Re: [OPE-L] is algebra dialectical and vice versa?

From: Ian Wright (iwright@GMAIL.COM)
Date: Fri Sep 16 2005 - 12:44:29 EDT

The negative feedback loop, Paul's oscillator, is also related to 
self-referential paradoxes, such as: "This sentence is false". If the 
sentence is true then the sentence must be false, but if the sentence is 
false then the sentence must be true, and round and round we go. A negative 
feedback loop is exactly like "reality arguing with itself" (very felicitous 

Godel's incompleteness theorems for formal logical systems are proved by 
constructing a direct analogue of this self-referential statement in 
first-order logic. My interpretation of his theorems is that truth and 
reference is not a syntactic property, but a semantic property, a feedback 
relation between a model (the formal system) and the objects it is modelling 
(in this case, the natural numbers).

Godel's results have direct parallels in computer science. They are 
equivalent to the halting problem: we cannot write an interpreter that 
determines whether any of its inputs encode a program that halts or not. 

It is remarkable that we can maybe view Hegel's opening gambits in Science 
of Logic as starting with a negative feedback loop that is unstable and 
necessarily generates continual dynamic change. It's intriguing that exactly 
this kind of mechanism was used by Godel to critique the ambitions of 
Hilbert's formalist program in mathematics. It is also very suggestive that 
the theory of computation derived from Turing's attempt to "mechanize" 
mathematical reasoning, or in other words, unify natural causality with 
logical deduction. For me, there are too many parallels between computation 
and Hegelian dialectics for it to be accidental, in particular the 
undecidability of their major premises, which are structurally similar: 
Church-Turing thesis, and identity of thought and being.


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