Final Remarks

  • Daniele Mundici
Part of the UNITEXT book series (UNITEXT)


We have prepared a formidable symbolic apparatus, with its logical calculus, and we can now launch it in the vast field of mathematics for which it was constructed. For example, if we wish to dedicate ourselves to the study of the problem of twin prime numbers p, p + 2 introduced on page 57, we cannot do anything else than accept the axioms for natural numbers, or for sets, and subsequently get down to calculate the consequences of the axioms — mentally, or with the help of lemmas and theorems previously obtained, or even with the help of a computer that generates for us pairs of twin primes with more than hundred thousand digits, hence suggesting that there are infinitely many of such pairs. The completeness theorem assures us that no consequence of the axioms will escape the logical calculus.


Natural Number Predicate Logic Completeness Theorem Incompleteness Theorem Geometric Entity 
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Copyright information

© Springer-Verlag Italia 2012

Authors and Affiliations

  • Daniele Mundici
    • 1
  1. 1.Department of Mathematics and Computer Science “U. Dini”University of FlorenceItaly

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