Philip Ronald Dutton
Registered: Feb 2004
I was pondering the logical statement: "x = x"
( 0 = 0, 5 = 5, etc.)
These kind of statements are so basic. But, I am wondering if there is a bit more complexity than what first appears. Hopefully, I can explain clear enough so that people can point out my mistake-- since, I am most likely making one here!
I think that "x=x" is coupled to (or encodes) a meta-mathematical version of substitution. Meta-mathematically speaking, you can distinguish the left 'x' from the right 'x.' Mathematically, speaking, you can not. Consider this "meta-mathematical" dialogue:
a:"hey look at that left 'x'!"
b:"Oh that is nice! I wonder what it is?"
a:"well, lets take a closer it..."
a:"hmmm, it appears to be the right 'x'!"
b:"well isn't that interesting?"
So, within the conversation, a substition was applied was it not? Also, the conversation could have gone back and forth for infinity because you have to look at the right side in terms of the left side also. I am calling this an "encapsulated meta-mathematically inherit recursion."
So, my thought experiment makes me think that the equals constant encapsulates some kind of meta substitution and some kind of meta recursion....
Such meta mathematical substitution will always have to be used within a computation model (i cant yet find words to explain why i think this..maybe, to start: you can not represent that statement within computation models and not have to use a substitution for analysis!?) Hence I smell seeds of computation being meta-mathematical.....oops: I should not have said that!
And now, I apologize for my rookie mistakes (whatever they are!).
P h i l i p . R . D u t t o n
Last edited by Philip Ronald Dutton on 03-16-2004 at 05:25 PM
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