Calculus as method or calculus as rules? Boole and Frege on the aims of a logical calculus.

By way of a close reading of Boole and Frege's solutions to the same logical problem, we highlight an underappreciated aspect of Boole's work—and of its difference with Frege's better-known approach—which we believe sheds light on the concepts of 'calculus' and 'mechanization' and on their history....

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Publicado en:Synthese Vol. 199; no. 5/6; pp. 11913 - 11944
Autores principales: Waszek, David, Schlimm, Dirk
Formato: Artículo
Publicado: Springer Nature Dec2021
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Acceso en línea:Ver este registro en EBSCOhost
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        atl: Calculus as method or calculus as rules? Boole and Frege on the aims of a logical calculus.
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        au:
          Waszek, David
          Schlimm, Dirk
        affil: Department of Philosophy, McGill University, Leacock Building, Room 414, 855 Sherbrooke St. W., H3A 2T7, Montreal, QC, Canada
      su:
        Mathematical notation
        Philosophy of mathematics
        Calculus
      sug:
        subj:
          Mathematical notation
          Philosophy of mathematics
          Calculus
      keyword:
        Boole
        Frege
        Logic
        Mechanization
        Notations
      ab: By way of a close reading of Boole and Frege's solutions to the same logical problem, we highlight an underappreciated aspect of Boole's work—and of its difference with Frege's better-known approach—which we believe sheds light on the concepts of 'calculus' and 'mechanization' and on their history. Boole has a clear notion of a logical problem; for him, the whole point of a logical calculus is to enable systematic and goal-directed solution methods for such problems. Frege's Begriffsschrift, on the other hand, is a visual tool to scrutinize concepts and inferences, and is a calculus only in the thin sense that every possible transition between sentences is fully and unambiguously specified in advance. While Frege's outlook has dominated much of philosophical thinking about logical symbolism, we believe there is value—particularly in light of recent interest in the role of notations in mathematics and logic—in reviving Boole's idea of an intrinsic link between, as he put it, a 'calculus' and a 'directive method' to solve problems.
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    language: English
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