David Peat

On Incompleteness 49our frameworks. Just because things make sense on paper does notnecessarily mean they will work in a practical way. Without our morehuman feelings logic will propel us forward, almost against our will.And when it overwhelms us it bends everything into its grip.Quantum theory offers us an alternative viewpoint. It dependsupon a logic that is inclusive and leaves room for both A and not-A. Itis a logic that depends on contexts and complementarity, one in whichwhat is A in one context becomes not-A in another. Instead of a mechanicallogic that forces us onward, line by line, quantum logic invitesus to step back and ask, In what context is this logic operating?The authoritarianism of logic is a form of confrontation in whichthere is no middle ground. It is a logic of the excluded middle. It is alogic of winners and losers. It is a showdown in which either we triumph,so that our opponent does our bidding, or we lose face and losepower. Far better is when each voice has been heard and each positionrespected, when everyone has made a creative contribution and feelshe or she has gained something while defeating no one. For how can“right action” flow out of anger and conflict? This is not compromise,in the sense of giving ground, but of creating a framework flexibleenough to tolerate multiple points of view and contexts. It is an approachin which each person can work out of his or her own centerand act in a gentle way. 66The Law of the Excluded Middle. Aristotle was the key philosopher to placelogic on a firm footing by showing the ways in which syllogisms (sets of logicallyconnected steps) can be used to establish rigorous arguments. He showed, for example,that if A and B are each related to C, then it must also be true that A and Bhave a relationship to each other. For example:Major Premise: All dogs (C) have four legs (A)Minor Premise: Spot (B) is a dog (C)Conclusion: Therefore Spot (B) has four legs (A)But Aristotle was concerned about statements made about the future. A famousexample is the proposition “there will be a sea battle tomorrow.” Since, from theperspective of today, no one knows if there will be a battle tomorrow, how can thisstatement be treated in logic? Aristotle proposed that at least we can say the followingwith certainty: “It is true (now) that either there will be a sea battle tomorrow orthere will not be a sea battle tomorrow.” Following this line of thought Aristotle