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Aug 23 2004
proving a universal negative?

In discussions of this type, I often hear it said that "You can't prove a universal negative". Both theists and agnostics who seek to deny that I can actually be an atheist will frequently state this as a fact, and it is often taken for granted even by so-called "skeptics".

The idea, I suppose, is that it seems easy to prove that something exists (if I want to prove that there is such a thing as a duckbilled platypus, I can just get one and show it to anyone who doubts their existence) but apparently harder to prove that something doesn't exist.

However, as a mathematician, I must say that this is simply not true. There are many proofs that something does not exist. Here is a simple example: I claim that I can prove that there is no positive whole number whose square is equal to 5. The proof goes as follows: 2 squared is four and 3 squared is 9. Then, if there is a number x such that x^2=5 it must be between 2 and 3. However, there are no whole numbers between 2 and 3. A similar, more famous proof shows that there are no fractions p/q with p and q both integers such that (p/q)^2=2. (The square root of 2 is not rational.)

Okay, let's move out of the mathematical realm. If something exists, then it generally has noticeable consequences. To prove a universal negative, that the thing does not exist, it is sufficient to show that those consequences fail to occur. In the case of God, I can say that if there was an all-loving, all-powerful God, then I believe the world would look noticeably different than it does. I would expect not to see so many innocent children being killed by violent nuts, I would expect to see a noticeable preference given by this God to the people who believe in and worship it, etc. Since that is not the case, I conclude that there is not an all-loving, all-powerful God.

Oct 18 2004

The concept of God as portrayed by Christianity and other monotheistic religions is contradictory and impossible. However, that doesn't rule out the possibility of a God or Creator that doesn't fit their precise criteria.

I think the philosophy of Deism, wherein it is suggested that a God created the universe and then abandoned it, has some merit. However, until I see some sort of proof that a God is necessary for the creation of the universe, I remain agnostic-atheist.

Jan 17 2008

i dont understand the first conjecture, as god is only said to be all powerfull and loving by those that have what they call belief, and a god or creator that made the univers could exist, but just not care about wether one of the objects, creations in that univers, is happy, believes in him/her/it, or survives longer than a blink of his eye ( if he/she/it has any), then a god/creator could exist, just not an all loveing one:).

as for a god in the image of man, like belivers of all denominations belive in, well thats just silly, they cant all be right, all the rules they put on membership to one or the other belife systems, negates the existence of such a god, and as for any one of them being right and all the others being wrong, how could his/her/it's creation come to that point withought his intervention ( so often quoted in these books of rules) to put us all back on the right track, lets face it the systems of belife in the world, are more responsible for the mess the world is in, than anything that nature and the devil ( yet another man made idea) could possible be held acountable for.

Jan 19 2008

Originally, this thread was about the question of whether it is possible to prove a universal negative. I still believe the answer is yes, but of course the claim has to be stated unambiguously. The reason we can prove, for example, that there are no positive whole numbers n, x, y and z such that n>3 and x^n+y^n=z^n is because we know quite specifically what we mean by numbers, powers, addition and equality.

This does present some problem when trying to apply these ideas to the question of existence of supernatural beings or gods of any kind. What exactly do we mean by "god" anyway?

The usually description of the Christian god is actually rather specific. It is specific enough for me to be confident that the vast majority of evidence points to the likelihood that this god does not exist but is only the creation of human imagination.

But, if we open up the question to "some sort of god" without being any more specific, then it becomes so vague that I don't see how we can say anything meaningful about its (non)existence...or the significance of whether such a thing exists.

Commonly for Deists (and for Nick above), there seems to be an assumption that if some conscious being created our universe, then that thing is "God". But, that isn't so clear to me.

Suppose we eventually found out that our universe was created by a scientist in some other universe with very different laws of physics. Suppose this scientist works for a government that gave him a large amount of what they consider money to develop a method of generating lots of energy, and his idea was to build a machine that created a universe filled with "stars" that turn hydrogen into helium through a fusion process and another machine to collect that energy (through the things we call "black holes") for use in his universe. Suppose he did not even realize that life would develop in this universe (since the laws of physics in his universe are so different and he thought that only THOSE laws were sufficient for life) we're just an accident.

This is really just science fiction. I'm not claiming I believe this story, only that I can imagine this story. Actually, I can imagine this story being true more easily than I can convince myself to believe in any of the more traditional creation myths of religions on Earth, but that's beside the point.

The point is, would we consider this extra-universal scientist to be "God" merely because he created ours? I think not. Several things are missing.

One important thing is that he doesn't really care about us. That, at least in my meaning of the word, is an important part of what would make something "God". Already, if the creator of the universe is something that doesn't care about us, then I'm less inclined to use the word "God" to describe it.

In this case also there does not seem to be anything "supernatural" going on. For certain my science fiction story speculates about another universe where the laws of physics are different, but this is not so much SUPER-natural as "an alternative nature". (Some of our own scientists have speculated about the use of String Theory to allow us to create tiny universes in our own particle accelerators. If we did create a tiny universe with different laws than ours in this way, would we become super-natural beings ourselves? Arguably, we would be to anything living in there...but then this seriously weakens the meaning of "supernatural", doesn't it?)

Moreover, and I think this is important too, there is something missing here as far as MORALITY goes. Even Deists (like Jefferson) refer to their god as the source of morality. But, this scientist in the other universe may not be a moral example (perhaps he sabotaged the career of the scientist in the lab next to his to advance his own, and perhaps he beats his children...we don't know) nor does his action necessarily have any moral implications for us, the inhabitants of his creation.

Finally, this scientist who created our universe does not necessarily possess either omniscience or omnipotence. Having the power to create the universe is certainly impressive, but it doesn't necessarily mean that he knows everything or can do anything.

In conclusion, let me repeat that I do not believe the universe was created by a child beating, money seeking scientist from another universe. I'm just using this as an example to illustrate my point:

Those who argue that "there must be a god because SOMETHING created the universe" have to explain to me what the word "god" means to them, because the universe could have been created by something I would not want to describe as "god".

(Also, they have to explain to me how they know that something sentient created the universe as opposed to the many alternatives I can imagine there as well...but that's another story!)

Feb 10 2008

there are no water breathing humans, there are no humans that can fly with only the attributes they were born with, there are no humans that can see in the ultraviolet or infra read unaided, these are universal truths, as for universal negative, i believe it only exists in math, and yes your right you can prove it, but what's the point, what use is it other than a math riddle that mathmaticians can enjoy.

Feb 10 2008

yes alex i wonder what kind of god would need a massive explosion to create the univers, if he was all powerful why not just create the univers as it says in the bible, 6000 years ago complete as it is, how come we can now date it to 13.7 billion years ago and started by a massive explosion, and how come we can see the start of life and evolution after that to get life on this planet to were it is, how many inconsistances do religious ppl need to see through the delusion of god the creator, and how do we expect to survive the next hundred years with so many deluded ideotic ppl in places of power and influence within our societies, i realy fear for the survival of the human race, we seem to have a death wish, and little rational ways to avoid our own destruction.

Feb 12 2009
Re: proving a universal negative?

I believe Alex was correct; it's more than just a math riddle. The idea is that you can disprove a specific negative with which details about it's possible existence are given. In the original math proposition. If the unknown number to equal 5 when squared has to be positive and has to be a whole number, it's easy to deduce and conclude that no such thing exists. Similarly, if you proclaim a deity exists and ascribe to it certain tangible features, you can verify the veracity of the attributes and thus the specific deity they're attached to.

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