Avon, Mauro
(2011)
A different approach to logic.
[Preprint]
Abstract
The paper is about an approach to logic that differs from the standard first-order logic and other
known approaches. It should be a new approach the author has created proposing to obtain a general
and unifying approach to logic and a faithful model of human mathematical deductive process. We
list the most relevant features of the system. In first-order logic there exist two different concepts of
term and formula, in place of these two concepts in our approach we have just one notion of
expression. The set-builder notation is enclosed as an expression-building pattern. In our system we
can easily express second-order and all-order conditions (the set to which a quantifier refers is
explicitly written in the expression). The meaning of a sentence will depend solely on the meaning
of the symbols it contains, it will not depend on external ‘structures’. Our deductive system is based
on a very simple definition of proof and provides a good model of human mathematical deductive
process. The soundness and consistency of the system are proved, as well as the fact that our system
is not affected by the most known types of paradox. The paper provides both the theoretical
material and two fully documented examples of deduction. The author believes his aims have been
achieved but obviously the reader is free to examine the system and get his own opinion about it.
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A different approach to logic. (deposited 08 Oct 2011 13:35)
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