Note that I'm not saying: ◇(Kp ∧ ¬p)
From here:
1. It is possible that I know everything and am wrong about something
2. I know everything and it is possible that I am wrong about something
The former is false but the latter seems possible as the argument above shows. — Michael
Well, yes, you are saying that in some possible world here age might not be 30. — Banno
(2) is only true when the modality of 'possible' is alethic, or if we know that p fallibly. — Kuro
I suppose the latter is the implication of fallibilism. If knowledge does not require certainty then I can know everything even if I am not certain about anything. — Michael
I'm saying that she might not be 30 in the actual world. — Michael
But the actual world is a possible world...
So when you say that she might be 30 in the actual world, you are saying she might be 30 in some possible world... — Banno
The counterintuitive conclusion is that I could be wrong in believing that something is true even though I know that this thing is true. — Michael
A better would be something like "I believe that in the actual worlds, p, although in other possible worlds, ~p" — Banno
by having to explain a fairly simple notation while trying to make a point with that notation to neophytes. — Banno
Well, you can. You know that her age is 30 even if it might have been that she was 29. There's no paradox here — Banno
Not about things you know - they are true. — Banno
"I could be wrong" can be true even if I'm not wrong. — Michael
Can you give a real-life example or does this have to firmly stay in propositional logic?
Say about your own attributes for example. I know I am male, could I be wrong? I know I am caucasian, could I be wrong? etc. — universeness
I think the reason that this conclusion seems counterintuitive is that even if we claim to be fallibilists there is this intuitive sense that knowledge entails certainty — Michael
This strikes me as a somewhat counterintuitive conclusion. — Michael
Exactly. Good point!the only system that could prove a system was omniscient would have to be itself, omniscient. As only an omniscient would know all possible questions. — universeness
This is good. We must test and challenge our logic on a constant base! — Alkis Piskas
Even if my belief is true it is still the case that it could be false. — Michael
A necessary truth is one that could not have been otherwise. It would have been true under all circumstances. A contingent truth is one that is true, but could have been false.
When I say "I believe that you are American but I could be wrong" I'm not saying "I believe that you are American but I am wrong" and I'm not saying "I believe that you are American but in some other possible world I am wrong". — Michael
"I believe that you are American but I could be wrong" is sensible, and possibly true, even if you are in fact an American. — Michael
I'm not wrong then I can't be wrong, but then via modus tollens it then follows that if I can be wrong then I am wrong. — Michael
Draw that out for me...? — Isaac
Again, it's just not clear how you're getting here. The "...I could be wrong" cannot be true if the proposition is it's referring to is true. — Isaac
I just wonder ... If you know that 'p' is true, why do you have also to believe it is true? What does "belief" add to it? Anyway, knowledge is stronger than belief. Beliefs are not knowledge. A belief may be an opinion, a certainly and at most a conviction. But all these are relative. They lie on a scale of of certainty: from very low to very high. Knlowledge on the other hand is not relative. It refers to something absolute or definite. "I know that this is true." That's all. (If it is true or not for you or most people, it's another story.) On the other hand, saying "I believe this is true" is quite different. I leave a window of uncertainly open, however small.If I know that p is true then I believe that p is true. — Michael
(I had to look up "musings". :smile:) I don't think we can discuss this without going off thread! :grin:Do you have any philosophical musings about why we are compelled to do this, without going off thread! — universeness
"Mods" ... It seems it's my vocabulary day ... But I wan't so lucky with this one! :smile:You don't want to invoke the wrath of the mighty titans, labeled 'mods,' and their terrifying siren call! — universeness
I think this is a wise idea. Well, it was, because I already replied in here! :grin:)If you don't feel you can comment without going off thread then you could PM me a response if you want. — universeness
If I'm not wrong then I can't be wrong
Therefore, if I can be wrong then I am wrong — Michael
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