TITLE:
A New History of Logic: The Laborious Birth of a Formal Pluralism
AUTHORS:
Antonino Drago
KEYWORDS:
Double Negation, Intuitionist Logic, Kolmogorov’s 1932 Paper, Problem-Based Organization of a Scientific Theory, Two Fundamental Dichotomies, Structure of a Theory, Kuhn’s Categories, Koyré’s Categories
JOURNAL NAME:
Advances in Historical Studies,
Vol.10 No.4,
December
23,
2021
ABSTRACT: The paper starts by remarking that the ancient Greek
word for “truth” was “alétheia” (unveiling), which is a double negation. But,
after Plato the affirmative meaning of the idea of truth has prevailed. The
same meaning was reiterated by Romans’s word for truth, veritas. Not before the year 1968 the double negation law was
re-evaluated, since its failure was recognized as representing, more
appropriately than the failure of the excluded middle law, the borderline
between classical logic and almost all non-classical kinds of logic. Moreover,
its failure is easily recognized within a (scientific) text; which therefore
can be analyzed in a new logical way. As an example, the analysis of Kolmogorov’s 1932 paper about the foundations of
the intuitionist logic shows many interesting results, in particular his
reasoning through arguments pertaining to the same intuitionist logic. In
addition, previous papers have suggested—through a comparative analysis of all
scientific theories which are based, like the previous one, on a general
problem—that there exists a new model of organization of a theory which is
alternative to the deductive-axiomatic model and it is governed by intuitionist
logic. Some important logical events pertaining to non-classical logic are
recognized by inspecting through both the double negations and this new model
of organizing the original texts of past theories; so that the entire history
of logic appears as a development along two main lines, one line representing
classical logic dominated all others for a very long period of time, although
at the origins the logical arguing had
pertained to the alternative line. This history of logic confirms both Kuhn’s
category of a paradigm and Koyré’s categories, represented by him through a
couple of “characteristic propositions” in mutual conflict; analogous couples
of propositions are suggested as representing the categories for adequately
interpreting the entire history of logic.