Occams razor has some underlying assumptions to it which we should examine:
Quote:
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Occam's Razor states that the explanation of any phenomenon should make as few assumptions as possible, eliminating those that make no difference in the observable predictions of the explanatory hypothesis or theory.
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This implies that between two theories,
both of which completely describe a phenomena, we should choose the simpler of the two as being the truth.
However, does reality work this way? Does the simpler explanation hold more merit, having any more "reality" to it?
If two mathematical formulations work out to be exactly the same thing in the end- is it correct to use the simpler formulation? Is this the underlying nature of reality? Simple?
Here it seems that instead what is happening is that human perception is taking its role in defining truth. That is, Occams razor is really saying:
human defined truths should exist in human defined terms.
But is this reality? Why would reality have any basis on our perception of it?
And it seems:
reality does rely on our perception of it to the degree which we can understand, make predictions, react to, and utilize the phenomena around us. In short, the perception of reality makes a big difference in our ability to "utilize" it so to speak, or apprehend it. If a simpler theory makes it easier to wrap our minds around it, then it is reality.
So we can imagine a culture which never invents the concept of zero as an item unto itself. Instead, they realize something exists there, but are unable to decide on a symbol to represent it by itself. Instead, because of the peculiar nature of their history, they use (7 apples - 3 people eating 1 apple each - 2 people eating 2 apples) to represent zero.
Thus, they must use this longish, semi literal sentence, any time they wish to represent zero. Does this make the representation of zero any less real? It appears to define it around a precedent- the existence of apples within a situation.
Thus to a novice using this representation of zero, he may not be able to comprehend the usage of zero in a math problem which does not involve seven apples. He will think- where are the apples? Since there are no apples to go away, how can I have no apples?
A more advanced thinker may be able to handle one to six apples, thinking in his mind: now I will append an additional fictional seven apples, which then will be eaten by these individuals. Thus, the math can be applied to greater domains.
And finally, a really advanced thinker may be able to add apples on even when the problem involves something completely different, like seashells.
In the final analysis, such a representation of zero is clearly workable, and meaningful. In fact, every number can be represented in such a way. Does this make the representations incorrect?
No. But for our conceptual system, it is easier to keep fewer things in mind at a time- but that does not mean reality does not exist as "the possibility of all things which can represent zero- actually are zero"
Therefore Occams razor should be looked at as a conceptual tool, for we can not tell if reality is or is not a simple phenomena.
one =all! -
04-14-2006, 06:29 AM
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