Raven paradox

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How is that a paradox?

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Posting because Veeky Forums needs more analytic philo.

It's not a very strong paradox, if you choose to retain that induction can prove anything, then the power of a non-black thing being equal to a raven can be justified in that the converse would completely disprove, i.e. a non-(non-black nonraven) the theory.

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I don't get it. That's the just the contrapositive of all ravens are black

the paradox is that proof of the contrapositive such as finding a yellow mango, is equally as strong as actually finding a black raven, it would be like me, having never seen a crocodile before, looking at a white mug and thinking, this is proof that all non-green things are non-crocodiles.

whether or not you think it's an actual paradox depends on how you think science works.

I fucked that up, the white mug would prove that all crocodiles are green, because it gives evidence to all non-green things being non-crocodiles.

The absence of evidence is evidence of absence.

>Nicod's criterion says that only observations of ravens should affect one's view as to whether all ravens are black. Observing more instances of black ravens should support the view, observing white or coloured ravens should contradict it, and observations of non-ravens should not have any influence
How is this a solution to the paradox? He just restates what we intuitively think without any logical arguments

Still not getting the paradox. If I combed through the set of all non-black things, and did indeed find all of them to be non-Ravens, where is the paradox? It is simply a true statement.

All non-odd integers are non-primes.

How is that a paradox?

That's not even true. Can we have a formal statement of the paradox?

It's not meant to be a solution just an explicit statement of the problem.

I agree, it's not a paradox. the problem only arises when you don't use probabilities, such as in classical logic, and can only derive true or false from statements.

Principle 1 (Nicod's condition) In the absence of other evidence, the evidence that some object is both F and G confirms that all F are G.

Principle 2 (Equivalence condition) If evidence confirms a proposition then it also confirms any proposition that is logically equivalent to that proposition.

Principle 3 In the absence of other evidence, non-black ravens do not confirm that all ravens are black.

This is a trilemma, one of these conditions must be false.

>Drops raven in purple paint
Your move, brainlet.

if you paint a raven white or find an albino raven it is still a raven
so his mind should be very easy to change or else he's just being irrational and refusing to admit he is wrong.

It's not properly a paradox; it's simply counter-intuitive. The idea is that I claim all ravens are black, you ask me for evidence, and I show you a bunch of purple grapes.

Which is equivalent to

It's not very counter intuitive.
The space of ravens is far smaller than the space of non-black things so gathering x ravens that are black provides a lot more evidence in favour of the statement "all ravens are black" than gathering x non-black things that are non-ravens does to provide evidence in favour of the statement " all non-black things are non-ravens".

In examples where the sizes of the two spaces are more equal then it would be much more viable to find evidence in this way

This is neither a paradox nor counter-intuitive.

If A therefore B is assumed true, then not-B therefore not-A is also true.
If you are a raven then you are black
If you are not black then you are not a raven

So a red apple can be taken as evidence that all ravens are black. Weak evidence, admittedly, but it supports the proposition.

But what if you say "All men are less than 12 feet tall"?
Every 5 or 6 foot man you find supports the proposition.
Then you find an 11 foot man.
This is ALSO evidence that the proposition is true -- but you start to wonder!!!

event A is evidence for event B if P(B|A) > P(B)

the event of finding an 11 foot man is not evidence for all men being less than 12 foot tall. It makes it less likely than prior the event of finding an 11 foot man because finding a man who is 11 foot makes it much more likely that there is a guy who is 12 foot or greater out there.

The paradox is that our intuition about what constitutes as proof that all ravens are black is wrong

Why is this a paradox? The logical structure is not paradoxical.
It only shows problem with simple induction.

It's not. It's a paradox in the sense that simpson's paradox is a paradox

>The absence of evidence is evidence of absence.
Wrong.

2 is a non-odd integer, therefore 2 is a non-prime?

I don't think those are equivalent. Showing purple grapes is not absence of evidence; it is positive evidence in favor of the claim.

>It's not very counter intuitive.
Perhaps not to you, but I think in daily life people would never accept a handful of grapes as being evidence of anything at all about ravens.

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Agreed. An 11 foot man is supposed to increase your CONFIDENCE that there are no 12 foot men, just as all non-black objects which are not ravens increase your confidence that all ravens ARE black.
But confidence is all it is. It's not a proof. A single albino raven would constitute a disproof.
What's funny about the 11 foot man is that it, logically, SHOULD increase your confidence but actually decreases it.

That's easy. All I need is a nutcracket and some cooperation on the part of the guy whose mind needs changing.

>I think in daily life people would never accept a handful of grapes as being evidence of anything at all about ravens.
That's because it's infinitesimally compelling evidence, which means it effectively isn't evidence.
The total number of non-ravens is in fact infinite because there's no limit on what you can identify as an object that counts as a non-raven. You could count abstract objects for example and then you wouldn't even be bound by real world physicality, or you could count just real world objects but use an infinite number of different approaches to classifying them e.g. a chair vs. the assembly parts of a chair like its legs vs. the wood of the chair vs. the molecules of the wood vs. the atoms of the molecules etc.
So while both:
A) An instance of an observed black raven and
B) An instance of an observed non-black non-raven
Would both technically be evidence for the claim, A would be a real number weighted amount of evidence (~16 million ravens in the world) while B would be a 1/ω weighted amount of evidence, which for most purposes means B is equivalent to zero evidence.
This explains why people don't intuitively think grapes say anything about the claim all ravens are black. Their intuition in this case is effectively true, equating 1/ω with 0 is something done formally all the time, and certainly acceptable for people to do informally in assessing what counts as evidence for a claim.