> This conclusion seems paradoxical, because it implies that information has been gained about ravens by looking at an apple. I remember how I used to be confu

> This conclusion seems paradoxical, because it implies that information has been gained about ravens by looking at an apple. I remember how I used to be confused about ad-hominems. It's known as fallacious because "an opponent's credibility has nothing to do with the truth-value of their argument". Yet common sense dictates that if a pathological liar makes a proposition, it would be unwise to take their proposition at face value. At some point, I realized that my distrust was not directed towards the proposal per se, it was directed towards what a bayesian would call "the likelihood" [0]. I.e. how much the proposition changed my beliefs. Therefore, the reputation for pathological lying did not imply that the proposition was false, but that I should hold my beliefs constant (set likelihood to zero) as if the liar had never said anything at all. I think my initial confusion is similar to the raven's paradox because we're confusing the hypothesis itself (our prior) with the weight we assign the evidence (the likelihood). Let's consider the two proposals. The original proposition is "all raven are black". Modus Ponens says "black, given a raven". Now if I were to see a raven though a monochromatic lens, then I would expect to see a black raven without the lens. Now consider the contraposition "everything non-black cannot be a raven". Modus Ponens says "not-raven, given non-blackness". So if I were to see a green object, I would expect to not see a raven. In the original proposition, the raven was the signal while the color was the hypothesis. But in the contraposition, the color was the signal while the raven was the hypothesis. The insight here is that when we contrapose the claim, we also switch the hypothesis with the evidence. Therefore, the sentence I quoted above is incorrect because a green (non-black) apple doesn't provide information about ravens, a green (non-black) apple provides information about non-blackness. Namely, whether non-blackness is a strong signal of non-ravenness. E.g. suppose we saw a raven and, upon closer inspection, the raven turned out to be a green raven. The correct reaction is "huh, I guess raven-ness isn't such a reliable signal of black-ness after all". And suppose we saw a blur of green and, upon closer inspection, the green object was a green raven. The correct reaction is "huh, I guess non-black-ness isn't such a reliable signal of non-raven-ness after all." [0] I didn't know the terminology back then, but I vaguely understood the concept on an intuitive level.