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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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