Reasons from Science for Limiting Classical Logic

Abstract

As is clear from the title, the paper defends the view that there are reasons from Science for limiting Classical Logic (CL). In this paper such reasons are especially given from physics; even if I think that other areas (Philosophy of Science, Epistemology, Action theory, Ethics... etc.) lead to similar or to the same limitations which are proposed here.¹ In general problems arise when logic is applied to fields outside logic and mathematics. These problems are of different kinds but many of them have the same source. The source is what I have called elsewhere “replaceable and reducible parts in the consequence class”. In other words: Classical valid inferences, (arguments) which have replaceable or reducible parts in their consequence class lead to paradoxical or incorrect results when applied to the respective area. Replaceable parts are parts which can be replaced by an arbitrary part (sentence, predicate) salva validitate of the argument. And reducible parts are parts which can be reduced to smaller parts salva validitate of the argument. In this paper I shall concentrate on problems which arise when logic is applied to physics. The paper is divided into 4 chapters. In the first chapter I want to deal with the problems of commensurability and to show that this problem is not specific to physics, but is much more general. The second chapter deals with commensurability in Quantum logic. In the third chapter special restrictions (filters) on CL are proposed for a solution of the above mentioned problems. In the fourth chapter it is shown how these restrictions can solve the problems concerning commensurability and distributivity when logic is applied to Quantum Theory.