Let's do a thought experiment.
Suppose there is a universe where there is only one of every thing. There's a baker, call him Joe, who bakes a single square and sells it each day. If you want to get a bit grotesque, imagine that he has only one eye, one arm, one hand, one finger, etc. And, since there are no collections in this universe, we don't add up all the single things into an aggregate. So one is the only number in town.
One day, Joe's knife slips and he ends up cutting the square in... two. For the first time there is now two of something. According to some of those who provided intelligent critiques of my previously post, numbers exist only as a conceptual reflection of material phenomenon, so now that we have two squares, the number two can now exist.
So far, so good.
One day Joe contemplates the reality of the split square, and realizes it was a money-maker. He says to himself, I could cut the square into more sections, call them "three", and "four", and make even more money from my squares! At this point, the square has not been cut, and there is only one of everything else, so can three and four exist at this point? According to the external-phenomenon-correspondence view, they can't exist because there isn't three or four of anything in the external world to describe. I think they can, and do. Three and four can exist as mental concepts, weightless, massless, without energy or matter or motion, and without any necessary correspondence to anything in the physical realm.
If and when Joe takes his knife and cuts the square into three and four, what once existed in Joe's mind now exists as material reality as well.
So, numbers are subtle things that seem to exist on the edge of materialism. It seems that the necessary correspondence to real-world phenomena is not as tight as some would insist, and that numbers can have, in some sense, independent existence.
A further point -- while the theist may argue that both numbers and mathematics existed in the mind of God before he (like Joe the baker) created his creation, the antitheist materialist insists that they exist only in the mind of man. But scientists, atheists among them, have noted the beauty that often accompanies the mathematical equations associated with the laws of physics. And this surprises them -- it's not what you would expect from a universe caused by nothing, for nothing, and governed by cold, unfeeling, unconscious, mindless processes.
Maybe it's because there's a beautiful mind behind them.
And that's the way the Ball bounces.
6 comments:
Hmmm..it seems you're saying in this alternate version of reality, premise X is true. Therefore, premise X is also true in our reality. Perhaps inspired by Plantinga?
If Joe the Baker realized he could make more money, that indicates a plurality of money already exists in this reality. There are also multiple days in this reality.
I realize it's just a thought experiment, but I don't think this one works - it's too difficult to conceive of what a universe with only one of everything would really be like...
One problem with this thought experiment is that although this fictional unverse might contain only one "Joe", it still contains lots of "things". What should stop Joe from counting his possessions etc.? Grouping is arbitrary and to really eliminate this problem you would have to conceive a universe that truly only contains one thing, i.e. one elementary particle and I don't think it would spent it's time cutting bread.
That having said, I tend to agree with you that mathematics is not restricted to the material world. While our understanding of mathematics has clearly developed from examination of the natural world there seem to be a lot of mathematical truths beyond application or even correspondence to the "real" world. However, many applications of new concepts have always been found. It is at least possible that every bit of mathematics conceivable has some sort of application to our world. Wouldn't that be exciting?
"But scientists, atheists among them, have noted the beauty that often accompanies the mathematical equations associated with the laws of physics. And this surprises them [...]"
If your refering to the equations themselves, they are beautiful because they are simple, elegant, and they are simple and elegant because they represent fundamental truths about nature, and that's what makes them beautiful. Anyway, don't try and argue that a god exists because we weird physicists find pleasure in looking at E = mc².
If you're refering to the beauty found in nature caused by these laws and equations, well, I'd say the question here is something else: What causes this "beauty" and how it causes it is, in many cases, known. the interesting question is why we would perceive such structures as beautiful.
Anon -- inspired by Plantinga? Perhaps. I have read more about Plantinga, than Plantinga himself.
LCTS -- indeed!
"Three and four can exist as mental concepts, weightless, massless, without energy or matter or motion, and without any necessary correspondence to anything in the physical realm."
Hate to go all science instead of logic, but "mental concepts" and thought in general is quantifiable. They are the result of the complex electrical interactions between neurons in that gray mass you seems to enjoy abusing so much. :)
You must keep in mind that our numbering system is a representative system, not an entity. In base one mathematics, there is in fact only one number involved. Though tedious, it can in fact be used to describe anything regular base ten can.
Ah, base one -- is that ones and zeroes? I remember learning how to code in ones and zeroes as a junior programmer at Canadian General Electric. Reminds me of DNA "switches" -- on, or off.
I'm a dualist, my friend. I believe that the mind resides in the brain, but is not equal to it. I believe that the brain can trigger the mind, and vice-versa. When an atheist invokes the image of the Flying Spaghetti Monster, does the brain trigger this image in the mind, or does the mind, operating with will, invoke the image which is stored in the brain? Hawking says, push-come-to-shove, no free will, we are determined creatures.
Which, if true, means the theist cannot but believe in God, and the atheist cannot but help invoke the FSM. Which suggests the futility of even pursuing such matters.
The fact that we are having this discussion means that, deep down, everyone is a philosophical theist when it comes to meaning, purpose, the possibility of rational dialog, and at least some modicum of real human freedom.
Ones and zeroes are binary, which is base two. base one consists of only zero. 0=0 00=1 000=2, etc. Its cumbersome.
I'd browse your archives to see if you've addressed it, but my time online is limited my RL factors. Are you aware of any logical arguments for the existence of the mind as separate from the brain? perhaps you could address this in a new post?
And I agree with the idea that freewill is a false one. However, since we were not going to do anything other than have this discussion, it cant be described as futile. Only inevitable.
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