Of course observing 99 black ravens doesn’t prove that the 100th raven will be also be black.
But which way are you going to bet?
Suppose I make a wager with you. I have a jar with 100 balls. I allow you to draw out 99 balls at random and observe their color. If you reached into my jar and pulled out 99 black balls, what odds would you give that the last remaining ball would be black as well?
Would you refuse to make such a bet? If I offered you an even money bet that the remaining ball was not black would you accept? It seems to me that after you’ve drawn out 99 black balls at random, odds of 99 to 1 that the remaining balls is not black would be fair. It would be foolish of you to refuse to bet if I gave you odds of 98 to 1 or better.
So the 99 black balls ARE evidence of the color of the remaining ball…if we are able to make certain assumptions about how those balls were selected. If we change the conditions and I don’t allow you to draw balls at random, but instead I look into the jar and hand you the ball of my choice, I’d agree that the 99 balls I showed you don’t provide evidence for the color of the remaining ball. Or if I was able to add extra balls after your 99 observations, or if I was able to change the color of a ball in your hand before you had a chance to observe it, and so on.
But human beings routinely bet their LIVES on things that aren’t “proven”. How do you know that apples aren’t poisonous? How do you know that the next time you step out of the house that you won’t fall into the sky? How do you know that when you turn around a leopard hasn’t crept up behind you? How do you know that when you say “Supercalifragilisticexpialidocious” it won’t cause the sun to explode?
All logic has to work this way, because for logic to “prove” anything, you have to accept the premises. All men are mortal, Socrates is a man, therefore that proves Socrates is mortal according to your logic. But how do you know that all men are mortal? How do you know Socrates is a man? What makes you willing to accept the premises? The only reason you have for accepting any premise is not deduction, but induction. You know that all men are mortal, but even if you deduced that from other premises, what caused you to accept those earlier premises? At some point you either have to throw up your hands and accept inductive reasoning, or declare that there are certain premises that you accept without proof.
And this is neccesary if you want to continue to survive, because how do you know that breathing and eating are neccesary for you to continue to survive? You can declare that you have no proof that human beings need to breathe to survive just because every living human being you’ve ever observed died if prevented from breathing. But if you don’t accept the need to breathe, you’re not going to be alive any more, and therefore you won’t be around to argue with any more. Every single living logician accepts inductive reasoning in their day to day life, the ones that didn’t wouldn’t be able to decide whether to drink water or hemlock.