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The dependence of computability on numerical notations

Ethan Brauer

Synthese 198 (11):10485-10511 (2021)

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Computability, Notation, and de re Knowledge of Numbers.Stewart Shapiro, Eric Snyder & Richard Samuels - 2022 - Philosophies 1 (7):20.details Saul Kripke once noted that there is a tight connection between computation and de re knowledge of whatever the computation acts upon. For example, the Euclidean algorithm can produce knowledge of which number is the greatest common divisor of two numbers. Arguably, algorithms operate directly on syntactic items, such as strings, and on numbers and the like only via how the numbers are represented. So we broach matters of notation. The purpose of this article is to explore the relationship between (...) Download Export citation Bookmark 1 citation
On Algorithms, Effective Procedures, and Their Definitions.Philippos Papayannopoulos - 2023 - Philosophia Mathematica 31 (3):291-329.details I examine the classical idea of ‘algorithm’ as a sequential, step-by-step, deterministic procedure (i.e., the idea of ‘algorithm’ that was already in use by the 1930s), with respect to three themes, its relation to the notion of an ‘effective procedure’, its different roles and uses in logic, computer science, and mathematics (focused on numerical analysis), and its different formal definitions proposed by practitioners in these areas. I argue that ‘algorithm’ has been conceptualized and used in contrasting ways in the above (...) Download Export citation Bookmark 1 citation

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