Quote:
|
Originally Posted by Doctordick
I suspect mathematics could probably be defined to be the design and study of internally self consistent systems.
|
I agree with you and we can also add, it's also a set of logical rules
Quote:
|
Originally Posted by Doctordick
That would make the "systems" invented;
|
I don't agree with this for the simple reason that a "consistent systems" is a system that all it's rules have to fulfill our mathematical postulates and laws...so we can only say that thoses "systems" are "deduced" and not invented.
Quote:
|
Originally Posted by Doctordick
however, if one conceives of mathematics as the entire set of all possible self consistent systems, then it would clearly be something to be discovered.
|
Mathematics can never make discovery, only deductions from it's basics laws (logic). Saying that mathematics can make discovery (or that it's discovered) is like saying that mathematics discovered the number "2" just because we can write in mathematical words : 1+1 = 2.
Can we say that mathematics discovered all numbers just because we can write [For every number "n" , there is a number "m" = "n+1"] ????? I don't think so...in fact, this is something that I have discovered long ago and that I simply used mathematics to put it down on a paper.
Sometime, a mathematicien can write down a very long and beautiful formula (based on simples mathematical and logical rules) but it'll be called a "theory" or "philosophy" until it'll be discovered by experimental science: I can say that, depending on my feeling (my own logic), an extraterrestrial life exist somewhere in the universe, we can call it "theory" or"philosophy" or SF. Suppose now that humans (in 1000 years from now) discovered that an extraterrestrial life exist in other planets... can we say that's it's me who discovered the extraterrestrial life? i don't think so even if I like the idea...
I think that mathematics was created and can only make theorys (which is mainly a very complicated and not simple or obvious deduction) which have to be discovered by other sciences.
