mitchellmckain wrote:Moonwood the Hare wrote:I think the whole issue of swans on other planets is a red herring if number of possible swans on earth is infinite.
But an infinite number of swans on the earth is not possible and so an infinite number of possible swans does not support your thesis. All that does is diminish the probability of any particular possibility.
If there are an infinite number of possible swans and a finite number of actual swans and an even smaller number of observed swans and the only swans we can know about directly are the observed ones and if we have no way of knowing which possible swans are actual the thesis stands. If there is another way of knowing about the actual but unobserved swans that must take the form of another theory about all swans which in turn will be subject to the same limitations.
Moonwood the Hare wrote: While the nunber of actual swans is finite but immeasurable
But it is not immeasurable.
How would you measure it?
Moonwood the Hare wrote:If the number of potential swans is massively larger than the number of observed swans then the probability of all swans sharing the properties of the ones we have observed approaches zero.
Incorrect. You cannot presume that all possibilities are equally likely, and howeverr large the number of potential swans may be, "all swans" is a finite number and so your conclusion does not follow.
Nor can you presume that all possibilities are not equally likely so any claim that they are not must take the form of another universal theory. If all swans is a finite and measurable number then the earth as a whole is a single exhaustively searchable location; a point in Popper's sense and that does change things.
By infinite universe, do you then actually mean an infinite earth (and thus an infinite number number of swans on the earth) or that by "all swans" you mean all the swans that ever exist assuming that they exist and reproduce forever? Then and only then does the nonzero probability of a non-white swan being produced become a certainty.
I would say as long as the potential number of swans is infinite we have the nonzero probability unless we can treat the earth as a single point.
I am not sure where we are going just now. My may point for a long time has been to get rid of the idea of universal theories being probably true in the formal sense. Do you think there is a way of measuring the truth of theories in terms of calculable probability?