Indeed. The trouble comes when those pontificating about Smith's thought/belief process conflate his belief that:((p v q) is true if...(insert belief statement(s) regarding what makes this particular disjunction true)) and ((p v q) is true because... (insert belief statement(s) corresponding to the prior 'if')) with belief that:((p v q) is true). The latter cannot exhaust the former, and thus belief that:((p v q) is true) is not an adequate representation of Smith's belief. — creativesoul

I hope it's clear from my preceding remarks that I agree: (p V q) is not an adequate representation of Smith's belief in the case we began by considering.

Who says it is?

To say it is not an adequate representation of Smith's belief is not to say it can have no part in an adequate representation of Smith's belief.

For one thing, Smith believes

1. p [for reasons assumed in the scenario]
2. if p then (p V q) [empty formalism]
3. p V q [by inference from 1 and 2]

For another, Smith believes or is disposed to affirm that he has no idea whether q is true -- which is not the same as merely believing the tautology (q V ~q).

The trouble comes this way:
If you have good reason to believe that p, then you have good reason to believe that p v q, and if p v q is true you have a well-founded true belief, but it is possible for p to be false and q true, in which case your reasons for believing that p turn out to be irrelevant. — Srap Tasmaner

Is there some reason to insist that we cannot have justified true beliefs of this sort? To say p is justified in some epistemic context is not to say p is justified in an epistemic context that includes all the relevant facts. Such cases may lead to trouble for the one who believes that p, but I don't see what special difficulties they present for our analysis of these cases.

My reasons for believing p are not "irrelevant" to my judgment (p V q) in the case you've just described. They are the reasons that justify my judgment that p, and it's only this judgment which grounds the inference to (p V q).

That whole epistemic context is reflected in my disposition to alter my judgments in light of future changes to my view of the relevant facts. Such changes alter the balance of reasons for judging that p, which undermines the chain of inferences that had previously supported the claim (p V q).

All of which goes to show how the reasons that support the judgment that p are crucial to the judgment that (p V q) in this case.

Surely we're agreed on such matters? There must be something else at issue here....

http://fitelson.org/proseminar/gettier.pdf

The original paper...

For one thing, Smith believes

1. p [for reasons assumed in the scenario]
2. if p then (p V q) [empty formalism]
3. p V q [by inference from 1 and 2]

That's been shown to be an inadequate account of what believing a disjunction requires...

Is there some reason to insist that we cannot have justified true beliefs of this sort? — Cabbage Farmer

No. But for many philosophers the intuition here is that the justified true beliefs in Gettier cases are not knowledge, so it's a problem for such accounts of what knowledge is.

My reasons for believing that p are obviously relevant to my believing that p v q, but it will turn out they have nothing to do with what makes p v q true. It's a bit of luck that I believe p v q for one reason but it turns out to be true for another. (Abusing the word "reason", I know.)

This thread is almost entirely about the B in JTB, for reasons that pass understanding.

The original paper... — creativesoul

It's not clear to me what position you take yourself to be arguing against or what position you take yourself to be defending, nor how your position is related to Gettier's .

"S believes that p" does not entail that p is true.

"S's belief, that p, is a justified belief" does not entail that p is true, nor that p is justified in every epistemic context.

"S knows that p" entails that p is true.

"T asserts that S knows p" does not entail that S knows p, and does not entail that p is true, even when T = S.

Sometimes knowledge claims are false claims. Like Wittgenstein says:

One always forgets the expression, 'I thought I knew'. — Wittgenstein

Gettier's paper is a critique of the concept of knowledge, not a critique of belief and justification, and not a critique of the validity of disjunction. It seems to me he takes ordinary epistemological concepts of belief, justification, and truth for granted in his paper. For instance:

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. — Gettier

Gettier's paper is a critique of the concept of knowledge, not a critique of belief and justification, and not a critique of the validity of disjunction. It seems to me he takes ordinary epistemological concepts of belief, justification, and truth for granted in his paper. For instance:

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.
— Gettier — Cabbage Farmer

Indeed, and this is really annoying. If justified true belief does not amount to knowledge, then what the eff is knowledge and what does amount to it? Where I'm at with this at the moment is that Smith does not arrive at his belief 'p' by formal logic, but by informal induction, and therefore he is not entitled (by logic) to treat his belief as a certainty, which is required to form the disjunction with a random 'q'. If Smith had the humility to assert in the first place, not 'p', but '(p v (I falsely believe p))', which is all he can confidently assert, he would save himself from justified true beliefs that he did not know, and us from a lot of head-scratching.

Where I'm at with this at the moment is that Smith does not arrive at his belief 'p' by formal logic, but by informal induction, — unenlightened

Together with abduction, yes. This is how we reason about matters of fact, sure.

and therefore he is not entitled (by logic) to treat his belief as a certainty, — unenlightened

Which he needn't; he only needs his belief to be justified. As Gettier puts this, he has "strong evidence" for (f).

which is required to form the disjunction with a random 'q'. — unenlightened

No, it's clearly not, as my jar model shows. You can form a disjunction of beliefs held only probable, not certain.

If Smith had the humility to assert in the first place, not 'p', but '(p v (I falsely believe p))' — unenlightened

But that just is to assert that p. Of course to say something is the case is to recognize that it might not be - it's the main reason we bother to make assertions. They are informative precisely because the facts they communicate are usually contingently so. And to recognize that is to recognize that you could be wrong. No one takes everything he says to be a necessary truth. But by asserting you commit yourself to the consequences of being right or being wrong. You place your bet, you answer the test questions, you test your hypothesis. What alternative is there?

I don't think humility saves you from Gettier. Suppose Smith never assents to p v q unadorned, but only as probable. We could still have a situation where Smith is right about the probability of p v q (and this is all we're talking about, not its truth) but his subjective probabilities are swapped: it's actually the "Jones" jar that is nearly all blue and the "Barcelona" jar that's nearly all red. Same problem, even without any claim of certainty or any belief held unconditionally true.

We could still have a situation where Smith is right about the probability — Srap Tasmaner

Weasel words these, if you don't mind my saying. If I'm right about something, probability no longer applies. If improbably I have the winning lottery ticket, what are the chances I have won the lottery?

Weasel words these, if you don't mind my saying. If I'm right about something, probability no longer applies. — unenlightened

?

I mean something as simple as this: I think there are 4 beers in the fridge because I think there are 3 Guinness and 1 Bud Light. Sadly, there's 1 Guinness and 3 Bud Light. I'm right about how many, but I've got the proportion wrong.

If you think about my stupid jars, it's obvious how this works.

If I'm weaseling about anything, it's that there are objective probabilities to get right or wrong. Sometimes there are, as with the jars. And sometimes you can be wrong about how probable an event is. I'm not offering a position in which there is no objective truth. Gettier gets dramatically reworked if you do that.

It's not clear to me what position you take yourself to be arguing against or what position you take yourself to be defending, nor how your position is related to Gettier's.

Understood and unsurprising given the novelty of my approach/position.

Gettier claims to show a case that satisfies the JTB formulation of knowing a proposition. The proposition in this case is a disjunction. Gettier claims that Smith meets the JTB criterion for knowing a disjunction. Gettier sets out a formula in the beginning of the paper that Smith's thought/belief process(as described by Gettier) follows in Case II.


1. I am claiming that believing a disjunction is necessary for knowing one
2. Believing a disjunction is not being taken proper account of
3. Belief that:((p v q) is true) is an utterly inadequate account of what believing a disjunction consists in/of
4. An adequate account of believing a disjunction clearly shows that Smith's belief is false
5. False belief is not a problem for JTB, no matter how it is arrived at
6. The underlying problem in Case II is a grossly inadequate (mis)understanding of what believing a disjunction consists in/of

It strikes me that perhaps you've not seen this...

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 believing a disjunction.

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 believing a disjunction. 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 believing a disjunction, 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 believing a disjunction 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 and it is false.

QED

You wrote:

I hope it's clear from my preceding remarks that I agree: (p V q) is not an adequate representation of Smith's belief...

Who says it is?

To say it is not an adequate representation of Smith's belief is not to say it can have no part in an adequate representation of Smith's belief.

For one thing, Smith believes

1. p [for reasons assumed in the scenario]
2. if p then (p V q) [empty formalism]
3. p V q [by inference from 1 and 2]

Seems that Gettier does as well as many many others including yourself. I mean, you say so immediately after saying that (p v q) is not an adequate representation of Smith's belief.

Gettier:

...Smith does believe that (h) is true...

Gettier claims that Smith believes that "Either Jones owns a Ford or Brown is in Barcelona" is true. I'm objecting that this account of Smith's believing Q is utterly inadequate. Believing Q when Q is a disjunction requires thinking about the rules of correct inference because believing a disjunction requires considering what makes the disjunction true.

My solution shows this and in doing so it also shows that Smith's belief is false. Given that Smith has false belief, Gettier has lost all justificatory ground regarding Case II. His critique of JTB is based upon falsehood. Smith's belief is not true. Gettier's Case II is unfounded...


----------------------------------------------------------------------------------------------------------------------


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'))

The above holds good for every imaginable disjunction arrived at from belief that:((p) is true). There is never a problem of any kind. It's a solution. Believing a disjunction - for a rational person - is nothing more and nothing less than knowing what makes it true and believing that those conditions have been met. Smith's thought/belief process for arriving at believing all three of his own disjunctions is adequately represented below...

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

Gettier claims to show a case of knowing a proposition. The proposition in this case is a disjunction. Gettier claims that Smith knows a disjunction. — creativesoul

No he doesn't. He shows a case of Smith having a justified true belief that isn't knowledge.

Fair enough, you're correct. Gettier himself says Smith does not know (h)...

I was more or less going from the three formulations of S knows that P...

Smith's belief is false. That's what matters...

A bit of irony though...

Gettier mistakenly claims to have satisfied the (JTB)necessary and sufficient conditions for knowing P, while failing miserably at providing the necessary and sufficient conditions for believing Q when Q is a disjunction arrived at from believing P.

No. But for many philosophers the intuition here is that the justified true beliefs in Gettier cases are not knowledge, so it's a problem for such accounts of what knowledge is. — Srap Tasmaner

Gettier gives two special cases in which a justified true belief arguably does not count as knowledge, due to inadequate fit between the justification for the proposition and the truth of the proposition in question.

I suppose one might conclude that, though JTB may be necessary for knowledge, it is not sufficient.

That's not a troubling claim in my book. Even less so, given that Gettier's first case involves a superficial error of description, and his second case involves an arbitrary and artificial inference. Does anyone really believe that way? What is in fact believed when such sentences are uttered in such contexts?

My reasons for believing that p are obviously relevant to my believing that p v q, but it will turn out they have nothing to do with what makes p v q true. It's a bit of luck that I believe p v q for one reason but it turns out to be true for another. (Abusing the word "reason", I know.) — Srap Tasmaner

Plato proposes that justification (account, logos) be added to true belief as a criterion for knowledge, to rule out cases in which a belief is only "accidentally" true.

Gettier helps us further specify the conception of knowledge as justified true belief, by indicating cases in which a justification for an accidentally true belief does not function the way the believer intends.

In both of Gettier's original cases, we expect the lucky believer, apprised of the relevant facts, to think something like "That's not what I meant".

His beliefs about the relevant state of affairs are on the whole contrary to fact, even though that view of the state of affairs disposes him to assent to a single proposition that is arbitrarily true with respect to his beliefs.

We might say the target propositions do not really reflect what is believed, and insist that beliefs be represented more thoroughly with respect to epistemic context.

Or we might say the ascribed "beliefs" are not really justified, though they seem justified from the point of view of the local epistemic context. A belief is true or false, independent of our grasp of the truth value of the proposition believed. Likewise, we might say, a justification for that proposition is "fit" or "unfit", independent of our grasp of the fitness of that justification.

Along such lines we could advocate for something like "fitness" as a "fourth criterion" to round off JTB, yielding Fit Justified True Belief. (Or try fullness, completeness, adequacy….). But this is only to clarify the original conception of "justification". For the thought was never that any old story that sounds good to me is good enough to warrant my beliefs, but rather that my story must line up with the relevant facts.

That sort of response should fly just as well for Barn Façade variations on Gettier's theme.

In both of Gettier's original cases, we expect the lucky believer, apprised of the relevant facts, to think something like "That's not what I meant".

His beliefs about the relevant state of affairs are on the whole contrary to fact, even though that view of the state of affairs disposes him to assent to a single proposition that is arbitrarily true with respect to his beliefs.

We might say the target propositions do not really reflect what is believed, and insist that beliefs be represented more thoroughly with respect to epistemic context.

Or we might say the ascribed "beliefs" are not really justified, though they seem justified from the point of view of the local epistemic context. A belief is true or false, independent of our grasp of the truth value of the proposition believed. Likewise, we might say, a justification for that proposition is "fit" or "unfit", independent of our grasp of the fitness of that justification.

Along such lines we could advocate for something like "fitness" as a "fourth criterion" to round off JTB, yielding Fit Justified True Belief. (Or try fullness, completeness, adequacy….). But this is only to clarify the original conception of "justification". For the thought was never that any old story that sounds good to me is good enough to warrant my beliefs, but rather that my story must line up with the relevant facts.

That sort of response should fly just as well for Barn Façade variations on Gettier's theme. — Cabbage Farmer

What about my example of Mary giving Smith £10?

1. Mary tells Smith that she will give him £10 if Jones owns a Ford or if Brown is in Barcelona
2. Smith justifiably believes that Jones owns a Ford
3. So, Smith justifiably believes that Mary will give him £10
4. Jones doesn't own a Ford but Brown is in Barcelona

Is this "unfit" justification? Is this a case of "that's not what I meant"?

For the thought was never that any old story that sounds good to me is good enough to warrant my beliefs, but rather that my story must line up with the relevant facts.

Are you saying that a belief is only justified if it's true?

Smith believes Jones owns a Ford. Smith believes that Mary will give him £10 if Jones owns a Ford or if Brown is in Barcelona. Smith believes that Mary will give him £10 because Jones owns a Ford.

Smith has false belief.

Smith believes that Mary will give him £10 because Jones owns a Ford.

Smith has false belief. — creativesoul

Smith believes that Mary will give him £10.

Smith has a true belief.

He's correct in his belief that Mary will give him £10, but incorrect in his belief that she will do so because Jones owns a Ford.

This is the nonsense scenario you're setting up: "I believe that Mary will give me £10 because Jones owns a Ford, but I don't believe that Mary will give me £10". It's utter rubbish.

Quick note on the linguistics here:

(1) Mary gave me £10 because I won; and
(2) Mary didn't give me £10 because I won

usually both presuppose that Mary gave me £10.

The point of the statement is to highlight the reason for the action. The implication of the negative statement is that there was some other reason for the action taken. (Compare: "Mary didn't give me £10 because I didn't win.")

You get this a lot in Hollywood screenplays: "I didn't put you in the game because you're my son. I put you in the game because you earned it."

Similarly, someone could tell Smith, "Mary didn't give you £10 because Jones owns a Ford; she gave you £10 because Brown is in Barcelona."

That doesn't follow from what I've been arguing. You'll have to do better than that Michael.

He's correct in his belief that Mary will give him £10, but incorrect in his belief that she will do so because Jones owns a Ford.

What grounds this move to split up Smith's belief? On what basis do you posit Smith holding two beliefs?

Mary says she'll pay Smith if either this or that is the case. Smith understands this. Smith believes Mary will pay him because this is the case.

You want to remove the operative content of Smith's thought/belief, and by doing so create a problem that is otherwise not there.

Smith's belief is about and therefore must include his considering the conditions under which Mary will pay him.

What grounds this move to split up Smith's belief? — creativesoul

The fact that there are two parts to Smith's belief. 1) Mary will give him £10, and 2) she will do this because Jones owns a Ford.

If someone were to ask Smith if he believes that Mary will give him £10, he will say that he does. It's really simple. You're clutching at straws.

What grounds this move to split up smith's belief? On what basis do you posit Smith holding two beliefs? — creativesoul

Just "because"?

I asked:

What grounds this move to split up Smith's belief?

Michael answered:

The fact that there are two parts to Smith's belief. 1) Mary will give him £10, and 2) she will do this because Jones owns a Ford.

The astute reader will note that Michael just conceded, perhaps unwittingly, that there are two parts of Smith's belief that:Mary will pay him because Jones owns a Ford.

Michael wants to eliminate one part. Doing so renders an incomplete account of Smith's belief. This is clear for all to see. "Mary will pay me" does not mean the same thing as "Mary will pay me because Jones owns a Ford".

Salva veritate

The problem is not with Smith's belief. The problem is how it's being accounted for.

"Mary will pay me" does not mean the same thing as "Mary will pay me because Jones owns a Ford". — creativesoul

I'm not saying they do, so this is a straw man. I'm saying that if he believes that Mary will pay me because Jones owns a Ford then he believes that Mary will pay me. I've gone over this several times.

p ∵ r ⊨ p

If Jones crashed his car into a tree then Jones crashed his car. If I believe that Jones crashed his car into a tree then I believe that Jones crashed his car. How is this so hard for you to understand?

I honestly think you're just being dishonest at this point.

Michael wants to eliminate one part. Doing so renders an incomplete account of Smith's belief. This is clear for all to see. "Mary will pay me" does not mean the same thing as "Mary will pay me because Jones owns a Ford".

A belief isn't justified if the justification is false.

But you are right; instead of being false, in this case the justification is insufficient.

@Creative, do you think that knowledge is equivalent to justified true belief?

Just wondering.

A belief isn't justified if the justification is false.

But you are right; instead of being false, in this case the justification is insufficient. — Banno

All Gettier says is that the Smith has "strong evidence" for the proposition that Jones owns a Ford.

Do you recommend holding out for justification that absolutely guarantees truth?