Fake Barn Country: Henry is looking at a (real) barn, and has impeccable visual and other evidence that it is a barn. He is not gettiered; his justification is sound in every way. However, in the neighborhood here are a number of fake, papiere-mâché barns, any of which would have fooled Henry into thinking it was a barn.

The idea here is that Henry's belief is too lucky -- if he had happened to form the same belief looking at one of the other "barns", he'd be wrong. So there is some doubt about whether his current belief counts as knowledge.

This is a slightly different way of putting the pieces together, but is still a Gettier descendant.

Again. Don't see the problem. If it is a barn, then his belief is true. If it is not, then his belief is false. That one's quite a stretch on the imagination as well. I mean, we can all think of some logically possible world in which things make different kinds of sense.

It all starts with thought/belief Srap...

We get that wrong and we get something or other wrong about everything ever spoken and/or written.

By the way, the argument from illusion is untenable.

It's ambiguous.

"S is justified in believing that P" could mean:
(1) If S were to believe that P, his belief that P would be justified, or
(2) S believes that P and his belief is justified.

In the quote you gave, Gettier seems to conflate the two, but it's harmless because he's talking about this:

(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.

That is, the belief that P is one of the three conditions, listed here in TBJ order. I say conflation is harmless here because he's specifically talking about cases where all of (i), (ii), and (iii) hold.

In the specific cases he offers -- I just glanced at Case I -- he does not attribute the belief for which there is justification, but only uses it as the premise from which a different belief is derived.

Case one specifies Smith's belief. Gettier refers to them as a "conjunctive proposition".

(d) Jones is the man who will get the job, and Jones has ten coins in his
pocket.

Smith's evidence for (d) might be that the president of the company assured him
that Jones would in the end be selected, and that he, Smith, had counted the
coins in Jones's pocket ten minutes ago. Proposition (d) entails:

(e) The man who will get the job has ten coins in his pocket

Let us suppose that Smith sees the entailment from (d) to (e), and accepts (e)
on the grounds of (d), for which he has strong evidence. In this case, Smith is
clearly justified in believing that (e) is true.

Looks like a problem with entailment. Truth conditions matter.

Case one specifies Smith's belief. Gettier refers to them as a "conjunctive proposition". — creativesoul

Same pattern as in Case II: Smith has strong evidence for the conjunctive proposition (d), but Gettier never says that he accepts it, only that he derives (e) from it, and that (d) is false while (e) is true. Smith does accept (e).

Here, he says "on the grounds of (d)", where in Case II he says "on the basis of (f)". That's somewhat ambiguous. Could mean that he's accepted (d) (and (f) in Case II), but then Gettier is explicit about him accepting (e) (and (g), (h), and (i) in Case II) so why not say so explicitly? His preamble I think does not require that the antecedent be believed, only that it be justified, since all we're going to get from these antecedents is justification anyway, as they never turn out to be true.

Suppose that Smith and Jones have applied for a certain job. And suppose that Smith has strong evidence for the following conjunctive proposition:

(d) Jones is the man who will get the job, and Jones has ten coins in his pocket.

Smith's evidence for (d) might be that the president of the company assured him that Jones would in the end be selected, and that he, Smith, had counted the coins in Jones's pocket ten minutes ago.

Proposition (d) entails:

(e) The man who will get the job has ten coins in his pocket.

Let us suppose that Smith sees the entailment from (d) to (e), and accepts (e) on the grounds of (d), for which he has strong evidence. In this case, Smith is clearly justified in believing that (e) is true.

But imagine, further, that unknown to Smith, he himself, not Jones, will get the job. And, also, unknown to Smith, he himself has ten coins in his pocket. Proposition (e) is then true, though proposition (d), from which Smith inferred (e), is false.

Looks like a problem with entailment. — creativesoul

Well you know I don't agree there.

He believes that:the proposition "Either Jones owns a Ford or Brown is in Barcelona" is true because Jones owns a Ford. — creativesoul

If he believes that the proposition "Either Jones owns a Ford or Brown is in Barcelona" is true because Jones owns a Ford then he believes that the proposition "Either Jones owns a Ford or Brown is in Barcelona" is true. And if the proposition "Either Jones owns a Ford or Brown is in Barcelona" is true because Brown is in Barcelona then the proposition "Either Jones owns a Ford or Brown is in Barcelona" is true.

So Smith has a true belief.

The conflation of being true and being called "true" as the result of being the conclusion of a valid inference. Validity is insufficient for truth. — creativesoul

I've addressed your confusion here. Nobody is saying that validity is sufficient for truth. Validity is one thing and truth is another. I've provided examples of valid arguments with false conclusions and valid arguments with true conclusions. Smith's case is a valid argument with a true conclusion.

Smith holds the belief that:((p v q) follows from (p)). — creativesoul

He also holds the belief that p is true, and so also holds the belief that p ∨ q is true.

It seems to me that you're making two mistakes.

The first is in thinking that the following is an exhaustive account of Smith's beliefs:

1. p
2. p → p ∨ q

But it isn't. There is also the conclusion:

3. p ∨ q

The second is in thinking that Smith's belief on p ∨ q being true is only:

4. p ∨ q ∵ p

But it isn't. It's also:

5. p ∨ q

And before you respond yet again with "salva veritate", I'm not saying that p ∨ q ∵ p is equivalent to p ∨ q, just as I'm not saying that p is equivalent to p ∨ q. I'm saying that p ∨ q ∵ p entails p ∨ q, just as I'm saying that p entails p ∨ q.

Michael I've made that case. Entailment doesn't matter. p1 and p2 exhaust everything Gettier says until his conclusion that Smith believes (p v q). He never got there and my argument shows how that's the case. It takes more than a single deduction.

Srap, there is another problem at hand. Belief and propositions are not equivalent.

p1 and p2 exhaust everything Gettier says until his conclusion that Smith believes (p v q). He never got there and my argument shows how that's the case. It takes more than a single deduction. — creativesoul

This is a valid argument:

1. p
2. p ⊨ p ∨ q
3. p ∨ q

Therefore the rational person who believes 1 and 2 will also believe 3. Consider:

4. Socrates is a man
5. If Socrates is a man then Socrates is mortal
6. Therefore, Socrates is mortal

A valid argument. Therefore the rational person who believes 4 and 5 will also believe 6.

It is true that Smith might not be rational and might not believe 3 (or 6) even though he believes 1 and 2 (or 4 and 5), but that's irrelevant. Gettier asserts that he is rational and does.

The problem that Gettier raises is that if Smith believes 3 because he believes 1 and 2 – and if 1 is justified but false, and 2 and 3 are true – then Smith has a justified true belief that intuitively isn't knowledge.

If all you're saying is that a belief in 3 doesn't necessarily follow from a belief in 1 and 2 then you're addressing a red herring.

This is a valid argument:

1. p
2. p ⊨ p ∨ q
3. p ∨ q

Therefore the rational person who believes 1 and 2 will also believe 3. Consider:

4. Socrates is a man
5. If Socrates is a man then Socrates is mortal
6. Therefore, Socrates is mortal

A valid argument. Therefore the rational person who believes 4 and 5 will also believe 6.

Can't get to 3 from 1 and 2. Can't get to 6 from 4 and 5. Missing premiss in both.

True premisses and valid form cannot yield false conclusions.
False premisses and valid form cannot yield true conclusions.

Gettier's Case II has Smith working from a false premiss. For whatever reason, convention has been bewitched for half a century. I've shown that arriving at belief that:((p v q) is true) because (p)) requires more than one deduction. Gettier's formulation requires only one. One cannot arrive at belief that:((p v q) is true). Can't be done. Prior to ever getting there, one must first go through belief that:((p v q) is true if...) and belief that:((p v q) is true because(insert appropriate corresponding belief to the prior 'if')).

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)

That's the solution. Gettier gets to p2(longwindedly) and wants to claim that 'therefore' Smith believes that ((p v q) is true). I've already argued for all this without subsequent refutation.

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.

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. So, as Gettier says, Smith believes Jones owns a Ford. Smith constructs (g), (h), and (i). All of which are (p v q). So, Smith believes p, and deduces (p v q) from p and accepts (p v q) as a result of this deduction. There is nothing in the above two quotes 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 hasn't yet gotten to the point where he has formed and/or holds belief that:((p v q) is true)...

But oddly enough, Gettier concludes that that is the case, 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...

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 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 that belief. I've shown all sorts of problems with Gettier's account. That want of Gettier is yet another.

Belief that:((p v q) is true) is not equivalent to belief that:((p v q) is true because(p)). We cannot swap one for the other. The latter consists in part of the deduction missing in Gettier's account.

Salva veritate

QED

What's the difference between a premise and an inference rule?

The same as the difference between a conclusion and an inference rule?

And what would that be?

pm me Srap...

I would hope that anyone voting 'no' would would bear the burden of valid objection.

There's quite a bit to consider here regarding the sheer scope of application that this refutation has for philosophy on a whole. Aside from the cottage industry that owes it's very existence to this particular case, there is more. Namely, anything and everything that has to do with deriving disjunction. Unless I'm missing something, in addition to refuting the Case II, this places the very notion of deriving disjunction under tremendous scrutiny, which in turn places para-consistent logic - in part at least - under the same.

True premisses and valid form cannot yield false conclusions.
False premisses and valid form cannot yield true conclusions.

Gettier's Case II has Smith working from a false premiss. For whatever reason, convention has been bewitched for half a century. I've shown that arriving at belief that:((p v q) is true) because (p)) requires more than one deduction. Gettier's formulation requires only one. One cannot arrive at belief that:((p v q) is true). It can't be done, unless that is; one wants to conflate being true with being called "true" as a result of being the product of a valid inference. Validity is insufficient for truth. Prior to ever getting to belief that:((p v q) is true), one must first go through belief that:((p v q) is true if...) and belief that:((p v q) is true because(insert belief statement(s) corresponding to the prior 'if')). That holds for any and all interpretations thereof.

Salva veritate

What I'm saying is that the following is not only my argument. It is not only an adequate account of Smith's thought/belief process, but it is also necessary for any and all disjunction. It's a formula that doubles as a solution. This can be tested by virtue of filling it 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'))(from p1,p3)

It shows us something about the difference between propositions and belief(s) as well. Case II was a thorn in the side of many folk due to the fact that it required us to say that Smith believed a proposition which contained a statement that Smith did not believe. My solution solves that.

It also sheds light upon what it actually takes to believe a disjunction, as compared/contrasted to just believing that it follows from some belief or other. Furthermore, it shows that Gettier's formulation is invalid.

That's huge.

False premisses and valid form cannot yield true conclusions. — creativesoul

Yes they can.

1. If my name is Susan then I am a man
2. My name is Susan
3. Therefore, I am a man

False premises, true conclusion.

Can't get to 3 from 1 and 2. Can't get to 6 from 4 and 5. — creativesoul

Yes you can. They're valid. The second is the stereotypical syllogism.

Invalid form

You are quite simply wrong. It's modus ponens.

This is a valid... Therefore the rational person who believes 1 and 2 will also believe 3...

The rational and wise person knows that validity is insufficient for truth.