You have p as a premise — Srap Tasmaner
The point is that if I'm asked what would follow if ¬p then I would withdraw the disjunction rather assert q. — Michael
S believes {1. p , 2. (p v q)}
Reality {3. ¬p , 4. (¬p v q)}
Logic (p v q) & (¬p v q) → q — unenlightened
The third step makes no sense in context. — Michael
Yes it does. It expresses the part of the story where Gettier infallibly tells us That Smith is wrong about Jones owning a Ford. It's like when God says "Let there be light". It is so, whether He has gotten around to giving you eyes or not. That's another teaching story, but it works the same way - the story is the story and you have to make sense of it the way it is. — unenlightened
The bit in bold is the bit that doesn't make sense:
(p ∨ q) ∧ (¬p ∨ q) → q
It's not that at all. It's:
B(p ∨ q) ∧ (¬p ∨ q) — Michael
Belief has to reach an accommodation with them or talk nonsense. — unenlightened
So I don't actually understand your criticism. — Michael
S doesn't believe (p v q) unconditionally as Gettier and others here claim, but the conditional, "If really p, then (p v q)". — unenlightened
Now, how do you test "If really p, then p v q"? — Srap Tasmaner
The sort of thing science busies itself with is connected disjunctions - "the glass contains water or vodka" - and then we get the hydrometer out. "The glass contains water or my neighbour has a beard" is not something it is sensible to consider, never mind claim as a belief, or try and test. — unenlightened
If Smith has a justified belief that the glass contains water, why would he want to think, claim or believe that it contains water or vodka? He wouldn't, he would think claim and believe it contains water - wrongly. The circumstance where he would perhaps form the disjunction is if he saw that it contained a clear, colourless liquid, and that someone had sipped from it (not white spirit then), but didn't know exactly what liquid. If he thinks he knows what is in the glass, he has no reason to think the disjunction. And then it is as arbitrary and pointless as an unconnected disjunction.Then what if Smith has strong evidence to suggest that it's water but in fact it's vodka? He has a justified true belief that "the glass contains water of vodka". — Michael
Science doesn't formulate unconnected disjunctions and then try and establish which arm is true. — unenlightened
it could always turn out to be the truth of q reinforcing your belief that p. — Srap Tasmaner
Gettier just constructs an artificial example to show how this works. It happens when you think you're testing p but you're actually testing p v q v r. — Srap Tasmaner
trying to save it from the disjunction case seems like a wasted effort anyway. — Michael
You wrote:
If I believe that the statement "Jones owns a Ford" is true and written in this book, and if I believe that "Brown is in Barcelona" is also written in this book, then I believe that the statement "one of the two statements written in this book" is true.
How is that any different to saying "I believe that this or that statement is true"? Or "I believe that 'Jones owns a Ford' is true or 'Brown is in Barcelona' is true"? Or "I believe that Jones owns a Ford or Brown is in Barcelona"?
You wrote:
I think what you're doing is conflating Smith's argument and Gettier's argument.
Smith's argument is:
1. p
2. p ⊨ p ∨ q
3. p ∨ q
He recognises it as valid, he believes the premises, and so he believes the conclusion.
Gettier's argument is:
1. Smith believes p
2. Smith believes p ⊨ p ∨ q
3. Smith believes p ∨ q
4. ¬p
5. q
6. p ∨ q
Smith's belief 3 is true because of 6.
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