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 phrase!). 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. -Ian.
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