Such a complex intertangling of nature could not have happened through random accidental misfirings of DNA copying. — MikeL

Why not?

There's only one truth to 2 + 2, which is 4 but an infinite number of wrong answers. — TheMadFool

This part is right and interesting. It's entropy. There are more possible ways for your car not to work than for it to work.

Not obvious that this applies to morality though. You can divide moralities broadly into two "styles": those that forbid certain things (don't kill, don't steal) and those that specify a standard (be this way) any deviation from which is forbidden. Wouldn't be a big surprise for deviation to be rare for a type 1 morality, but it's basically inevitable for a type 2.

Hey, when you put it like that, you have an argument that works. — apokrisis

I'm not sure. Think I rushed it.

Better might be:
4. If Big Pharma did not fund them, biologists would not tell people they are only chemicals.
5. Big Pharma wants to sell people addictive and destructive chemicals.
Therefore,
6. Big Pharma funds biologists.

Should probably try a version that isn't all counterfactuals ...

Materialism is fundamental to these drug scandals. The industry needs to propagate the myth that chemicals are beautiful things because that is all humans are. — Rich

So your argument is:
1. If biologists did not tell them so, people would not believe they are only chemicals.
2. If people did not believe they were only chemicals, they would not believe that chemicals are beautiful things.
3. If people did not believe chemicals were beautiful things, Big Pharma could not sell them addictive and destructive chemicals.
4. Big Pharma wants to sell people addictive and destructive chemicals.
Therefore,
5. Big Pharma funds biologists to tell people they are only chemicals.

And what would that be?

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

Let S be the set of all statements.
Let z be the string "If x ∈ S, then x is false."
Assume z ∈ S.
If z is true, then z is false.
If z is false, then it is false that if x ∈ S, then x is false.
Therefore if z ∈ S, z is false, and it is false that if x ∈ S, then x is false.

Let z* be the string "z* is false and if x ∈ S/z*, then x is false."
Assume z* ∈ S.
Let S/z* be the complement of z* in S.
If z* is true, then z* is false.
If z* is false, then either z* is true or it is false that if x ∈ S/z*, then x is false.
Therefore if z* ∈ S, z* is false, and it is false that if x ∈ S/z*, then x is false.

Even biologists are running away from. — Rich

Jerry Fodor made a very similar claim about biologists en masse giving up the idea of adaptation. The LRB, which published a precis of his book about Darwin, received more than a few letters from evolutionary biologists saying this was hogwash, that there is no such flight from adaptation. The debate is worth reading and skimming.

Looks like a problem with entailment. — creativesoul

Well you know I don't agree there.

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.

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.

Gettier most certainly attributes belief that Jones owns a Ford to Smith. — creativesoul

No he really doesn't and I suspect it was deliberate.

and barns — creativesoul

From the Lycan paper I linked:

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.

I'm not sure where I went 'wrong'...

Seriously. Show me. — creativesoul

Those are from the first 5 pages:

So, Smith's belief is that Jones owns a Ford, and that each of the three propositions derived from that follow the rules of logic. — creativesoul

He believes that all three are true by virtue of believing p and accepting the rules of valid inference. — creativesoul

His believing that they are true is nothing more and nothing less than his believing that the rules of disjunction allow him to randomly add any other statement to his belief that p and then call it "true" as a result of his believing that p. — creativesoul

Jones owns a Ford or Brown is in Barcelona
Jones owns a Ford or Brown is in Boston

These are both valid inferences from a belief that p. Because p is false, they cannot both be true. They cannot both be true, because p is false and they state contradictory locations regarding the whereabouts of Brown. Smith believes that p, and has no idea of Brown's location. — creativesoul

He believes that p v q is true because he believes that p, and he believes that the rules of correct inference allow him to derive p v q based upon p. — creativesoul

There's nothing more to believing that (p v q) aside from believing that p, knowing that p v q follows from p, and knowing that if p is true, then so too is (p v q). — creativesoul

I have been at pains to show that belief that (p v q) is nothing more than believing that the rules of correct inference say that (p v q) follows from p. — creativesoul

Believing that (p v q) is true, if based upon belief that p, is to believe that if p is true then so too is (p v q). — creativesoul

These are from the last five pages:

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) — creativesoul

So, Smith believes p, and deduces (p v q) from p and accepts (p v q) as a result of this deduction. — creativesoul

Smith believes Jones owns a Ford. — creativesoul

He believes that 'Either Jones owns a Ford or Brown is in Barcelona' follows from 'Jones owns a Ford'. He believes Jones owns a Ford. He believes that 'Jones owns a Ford' is true. — creativesoul

He believes that 'Jones owns a Ford or Brown is in Barcelona' follows from 'Jones owns a Ford'. He believes that 'Jones owns a Ford' is true. He believes Jones owns a Ford. — creativesoul

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. — creativesoul

You can't seriously suggest that you haven't been arguing that Smith believed P∨Q only because he believed P, and that you almost continually, with a few momentary lapses, refused to allow that Smith actually believed P∨Q.

We were both wrong there. Gettier never attributes to Smith the belief that Jones owns a Ford. The only beliefs he ever attributes to Smith are (g), (h), and (i).

We were both wrong. Let's leave it at that.

I don't remember ever saying that. — creativesoul

Good one.

More specifically, do they all follow Gettier's above formulation and if so, do all the Q's involve disjunction? — creativesoul

Yes to the first, no to the second.

For instance, there's the dog-sheep:

You see in a field what looks to be a sheep and form the belief, based on direct observation, that there is a sheep in the field you are observing. But what you observe is actually a dog disguised (?) as a sheep. But there is in fact a sheep in that field; it's just behind a rise where you can't see it.

Your direct observation of the dog-sheep justifies your that there is a sheep in the field, and there is, but this doesn't seem like knowledge.

The upshot for our discussion here:

Everywhere I said all Smith's troubles flow from his having a false belief that Jones owns a Ford, I was wrong.

Everywhere you suggested that Smith really only believes that Jones owns a Ford, you were wrong.

Do they all involve disjunction? — creativesoul

No. Many involve something like faulty definite descriptions along the lines of Case I, and many involve more than a passing resemblance to the argument from illusion.

I suppose the SEP article is good, but I haven't looked in a while. I remember finding this article helpful.

Are there any other example besides Gettier's that place JTB under suspicion? — creativesoul

Do you mean besides all of the cases inspired by Gettier?

6. Smith's evidence for (f) justifies his belief that (h) — Srap Tasmaner

Should probably change that to:
6a. If the evidence for (h) is strong enough, it justifies Smith's belief that (h)
6b. Smith's evidence for (h) is strong enough (from 1 and 4)
6c. Smith's evidence for (h) justifies his belief that (h)

I think I'd read somewhere before that there are doubts about how Gettier's original cases are constructed, but I hadn't though much about it, as we had other fish to fry in this thread. (As I said before, no one particularly cares because it's the not these particular cases but the pattern that's of interest.)

At any rate, none of us paid much attention to this.

So the form of the argument is actually this:

1. Smith has strong evidence for (f)
2. If (f) entails (h), evidence for (f) is evidence for (h)
3. (f) entails (h)
4. Smith's evidence for (f) is evidence for (h) (from 1-3)
5. Smith accepts (h) on the basis of the evidence he has for (f)

He certainly could accept (f) on the basis of the evidence he has. If that evidence is strong enough for him to accept (h), it's certainly strong enough for him to accept (f). But as it happens, Gettier never says that he does.

6. Smith's evidence for (f) justifies his belief that (h)
7. (h) is true

Let's talk about something else for a moment.

Smith believes Jones owns a Ford. — creativesoul

Notice anything odd here:

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 (f), 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.

Where does Gettier say that Smith believes that Jones owns a Ford?

So Smith believes that the proposition "Either Jones owns a Ford or Brown is in Barcelona" is true because Jones owns a Ford, and he does not believe that the proposition "Either Jones owns a Ford or Brown is in Barcelona" is true.

Is that correct?

Does Smith believe that the proposition "Either Jones owns a Ford or Brown is in Barcelona" is true?

Does Smith believe that the proposition "Either Jones owns a Ford or Brown is in Barcelona" is true?

But he does not believe that the proposition "Either Jones owns a Ford or Brown is in Barcelona" is true?

So Smith does not believe that the proposition "Either Jones owns a Ford or Brown is in Barcelona" is true?

So Smith does believe that "Either Jones owns a Ford or Brown is in Barcelona" is true?

But he does not believe that Jones owns a Ford or Brown is in Barcelona, and he does not believe that "Jones owns a Ford or Brown is in Barcelona" is true?

But he does not believe that Jones owns a Ford or Brown is in Barcelona?

But he does not believe that Jones owns a Ford or Brown is in Barcelona?

Does Smith believe that Jones owns a Ford or Brown is in Barcelona?

So he does believe "Jones owns a Ford or Brown is in Barcelona" is true?

But he does not believe that Jones owns a Ford or Brown is in Barcelona?

So does Smith believe that "Jones owns a Ford or Brown is in Barcelona" is true?

EDIT: left off "is true".

Does Smith believe that pvq is true?

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) — creativesoul

Just to be clear, you are claiming that Smith does not actually believe that p∨q is true, right?

Smiths belief that:((p v q) follows from (p)) shows it. — creativesoul

No it doesn't. That's a conditional. It says only that if p, then p∨q. We have p, therefore we have p∨q.

And Gettier characterizes this conditional as a true belief of Smith. That is, p∨q does in fact follow from p -- it's not "merely", so to speak, a belief of Smith. It's one of Gettier's conditions that the entailment be correct.

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 that the first two premisses below cannot effectively exhaust...

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

Except you don't show the actual deduction of p∨q. In truth, it's barely a deduction at all. It's just or introduction.

(P v Q) is the conclusion to an argument. "Because" operates the same as "therefore." Smith believes (P v Q). Why? Because P and the rule of addition. — Chany

Yes. It's really that simple.

And because you can't assume that Smith knows the law of addition, Gettier specifies that he does; and because you can't assume that he actually makes the inference he is entitled to, Gettier specifies that he does.