There is a problem—length isn’t the only way to order hypotheses. If there was some other method of ordering that fulfilled the right conditions (even just some obvious function of length, e.g. length char value of the first letter), it could be used instead to order hypotheses, which would then be decreasing in probability on that* parameter instead. You could give bonus points for mentioning the Flying Spaghetti Monster if you wanted, and it would be a perfectly fine ordering.
Yes, it demonstrates that this statement is too weak to be really called “Occam’s razor”. But it doesn’t contradict the statement. Is this standard, to use “contradict” to mean “contradict the intended connotation of”? That seems confusing.
I feel like at the very least, a demonstration that the argument, while technically correct, doesn’t achieve the real-world implications it intended to should be taken as an invalidation of the point. I find that it is far too often that someone clings to the fact that their argument is technically correct even though it is irrelevant practically.
Not that anyone is doing that in this thread, as far as I can tell. But it’s something to watch out for.
There is a problem—length isn’t the only way to order hypotheses. If there was some other method of ordering that fulfilled the right conditions (even just some obvious function of length, e.g. length char value of the first letter), it could be used instead to order hypotheses, which would then be decreasing in probability on that* parameter instead. You could give bonus points for mentioning the Flying Spaghetti Monster if you wanted, and it would be a perfectly fine ordering.
That doesn’t in any way contradict this, that just demonstrates the fact that limits of sequences are invariant under a permutation of that sequence.
It quite thoroughly contradicts this, since it means that this isn’t a proof of Occam’s razor, merely a proof that there is some sequence.
Yes, it demonstrates that this statement is too weak to be really called “Occam’s razor”. But it doesn’t contradict the statement. Is this standard, to use “contradict” to mean “contradict the intended connotation of”? That seems confusing.
I feel like at the very least, a demonstration that the argument, while technically correct, doesn’t achieve the real-world implications it intended to should be taken as an invalidation of the point. I find that it is far too often that someone clings to the fact that their argument is technically correct even though it is irrelevant practically.
Not that anyone is doing that in this thread, as far as I can tell. But it’s something to watch out for.