Posted: Apr 24, 2011 2:40 am
Paul Almond wrote:
It seems to me that the issue here is what we classify as "a possible world". For example, I could easily say this, paraphrasing Swinburne:
"It seems coherent to suppose that there exists a world in which the Goldbach conjecture is not true, from which it follows that it is coherent to suppose that the Goldbach conjecture is not true, from which in turn it follows that the Goldbach conjecture is not logically necessary."
and the problem of this, of course, is that we can't be sure, right now, whether the Goldbach conjecture is true or not - but if it is true it seems that it is necessarily true - something which we seem to have just ruled out merely by being able to conceive of the possibility that it is not true.
Necessary existence is not the same as necessary truth, is it?
But I think I see your point: If the GC is possibly true, then it is possibly necessarily true; and if the GC is possibly false, then it is possibly necessarily false. To be possibly necessarily true/false is to be necessarily true/false, i.e. to be true/false in all possible worlds. So we cannot consistently say that the GC is true in some possible worlds and false in some other possible worlds, and we cannot consistently say either that the GC is both true and false in all possible worlds. All we can consistently say is that if the GC exists as a true/false proposition in some possible worlds, then it exists as a true/false proposition in all possible worlds in which it exists.
Paul Almond wrote:One thing I don't like about this subject is that some of the vocabulary can be hard to pin down.
Yes, indeed.