One of my favorite arguments for the existence of God was developed by St. Augustine. It goes like this: Mathematical and geometric truths, like the Pythagorean Theorem for example, exist even if no human mind ever thought them. So they are not reducible to human mind or brain. Using another example, the interior angles of different triangles always add up to the same number of degrees even if there had never been a single human to discover or know that. But they are abstractions and are immaterial and mind-like phenomena, so it is difficult to conceive of them existing independently of minds as in Plato's world of Forms. Their nature requires they reside in an eternal mind, and that is God.
It's a powerful metaphysical argument - and there are others (especially Aquinas's 'five ways').
ReplyDeleteHowever, people have (for some hundreds of years) been too impatient to follow metaphysical arguments, or even to admit that there is such a subject.
It requires at least 10 minutes of hard consecutive thinking to be devoted to the subject - and obviously that is too much to ask nowadays - we are busy people, after all!
Even Bertrand Russell couldn't be bothered to refute metaphysical arguments - he simply claimed not to understand them:
http://www.bringyou.to/apologetics/p20.htm
Despite that many people, including the greatest minds, for a couple of thousand years had understood these arguments - Russell clearly believed that his failure to make sense of metaphysics was not a deficit in himself; but the problem that everybody else who preceded him historically had been dazzled by nonsense.
I, for example, managed to avoid thinking about metaphysics for about 40 years - it really is easy, with so many distractions available!
Pithagorus theorem (which I like very much) is valid for planar geometry only.
ReplyDeleteIt is not valid for triangles on the sphere (e.g. on the surface of the Earth).
It is not valid for larger scales: about 10^11 light years of distance.
Among many branches of Physics, I have never thought aobout the meta-one.
Respectfully, Florida resident.
While the flow of the argument seems sound, I contest the premise that the Pythagorean Theorem exists. It's a true statement, like saying that equality is transitive, but it doesn't become an existing "thing" by being true or by having a name.
ReplyDeleteThat is good argument? It is like saying a sculpture already exists in a block of marble and all one has to do is chisel away at the marble to find it.
ReplyDeleteInteresting argument...but ultimately without any proof. To say something exists whether you know of it or not and then to say...well...it has to be known by someone for it to exist...and drumroll that some one is God...is well...empty.
ReplyDeleteThose examples you state are nothing more than MAN's attempt at interacting with his world. Man's world...man's tools. Man develops the tools and math is a tool...in order to find a place for himself.
There is no metaphysical argument that can prove the existence of an entity that can't be proven to exist. Either you can see it and touch it or prove through experiment that it is there...or you can't. Arguments are just that...empty and without proof.
But good try.
C'mon, you can update this for today!
ReplyDeleteWhat about the Mandelbrot set, which literally contains an infinite set of beautifully, complex, artistic images that look like they must have been designed by someone.
http://images.google.com/images?hl=en&source=hp&biw=1162&bih=703&q=mandelbrot+set&gbv=2&aq=f&aqi=g10&aql=&oq=
Who could have designed and created an infinity of artful images but an infinite artistically creative mind? (Though God appears to be a little bit of a hippy)
Universal addressed it as did Erik to a limited extent. The questionable/faulty premise here is that immaterial truths require a mind to be so. There isn't a good reason to suspect that a world of Platonic forms need exist either. If one were to seriously present this as a proof (and to be fair, you only presented it as an argument), one would have to show that properties of mathematics and geometry among other principles need a processing agent aware of them in order to operate.
ReplyDeleteThat premise seems so risible to me that I'd assume that it arose out of man's natural tendency toward assumption of dualism rather than any rigorous, deep contemplation of the matter.
It is not valid for triangles on the sphere (e.g. on the surface of the Earth).
ReplyDeleteActually it's only valid in space where there's no matter to curve the space; IOW it's a creation of the human mind, and merely a close approximation to reality - as is all human-created mathematics:
"As far as the laws of mathematics refer to reality, they are not certain, as far as they are certain, they do not refer to reality."
Augustine's argument applies to mathematics as a whole; he didn't know Rienmann. I prefer Anselm's argument from perfection. Russell despised it.
ReplyDeleteAnyway modern cosmology itself is an argument for a creator God. But, the bigger point is that there is no logical argument that either proves or disproves the existence or nonexistence of God. Both religion and atheism are acts of faith.
One thing you can demonstrate is that there is no benevolent, caring God.
"But they are abstractions and are immaterial and mind-like phenomena, so it is difficult to conceive of them existing independently of minds as in Plato's world of Forms. Their nature requires they reside in an eternal mind..."
ReplyDeleteI don't buy it. Not as a mathematician, not as a secularist. The highlighted statements are totally unjustified.
Also, the kind of "eternal mind" that's crammed full of mathematical theorems bears zero resemblance to any god anyone has ever believed in.
If that's God, I have to ask what the big deal is.
ReplyDelete"There is no metaphysical argument that can prove the existence of an entity that can't be proven to exist"
ReplyDeleteDo you mean scientifically prove? Because there are metaphysical arguments that can prove something's existence by showing the assertion of its non-existence entails a contradiction. This would get us to establishing the things that science takes for granted like the existence of an objective reality or parsimony.
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ReplyDelete"That is good argument? It is like saying a sculpture already exists in a block of marble and all one has to do is chisel away at the marble to find it."
ReplyDeleteReminds me of the bird and the nest. It exists in the mind of the bird before the twigs and scrap are placed. Or the beaver dam which exists in the mind of the beaver. Honey combs, etc. There is something of a mystery about the creative force of critters. Envisioning and creating.
The statue, honey comb, nest and dam exist both as abstract ideas and as concrete material before they are arranged by the creative force of the critter.
We observe that reality has certain properties.
ReplyDeleteWhy should that require a mind? It well could be a mindless, unthought universe.