1: You say "all the possible future variations concerning a particular state of affairs are known" and that there is a "similarity is present among the majority of the possible states of affairs".
Therefore we know that among the possible outcomes there is a majority with similarity 'x'.
So if asked to make a prediction on whether 'x' will occur or not, clearly the probability is greater than 0.5 (the definition of 'majority') and thus "more reasonable to believe".
On this basis I say it is impossible in this case that "no probability can be assigned concerning the potential occurrence to those states of affairs".
Furthermore, your conclusion "it is reasonable to believe that an outcome will occur in which the similarity is present." seems simply to be a rewording of 'more probable.' The 'no probability' premise is an attempt to bracket off probability and bring in your account of 'reasonable', but they are one in the same and the 'no probability' premise is false.
2: In the dice example, you say there is a die (6 faces, it will land on one of them) and the claim is:
"It is more reasonable to believe that it will land on a face higher than 1 than it is reasonable to believe it will land on 1"
In a single roll, there is a 1/6 chance it will land on 1, and there is a 5/6 chance it will land on not-1.
Changing 'probable' for 'reasonable' does not change the fact that this is a prediction based on the outcomes of 5/6 vs 1/6, where anyone can see 5/6 is "more reasonable to believe".
3: the same issue of swapping 'probable' for 'reasonable' is the case in your next example:
"It
is more reasonable to believe that the pattern will continue at least
once than it is reasonable to believe that the pattern will not continue
at least once."
has the same form as:
'the pattern will continue at least
once' is more probable than 'the pattern will not continue
at least once.'
You can only get to 'more reasonable to believe outcome x over outcome y' through a probabalistic principle.
yes a probabilistic principle is assumed in both predictions. This principle is the argument stated at the top of my last post. Also note that the dice should not be considered fair. the chances of the dice landing on any face are not equal but unknown, like the chances of the pattern continuing any particular number of times is unknown.
ReplyDeleteEither the dice is has known probabilities (these don't necessarily have to be exact probabilities) and it's reasonable to bet on a side other than "1", or it has truly unknown probabilities and it's unreasonable to assume that it won't land on "1", because the "1" square could be a mile wide.
ReplyDelete-M
I assume that the dice will land on a number higher than 1 (not 1) as apposed to landing on 1. you say this is unreasonable because 1 may have a higher chance of occuring. this does not show that it is unreasonalbe. to choose "1" over "not 1" is to assume that "one" has a higher chance of occuring (an unjustified assumption) to choose "not 1" over "1" is to not make such an assumption.
Deleteyou do bring up the point that my argument relies on a premise such as "we must decide whether or not the pattern will continue". but if this is accepted it is intuitively more reasonable to assume that it will. to disagree is to say that we should assume 1 is more likely than not 1 which is silly because the probs are unknown.