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Re: mathematics
Date: 2005-08-19 07:07 pm (UTC)Point #1. It is impossible for you or I to perceive the world without the filter of this symbolic system. The very fact that we quantify 'more' by enumerating individuals means that we are seeing from inside the symbolic system. The concept of more and less and enough (for a specific reaction to happen) are probably external and transcendent.
Point #2. The very act of abstracting things in the real world into arithmetic is using the symbolic system. The very act of manipulating those abstractions and expecting the result to match up with the observable is using the system. Your example is an example of the symbolic system at work.
Point #3. I will concede that perhaps the initial level of abstraction (counting, basic arithmetic) may be instinctive to our species. But then, so is the abstraction of language itself. It's one of the things we humans do.
Point #4. It may be that the perception of things as units is a sensory artifact. For example, if you look at one of Bob's apples, you see a single apple. But if you could see the atoms and not the apple, you would say it is a heterogeneous mass of mostly hydrogen and oxygen. This extends until you are seeing sub-atomic particles, and if at some level everything turns out to be quanta of energy, your perception of objects turns out to be a trick of the light in the first place.
It is inescapable that we live in the well of our own perceptions, and our symbolic models for abstracting those perceptions will reflect those perceptions back. Since this system of symbols and abstraction is dependent on our perceptual mechanism, I'd have to say no, it is not transcendent.
-HH