Posted: Jan 07, 2015 1:09 pm
Thommo wrote:If you don't know the probability distribution, it does rather beg the question what is meant by "probability", does it not?
Similarly excluding some unknown subset of possible designers of unknown size from a superset of designers, also of unknown size does not in fact show that the probability is less than 1, because we don't know the cardinalities of the sets involved (which is hardly surprising - we don't know anything about these sets, if they are even sets, rather than classes which are an improper domain for discussing probability in the first place). It still might almost surely be the case.
Also, we must not forget that the restriction of naturally generated universes to only those sustaining life is a choice made by an arguer for rhetorical effect, similarly the lack of restriction of gods to those gods who would choose to create via natural laws is a choice made by an arguer for rhetorical effect. Neither choice can or does reflect reality, or any real probability distribution.
If anything the argument is slightly worse than the completely fallacious fine tuning argument. It's absolutely riddled with holes. I can't understand why anyone would be able to see through one but not the other.
Mathematics is very precise and very technical. If you don't obey simple rules then you can't use terms like "probability". One is honestly better waving ones hands around and saying "it sounds about right to me" than invoking this kind of specious appeal to the authority of probability theory.
I can try and explain this on a more technical level if my attempts at speaking plainly aren't communicating the point precisely enough. I'm not sure it will be clearer, but it should be more accurate to do so.
But Thommo, it absolutely doesn't matter what exactly the real probability distribution is, or the total sizes of the sets.
As long as it is 100% on the one set, and less than 100% on the other, the actual sizes of the sets are irrelevant. What matters is that the probability is 100% on the one, that means what we observe will ALWAYS be the case on that hypothesis.
It doesn't matter if the other set is 10, 100 or infinitely infinite in total size, as long as the observed evidence is less than 100% of that size, it will have a probability below 100%. That is all we need to know.
=100% vs <100%. Then =100% wins, regardless of how big you make those two sets, or how much less than 100% it is.
There's nothing wrong with this argument. The question comes down to "how probable is what we observe on hypothesis X vs hypothesis Y"?
If one probability is greater than the other, and it is because it is 100% on X while it's <100% on Y, then it doesn't matter whether it's actually 99.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999%, or 20%, on Y, what we can say then is that there is some probability it could be different on Y. This is not the case on X, so the evidence is more probable on X, because it is 100% expected on X.