Gettier wrote:
Imagine that Smith a)realizes the entailment of each of these propositions he has constructed and b)proceeds to accept (g), (h), and (i) on the basis of (f)...
"This immediately reminded me of Gettier 'problems' with the JTB account."
— creativesoul
There is a kind of connection to the argument here. Gettier cases are examples of epistemic luck -- you have a belief, it's true, it's got something that counts as justification, but the proposition believed to be true is true under a different interpretation than the one you intended, and our intuition that these are not examples of knowledge is because the justification you had fit the interpretation under which your sentence was false, not the one under which your sentence was true. (That's probably not all cases -- if it were, I would have just solved the Gettier problem.)
There's another sort of luck that's even easier to get at because there's no question of knowledge at all: that's when you're asked a question on an exam (or a game show, whatever) and you guess -- and your guess is right! If you're asked when the Battle of Hastings was, "1066" is the right answer whether you've ever even heard of the Battle of Hastings or not, because truth is not the same thing as knowledge.
(Not getting into the disjunction thing yet, as I have an argument that uses disjunction still under litigation.) — Srap Tasmaner
C1. ((q) is not true)(from p1,p3) — creativesoul
Gettier wrote:
Imagine that Smith realizes the entailment of each of these propositions he has constructed and proceeds to accept (g), (h), and (i) on the basis of (f)...
...Smith is therefore completely justified in believing each of these three propositions. Smith, of course, has no idea where Brown is.
The exclusive/inclusive distinction is irrelevant here. Smith, given what he believes, posits all three q's as a means to create a proposition, not as a means to state belief. Gettier says as much. — creativesoul
Gettier wrote:
Imagine that Smith a)realizes the entailment of each of these propositions he has constructed and b)proceeds to accept (g), (h), and (i) on the basis of (f)...
...It is clear that Smith's belief that P is the grounds upon which he accepts that P ∨ Q, but by accepting that P ∨ Q he is committed to accepting all four possible models...
You wrote:
You're on the wrong track, in my view. I have explained why as best I can.
The idea I sketched a couple months ago, that justification cannot cross the boundary between one interpretation and another, is essentially the mainstream response to Gettier, that something is needed to guarantee the relevance of the belief's justification to its truth for that belief to count as knowledge. You must get the right answer for the right (sort of) reasons.
Gettier wrote:
Imagine that Smith a)realizes the entailment of each of these propositions he has constructed and b)proceeds to accept (g), (h), and (i) on the basis of (f)...
Gettier continues:
...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.
creative wrote:
This immediately reminded me of Gettier 'problems' with the JTB account.
Srap replied:
There is a kind of connection to the argument here. Gettier cases are examples of epistemic luck -- you have a belief, it's true, it's got something that counts as justification, but the proposition believed to be true is true under a different interpretation than the one you intended, and our intuition that these are not examples of knowledge is because the justification you had fit the interpretation under which your sentence was false, not the one under which your sentence was true. (That's probably not all cases -- if it were, I would have just solved the Gettier problem.)
There's another sort of luck that's even easier to get at because there's no question of knowledge at all: that's when you're asked a question on an exam (or a game show, whatever) and you guess -- and your guess is right! If you're asked when the Battle of Hastings was, "1066" is the right answer whether you've ever even heard of the Battle of Hastings or not, because truth is not the same thing as knowledge.
(Not getting into the disjunction thing yet, as I have an argument that uses disjunction still under litigation.)
Srap continued:
That was a couple months ago in the "'True' and 'Truth'"" thread, and might be worth revisiting now.
P ∨ Q has four possible models:
(1) P=0, Q=0
(2) P=1, Q=0
(3) P=0, Q=1
(4) P=1, Q=1
The gist of the above remarks was that, to take Case II as the example, Smith's justification relates to the models in which P is true (2 or 4), but it turns out P ∨ Q is in fact true under the third model, in which only Q is true.
Gettier set out Smith's thought/belief:
...Imagine that a)Smith realizes the entailment of each of these propositions he has constructed and b)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 has false belief. There is no issue with JTB. — creativesoul
Smith's belief that:((p v q) is true because (p) is true) is not equivalent to belief that:((p v q) is true) — creativesoul
Gettier wrote:
Imagine that Smith a)realizes the entailment of each of these propositions he has constructed and b)proceeds to accept (g), (h), and (i) on the basis of (f)...
"Donald Trump is the President" is not existentially contingent upon "Donald Trump is the President because he won the popular vote." You can arrive at the former without going through the latter. That is not the case with Smith's thought/belief process. — creativesoul
That doesn't follow from Gettier's description of Smith's thought/belief processes Michael. — creativesoul
p1. ((p) is true)
p2. ((p v q) follows from (p))(from a)
p3. ((p v q) is true if either (p) or (q) is true)(from a,b)
C1. ((p v q) is true because (p) is true)(from p1,p3)
C2. ((p v q) is true)(from p3,C1)
I believe that X entails Y, I believe that X is true, and so I believe that Y is true. But X isn't true. This is the same as in Smith's case.
You wrote:
p1. ((p) is true)
p2. ((p v q) follows from (p))(from a)
p3. ((p v q) is true if either (p) or (q) is true)(from a,b)
C1. ((p v q) is true because (p) is true)(from p1,p3)
C2. ((p v q) is true)(from p3,C1)
p1. "John is a widower" is true
p2. "John was married" follows from "John is a widower"
p3. "John was married" is true if either "John is a widower" or "John is a divorcee" is true
C1 "John was married" is true because "John is a widower" is true
C2. "John was married" is true
You wrote the following:
p1. "John is a widower" is true
p2. "John was married" follows from "John is a widower"
p3. "John was married" is true if either "John is a widower" or "John is a divorcee" is true
C1 "John was married" is true because "John is a widower" is true
C2. "John was married" is true
You wrote:
..But John isn't a widower; he's a divorcee. According to you, if I believe that John is a widower then I cannot have a true belief that John was married, because what I really have is the false belief that John was married because he is a widower.
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