Bebbo
September 9, 2003, 12:58 PM
I've seen the phrase "up to isomorphism" used a lot in Chris Langan's CTMU related writings, for example:
http://www.megafoundation.org/Ubiquity/Spring02/Atheist.htm
"Again, we have the distinction between particular theoretic languages, which may indeed be fantastic, and the basic syntactic relations of which they are composed. With respect to ordinary theories, the map is not the terrain; with respect to cognitive and perceptual syntax, it sure as hell is, right up to isomorphism. (By the way, "up to isomorphism" is not an escape clause. Beyond the maximum scope and resolution at which the real universe can internally sustain a syntax <--> content, mind <--> reality, cognition <--> information, time <--> space isomorphism, there is no more reality; the isomorphism is the entire basis of the coherence of the real universe! This should readily become apparent to anyone who tries, logically of course, to find an alternative basis.)"
I've looked up the phrase on Wikipedia but that doesn't really help me understand it in regard to what Langan is saying.
Can anyone explain what "up to isomorphism" means generally, and specifically in regard to the quoted paragraph?
Thanks,
Dene
http://www.megafoundation.org/Ubiquity/Spring02/Atheist.htm
"Again, we have the distinction between particular theoretic languages, which may indeed be fantastic, and the basic syntactic relations of which they are composed. With respect to ordinary theories, the map is not the terrain; with respect to cognitive and perceptual syntax, it sure as hell is, right up to isomorphism. (By the way, "up to isomorphism" is not an escape clause. Beyond the maximum scope and resolution at which the real universe can internally sustain a syntax <--> content, mind <--> reality, cognition <--> information, time <--> space isomorphism, there is no more reality; the isomorphism is the entire basis of the coherence of the real universe! This should readily become apparent to anyone who tries, logically of course, to find an alternative basis.)"
I've looked up the phrase on Wikipedia but that doesn't really help me understand it in regard to what Langan is saying.
Can anyone explain what "up to isomorphism" means generally, and specifically in regard to the quoted paragraph?
Thanks,
Dene