Husserl on the 'Totality of all conceivable arithmetical operations'

History and Philosophy of Logic 27 (3):211-228 (2006)
Abstract
In the present paper, we discuss Husserl's deep account of the notions of ?calculation? and of arithmetical ?operation? which is found in the final chapter of the Philosophy of Arithmetic, arguing that Husserl is ? as far as we know ? the first scholar to reflect seriously on and to investigate the problem of circumscribing the totality of computable numerical operations. We pursue two complementary goals, namely: (i) to provide a formal reconstruction of Husserl's intuitions, and (ii) to demonstrate ? on the basis of our reconstruction ? that the class of operations that Husserl has in mind turns out to be extensionally equivalent to the one that, in contemporary logic, is known as the class of ?partial recursive functions?
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DOI 10.1080/01445340600553151
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References found in this work BETA
An Unsolvable Problem of Elementary Number Theory.Alonzo Church - 1936 - Journal of Symbolic Logic 1 (2):73-74.
Philosophie der Arithmetik.E. G. Husserl - 1891 - The Monist 2:627.
General Recursive Functions.Julia Robinson - 1951 - Journal of Symbolic Logic 16 (4):280-280.
Recursive Function Theory and Logic.Ann Yasuhara - 1975 - Journal of Symbolic Logic 40 (4):619-620.

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Citations of this work BETA
Functions in Frege, Bolzano and Husserl.Stefania Centrone - 2010 - History and Philosophy of Logic 31 (4):315-336.

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