Antonino Drago

Dept. of Physical Sciences, Univ. "Federico II", Napoli

Abstract

Recent works on non-classical logic emphasised that its borderline with classical logic has to be put on the validity of the law of double negation.
This law gives reason of the radical change Popper introduced in Vienna Circle's attitude. Vienna circle wanted to state full empirical evidence for a scientific truth. Rather, Popper considered this positive statement as lacking of decisive support; hence, he suggested to qualify as non-scientific - i.e. metaphysical in nature - those sentences which do not enjoy empirical evidence; shortly, he doubly negated Vienna Circle's basic thesis; which is obtained by dropping out the two negations, but it is not implied by Popper's thesis. This statement constitutes a failure of double negation law. (one may recall two more celebrated Popper's statements which are double negated statements: "To minimize [= reduce, annihilate] sufference"[¹ to enhance joy] and "To minimize the risks of bad rulers" [¹ to enhance good rulers])
When a theory includes a DNS of this kind, no deductive theory from positive axioms is possible. The theory is thus open to novelties; it is rather a process for discovery new truths, or rather a new method for solving a general problem.In fact, in Popper's reflection the general problem is: What is science? His investigation is aimed to discover in which way to analyse scientific truths. We can re-visit all characteristic features of Popper's philosophy under this light. However, he was not always consistent with the introduction of a choice on the kind of logic -either classical one or non-classical one -, which opens new perspectives on the relationship between empirical validification and an hypothesis, since this hypothesis may be also a double negated hypotesis.
The change of emphasis from LEM to DN in differentiating classical logic from non-classical logic is remarkable under one more aspect. A failure of double negation law is easier to be scrutinised in original writings than a failure of LEM. Since 1989 I found out a list of DN in the original writings belonging to some scientific theories, i.e. classical chemistry, L. Carnot's calculus geometry and mechanics, S. Carnot's thermodynamics, Avogadro's atomic theory, Galois' theory, Klein's Erlangen program, Einstein's special relativity, quantum mechanics (strategists' theories too, by Sun Tzu, L. Carnot, Clausewitz, and even S. Freud's psycho-analysis ). In some cases the number of DNS is so high to allow an easy re-construction of the contents in the whole text; one has to merely extract all DNS's and then grouping them in units of arguing. The best instance of this kind of analysis is S. Carnot's book on thermodynamics.
One may remark that Popper's innovation (1933) represents the introduction in the philosophical attitude of Vienna Circle, of the pluralism on the kinds of logic, just in the same time Glyvenko, Kolmogoroff and Goedel independently emphasised the irreducible distance between classical logic and the most representative non-classical logic, i.e. the intuitionistic one.
All that shows that the logic of "logical empirism" has to be enlarged till to include non-classical logic too, and moreover, the domain of "empirism" has to be enlarged till to include the original writings by the founders of scientific theories.

Drago A.: "Logical Empirism and non-classical Logic", in Proceedings Wien Circle and Logical Empirism, 12-14 July, 2001, in press

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