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Husserl on the ‘Totality of all conceivable arithmetical operations'

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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'.

Document Type: Research Article

DOI: https://doi.org/10.1080/01445340600553151

Affiliations: Scuola Normale Superiore, Piazza dei Cavalieri, 7, 56126, Pisa, Italy

Publication date: 2006-08-01

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