Art. 03 – Vol. 23 – No. 4 – 2013

Definitions and Theorems


National Institute for Research & Development in Informatics – ICI Bucharest

Abstract: In this article we review the facts that led to the crisis of mathematics and then to the quest of their fundaments, by which the foundation of sciences is found. We point out that the definition is not unique and that it is the dynamical factor of mathematics, allowing the intelectual act of creation all its liberty of movement.

Key words: definition, propositional function, metamathematics, proof.


  1. Aristoteles:Analiticele secunde; Metaphysica.
  2. Dumitriu, A.: Istoria logicii. Ediţia a III-a, Ed. tehnică, 1992-1998.
  3. Heyting, A.: Mathematische Grundlagenforschungen. Intuitionismus, Beweistheorie (Springer, Berlin, 1934).
  4. Fraenkel, A.; Bar-Hillel, J.: Foundations of Set Theory. North Holland Publishing Company, 1958.
  5. Putnam, H: Mathematics without Foundations. «The Journal of Philosophy», LXIV, 1, 1967.

Vew full article

  1. Körner, S.: On the Relevance of Post-Gödelian Mathematics to Philosophy. «Problems in the Philosophy of Mathematics», Amsterdam, 1967.
  2. Mostowski, A.: The Present Sfate of Investigation on the Foundations of Mathematics. Polska Akademia Nauk – Instytut Matematyczny, 1955.
  3. Einstein, A.: The Meaning of Relativity. Methuen, Londra, 1922.
  4. Porphyrios: Isagogé.
  5. Wittgenstein, L.: Tractatus logico-philosophicus. Ed. Kegan Paul, Londra, 1933.
  6. Russell, B.: Introduction to Mathematical Philosophy. franc., ed. Payot, Paris, 1926; Introduction to Mathematical Philosophy.
  7. Goblot, L.: Traité de logique. A. Colin, ed. a VI-a, Paris, 1937.
  8. Leibniz, G. W.:De arte combinatoria.
  9. Pascal, B.:De l’esprit géometrique.
  10. Hobbes, T.: Computatio sive logica.
  11. Poincaré, H.: Science et méthode.
  12. KANT, Imm.: Kants gesammelte Schriften, Band XVI, Berlin, Georg Reiner, 1912.