Are you using "entail" in some special sense? — Srap Tasmaner
Isn't this what "probably p" already says? Why do this superposition analysis at all? — Srap Tasmaner
Yes, you could use probably and possibly instead. I think the superposition idea is a neat way of doing it, but if we go your way, we have something like this:]S believes {
1. Probably p & possibly ¬p
2. p ⊨ p ∨ q
3. p ∨ q
4. p ∨ q ⊨ ¬p → q
5. ¬p → q
6. p ⊨ ¬p → q) }
7. ¬p (Gettier's stipulation)
Without the unadorned premise "p", one cannot make the move to (p v q), and Gettier's justified true belief that is not knowledge cannot arise. — unenlightened
So what? — unenlightened
The point is that if I'm asked what would follow if ¬p then I would withdraw the disjunction rather assert q. — Michael
Smith's belief that Jones owns a Ford is true if and only if Jones owns a Ford. — Michael
Smith's belief that Jones owns a Ford is false, Gettier insists. Jones does not own a Ford. — unenlightened
But this is not an issue with logic per see, but something else. That something else could be Grice's maxims, for instance.
So this is similar to the path of constraining justification: there are other rules besides logic in play. — Srap Tasmaner
Yes, you could use probably and possibly instead. — unenlightened
I think the issue is that whereas this is valid:
1. p
2. p ∨ q
3. ¬p → q
This probably isn't:
1. B(p)
2. B(p ∨ q)
3. B(¬p → q)
Perhaps relevance logic is more appropriate here, denying the disjunctive syllogism. — Michael
Well this second 3 is still a conditional. We don't yet have something like
4. B(¬p)
That would force is to conclude that q. Once we get 4, our beliefs are inconsistent and something must be done. — Srap Tasmaner
But this is not an issue with logic per see, but something else. That something else could be Grice's maxims, for instance. — Srap Tasmaner
Yes. But my point is that premise 1 is "p", not "probably p and possibly not p". — Michael
Whatever dude. As long as it is clear that you can't derive the disjunction. Annoyingly, Michael's quote ate my vital strike."Possibly" is already in the background underwriting "probably". — Srap Tasmaner
Perhaps relevance logic is more appropriate here — Michael
As long as it is clear that you can't derive the disjunction. — unenlightened
And I'm not willing yet either to give up using or forbid others from using standard rules of inference. — Srap Tasmaner
But my point is that premise 1 is "p", not "probably p and possibly not p". — Michael
Yes yes, premise 1 is p, the disjunction applies, and explosion happens such that Smith believes anything and anything because with authorial infallibility, ¬p. — unenlightened
We're just discussing what Smith believes. Specifically, does he believe p ∨ q? — Michael
And I still find this peculiar. Gettier tells us in so many words that he accepts (g), (h), and (i). The argument has to be that shouldn't or couldn't. I guess you could go with "wouldn't" but that's not especially persuasive. — Srap Tasmaner
Where does 1 come from? Smith does not believe Brown is in Barcelona, but he doesn't believe Brown is not in Barcelona.
If he did, the whole exercise makes no sense. — Srap Tasmaner
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.