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Posted by trofimov on February 19, 1998 at 18:13:58:
In Reply to: Re: Status of math posted by Claude Kordo on February 11, 1998 at 15:54:41:
: I think the stronger argument would begin from the idea of "invention," and would then proceed from these axiomatic-inventions, through a series of extensions to discoveries that would link a Human-frame-of-reference to the idea of "measurement." Measurement is arguably the single most important idea in the formation of all human concepts, and allows minds imbued with reason to reach a level called Abstraction.
: Again, I must emphasize the idea of "invention." This was done from a human perspective, .and was done in order to have a frame of reference for Human conceptualization.
: If a Xenomorph, or alien consciousness, could be identified or defined, its Xeno-psychological matrix would not necessarily "invent" mathematics as we did - the frame of reference would be far different.
: I think the question you are really asking is whether mathematics exists "independent of consciousness." I don't think so - someone or something must point to "it" and say, in whatever terms, "this relationship is true."
Of course, another way to look at it is biological--it is commonly noted that not all humans have equal biological predispositions to math, and most animals have little to none. This is independant from the existence of the power of reason. So once the ability for measurement existed, it must have been discovered by some intrepid hairy pre-man. As civilization progressed, it is very likely that various aspects of mathematics
can be said to have been "discovered" as always having been present,conceptualized by reason, but not an invention of it. Advances in mathematics to this point were made by observation of the physical world. In this case, it is only the language and vocabulary of mathematics that can be said to be invented--for the properties are always there to be discovered.
Of course, mathematics does not exist without consiousness.
But then, what concept does?
-trofimov
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