But all black things are not ravens, so you would also have to add it's direct definition. What you have then is so close to a raven, you might as well call it a raven. Non-ravens are other.

The fact that a raven is black doesn't mean mathmatically all non-black things are Non-ravens.

This statement doesn't make sense, part B of R2 is strange. I feel like I was taken on a ride.

Your statements do not falsify, R1 and R2.

You're honestly onto a red herring here.

The fact that a raven is black doesn't mean mathmatically all non-black things are Non-ravens. — Qwex

It does. We can symbolize "all ravens are black" as "R -> B". That's equivalent to "~(R ^ ~B)" or "~R v B" or "~B -> ~R", which we would say as "nothing is both a raven and non-black", "everything is either not a raven or black (or both)", and "everything that is not black is not a raven", respectively.

You're misunderstanding the relationship between Popper and Hempel. Popper uses Hempel's paradox as a disproof of confirmationism, not as a consequence of falsificationism. Hempel's paradox only follows from confirmationist inference, and the absurdities it leads to are a reason Popper gives to reject confirmationism, leaving falsificationism instead.

You're correct that under a confirmationist view, the non-existence of unicorns would be reason to believe the existence of God. And that is absurd. Which is why you should reject confirmationism, like Popper does.

But what a pointless expression that is.

It proves if unicorns exist God might/does exist.

All non black things are non-ravens, no all non black things are non black. I don't see where the relationship is between non black things and ravens. I believe it's lesser perception than what ravens are entirely.

We have only taken a raven partially, we think we have defined R with B so raven is fitted oddly into the statement. Non black things =/= non ravens, as math?

B = R.

Why if we take only a raven's black? The statement is tactile or means nothing. It is not a statement about fundemental nature.

You've created a random category.

A good question may be if black exists, might ravens exist?'

non black things =/= non black non ravens

Take a look at this image:



Everything in B is in A. Everything that is not in A is also not in B. Right? Obvious.

B = ravens and A = black things. Everything that's not black is also not a raven, because if it was a raven, it would be black.

That part isn't weird at all. That's just straightforward logic and sets.

The weird part is that if we think finding a black raven counts as evidence for "all ravens are black" (P), then finding a non-black non-raven (like a green apple) should likewise count as evidence that "all non-black things are non-ravens" (Q). But sentences P and Q are equivalent -- both sentences paint the same picture, like that one above -- so evidence for Q is the same thing as evidence for P. Which would mean a green apple is evidence that all ravens are black, if we accepted that we could make inferences from particulars to universals like that.

Which suggests that we shouldn't accept that we can make such inferences. A green apple, despite being a non-black non-raven, isn't evidence that all non-black things are non-ravens. A black raven, likewise, is not evidence that all ravens are black. No number of non-black non-ravens can prove that all non-black things are non-ravens, and no number of black ravens can prove that all ravens are black. You can't positively prove (or confirm) anything.

But you can disprove (or falsify) them. A single non-black raven would disprove both P and Q.

Why is B = R?

You might as well say ravens are black winged birds, etx. Rather than going through thought-process on primarily their blackness, consider whole ravens in the statement. All non raven things =/= non ravens. Implying a non raven raven.

All non black things =/= non-ravens

Nobody is saying black things EQUAL ravens. Black things are a SUPERSET of ravens; at least, that's the claim in question. That claim might be false; if a bloody red wounded raven counts as a non-black raven, then it is false. That's not the point.

"All ravens are black" is just an example of a hypothesis. Substitute what ever other terms you want. Pick some A and B such that maybe all B are A. It doesn't matter what you pick. If all B are A, then all non-A are non-B. So if you find something both non-A and non-B, that would count as evidence for "all non-A are non-B" just as much as finding something both B and A would count as evidence for "all A are B". And since those are equivalent, the non-A and non-B thing would count as evidence that all B are A. Which is absurd. So we shouldn't make inferences like that.

So a raven is a black thing? Okay, I'm with you.

all black things are black, all non black things are non-black. A raven is a raven.

l You're misunderstanding the relationship between Popper and Hempel. Popper uses Hempel's paradox as a disproof of confirmationism, not as a consequence of falsificationism. Hempel's paradox only follows from confirmationist inference, and the absurdities it leads to are a reason Popper gives to reject confirmationism, leaving falsificationism instead.

You're correct that under a confirmationist view, the non-existence of unicorns would be reason to believe the existence of God. And that is absurd. Which is why you should reject confirmationism, like Popper does. — Pfhorrest

Well said. Thank you very much for the clarification. Much appreciated.

My reasoning is as follows:

R1 = all ravens are black
Contraposition of R2 = all non-black are non-ravens

Observing green apples, red tomatos, etc. i.e. non-black non-ravens doesn't falsify the claim R1 because these observations don't falsify claim R2 and R1 is equivalent to R2. If so, then R1 remains unfalsified and should be, if there are direct confirmatory observations e.g. a considerable number of black raven observations, considered as a scientific claim - true for all intents and purposes.

Observing green apples, red tomatos, etc. i.e. non-black non-ravens doesn't falsify the claim R1 because these observations don't falsify claim R2 and R1 is equivalent to R2. If so, then R1 remains unfalsified ... — TheMadFool

Correct so far.

... and should be, if there are direct confirmatory observations e.g. a considerable number of black raven observations, considered as a scientific claim - true for all intents and purposes. — TheMadFool

Not so correct according to a falsificationist like Popper. A claim being scientific has nothing to do with whether it is true or not: there can be false scientific claims, like for example Modified Newtonian Dynamics as a theory of dark matter is pretty much known to be false now (because of the Bullet Cluster observation), but it's still a scientific claim. That's because it's falsifiable: if it were false, we could show that it was false (and in this case it is, and we have).

Most importantly, the falsificationist says that that "if there are direct confirmatory observations e.g. a considerable number of black raven observations" part means nothing. Finding a whole bunch of black ravens tells us nothing at all about whether all ravens are black, according to the falsificationist. And likewise finding a whole bunch of non-black non-ravens tells us nothing at all about whether all non-ravens are non-black. That's the key point of falsificationism: you cannot confirm things. Failing to falsify things still isn't confirming them. Every hypothesis starts off with the status of "possible", and then either keeps that status, or loses it if it's falsified. A bunch of failed falsifications never boosts its status higher than the initial status of just "possible".

So on a falsificationist account, finding a non-black non-raven has no impact on the likelihood of all ravens being black -- as we'd expect. That comes at the "cost" of the implication that finding a black raven also has no impact on the likelihood of all ravens being black. But that cost, the falsificationist argues, is much less; it's a little unintuitive, because we have confirmationist intuitions, but it's much less unintuitive than green apples proving that all ravens are black, and more importantly much less logically problematic than confirmationism, since that's just straightforwardly a case of affirming the consequent (as it's trivially fallacious to argue "if P then Q; Q; therefore P").

One more thing. There are two types of evidence to wit confirmatory and disconfirmatory.

In the case of the claim R1 = all ravens are black, a confimatory evidence would be one or more black ravens. Since R1 = R2 = all non-black are non-ravens, observing a green apple or a red hat i.e. observing non-black non-ravens would also be confirmatory evidence.

Why?

Consider a world of only birds with 5 black ravens and 5 white pigeons. Observing 3 black ravens would suggest a pattern viz. R1 = all ravens are black. Now, instead of R1 if we use the different but logically equivalent R2 = all non-black are non-ravens, we'd be looking at the white birds and checking if they're ravens or not.

A few white pigeons would be confirmatory evidence of R2 which, because R2 = R1, would also confirm R1. We may take the position that observing white pigeons as evidence for black ravens as absurd but if it is really absurd we should be able to get to a contradiction which isn't the case.

Also, in this bird world, it's possible to exhaustively search all non-black objects, here white pigeons, and from this conclude that R2 = all non-blacks are indeed truly non-ravens and the next step in the deduction is R1 = all ravens are black. In other words, no logical error can be detected in working from non-ravens to ravens.

The problem, it seems to me, is that claims like R1 = all ravens are black and R2 = all non-blacks are non-ravens have a huge domain of concern. It isn't practical to make a thorough exhaustive search for either all ravens or all non-blacks. Ergo, as so many have repeatedly asserted, confirmatory evidence simply lacks certainty in terms of proof. However, disconfirmatory evidence, despite being equally difficult to find, because it too requires the same level of thoroughness in our search for it, has absolute certainty in terms of ruling out as false claims like R1 = all ravens are black (universal affirmative claims, claims science is very fond of).

Not so correct according to a falsificationist like Popper. — Pfhorrest

Theory of gravity T1 = all matter are things that attract
R1 = all raven are black

We have inductive evidence that T1 and R1 are both true

Contrapositive of T1 = T2 = all things that don't attract are non-matter
Contrapositive of R1 = R2 = all non-blacks are non-ravens

We have evidence for both R2 (green apples) and T2 (thoughts don't exhibit attraction)

We have T1 and R1, both have confirmatory evidence and no disconfirmatory evidence. Ergo both T1 and R1 are acceptable as scientific claims. They can both be falsified but haven't been so.

The heart of the issue for me is statements like R2 = all non-blacks are non-ravens do not contradict their logial equivalents, the contrapositives, here R1 = all ravens are black. So, there's nothing actually absurd about it.

The issue isn't that R2 supposedly contradicts R1. Nobody thinks it does, not even Popper.

Popper's whole falsificationist program is saying that "confirmatory evidence" is no evidence at all. Only disconfirmatory evidence counts. That's why it's "falsificationism", the opposite of "confirmationism". It's explicitly anti-confirmationist.

There are more reasons to be anti-confirmationist than just this, but Hempel's paradox illustrates a problem with confirmationism. It's absurd to think that green apples tell you anything about the relationship between ravens and blackness. But because R2 = R1, it's equally absurd to think that black ravens tell you anything about the relationship between ravens and blackness. Falsificationism points out what's wrong with both of those things: they take evidence to confirm a hypothesis, when it can do no such thing. It can only falsify it.

Observing 3 black ravens would suggest a pattern viz. R1 = all ravens are black. — TheMadFool

Popper would say no, it doesn't. Well, maybe it suggests it, in an entirely non-rigorous way -- maybe seeing three black ravens gives someone the idea that maybe all ravens are black -- but it doesn't provide any evidence for it, on a falsificationist account. On a falsificationist account, you can come up with the idea that all ravens are black out of wherever you come up with it, even if you've never seen a raven, and its status is "maybe possible". Then you find a black raven... and that doesn't change its status. Then you find another black raven... still no change. You can find as many black ravens as you want and that tells you nothing at all about whether or not all ravens are black: it's still a possibility, but it already was a possibility. It's not until you find a non-black raven that anything changes.

Popper's whole falsificationist program is saying that "confirmatory evidence" is no evidence at all. — Pfhorrest

It's absurd to think that green apples tell you anything about the relationship between ravens and blackness. — Pfhorrest

you nothing at all about whether or not all ravens are black: it's still a possibility, but it already was a possibility. It's not until you find a non-black raven that anything changes. — Pfhorrest

You say that there's no such thing as confirmatory evidence but if I'm not wrong that everyday objects fell to the earth and the heavenly bodies revolved around others were considered as confirmatory evidence for Newton's theory of gravity, considered as the greatest scientific achievement of all time.

Coincidentally, Popper was moved by the failure to disconfirm Einstein's theory of gravity, relativity, which supplanted Newton's own theory. Point is the scientific method, in fact anything empirical, requires both confirmation and failure to disconfirm to prop it up.

Otherwise, as I realized sometime ago, we'd be committing the fallacy of argument from ignorance viz. if it's not false then it must be true.

Also how do scientists come up with theories? From observations that have a pattern and that means repetition and that in turn allows us posit a universal affirmative such as "all As are Bs". Claims aren't pulled out of thin air - they usually have some confirmatory evidence.


I understand now why Popper laid so much stress on falsifiability because he knew that many theories fit a particular data set i.e. all theories are confirmed but these theories are mutually inconsistent and so to get ahold of the truth we must eliminate all except one and for that we need disconfirmatory evidence for each.

NB that I’m not trying to argue for falsificationism here (though I do support it), just clarifying what it is and how it’s related to Hempel’s paradox. Hempel was not a falsificationist but a “hypothetico-deductivist” (which became the standard type of confirmationism, before “confirmationism” was a word).

NB that I’m not trying to argue for falsificationism here (though I do support it), just clarifying what it is and how it’s related to Hempel’s paradox. Hempel was not a falsificationist but a “hypothetico-deductivist” (which became the standard type of confirmationism, before “confirmationism” was a word). — Pfhorrest

I'm not saying you are. Anyway, very helpful. Thanks. :up: