We know the relevant set to do so.

By seeing one green apple, you niether know the number of green apples, number of ravens, their relationship to each other nor to the rest of the world.

You can put no probability on what the presence of a green apple means for ravens.

You can put no probability on what the presence of a green apple means for ravens. — TheWillowOfDarkness

Yes you can. Observing a green apple increases the probability that "if something isn't black then it isn't a raven" is true from (1/x)ⁿ to (1/x)^{n - 1}, where n is the number of non-black things.

And so due to contraposition, observing a green apple increases the probability that "if something is a raven then it is black" is true.

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.

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

This doesn't address the point.

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 if 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)?

Out of curiosity, how do you deal with ontic uncertainty? Do you treat vagueness and propensity as elements of reality? — apokrisis

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."

Would you go as far as extending the principle of indifference to nature itself? — apokrisis

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."

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

I don't need to know the actual probability. It could be 1 in 10 or it could be 1 in a trillion. Whatever the probability is, (1/x)ⁿ is less than (1/x)^{n - 1}.

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.

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

We know that n isn't 0 given that we have an example of something that isn't black. So n is at least 1.

You don't. n may be 0 for black ravens. Knowing n= at least 1 for green apples doesn't give you number of black ravens.

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

The claim we're considering is "if something isn't black then it isn't a raven". Where n is the number of things that aren't black and 1/x is the probability that such things aren't ravens, the probability of the claim being true is (1/x)ⁿ before any observation and (1/x)^{n - 1} after the first successful observation (e.g. observing a green apple).

Therefore, observing a green apple increases the probability that "if something isn't black then it isn't a raven" is true.

x is the problem. If there are non-black ravens, x=0 and the probability is incohrent. Currently, you have no definition of x, so you can't say what's probable or not.

Now if you knew x, the probability of a non-black raven in a certain area, you could say how probable it was. But in that case, you already know and so have no need for green apples.

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

No, if there are non-black ravens then x wouldn't be 1. And given that there's a non-black non-raven we know that the probability isn't 0.

So, again, the probability that "if something isn't black then it isn't a raven" is true is increased by observing a green apple.

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 about it or not.

For your probability to function, x cannot equal zero. Non-black ravens must be known to be impossible-- which renders the probability useless in the way you are using it. We would already know there were no non-black ravens.

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

Where is this x = 0 coming from? x can never equal 0. So, no, in the instance of a non-black raven, x doesn't equal 0.

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.

So unless you can discount that possible (i.e. black ravens are impossible), your probability cannot function.

Only if we embrace a sloppy usage of "probability." You refuse to acknowledge the objective/subjective distinction. There is nothing strange about it. — aletheist

So, probabilities in this case must be either 1 or 0?

Well, given the existence of a green apple we know that the probability of a non-black thing not being a raven isn't 0. So, using your logic, the probability of a non-black thing not being a raven is 1. Therefore, the existence of a green apple is proof that if something is a raven then it is black.

If you don't like the conclusion then you must accept that the probability of a non-black thing not being a raven is greater than 0 but less than 1.

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

No it isn't. A green apple is a non-black thing that is not a raven. So the probability isn't 0.

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.

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

Yep and yep.

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

This is the tricky bit. I think you may be arguing towards the subjective as being real, and indeed the ultimately real. And I can't deny that Peirceanism heads in the direction of embracing frank idealism or panpsychism of that kind.

But I instead go in the other direction which would attempt to deflate "subjectivity" and reduce it to a scientific notion of pansemiosis. So there is a divide between the objective and subjective, the ontic and epistemic, the observables and the observer. But it is not a dichotomy of matter and mind, but matter and sign. The human observer becomes thus simply a highly complex and particular example of an ontologically general semiotic relation. And there is nothing causally mystic about a sign relation.

So when I talk about nature exhibiting the principle of indifference, it is in that deflationary sense. Nature really is a kind of mind, but only in the sense that minds are a kind of sign relation.

And with quantum physics especially, science now supports that. Quantum theory is not probabilistic in the standard sense (ie: there are hidden variables, so any sense of surprise is simply due to our epistemic ignorance of the details). Instead it supports the more radical view that events like the decay of a particle actually are just propensities. The world is set up in a general way as a state of constraint. Then after that, tychic chance or pure spontaneity takes over - because the world just doesn't care when some atom actually does go pop.

So when it comes to human concepts of probability, as I say, there is this sly trick going on. We impose deterministic constraints on the world (notions about what constitutes a fair coin toss, a fair roulette wheel spin, a fair shuffle of the deck) so as to ensure maximum epistemic uncertainty about the outcomes.

And that kind of modelling of randomness is great for pragmatic purposes. It really helps in constructing the human realm to divide our reality so clearly and counterfactually into the determined and the random.

But now getting back to metaphysics, we have to see past the very instruments we have constructed to "see the world more clearly". And that leads to the radical holism of firstness, secondness, thirdness, as you say. However then there is still a difference between accepting the traditional metaphysical dualism of objective and subjective as talking about world and soul, or matter and mind, and instead making the further radical break of following through pan-semiotically and seeing the mind as a species of sign.

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

You're talking nonsense.

No, you are ignoring the knowledge required to define a probability.

You see a green apple and say it must mean non-black ravens are unlikely, as if its presence meant there couldn't be that other non-black things of a particular type were likely.

Yet there might be a thousand white ravens sitting in the trees behind you.

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

I haven't said anything of the sort. What I've said is that observing a green apple increases the probability that "if something isn't black then it isn't a raven" is true.

That's sorts of true, but it has nothing to do with judging the chance of ravens being non-black.

An instance of a green apple means the probability of something non-black and not a raven is 1, and for anyone looking for something that is not a raven and not black, they have a higher chance of finding such an instance-- they might see this green apple we are talking about.

Doesn't tell us anything about the chance of non-black raven though, just that someone is more likely to find something that is not a raven and not black when it exists (as opposed to if it didn't).

That's sorts of true, but it has nothing to do with judging the chance of ravens being non-black. — TheWillowOfDarkness

Yes it does, due to contraposition. "if something isn't black then it isn't a raven" is logically equivalent to "if something is a raven then it is black". So, given that observing a green apple increases the probability that "if something isn't black then it isn't a raven" is true, it also increases the probability that "if something is a raven then it is black" is true. That's the paradox.

So, using your logic, the probability of a non-black thing not being a raven is 1. — Michael

Now you are losing track of the quantifiers. Given the observation of a green apple, the probability that some non-black thing is a non-raven is 1. It tells us absolutely nothing about the probability that all non-black things are non-ravens; that is still either 0 or 1.

No it doesn't. How have you derived that? Certainly not with the law of contraposition. — Michael

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.

The definition of logically equivalent is "Two statements have the same truth value in every model." It is evident that "all ravens are black" is not true in model #1, but true in model #2, yet "everything that is not black is not a raven" is true in models #1 and #2. Therefore "everything that is not black is not a raven" is not logically equivalent to "all ravens are black", according to the definition.

Yes they are. It's guaranteed by contraposition. — Michael

If contraposition guarantees a type of equivalence, then clearly it is other than "logically equivalent" as per your definition.

Here is the issue. Logically equivalent, as per the definition ensures that logically equivalent statements have the very same meaning, as you've been arguing. But two statements which are equivalent by contraposition do not necessarily have the very same meaning, as I've been arguing. Therefore logical equivalence, as per the definition, and "equivalence" as guaranteed by contraposition are not both the same form of "equivalence".

I think you may be arguing towards the subjective as being real, and indeed the ultimately real. — apokrisis

No, I am just taking exception to using the term "probability" for subjective confidence or degree of belief - as did Peirce, if I remember right. As a theist, physicalism is a non-starter for me; but as I said in the dualism thread, I am intrigued by Peirce's alternative of objective idealism, where mind is primordial and matter is the same "stuff" but with "inveterate habits."

I remember learning about this paradox and thinking it was kind of cool. My first response was: is there a problem? It might be that seeing a green apple does indeed provide a miniscule amount of evidence for the hypothesis that all ravens are black, but also that this miniscule evidence is provided to each raven color-hypothesis other than the green one, not allowing one to favor one over the other based on the evidence, and so making it of little help.

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

This is easier to understand if you use the phrases "if something is not black then it is not a raven" and "if something is a raven then it is black". The models are consistent.

It is a simple fact of logic that P → Q is logically equivalent to ¬Q → ¬ P.

If contraposition guarantees a type of equivalence, then clearly it is other than "logically equivalent" as per your definition.

No, it's logical equivalence. As explained here, "In logic, contraposition is an inference that says that a conditional statement is logically equivalent to its contrapositive", and as explained here, "In logic, statements p and q are logically equivalent if they have the same logical content. This is a semantic concept; two statements are equivalent if they have the same truth value in every model".

There really isn't anything to argue here.