On the heuristic view, mathematics is a fallible, anti-reductionist problem-solving activity that employs the analytic method (i.e., the generation of hypotheses for problem-solving via non-deductive inferences and the assessment of hypotheses’ plausibility by comparing them with experience). Central to Carlo Cellucci’s articulation of the view is the use of non-deductive inferences in the formulation of new hypotheses. Cellucci criticizes Lakatos’s version of the view for being unable to provide a proper heuristics for mathematics. In this paper, I respond to Cellucci’s challenge, advancing a Lakatosian, deductivist version of the proposal that can accommodate the nature and role of heuristics in mathematical practice. A form of pluralism about the heuristic view then emerges.

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Lakatos, Cellucci, and Heuristic Philosophy of Mathematics

  • Otávio Bueno

摘要

On the heuristic view, mathematics is a fallible, anti-reductionist problem-solving activity that employs the analytic method (i.e., the generation of hypotheses for problem-solving via non-deductive inferences and the assessment of hypotheses’ plausibility by comparing them with experience). Central to Carlo Cellucci’s articulation of the view is the use of non-deductive inferences in the formulation of new hypotheses. Cellucci criticizes Lakatos’s version of the view for being unable to provide a proper heuristics for mathematics. In this paper, I respond to Cellucci’s challenge, advancing a Lakatosian, deductivist version of the proposal that can accommodate the nature and role of heuristics in mathematical practice. A form of pluralism about the heuristic view then emerges.