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Deductive foundation and analytic propositions

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References

  1. G. Frege:Über formale Theorien der Arithmetik. The text cited in the book:I. M. Bocheński:Formale Logik, pp. 337–338.

  2. K. Ajdukiewicz:Le problème du fondement des propositions analytiques. Studia Logica VIII (1958).

  3. G. Frege:Die Grundlagen der Arithmetik, p. 4.

  4. The definition of propositions analytic in the synatic sense and the remarks about analytic propositions formulated in this article were presented in my lecture delivered at the conference of the Institute of Logic of the Polish Academy of Sciences in Wroclaw on June, 1958. I was aware of the consequences of this definition for the notion of a deductive foundation in connection with the problem of foundation of statements and decisions, formulated byK. Ajdukiewicz as the main theme of the international logical conference in Warsaw in 1961.

  5. L. Borkowski, J. Słupecki:A Logical System Based on Rules and Its Application in Teaching Mathematical Logic, Studia Logica VII (1958).

  6. Cf. Studia Logica VII, p. 93.

  7. Cf.L. Borkowski:Systems of the Propositional and of the Functional Calculus Based on One Primitive Term, Studia Logica VI, p. 28.

  8. The abbreviation of the expression: the suppositions of a proof (called also sometimes the assumptions of a proof).

  9. This notation is explained in my paper cited in footnote 7, Studia Logica VI, pp. 28–29.

  10. E.g.D. Hilbert-W. Ackermann:Grudzüge der theoretischen Logik.

  11. K. Ajdukiewicz:Le problème du fondement des propositions analytiques.

  12. L. Borkowski:Reduction of Arithmetic to Logic Based on the Theory of Types without the Axiom of Infinity and the Typical Ambiguity of Arithmetical Constants, Studia Logica VIII (1958).

  13. This definition is an interpretation of the definition of structural rules given byK. Ajdukiewics in his book:Główne zasady metodologii nauk i logiki formalnej, p. 94.

  14. K. Ajdukiewicz:Zarys logiki, p. 149.

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  1. Uniwersytet Wrocławski, Wrocław

    Ludwik Borkowski

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  1. Ludwik Borkowski
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To the memory of Professor Kazimierz Ajdukiewicz

Allatum est die 26 Martii 1965

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Borkowski, L. Deductive foundation and analytic propositions. Stud Logica 19, 59–72 (1966). https://doi.org/10.1007/BF02186725

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