We then conclude that I could be wrong even if I know everything (and assuming that some p is not necessarily true): — Michael
I believe jgill is a mathematician but is he the best mathematician that has ever existed in human history? — universeness
If "aliens exists" is true then "aliens exist" is not false.
"is not" does not mean "is not possibly". ¬p does not mean ¬◇p.
Again, see the valid modal logic: — Michael
if "aliens exist" is true then "aliens exist" is not false, and it could not possibly be false without negating "aliens exist" being true — Janus
I thought the very basis of modal logic is that contingent truths, which cannot be false (obviously) could have been false (which means could be false in other possible worlds). — Janus
"Necessarily" always includes our world because it always includes all possible worlds. "Possibly" is explicitly non-committal on whether our world is the one described. If aliens are known to exist here, they are known to be possible; they may even be necessary, who's to say? But if you claim their existence is contingent, you're explicitly not claiming that in addition to existing here they don't exist here; you are claiming there is a possible world (maybe nearby, maybe accessible, whatever) in which they do not. Again: in that world, they do not; in this one, they still do. "Possibly not" just isn't about the facts here being different here. That rather misses the whole point. — Srap Tasmaner
I'm just talking about claims like "I believe that you are American but it's possible that I'm wrong". My claim is true if my belief is right and my claim is true if my belief is wrong.
I don't have any knowledge of your nationality whatsoever. — Michael
The 'possibility' of something is a measure of our uncertainty about it, so once we know x is the case, the possibility P(x)=1 which is the same as just x. — Isaac
So you reject fallibilism and claim that knowledge requires certainty? — Michael
We then conclude that I could be wrong even if I think I know everything (and assuming that some p is not necessarily true): — Michael
"It is possible that aliens exist" means [ There is at least one possible world in which aliens do in fact exist, and in that world it would be true to say "Aliens exist" ]. This might or might not be our ("this", "the actual") world. — Srap Tasmaner
As Janus, @Banno and I have all been arguing (I think) the matter is about what could have been, and the temporal aspect makes a difference. Here we are saying that our uncertainty about the present is low, but our uncertainty about hard determinism is higher. We know what is the case, but we're not so sure that it was pre-determined and so could never have been otherwise. — Isaac
Again, seems as the modals are being muddled. What we can conclude is that omniscience can know everything and yet things might have been other than they are; not that the omniscience might be wrong.
There's nothing more here. — Banno
As Janus, @Banno and I have all been arguing (I think) the matter is about what could have been, and the temporal aspect makes a difference. Here we are saying that our uncertainty about the present is low, but our uncertainty about hard determinism is higher. We know what is the case, but we're not so sure that it was pre-determined and so could never have been otherwise. — Isaac
When we admit to the possibility of being wrong we're not saying "I'm actually right, but in some possible world I'm wrong". We're saying "I might actually be wrong." That's fallibilism.
But when you know something, you are not wrong. — Banno
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
My claim that I might actually be wrong is true even if I'm not wrong. — Michael
And the way to make this consistent is to observer that if you know something to be the case in reality, you cannot be wrongin reality; but there might be an alternate state of affairs in which you thought you knew, but you were wrong. — Banno
I believe that aliens exist but I don't know that aliens exist. — Michael
My claim that I might actually be wrong is true even aliens exist and I'm not wrong. — Michael
If you know, you cannot actually be wrong. — Banno
I have a true belief and yet "I might actually be wrong" is true. — Michael
IF your belief is true in reality, it cannot be false, and so you could not in reality be wrong. — Banno
"I am not" doesn't mean the same thing as "I could not be". — Michael
I believe that aliens exist but I don't know that aliens exist.
I claim that I might actually be wrong.
My claim that I might actually be wrong is true even if aliens happen to exist and I'm not wrong. — Michael
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