Un wrote:...
But since there is in fact no connection between p and q, there is no justification for saying it.
Michael wrote:
If I believe that my child is eating cake, and if I believe that three children are eating cake, then I believe that the statement "my child is one of the three eating cake" is true. This seems perfectly reasonable.
Nothing at all unreasonable there.
I would just note something that is not like Gettier Case II. Michael is talking about combining two separate beliefs of his own. Case II only uses one belief of Smith's.
The similarity is that what's being derived has two different sets of truth conditions being combined into one. That is notable, I think, because of the historical notion of "proposition". A disjunction is called a "proposition", as is a conjunction. However, a disjunction consists of two separate propositions, each with it's own set of truth conditions, and in Case II, one of which need not be believed by the speaker/author.
Propositions are not equivalent to belief. — creativesoul
Exactly so. which is to say it is rhetorical. It only follows and then trivially if he is right about Jones.The justification for Smith saying it, is the fact that there is no connection. "Either Jones owns a Ford or Brown is in Barcelona" is Smith's certainty being put on display. The problem, of course, is that Gettier's account is inadequate for properly representing Smith's believing the disjunction. — creativesoul
This changes with Gettier though. Gettier knows Jones does not own a Ford. Gettier knows Brown is in Barcelona. Gettier also knows that Smith believes the disjunction because Smith believes Jones owns a Ford. If we fill out my solution with Gettier's belief we arrive at a different disjunction(s) than Smith. None of which are problematic. — creativesoul
Two kids, Bill and Ted. One of them is yours. If it's not Ted, it must be Bill, and if it's not Bill, it must be Ted. — unenlightened
Sure, but we're talking about belief. — Michael
But let's continue with this example, as you seem to be OK with it. — Michael
Let's not. Let's look at the formal implications of a disjunction that I laid out and you ignored. — unenlightened
p1. (B v T)
p2. ~B
c1 T
p1. (B v T)
p3. ~T
c2. B — unenlightened
p1. (B v T)
p2. ~B
c1 T
p1. (B v T)
p3. ~T
c2. B — unenlightened
That's an implication of p, that I am questioning. — unenlightened
What's the problem? — Michael
1. One or both of "Jones owns a Ford" and "Brown is in Barcelona" is false — Michael
Incidentally, the only mentions I can find of rejecting disjunction introduction are paraconsistent logics. — Michael
No that won't do. Firstly, it is more like your 3 than your 1. And secondly, they could both have been true. — unenlightened
1a. " Believably p, but conceivably ¬p." — unenlightened
2b. Believably (p v q) but conceivably (¬p v q) — unenlightened
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