You can put no probability on what the presence of a green apple means for ravens. — TheWillowOfDarkness
You don't know the number of black or non-black ravens. In seeing one green apple, you can't tell if the probability of a black raven is 99.999999999999999999999999% or 0.000000000000000001%, or any of the numbers in between, before or after.
For all you know, all ravens might be white. — TheWillowOfDarkness
Out of curiosity, how do you deal with ontic uncertainty? Do you treat vagueness and propensity as elements of reality? — apokrisis
Would you go as far as extending the principle of indifference to nature itself? — apokrisis
It shows your point is meaningless. You say that seeing a green apple allows you knowledge of the probability a raven is black, yet you do not name any relevant probability.
How exactly do you know the probability of you can't even define it (e.g. as 1/2 or 1/52, like the examples you keep bringing up, which supposedly reflect how you are using a green apple to tell the probability of a black raven)? — TheWillowOfDarkness
Not if n=0... which you have no way of discounting or naming a probability for. You do need to know the actual probably or we can't tell what applies in a given situation. — TheWillowOfDarkness
You don't. n may be 0 for black ravens. Knowing n= at least 1 for green apples doesn't give you n of black ravens. — TheWillowOfDarkness
x is the problem. If there are non-black ravens, x=o and the probability is incohrent. Currently, you have no definition of x, so you can't say what's probable or not. — TheWillowOfDarkness
The problem is when x=0, not when it equals 1. In the instance of non-black raven, x=0, as the probability of the non-black thing not being a raven is 0. And this is true whether we know there's a non-black raven or not.
For your probability to function, x cannot equal zero. Non-black ravens must be know to be impossible. — TheWillowOfDarkness
Only if we embrace a sloppy usage of "probability." You refuse to acknowledge the objective/subjective distinction. There is nothing strange about it. — aletheist
But that's the whole point. In an instance of a non-black raven, the probability of a non-black thing that is not a raven is 0. — TheWillowOfDarkness
If by "vagueness and propensity" you mean what Peirce called 1ns and 3ns, then yes, that is the working hypothesis that I have currently adopted and continue to explore. So by "ontic uncertainty," I assume you mean what he called "absolute chance." — aletheist
Again, it depends on exactly what you mean by that. As should be clear by now, I am opposed to using the term "probability" when what we really mean is (subjective) "confidence" or "degree of belief." — aletheist
Yes, but that doesn't help you. That only gives you n. You still don't know x. The green apple doesn't tell you non-black ravens are impossible, which is what you need to avoid incohrenence to the probability. — TheWillowOfDarkness
No, you are ignoring the knowledge required to define a probability in the world.
You see a green apple and say it must mean non-black ravens are unlikely, as if its presence meant there couldn't be other non-black things of a particular type.
Yet there might be a thousand white ravens sitting in the trees behind you. — TheWillowOfDarkness
That's sorts of true, but it has nothing to do with judging the chance of ravens being non-black. — TheWillowOfDarkness
So, using your logic, the probability of a non-black thing not being a raven is 1. — Michael
No it doesn't. How have you derived that? Certainly not with the law of contraposition. — Michael
Yes they are. It's guaranteed by contraposition. — Michael
I think you may be arguing towards the subjective as being real, and indeed the ultimately real. — apokrisis
Look Michael, take (2) as a proposition. "Everything that is not black is not a raven.". Now take the proposition "Everything that is black is not a raven". Is there any contradiction evident here which would exclude those two propositions from being consistent within a particular model? I don't see any. This is model #1.
Now take a model which has as a proposition "All ravens are black". This is model #2. Model #2 is not consistent with model #1 because "all ravens are black" contradicts "everything that is black is not a raven. — Metaphysician Undercover
If contraposition guarantees a type of equivalence, then clearly it is other than "logically equivalent" as per your definition.
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