Mathematics – Logic
Scientific paper
2011-07-23
Mathematics
Logic
159 pages; in the last version i made some slight modifications
Scientific paper
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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