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.

That's not what Gettier sets out.

I think now that going down this road eviscerates entailment in a way we don't want. If we have a web of beliefs, connected by various degrees of the relation "is a reason for", we still need to individuate those beliefs, even if they confront reality in groups or as a totality, not singly, because we have to be able to revise them individually.

Perhaps maybe it simply place certain kinds of entailment under scrutiny. As you say, each thought/belief has it's own set of truth conditions(although, unlike yourself, I think that some share those).

I think the usual approach to Gettier is probably right: we feel that the justification Smith has for believing (f) turns out to be irrelevant to the truth of (h). It's that irrelevance we want to capture. We need rules about how justification passes from one belief to another, something more precise than Gettier's principle that entailment preserves justification just as it preserves truth.

My formulation of Smith's thought/belief process avoids the issue, does it not?

(1) Smith does not believe that (h).

(2) Smith's inference of (h) from (f) is faulty.

What is your claim?

Smith does not believe that:((h) is true) That is too simplistic an account. Rather, Smith believes that:((h) is true because (f)). Gettier says much the same thing when he writes...

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).

Salva veritate

Belief that:((h) is true) is not equivalent to belief that:((h) is true because (f))

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.

Seems to me that Smith's belief is explicit. As above, Smith believes that:((p v q) is true because (p)). That most certainly does not obligate Smith to accept different senses of "or". As a matter of fact, I think that in order to validly criticize another's argument(Smith's belief in this case), the first step is to accept their meaning; sense; definitions; etc. Given that, it doesn't make any sense to misattribute meaning to Smith's thought/belief as a means for scrutinizing it. That's what non-sequiturs(strawdogs) are made of. The notable exception, of course, is if one can effectively show that something is wrong with their usage(equivocation, nonsensical, etc.).

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.

I'm wondering if these sorts of considerations are even able to arise if it turns out that the Gettier problem is nothing more than a half-century worth of misunderstanding.

You wrote:

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.

Belief that:((p v q) is true) is inferred from belief that:((p v q) is true because (p) is true) which is inferred from his belief that:((p) is true), ((p v q) follows from (p)), and ((p v q) is true if either (p) or (q) is true).

Salva veritate

Belief that:((p v q) is true) is not equivalent to belief that:((p v q) is true because (p) is 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.

As above... Therefore the traditional means of accounting for Smith's thought/belief process fails. The traditional account remains untouched. Smith has false belief. False belief is not a problem for JTB no matter how it is arrived at.

a half-century worth of misunderstanding — creativesoul

No.

1. Your reading of Gettier's original paper is wrong on its face and you're never going to convince anyone.

2. Even if you were right, and there was something faulty in Gettier's original cases, no one would care. Once you've seen the trick, it is child's play to construct new Gettier-type cases. The Gettier problem is this whole family of cases, and its seemingly endless adaptability. There is no broad agreement on any version of the JTB theory that meets our intuition of what counts as knowledge while blocking the creation of a Gettier-type case to undermine that specific approach.

You wrote:

No.

1. Your reading of Gettier's original paper is wrong on its face and you're never going to convince anyone.

Gratuitous assertions won't do at this juncture in the discussion. I'll convince anyone and everyone who is capable of following along.

2. Even if you were right, and there was something faulty in Gettier's original cases, no one would care. Once you've seen the trick, it is child's play to construct new Gettier-type cases.

If it's a Gettier case, then it ought follow the thought/belief process that Gettier himself lays out. If it does then you'll end up with false belief. False belief, no matter how it is arrived at, does not pose a problem for JTB.

Show me how one arrives at belief that:((p v q) is true) without going through the thought/belief process that I've been painstakingly laying out since the very beginning of this thread.

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)

Just in case inquiring minds want to know...

Gettier wrote:

Various attempts have been made in recent years to state necessary and sufficient conditions for someone's knowing a given proposition. The attempts have often been such that they can be stated in a form similar to the following:1

(a) S knows that P IFF (i.e., if and only if)

(i) P is true,
(ii) S believes that P, and
(iii) S is justified in believing that P.



For example, Chisholm has held that the following gives the necessary and sufficient conditions for knowledge:2

(b) S knows that P IFF (i.e., if and only if)

(i) S accepts P,
(ii) S has adequate evidence for P, and
(iii) P is true.



Ayer has stated the necessary and sufficient conditions for knowledge as
follows:3

(c) S knows that P IFF

(i) P is true,
(ii) S is sure that P is true, and
(iii) S has the right to be sure that P is true.



I shall argue that (a) is false in that the conditions stated therein do not constitute a sufficient condition for the truth of the proposition that S knows that P. The same argument will show that (b) and (c) fail if "has adequate evidence for" or "has the right to be sure that" is substituted for "is justified in believing that" throughout.

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. 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. 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.

<snip>


CASE II

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

But imagine now that two further conditions hold. First, Jones does not own a Ford, but is at present driving a rented car. And secondly, by the sheerest coincidence, and entirely unknown to Smith, the place mentioned in proposition (h) happens really to be the place where Brown is. If these two conditions hold, then Smith does not KNOW that (h) is true, even though (i) (h) is true, (ii) Smith does believe that (h) is true, and (iii) Smith is justified in believing that (h) is true.

These two examples show that definition (a) does not state a sufficient condition for someone's knowing a given proposition. The same cases, with appropriate changes, will suffice to show that neither definition (b) nor definition (c) do so either

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. — Michael

That's not what Gettier sets out. — creativesoul

It's exactly that. "A" is "p" and "B" is "p ∨ q".

(p v q) is true because (p) is true — creativesoul

Could you write this out in formal logic, or, at least, explain what it is the formal relationship between the two propositions: [(p v q) is true] and [(p) is true]?

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).

You're misreading.

1. S believes P
2. S deduces Q from P
3. S believes Q
4, S is justified in believing P
5. S is justified in believing Q

1. S believes P
2. S deduces Q from P
3. S believes Q
4, S is justified in believing P
5. S is justified in believing Q

I'm not misreading. I'm strongly asserting that 1 and 2 are not always adequate for believing Q. In Case II, another deduction is necessary for arriving at belief that:((p v q) is true).

I'm not misreading. I'm strongly asserting that 1 and 2 are not always adequate for believing Q. — creativesoul

They are if you're a rational person. How can you believe A but not believe some B that you recognise to follow from it? You'd have to be an idiot.

You'd have to be an idiot. — Michael

Now, now.

Now, now. — Srap Tasmaner

Heh, I can see how that could be misread. I was saying that the person who believes A but not what they recognise to follow from A is an idiot. I wasn't calling creative an idiot. ;)

Charming.

It's still not a nice word to use, Mr. Michael. Now mind your manners, there's a good boy. ;-)

Ready?

P: My username is Chany.

I think I'm pretty justified in believing P is true.

Q: There are currently 300 billion flying pigs on the earth.

I think I'm pretty sure this is false.

P v Q.

I arrive at this by the addition rule of logic. I am justified in believing it is true. I believe it is true. It has to be, because P is true. If I were taking a test and I was asked, "is (P v Q) true or false," I'd answer true and be absolutely correct.

Is this wrong in any way?

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)

Fill it out.

Works fine.

Not a Gettier case though.

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)

...

Works fine.

Not a Gettier case though. — creativesoul

C2. p ∨ q is true (from C1).

This is the Gettier case.

Salva veritate

Smith cannot get to belief that:((p v q) is true) without ((p v q) is true because (p)).

Belief that:((p v q) is true) is not equivalent to ((p v q) is true because (p)).

The "because" is the other necessary deduction.

Belief that:((p v q) is true) is not equivalent to ((p v q) is true because (p)). — creativesoul

I know they're not equivalent. But the latter entails the former, and the former is true. Smith has a true belief.

Salva veritate

That has nothing to do with what I'm saying.

Let's change P: I am not adopted.

I think I am fairly justified in this belief. No one said anything, I look like a bit like my father, and such.

Let's change Q: Michael lives in New York City.

I have no idea whether this is true or not. I suspend judgement. I can't be justified in believing Q.

Now, we look at (P v Q).

I am justified in believing (P v Q) is true on account of my justification in P.

Is this correct?

Smith cannot arrive at belief that:((p v q) is true) with a single deduction. Gettier's formulation for Smith's arrival at belief that:((p v q) is true) is found to be utterly inadequate as a direct result. To arrive at belief that:((p v q) is true) Smith must go through belief that:((p v q) is true because (p)). The argument shows precisely that.

Salva veritate is germane because belief that:((p v q) is true) is not equivalent to belief that:((p v q) is true because (p)). The former cannot be substituted for the latter, for it leaves out the necessary deduction within Smith's thought/belief process. The latter is Smith's thought/belief.

Let's change P: I am not adopted.

I think I am fairly justified in this belief. No one said anything, I look like a bit like my father, and such.

Let's change Q: Michael lives in New York City.

I have no idea whether this is true or not. I suspend judgement. I can't be justified in believing Q.

Now, we look at (P v Q).

I am justified in believing (P v Q) is true on account of my justification in P.

Is this correct?

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)

You arrive at true belief. The justification aspect is not a current concern of mine. Also not a Gettier case.

(p v q) is true because (p) — creativesoul

You still haven't explained what this proposition in formal logic. What does "because" translate as?

p ∨ q ∵ p

The former cannot be substituted for the latter, for it leaves out the necessary deduction within Smith's thought/belief process. The latter is Smith's thought/belief — creativesoul

I'm not saying that they can be substituted. I'm saying that the latter entails the former.

If I believe that Donald Trump is the President because he won the popular vote then I believe that Donald Trump is the President. If Smith believes that p ∨ q is true because p is true then Smith believes that p ∨ q is true.

In both of our cases we have a false belief and a true belief. You haven't shown that Smith doesn't have this true belief. You're just ignoring it and falsely claiming that the buck stops at the false belief.