If
X, Y and Z are possible future occurrences
that contradict each other. (future swans are white(X), future swans are green(Y), future swans are yellow(Z))
and
one of them
logically must occur (There is no way that future swans could be any other colour)
and
X, Y and Z all
have an equal chance of occurring
then
it is reasonable to believe that it is likely
that X or Y will occur. Because X Y and Z all have equal probability of occurring it is reasonable to expect that one of any two of the possibilities will occur. (one of two has a 66% chance of occurring)
Me and J were looking at this the other night and we thought there was a problem with it somewhere but now i dont see it so point it out if its still there.
Moving on to J's objection, I think it was something along the lines of "although this argument is sound.." or "even if this argument is sound... it would justify thinking that the swans will be grue". This is true! by the reasoning above it is reasonable to believe that at least the next one swan you see will be grue.
the objection can work for all kinds of things. any question phrased in the following way will lead to similar bizarre conclusions..
"on how many future occasions, in a row, starting with the next one i see, will...swans be grue? swans have big teeth? swans have two heads?
in all these scenarios the reasonable answer is "at least once" (by reasoning similar to the argument above)
A response to this objection is that it would be silly to expect anything but a contradiction when asking such questions.
for example there is no point in asking "on how many future occasions, in a row, starting with the next one i see, will...future swans be grue?" because you know you can ask the opposite question "...future swans be a colour other than grue?" and you will get contradicting answers.
However not all questions suffer this fate. take the question "on how many future occasions, in a row, will past pattern X continue?" This question is immune to the criticisms of the previous question because its opposite question doesn't lead to contradicting answers; "on how many future occasions, in a row, will past pattern X cease?" This question only has 2 possible answers: either "Once" or "Never".
The other questions we have looked at had an infinite amont of answers. this question however only has two so the reasoning we were using before doesn't work.
The reasoning relies on three (X,Y and Z)or more possible answers (X, Y, Z and so on for infinity ).
The criticism works against almost any question accept the "past pattern" question. that is why we can only use the kind of reasoning at the top of the page on the the "past pattern" question.
