There's coffee.

There had been, a long time ago, a study linking coffee consumption to increased risk of cancer. But coffee drinkers are more likely to be smokers. Controlling for smoking, coffee's risk was downgraded. Then it went back up. The latest I think is that there's a risk associated with very hot drinks, not coffee per se.

Tests produce results, but they don't tell you why they produce the result they do. That's why justification can point away from the truth instead of toward it.

"Jones owns a Ford" is true. "Jones owns a Ford" entails "Either Jones owns a Ford or Brown is in Barcelona". Therefore, "Either Jones owns a Ford or Brown is in Barcelona" is true.

Is that an accurate rendition of what you're claiming Smith's 'argument' is? — creativesoul

Yes. Except I wouldn't use the "either ... or ..." terminology as that implies an exclusive or, which isn't actually entailed by Jones owning a Ford. Gettier clearly meant for it to be an inclusive or, and so "Jones owns a Ford or Brown is in Barcelona" is the better wording. Charitable readings and all.

One of the two statements is believed. To state that one or the other is true is to believe that they both could be. It shows uncertainty where none exists. One of the two is believed. — creativesoul

No it isn't. The statement "London is the capital city of England or pigs can fly" is true if London is the capital city of England. Therefore I believe that the statement "London is the capital city of England or pigs can fly" is true because I believe that London is the capital city of England. Given that the statement is true even if pigs can't fly, I can believe that the statement is true even if I believe that pigs can't fly.

Like unenlightened you're setting up a situation where:

1. I know that "Jones owns a Ford or Brown is in Barcelona" is true if Jones owns a Ford,
2. I believe that Jones owns a Ford, and
3. I don't believe that "Jones owns a Ford or Brown is in Barcelona" is true.

This strikes me as untenable. Anyone in this situation is clearly suffering from cognitive dissonance. And although it's entirely possible that Smith is in this state of cognitive dissonance, it's also entirely possible that he isn't, and Gettier is quite within his right to assert that Smith isn't.

Besides, Smith likely does believe that "Brown is in Barcelona" could be true. So your counter-argument isn't actually a counter-argument at all.

There had been, a long time ago, a study linking coffee consumption to increased risk of cancer. But coffee drinkers are more likely to be smokers. Controlling for smoking, coffee's risk was downgraded. Then it went back up. The latest I think is that there's a risk associated with very hot drinks, not coffee per se.

Tests produce results, but they don't tell you why they produce the result they do. That's why justification can point away from the truth instead of toward it. — Srap Tasmaner

Well you have set up the beginning of a Gettier; Smith reads the study and believes that coffee causes cancer, a JFB. And then he sets up a connected disjunction "coffee causes cancer, or something else that coffee drinkers do causes cancer." Which is perfectly reasonable, and leads to further investigation. It is in fact a way of sceptically questioning his belief. Whereas Smith's arbitrary disjunction per Gettier does the opposite, it relies entirely on the unquestioned truth of his belief to make a claim that has no value in itself and can lead only to the entrenchment of his belief. It neither leads to a test of his belief nor an expansion of his knowledge in terms of Jones' whereabouts or anything else.

And since we all agree that it is possible and quite likely that we we all have the odd justified false belief, our attitude as scientists and equally as philosophers ought to be, because we are justified in being, sceptical rather than complacent concerning our beliefs.

So, I think we agree that "S believes p" does not imply "p". And if we can see that as reasonable people, Smith should also see it as a reasonable person. And if that is the case, he cannot assert p in the first place. Instead, he can only assert a connected disjunction along these lines: "(p, or some other explanation of whatever justifies my belief)". Call that "(p v ae)" (This disjunction is of the either/or variety, I think, so the logicians must amend the formula as necessary.)

And then, even if he is so ill-advised as to form the logically implied assertion, ((p v ae) v q), he is safe from ever believing or seeming to believe q, because (p v ae) is necessarily true, given justification - J, even if the substance of "ae" is that J is a lie, or an hallucination, and so it can be safely reasoned from.

...I believe that the statement "London is the capital city of England or pigs can fly" is true because I believe that London is the capital city of England...

Salva veritate

As I've asked before, why do you think that this term is relevant?

Because p3 and C1 cannot be further reduced/simplified without losing the because p part. That is true belief on your part here and now. Smith has false belief.

Because p3 and C1 cannot be further reduced/simplified without losing the because p part. That is true belief on your part here and now. Smith has false belief. — creativesoul

He also has a true belief. "Jones owns a Ford or Brown is in Barcelona" is true if Brown is in Barcelona. Brown is in Barcelona, therefore "Jones owns a Ford or Brown is in Barcelona" is true. Smith believes that "Jones owns a Ford or Brown is in Barcelona" is true because he believes that Jones owns a Ford and knows that "Jones owns a Ford or Brown is in Barcelona" is true if Jones owns a Ford.

Again, you're setting up the untenable situation where:

1. I know that "Jones owns a Ford or Brown is in Barcelona" is true if Jones owns a Ford,
2. I believe that Jones owns a Ford, and
3. I don't believe that "Jones owns a Ford or Brown is in Barcelona" is true.

It's nonsense.

He also has a true belief. "Jones owns a Ford or Brown is in Barcelona" is true if Brown is in Barcelona. Brown is in Barcelona, therefore "Jones owns a Ford or Brown is in Barcelona" is true.

No.

When you combine the two statements into one monolith and talk about Smith's belief like you've done above, you must remember and properly take into account that Smith's belief is about the rules of correct inference. If Smith believes that the disjunction is true if either one of the disjuncts is true, then he holds true belief about what makes the disjunction true.

That is not equivalent to believing the disjunction.

Smith believes that "Jones owns a Ford or Brown is in Barcelona" is true because Jones owns a Ford. Just like you believe your disjunction is true because London is the capital city of England.

Smith believes that "Jones owns a Ford or Brown is in Barcelona" is true because he believes that Jones owns a Ford and knows that "Jones owns a Ford or Brown is in Barcelona" is true if Jones owns a Ford.

Again, you're setting up the untenable situation where:

1. I know that "Jones owns a Ford or Brown is in Barcelona" is true if Jones owns a Ford,
2. I believe that Jones owns a Ford, and
3. I don't believe that "Jones owns a Ford or Brown is in Barcelona" is true.

It's nonsense.

That's a very poor reading of what I've set out here. What follows immediately below is the thought/belief process that is required in order to arrive at believing Q when Q is a disjunction. Which part are you denying?

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'))

That's a very poor reading of what I've set out here. — creativesoul

It's exactly what you're saying. You're saying that Smith doesn't believe that "Jones owns a Ford or Brown is in Barcelona" is true, despite the fact that he believes that Jones owns a Ford and knows that "Jones owns a Ford or Brown is in Barcelona" is true if Jones owns a Ford. It's untenable.

It's a simple fact that:

1. Smith knows that "Jones owns a Ford or Brown is in Barcelona" is true if Jones owns a Ford,
2. Smith believes that Jones owns a Ford, and so
3. Smith believes that "Jones owns a Ford or Brown is in Barcelona" is true.

And given that "Jones owns a Ford or Brown is in Barcelona" is true because Brown is in Barcelona, Smith's belief that "Jones owns a Ford or Brown is in Barcelona" is true is true.

I'm saying that belief that:((p v q) is true) is not equivalent to belief that:((p v q) is true because (p)). I'm saying that the way you've been accounting for Smith's thought/belief is inadequate, and by virtue of over simplifying what believing a disjunction takes we've arrived at bewitchment.

What follows immediately below is the thought/belief process that is required in order to arrive at believing Q when Q is a disjunction. Which part are you denying?

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'))

I ask the careful reader to compare the following...

Michael wrote:

It's a simple fact that:

1. Smith knows that "Jones owns a Ford or Brown is in Barcelona" is true if Jones owns a Ford,
2. Smith believes that Jones owns a Ford, and so
3. Smith believes that "Jones owns a Ford or Brown is in Barcelona" is true.

Again the pattern of oversimplifying Smith's believing a disjunction continues unabated, despite the fact that Michael himself follows the below...


It's a simple fact that:

1. Smith knows that "Jones owns a Ford or Brown is in Barcelona" is true if either "Jones owns a Ford" or "Brown is in Barcelona" is true.(p3)
2. Smith believes that Jones owns a Ford.(p1)
3. Smith believes that "Jones owns a Ford or Brown is in Barcelona" is true because Jones owns a Ford.(C1)

Michael just wrote:

Smith believes that "Jones owns a Ford or Brown is in Barcelona" is true because he believes that Jones owns a Ford...

Precisely. Now account for it correctly.

I predict great success for the hypothesis that it was either coffee or something else. But the issue is getting past tautology and giving some substance to the something else. (We're also in the neighborhood of Nelson Goodman's discussion of ceteris paribus in FF&F.)

Here's another tack. Smith's original approach to Jones's car ownership is in part an abduction: if Jones owns a Ford, he'll drive a Ford. There's additional support for the abductive thesis in Jones's history of Ford ownership. An alternative abductive thesis would have been that Jones is renting a Ford, but there's no additional support for that.

The two abductive theses are connected by having a common result, that Jones drives a Ford. Which brings us to an issue we haven't specifically discussed, which is disjunction elimination. That works like this:
1. A→C
2. B→C
3. A v B
4. C
Given that Jones drives a Ford, we could form the abductive hypothesis that Jones owns a Ford or Jones rents a Ford. That's clearly an improvement, as it would in fact be true. But it's not a foolproof method. Maybe Jones borrowed a Ford. How can you be sure you've thought of every possible explanation of Jones driving a Ford? (Or coffee drinkers getting cancer.)

On the other end, I think what bothers people about (g), (h), and (i), the arbitrariness of those distinctions, is that it's not obvious how you could eliminate them. What would be a consequence either of Jones owning a Ford or Brown being in Barcelona?

This is actually the same problem as above. It's the sort of thing that the TV show House relied on. "By any chance, have you been to Barcelona recently?" Wildly unconnected underlying issues can produce similar symptoms.

The mistake here is conflating knowledge of(justified true belief about) the rules of entailment/disjunction with believing a disjunction.

I wrote:

"Jones owns a Ford" is true. "Jones owns a Ford" entails "Either Jones owns a Ford or Brown is in Barcelona". Therefore, "Either Jones owns a Ford or Brown is in Barcelona" is true.

Is that an accurate rendition of what you're claiming Smith's 'argument' is?

Michael answered:

Yes. Except I wouldn't use the "either ... or ..." terminology as that implies an exclusive or, which isn't actually entailed by Jones owning a Ford. Gettier clearly meant for it to be an inclusive or, and so "Jones owns a Ford or Brown is in Barcelona" is the better wording. Charitable readings and all.

Charitable readings and all...

Smith doesn't believe that Brown is in Barcelona. So Smith's thought/belief process - since it involves invoking an inclusive 'or' - is about the rules of correct inference. And yet that is not being taken into proper account.

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 place names 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). — creativesoul

Do you mean to say that (g)-(i) are exclusive disjunctions, and that each of these exclusive disjunctions is entailed by (f)? That just seems wrong. For it's logically possible that Jones owns a Ford while Brown is in any one of those three locations.

If instead you mean that (g)-(i) are ordinary (inclusive) disjunctions, then they are trivially entailed by (f). In that case these propositions should not be expressed with the form "either (f) or (p)", but rather with the more modest form "(f) or (p)".


Redraft accordingly:

(f) Jones owns a Ford.

(g') Jones owns a Ford, or Brown is in Boston.
(h') Jones owns a Ford, or Brown is in Barcelona.
(i') Jones owns a Ford, or Brown is in Brest-Litovsk.


Smith believes that (f).

If Smith believes that (f), and Smith's beliefs are rational, and Smith understands the conventional meaning of logical disjunction, then:

1. Smith's beliefs are consistent with (g')-(i').
2. Smith is disposed to assent to (g')-(i')

None of those propositions commit Smith to having any expectations about the whereabouts of Brown. The belief that (f) does not commit Smith to having expectations about the whereabouts of Brown. Consider:

(u) Jones owns a Ford, or Brown is a unicorn.

The belief that (f) does not commit Smith to having beliefs about Brown or about unicorns. If Smith is rational then his beliefs are consistent with (u). If Smith is rational and understands the conventions of propositional logic, then Smith is disposed to assent to (u).

To all appearances, the truth of the second term in each disjunction is independent of the truth of (f) -- not only as a matter of logical form, but also as a matter of fact. Such propositions are utterly arbitrary and uninformative. To believe them, to have beliefs consistent with them, or to be disposed to assent to them, is merely to be a rational person who believes that one term in the disjunction is true.

I see nothing especially troubling in this way of speaking.

I see nothing especially troubling in this way of speaking. — Cabbage Farmer

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.

To believe them, to have beliefs consistent with them, or to be disposed to assent to them, is merely to be a rational person who believes that one term in the disjunction is true.

I see nothing especially troubling in this way of speaking.

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.

You're hopelessly confused, @creativesoul, so let's try a simpler example.

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

He might be wrong in believing that she will give him £10 because Jones owns a Ford, but he's right in believing that she will give him £10.

You're playing silly word games that do nothing to refute Gettier's argument. You ain't gettin' famous for it.

Smith believes that he will receive payment because Jones owns a Ford. His belief is false.

There's no word games being played Michael. I'm letting the fly out of the bottle.

I predict great success for the hypothesis that it was either coffee or something else. But the issue is getting past tautology and giving some substance to the something else. — Srap Tasmaner

Indeed, the whole idea is that such a formulation is necessarily true. Because otherwise S is only reasoning about his beliefs and giving substance to nothing. "I believe p, therefore I believe p v q." I tells us nothing about the world.

To put it another way, if S or any other philosopher wants to adhere to the strict implications of logic, they have to do so from the start. What is hidden in Gettier's account is what I have been accused of here, which is conflating what S believes with what Gettier defines to be the truth in his world. S believes p, but S doesn't assert ' I believe p', he asserts 'p'. He is not entitled to assert 'p' as a logical necessity, but he can assert my disjunction (p v ae) which is necessary and says in effect 'what I believe is true unless I am wrong in my belief.' It is S's failure to acknowledge in his assertion the real possibility of error on his part that leads him and us into the logical quagmire when he then makes strict logical deductions.

Using (p v q) as a means to represent Smith's belief is problematic. The content of Smith's thought/belief is precisely what's in question. Smith's believing Q cannot be adequately represented with belief that:((p v q) is true). Rational people do not believe something if they do not know what it means. Considering the truth conditions of (p v q) is required for knowing what (p v q) means. That's what rational people do. Smith is rational. As argued heretofore, Gettier's formula cannot take an account of Smith's consideration of the truth conditions of his particular disjunction(s).

Smith must think about the rules of correct inference. The earlier post of Smith running modus ponens through his mind is a more than apt demonstration of what that looks like. Belief that P and belief that Q are belief statements about the world while 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')) is belief about the rules. Gettier claims Smith recognized the entailment, which is thinking about the rules of correct inference. Smith must think about the rules. Gettier's paper does not take proper account of this.

Who here would argue that thinking about the rules of correct inference is not required in order to arrive at believing Q ,when Q is derived from P, P entails Q, and the thinking/believing agent recognizes this entailment and the proceed to accept Q on the basis of P?

The process I'm setting out, when absent, results in a Smith that cannot believe a disjunction because without thinking about the rules, one cannot recognize the entailment.

Again, rational people do not assent to believing Q unless they understand what Q means, Q's following from P's notwithstanding. Rational people do not assent to believing Q simply because they believe P and some folk say that Q's following from P is necessary and sufficient for believing Q.

That is particularly germane when believing Q is believing a disjunction.

If it's true that one statement follows from(and/or is entailed by) another then it is so solely by virtue of the rules of correct inference saying so. One statement's following from another, in and of itself, neither warrants believing nor counts as believing the statement which is said to follow.

That is particularly germane when discussing believing a disjunction.

Various attempts have been made in recent years to state necessary and sufficient conditions for someone's knowing a given proposition.

To this there is only thing to state...

One must believe a proposition in order to know it. Smith does not believe that ((p v q) is true) except in the sense that "true" indicates being the result of correct inference. Gettier's formula does not have what it takes for Smith to arrive at believing Q.

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 is what believing Q requires when Q is a disjunction arrived at from believing P. Gettier's account of Smith's thought/belief process only gets to p2.

Smith believes that he will receive payment because Jones owns a Ford. His belief is false. — creativesoul

Smith believes that he will receive payment. His belief is true. You're just playing word games.

I'm charging you with inadequately accounting for Smith's thought/belief by virtue of not taking account of the process that is necessary for believing a disjunction. The oversimplification that both you and Gettier are guilty of results in the Gettier problem. It's not a problem for believing a disjunction. It's a problem with how that's being accounted for. It's a pseudo-problem:The self-induced bewitchment of inadequate language use.

That's not a word game, and you know it.

A proper account of believing a disjunction has been offered. There are no problems with it, and no disjunction is immune. None. Here it is again...

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'))

That is what it takes. That is what it consists in/of. I've invited you and/or anyone else to imagine a disjunction arrived at by a rational agent on the basis of believing P that is not completely exhausted by the above solution. There are no problems. Fill it out.

The added beauty, of course, is that this eliminates any and all confusion about senses of 'or' as well as the fact that an insincere purveyor of disjunction cannot get through it, for it puts his/her actual belief on display for everyone to see. It also stops Gettier and anyone else from just mentioning - in passing - that Smith recognizes the entailment. The solution above spells out exactly what that means by virtue of showing what it requires.

I've given you an example with Mary giving Smith £10.

You've given an example of what, exactly?

Set it out in a way that follows Gettier's formula, then we'll talk...

An example of the Gettier problem. And I've set it out quite clearly:

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

Mary will give him £10. Smith has a true belief.

Gettier problems follow Gettier's formula...

...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.

Set it out by adding the values...

(Since @Michael has made a gambling argument, here's the argument I've put off making on the grounds that it's a lot of trouble for little chance of success. It does complete the record, though. ;-/)

If you believe that p and refuse to believe that p v q, then your beliefs are inconsistent. If you hold inconsistent beliefs then you are vulnerable to a Dutch book, as follows.

You're a bookie and you believe the odds that Jones owns a Ford are 10-to-1, and those are the odds you offer. That is, if Jones does own a Ford, you pay out just $11 on a $10 bet that Jones owns a Ford - Jones owning a Ford is the heavy favorite -and nothing on bets that he doesn't; if Jones does not own a Ford, you pay out nothing on bets that he does, and $110 on bets that he does not.

For some reason, you think it's less likely that Jones owns a Ford or Brown is in Boston than it is that Jones owns a Ford. (No matter where Brown is, the chances are at least equal. You don't agree.) You set the odds that Jones owns a Ford or Brown is in Boston at even money. That is, if either is true, you pay out $20 on a $10 bet that either is true, and nothing on a bet that both are false; if both are false, you pay out nothing on a bet that at least one is true, and $20 on a $10 bet that both are false. (If you think it's irrational to believe that Jones owns a Ford or Brown is in Boston, you might even offer something crazy like 1000-to-1 against. You just have no opinion and offer even money.)

Suppose I strongly believe Jones owns a Ford, and I bet $10 that he does and another $10 that Jones owns a Ford or Brown is in Boston. I figure I'll win both. Here are my actual payouts:
Ford & Boston: $31
Ford & not Boston: $31
No Ford & Boston: $20
No Ford & not Boston: $0
It costs me $20 to play, so my results range from clearing $11 to losing $20.

Now suppose instead I bet $10 that Jones does not own a Ford, and I bet $50 that Jones owns a Ford or Brown is in Boston. Here are my payouts:
Ford & Boston: $100
Ford & not Boston: $100
No Ford & Boston: $210
No Ford & not Boston: $110
The point here is that it only costs me $60 to play. No matter what happens, I clear at least $40. For nothing. With no risk whatsoever. No matter what Jones owns or where Brown is, I am guaranteed to clear at least $40.


Appendix

Assuming a negligible chance that Brown is in Boston and that you're right about the likelihood of Jones owning a Ford, these are the expected payouts:
First player: about $28 for a $20 stake;
Second player, who makes the Dutch book against you: about $100 on a $60 stake.

Gettier's scenario (no Ford, not Boston):
First player loses $20 to you;
Second player takes $50 from you.

Various attempts have been made in recent years to state necessary and sufficient conditions for someone's knowing a given proposition.

Getting thought/belief right is necessary for getting the above right. I've shown that believing Q when Q is a disjunction arrived at from believing P is not adequately accounted for in terms of belief that:((p v q) is true). Believing Q in these cases requires thinking about the rules. As such it needs to be represented and/or properly accounted for.