john doran:
the definition is unhelpful simply because there is goingg to be no mere definition that will entail what you want it to entail: that there are no necessary truths (which is the necessary result of there being at least one world with nothing in it).
Funny thing is that you accuse me of trying to create the circumstances which would validate my position. I am simply trying to lay the groundwork to conduct a conversation, and I am taking pains to make as few assumptions as possible, and let the chips fall where they may. I am not interested in “winning” arguments here.
Indeed there are more definitions which have to be contemplated. Your argument, which you reiterated in this post (and I am grateful you did), has four different fundamental pieces: “possible world”, “being”, “existence” and “necessary”.
Of these, the concept of necessary is clear enough, we both mean the same thing by it: “if something exists in all the possible worlds, then its existence is necessary”. So far, so good.
Of the other concepts, I tried to give a short and very general definition of the “world”, making as few assumptions as possible. If and when we can agree on a suitable definition, then we can attack the problem of “being” and “object” (they go hand-in-hand) and then we can contemplate the problem of “existence”. It may be a long road, and if you do not wish to do it, I will accept it.
john doran:
look, the problem with your suggestion is that it makes nonsense out of our deepest convictions about the world .
I don’t think so. These are all considered axioms, self-evident truths. They are considered “true” in this world, the only one we actually know of. If you wish to postulate that they are true across all the possible worlds, you have to argue for it and not assume it. I am convinced that in any “world” which contains thinking beings, those beings will arrive at these truths, and in that respect I think they are universal.
But I don’t think that a question “Where were the rules of chess, before chess was invented?” (you see, I read the article you pointed out to me) is a valid question. By the same token one could ask: “Where was ‘East of Eden’ before Steinbeck wrote it?” Or “Where was the Rubik’s cube before Rubik thought about it?” These questions are sheer nonsense. I could take it a step further, and ask an even more absurd question: “Where is the variant of ‘East of Eden’ which Steinbeck would have written, if he had a constant migraine?” If one accepts the idea of “abstract objects” vs. “abstract concepts”, these questions are “legitimate”. I strongly deny this.
Our brain works with information, sometimes rearranges old information sometimes comes up with ideas that no one has ever though about before.
john doran:
we know and develop these things independently of experience, and believe that it is impossible that they could be false. we are certain of the truths of these disciplines in a manner that is categorically different (and higher) than the conviction we place in our conclusions in the empirical sciences.
Not independent of experience. The primitive people observed the world and one of them suddenly realized that “two” apples are more than “one” apple. That was the great conceptual breakthrough, and mathematics was “crerated”.
john doran:
in the end, philosophers have given all kinds of arguments to account for the special epistemological status of math and logic and the other a priori disciplines (formal sciences, if you will) without admitting that there is anything like necessarily existent abstract objects that ground the certainty, but none of them work.
What do you mean, they don’t “work”?
john doran:
the only positive argument i will present (again) is this: a necessary being is either necessary or impossible (it cannot just happen to begin to exist, nor can it just happen to cease to exist); if it is not impossible, then it exists (whatever it is, and however many of them there may be); but the concept of “necessary being” is not impossible (i.e. logically contradictory); therefore there is at least one necessary being.
I disagree with the highlighted part. Absolute zero degree is a hypothetical limit of temperature; when the Brownian motion of molecules slows down, the temperature drops; but it can never actyally achieve this theoretical limit. So this limit exists as a conceptual limit, but it does not mean that it exists in a physical manner.
Moreover this line of reasoning is distinctly tautological: A necessary being exists necessarily, because its existence is necessary.
