf a minute. Consider justification, consider inference. Can we say that inference transforms one or more propositions into another proposition? Can we say that it would be foolish, if not impossible to believe, and thus to honestly assert a proposition one does not believe, unless bracketed in an "If (p)"? So one makes inferences from (justified?) beliefs to new propositions that are justified by the inference. One does not, thought one theoretically could, infer (p v q) from p, because - there's no point, apart from sowing dissent in the ranks of philosophers.

(a) If I have performed the rain dance, it will rain tomorrow.
(b) I have performed the rain dance.
(c) It will rain tomorrow.

(a) is justified inductively (probabilistically?) by the fact (videos enclosed) that I have performed the rain dance five times, and each time it has rained the next day.
(b) is justified by my memory augmented by the video (enclosed).
(c) is justified by inference.

Where is your belief at this point? I'm betting you are somewhat sceptical of (a) because (insert long-winded justification of choice). Your justification and mine are competing, conflicting.

Here in the Welsh mountains, it rains very nearly every day. Thus (a) is probably true, even though (a1) 'If I have not performed the rain dance, it will rain tomorrow' is also probably true. Does that change your belief in (a)?