I think it does relate to Bayesian statistics. What you’ve been concluding, with all your observations, is not just “no ravens are red” but “all ravens are the same color AND that color is black.”
Given that conjunction, you can conclude that no ravens are red a fortiori.
The reason I think you’ve been intuitively concluding this is that the prior likelihood that a species is all one color is fairly high (we know plenty of species like that, like robins and bluejays), and the probability that you’ve sampled so many thousands of ravens and just happened to have not seen all the ones of other colors is fairly low.
Your discovery of a green raven throws that last supposition for a loop. Now what is more likely: that you’ve had a fair sample so far, and just have happened to have missed a green raven, or that you’ve been systematically biased in your sampling? Where did that green raven come from? A continent you’ve never been to, perhaps? What else might you find there?
Further, now the conclusion you were coming to (“all ravens are the same color AND that color is black”) is false, so you have to throw out that reasonable hypothesis that “this is one of the many species that is all the same color.” So now you’ve got a species that can be many colors. The a priori likelihood that those other colors includes red is suddenly much higher.
No, it doesn’t.
See…this right here. This is the kind of stuff that killed any interest I might have had in formally studying philosophy.
Sorry.
- SERIOUS PHILOSOPHICAL QUESTION
- PREMISE FOR A SKIT ON “THE MUPPET SHOW”
alls i know is this:
if god didn’t make little green apples, and all ravens are not black,
what is the flight velocity of the unladen sparrow?
and, seriously, it must rain in Indianapolis sometime in the summer, que no?
Counterpoint: Nuh-uh.
Until I see a rigorous mathematical derivation of this, I ain’t buying it.
Here’s how it works. You think all non-black objects are not ravens – which is logically equivalent to saying all ravens are black. But then one day you see something green, and…could it be a raven? Even though it’s a different color? In that case your hypothesis would be all wrong. You’d better take a closer look and…oh wait, it’s actually an apple. Guess it’s not a counter-example after all, and the theory is supported.
It doesn’t sound intuitive because it’s stupid, people don’t actually mistake apples for ravens, and so the amount of evidence it provides is so minuscule you’d never even notice it. But yeah, it’s technically non-zero.
And this is why I don’t buy it as even only technically true. Because in our hypothetical, there is never uncertainty. An apple is an apple, a raven is a raven, two separate and distinct categories that are not confusable, and so would be statistically independent. In a real-world situation, maybe there would be some uncertainty, and so some incremental evidence would accrue. But in a pure, hypothetical sense I don’t see any reason for it be true at all.
(ETA: Should add that I’m no statistics denier. I’m perfectly happy with the solution to the Monty Hall problem, for example. I’m just not convinced in this case.)
All right, that’s fair. Then in a pure hypothetical sense, we can say that if you checked every single non-black object in the universe and confirmed none of them were ravens, that would prove that ravens could only be black even if you’ve never checked any. Seeing this green object is an apple is the first step on that very, very long but not quite infinite journey.
unless you believe there’s a quantum branching multiverse where every possibility is expressed. then the journey probably is infinite.
there also might be some issues with just our own universe and the space time bubble. there are places we can never reach even traveling at light speed because of the expanding universe. and the ravens could have had a head start
I’m only talking about the universe this version of us inhabits, and as mentioned from a strictly theoretical perspective. In a multiverse where all possibilities occur there will obviously be some universes where ravens are occasionally green, talk reasonably well in Spanish, and so on.
But birds aren’t real™️
But they do mistake wives for hats, therefore
How about if I said “every 8-ball on this billiard table is black?”
If you then systematically gathered up every single non-black thing on the table (including any cues and little bits of chalk), and you checked them out and confirmed that none of them was an 8-ball, would you be satisfied that my statement was correct?
I think you should be.
That said, I think the real issue is mixing True/False formal logic statements with statistics. The truthfulness of the statement “All humans are mortal” has nothing to do with us gathering “evidence” that there are lots of mortal humans. Logical proofs, of the “Logic 101”-kind – propositional and predicate logic – have nothing to do with incremental evidence and statistics. The statement is either true or not.
I think this is what rubs people the wrong way with the idea that a green apple is a piece of “infinitesimal evidence.” It’s a category error with the way people want to think about the initial statement, because now we’re talking about statistics and inductive logic.
I see a black bird and I want to paint it red….
Ok, this works better for me. At least, running possible objections through my head has not resulted in anything that works. Gotta think on it a bit more, though. 
