David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Studia Logica 79 (2):163 - 230 (2005)
In the present paper the well-known Gödels – Churchs argument concerning the undecidability of logic (of the first order functional calculus) is exhibited in a way which seems to be philosophically interestingfi The natural numbers are not used. (Neither Chinese Theorem nor other specifically mathematical tricks are applied.) Only elementary logic and very simple set-theoretical constructions are put into the proof. Instead of the arithmetization I use the theory of concatenation (formalized by Alfred Tarski). This theory proves to be an appropriate tool. The decidability is defined directly as the property of graphical discernibility of formulas.
|Keywords||Philosophy Logic Mathematical Logic and Foundations Computational Linguistics|
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Simon Friederich (2010). Structuralism and Meta-Mathematics. Erkenntnis 73 (1):67 - 81.
Felix Mühlhölzer (2010). Mathematical Intuition and Natural Numbers: A Critical Discussion. [REVIEW] Erkenntnis 73 (2):265–292.
Walter Dean & Hidenori Kurokawa (2014). The Paradox of the Knower Revisited. Annals of Pure and Applied Logic 165 (1):199-224.
Albert Visser (2014). Peano Corto and Peano Basso: A Study of Local Induction in the Context of Weak Theories. Mathematical Logic Quarterly 60 (1-2):92-117.
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