Again, my assertion is that it exists in reality in exactly the same way that it currently exists in reality. We haven't even touched on pi or sqrt(2), either. You can deny the existence, but then you are the one who has to deal with the reality of 1+1 in a universe with only one particle in it. If you object to the idea that 1+1 becomes meaningless in the reality of your single-particle universe, then you're the one who has something to resolve.

The reasoning is right in front of you. There's very little left to reason about it. If you claim that the lack of a sufficient number of particles implies the non-reality of bigger numbers, then you're the one with issues to resolve. They pose no problem from my perspective.

Who said that it's a calculation to "perform"? I doubt that anybody has yet computed 34897397852647896*239746128934621378946, but I maintain that these numbers are real and that the result is defined by reality (that is, there's a right answer, and lots of wrong answers, and this is a mind-independent reality).

What do you mean to "realize" it? 1+1=2 because it does, not because someone realized it. Just like gravity operates the way it does, even if minds were around to observe it happening.

This made me think of another point. In a universe with exactly one particle in it, what is the status of one-half? You don't even have two objects to create the denominator. Is it a real value? Does it exist in reality?

Just to add slightly to this (although there isn't much to add), it's a lot like setting up a physics experiment. If you arrange a bunch of objects in a box in a certain way, and then allow the universe to act on them (gravity, magnetism, whatever), then there is a set pattern of behavior that will be exhibited by the objects. And this behavior is not dictated by humans, simply observed. We do not *make* gravity act and we do not *make* the charged particles attract. They just do.

It's much the same way in mathematics. Once the axioms have been established (initial conditions), there are certain consequences that *necessarily* follow. This is not because of any sort of power we exert over the axioms or the logic. It just works out that way. We don't *make* the natural numbers have unique factorizations into primes (we don't *make* the primes, either). They just do.

In both cases, the "universe" (whatever it is) dictates to us the consequences, and the best we can do is try to make sense of it.

Aaron and bunny,

I'm making this up as I go along so it may take me a bit to formulate a response. Both of your responses were good imo.

Of course, I would say it has no status except if a brain were around to ponder what would happen if the particle were divided into 2. So let me makes sure I understand your position exactly...

You are essentially saying that numbers (and math) exist in this universe... Would exist in a universe devoid of particles... And would exist even if no universes existed! Is that correct?

I'd like to challenge you to think very hard about what nothing really is. What it would mean if no universes ever existed. It's not easy to do, because it requires that you shed biases and completely detach yourself from the way you view the meaning of numbers and math now. I'll do the same and try to think hard about numbers existing even if nothing else does. In the meantime, we're at an impasse. Btw...

What other things do you feel must exist even if nothing else does? I presume god would be one. Anything else? Evil, love, lust, right, wrong, good, and bad? Do these things fall in the category of things that don't need a universe (or a brain) to exist in? Also, I'm sure there is a name for this, but I don't know what it is. It's not empirical. Would it be existential truth or existence?

platonism?

It depends on what you mean by "in" here. I am saying (and have been saying) that the numbers exist, but are not dependent upon any particular physical manifestation for it to exist. I'm saying that these mathematical objects are real, mind-independent objects.

I also balk at the statement of "no universes existed" because I'm not sure what you mean by that. This is different from talking about vacuums and that sort of thing.

There comes a point where you're talking in absolutely meaningless terms. This looks like one of those cases.

This article is probably worth your time:

http://plato.stanford.edu/entries/god-necessary-being/

It's also *very* important here that the discussion of "mind-independent" is talking about minds *within* the universe, not the mind that sustains the universe. This is a subtle theological thing that I don't think is absolutely necessary to understand. You can replace "the mind of God" with "fact of reality" or something else like that (in the same way that gravity would exist even if humans weren't around to observe it -- assuming that you believe in the existence of an external universe that is not contingent upon your awareness of it to exist).

Mathematical objects are Mind Dependant, it's just an expression of reality. Like a language or images.

This, obv.

Good point. I have heard that math is considered a language. So does language exist outside of the universe in the same way that bunny and Aaron W think math and numbers do? Does "fire burns human flesh" exist in a universe with no fire or human flesh, just as 1+1=2 would? Do the English vowels of A,E,I,O,U exist independent of the universe?

This is not what is meant by math being considered a language. Math is a language in the sense that it is used to communicate ideas. It's not about reducing it to a collection of symbols. There would still be such as thing as "fire" even if we didn't have a name for it in English. And yes, fire would still burn human flesh even if we didn't have words to describe it.

I strongly suggest you slow yourself down and actually think about the topics at hand instead of chasing these tangents. I don't think they're quite as interesting as you believe they are.

It's endless, and therefore noone know's. You may be only a dream of a dream of someone.

Yeah. We experience the reality of our dreams the same as when we're awake. Other than convenience, there's really no reason to suppose the reality we experience when awake is "made up of" anything different than the reality of our dreams. Nor is there any reason to suppose that we're not all experiencing the same dream from different perspectives and there's really nothing out-there, or no out-there to begin with.

This isn't quite right. Modern philosophy of language began when Gottlob Frege, who was primarily interested in the foundations of mathematics, started trying to work out how ordinary language is a language in the same way that math is a language. In developing an ontology for arithmetic, he came to the conclusion that numbers were concepts and so were not different in kind from other concepts in ordinary language such as "fire," "horse," and so on. At the end, he'll argue that ordinary language is only possible because of the existence of a non-psychological and non-physical realm of concepts. So if you are going to accept the idea that mathematics depend on a realm of abstract objects for its soundness, then you might have to do so for language and logic more generally.

So the issue isn't whether fire would continue to burn you if you didn't have a word for it, but whether the concept of "fire" would exist even if there were no fires in a similar way that the concept of "one" would exist even if not instantiated in the universe (you can use a predicate like "red" instead of "fire" if you think "fire" and "one" are disanalogous).

Thanks for the clarification. I hope to read the Frege article when I have time. I was responding more to the second question (Do the English vowels of A,E,I,O,U exist independent of the universe?).

I'm curious (and maybe I'll understand better after I read the article) what this would say about the concept of "unicorns." We have a concept of a "unicorn" in a universe that (presumably) doesn't have any instances of it.

Yes, I think Tillich's views are relevant. To say that "G-d is a being" may be putting G-d in a "black box" which may be impossible, although I suppose that theists ( yours truly included ) and atheists are often guilty of this.

The ultimate state of reality is EMPTINESS.

*grunch*

No. If he created atoms, he cannot be made up of them.

In my view, yes.

It is interesting to me. Especially, since bunny agrees that vowels exist independently of brains. I cannot accept this. It seems to me that you guys are creating something of a ghost or shadow reality alongside the one we live in as a placeholder for things to exist when nothing else does. This most likely is the reason why you are theists and I am not. I simply do not accept this figment place where things are said to exist while nothing else can or does.

We've had this discussion before, but I thought I'd reiterate that I was a platonist as an atheist too. I don't think the two beliefs are particularly related (unless they're both just symptoms of my willingness to believe in spooky stuff, of course) since I think god exists in a different way from the way I think the concept of "a" exists.