His believing Q is exhausted by C1. — creativesoul
I've already refuted that attempt. — creativesoul
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.
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.
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...
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...
Gettier:
...Smith is therefore completely justified in believing each of these three propositions...
...S is justified in believing Q.
I agree Smith knows what the disjunction means.
Knowing what a disjunction means requires knowing what makes it true.
— creativesoul
Yes, and he believes it to be true. And it's true. So he has a true belief. — Michael
Looking at the problem again, notice that (p1) means that what unenlightened does is unconnected to the rain, whereas (c) makes just such a connection. — unenlightened
"London is the capital city of England or pigs can fly" is true if London is the capital city of England or if pigs can fly, and so if I believe that London is the capital city of England then I will believe that "London is the capital city of England or pigs can fly" is true. — Michael
I believe that there is no connection between the name of the capital of England and the aerial abilities of pigs. So I believe you are making an unjustified disjunction devoid of meaning. All you really believe, and all you can honestly assert is that London is the capital of England. As it happens, I can assure you that pigs can and do fly on a regular basis, but they invariably fly as baggage, so you are unlikely to have noticed them unless you are involved with baggage handling.
The relevance of this is that it solves the problems raised by Gettier, and prevents people from claiming as 'logical truth' certain things that are patent nonsense. — unenlightened
Surely you understand what I mean when I say that one or both of "London is the capital city of England" and "pigs can fly" is true? Because that's all the disjunction is saying. — Michael
Indeed, I understand and accept your conjunction as phrased in the first sentence, because there is a connection made between the statements mentioned as distinct from used concerning their truth or falsity. But this connection is not made when they are conjoined in use in the disjunction. A claim that mentions statements is not identical to a claim that uses them, and your use of quotation marks indicates that you understand that. — unenlightened
Regardless, you can always apply Gettier's reasoning to the second. — Michael
I don't think you can. Smith's belief that "at least one of two statements, 1 and 2, is true" is not the same as the belief that "statement1 and/or statement 2", for reasons that you have dismissed without criticism. — unenlightened
Why? — Michael
No rational person would think it's reasonable to believe A but unreasonable to believe A ∨ B. — Srap Tasmaner
Because the disjunction is explicitly saying that one or other may be false. So it does not say p is true it says p might be false, but in case p is false, then q must be true. And it also says that q might be false, but in case q is false p must be true.
But since there is in fact no connection between p and q, there is no justification for saying it. — unenlightened
"Probably A, but if not A then definitely B" — unenlightened
Because A ∨ B ↔(¬A→B), I guess.
That means ∨-introduction comes to P→(¬P→Q) for any Q, which, duh. — Srap Tasmaner
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