JustJim wrote:Moonwood the Hare wrote:I find a large chest filled with small boxes and I open a box at random and find that it contains 107 red marbles. What is the probability that all the other boxes contain 107 red marbles. On the basis of that one find I have no way of predicting whether the other boxes contain marbles or whether they are red. The probability remains at zero. Suppose I open a second box and find this contains 113 green marbles. I know more than I did because I have falsified the claim that all the boxes contain red marbles. This has not changed the probability at all. Single observations do not raise the probability above zero and in terms of mathematical probability even if there are a thousand boxes and I have opened 999 of them and they are all full of red marbles the probability that the final box will contain red marbles remains at zero.
Suppose someone intervenes at this point and, holding a gun to your head, says, "What color are the marbles in the final box? Answer the question! If you don't answer, or if you answer incorrectly, I'll blow your brains out!" What would your answer be?
If you're like the rest of us, I think you'd say the marbles in the final box are red. But why? If the probability that the marbles in the final box are red is ZERO, what makes virtually all of us, if our lives depend on it, answer that those marbles are red? If it's not probability, then what is it? Surely, the marbles might NOT be red, but, after the first 999 contained red marbles, would you predict any OTHER color for the marbles in the final box? Of course not! But WHY not? Why do we think that answering "red" is our best chance for keeping our brains inside our heads?
Do you think our unconscious minds nearly instantly go through all those reasoning processes you outlined in the rest of your post and determine that red is the best answer to the question, given the information we have? If so, what would you call that? If we're not somehow "calculating the odds" that the marbles in the final box are red, then what ARE we doing? It's not intuition, it's not pure guess work, it's not the same as flipping a coin... so what is it?
Well I'd say it's a personal judgement, a gut reaction, and that it is totally right to go with your gut reaction especially in a life or death situation; I think our evolutionary programming has prepared us to do that and do it well. I would say ultimately science rests on personal judgement that it is not purely objective and that there is nothing wrong with that. I think Popper's is the best attempt to square science and reason and ultimately it fails. Science is not a purely objective purely rational activity.