By Ben Goertzel
This e-book summarizes a community of interrelated principles which i've got built, on and off, during the last 8 or ten years. The underlying subject matter is the mental interaction of order and chaos. Or, to place it differently, the interaction of deduction and induction. i'm going to try and clarify the connection among logical, orderly, awake, rule-following cause and fluid, self organizing, habit-governed, subconscious, chaos-infused instinct. My earlier books, The constitution of Intelligence and The Evolving brain, in short touched in this courting. yet those books have been basically involved in different issues: SI with developing a proper language for discussing mentality and its mechanization, and EM with exploring the position of evolution in concept. They danced round the edges of the order/chaos challenge, with no ever absolutely moving into it. My target in scripting this publication was once to move on to the center of psychological technique, "where angels worry to tread" -- to take on the entire sticky matters which it really is thought of prudent to prevent: the character of awareness, the relation among brain and fact, the justification of trust platforms, the relationship among creativity and psychological illness,.... All of those matters are handled the following in a simple and unified manner, utilizing a mix of techniques from my earlier paintings with principles from chaos idea and intricate structures technology.
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Additional resources for Chaotic Logic - Language, Mind and Reality from the Perspective of Complex Systems Science
Example text
The time has come to enrich formal logic by adding to it some other fundamental notions. Do not lose your faith," concluded Stan. "A mighty fortress is mathematics. It will rise to the challenge. " More specifically, I suggest that we must enrich formal logic by adding to it the fundamental notions of pattern and multilevel control, as discussed above. The remainder of this chapter is devoted to explaining how, if one views logic in the context of pattern and multilevel control, all four of the "paradoxes" listed above are either resolved or avoided.
If these true statements also happen to be useful, then from a practical point of view it may be advisable to append A to I. Deductively such a move is not justified, but inductively it is justified. This fits in with the general analysis of deduction given in SI, according to which deduction is useful only insofar as induction justifies it. 4. com 50 CHAOTIC LOGIC Having dealt with implication, let us now turn to the paradox of contradiction sensitivity. According to reasoning given above, if one uses propositional or predicate calculus to define the transformation system T, one easily arrives at the following conclusion: if any two of the propositions in I contradict each other, then D(I,T) is the entire set of all propositions.
Roughly, clause (3) says that Y is an "approximate local minimum" of simplicity, in proof space. This is the kind of implication that is useful in building up a belief system. ,N, and the Bi are true, A might be worth assuming. After all, by contradiction sensitivity a false statement implies everything. But things are not so simple under relevant implication. If a statement A significantly implies a number of true statements, that means that by appending the statement A to one's assumption set I, one can obtain quality proofs of a number of true statements.