Smith believes Jones owns a Ford. — creativesoul
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.
Gettier states:
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.
6. Smith's evidence for (f) justifies his belief that (h) — Srap Tasmaner
Are there any other example besides Gettier's that place JTB under suspicion? — creativesoul
Do they all involve disjunction? — creativesoul
...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.
More specifically, do they all follow Gettier's above formulation and if so, do all the Q's involve disjunction? — creativesoul
Srap:
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.
Gettier:...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
I'm not sure where I went 'wrong'...
Seriously. Show me. — creativesoul
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
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
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.
and barns — creativesoul
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.
...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).
Gettier most certainly attributes belief that Jones owns a Ford to Smith. — creativesoul
Gettier states it all rather clearly:
...I shall argue that (a) is false in that the conditions stated therein do not constitute a sufficient condition for the truth of the proposition that S knows that P. The same argument will show that (b) and (c) fail if "has adequate evidence for" or "has the right to be sure that" is substituted for "is justified in believing that" throughout.
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. 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. 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.
Get involved in philosophical discussions about knowledge, truth, language, consciousness, science, politics, religion, logic and mathematics, art, history, and lots more. No ads, no clutter, and very little agreement — just fascinating conversations.