How can you show "more" or "less" plausible with ">=" and "<="? It is the "=" part I struggle with. "Greater than or equal" means it can be merely equal, and if merely equal, how can it be said to be "more plausible"? In that case wouldn't the plausibility be exactly the same?
Yes, it can be equal. But it can also be unequal, and hence more or less plausible. That's all the inequality means. We haven't shown how much more or less unequal, because the premises do not give us any clue.
Thanks for reply. But since "can be" and "must be" are different, this still makes me think we can not conclude "more plausible" but only "might be more plausible" or "at least as plausible", something like that. The question bugging me here, is in the very common argument form of "if A then B; B; A?" can we conclude after evidence B that the probability of A has increased? It seems to me that we cannot, at least based on ">=", since one possibility is that it did not (= case). But it also seems to me that it IS reasonable to conclude that A has increased, based perhaps on some other ground? We've restricted all possibilities to the subset where B is always true. Then again, maybe that subset isn't a subset and just the set, lol. Ok so now I'm thinking we can conclude probability of A has increased, but provided we know that B is sometimes not true. Whew. Regardless, feel free to ignore this, I'm sure there are many demands upon your attention. I'm having a blast and appreciate you've worked through all this and come up with something more unique than I expected, even if I get stuck on a few points. Plus you've pointed out many good references I hope to jump into someday, to retrace your steps. So thanks again for doing all this. One other note, I use "plausible" and "probably" interchangeably. If that doesn't fit your definition could be the issue.
“BECAUSE I AM ONCE AGAIN IN TWITTER JAIL”
Thank GOD his highness St. Elon is SAVING FREE SPEECH!
Now I hope he gives us all free rides on the Hype-R-Loop.
I'm late to the party and surely missing something obvious, but I have to ask, why is
`Pr(not-B|C)=1`
given C=if A is true B is true, what is the provability of B being false.
if I know nothing of A, how can I be sure B is false given C is 100% certain?
Excellent question. That's a typo from thinking about truth tables. See the link for the truth table P -> Q.
In this case, it doesn't matter what Pr(not-B|C) is, as long as it's not 0, since the numerator is 0.
How can you show "more" or "less" plausible with ">=" and "<="? It is the "=" part I struggle with. "Greater than or equal" means it can be merely equal, and if merely equal, how can it be said to be "more plausible"? In that case wouldn't the plausibility be exactly the same?
Good question.
Yes, it can be equal. But it can also be unequal, and hence more or less plausible. That's all the inequality means. We haven't shown how much more or less unequal, because the premises do not give us any clue.
Thanks for reply. But since "can be" and "must be" are different, this still makes me think we can not conclude "more plausible" but only "might be more plausible" or "at least as plausible", something like that. The question bugging me here, is in the very common argument form of "if A then B; B; A?" can we conclude after evidence B that the probability of A has increased? It seems to me that we cannot, at least based on ">=", since one possibility is that it did not (= case). But it also seems to me that it IS reasonable to conclude that A has increased, based perhaps on some other ground? We've restricted all possibilities to the subset where B is always true. Then again, maybe that subset isn't a subset and just the set, lol. Ok so now I'm thinking we can conclude probability of A has increased, but provided we know that B is sometimes not true. Whew. Regardless, feel free to ignore this, I'm sure there are many demands upon your attention. I'm having a blast and appreciate you've worked through all this and come up with something more unique than I expected, even if I get stuck on a few points. Plus you've pointed out many good references I hope to jump into someday, to retrace your steps. So thanks again for doing all this. One other note, I use "plausible" and "probably" interchangeably. If that doesn't fit your definition could be the issue.