https://math.stackexchange.com/quest...e-or-deductive
"Mathematics is deductive. To be more precise, only deductive proofs are accepted in mathematics. Your "inductive proof" of the distributive property wouldn't be accepted as a proof at all, merely as verification for a finite number of cases (1 case in your question)."
https://en.wikipedia.org/wiki/Problem_of_induction
"induction is the glory of science and the scandal of philosophy"
https://www.researchgate.net/publica...s_in_Reasoning
"A general two-stage theory of human inference is proposed. A distinction is drawn between heuristic processes which select items of task information as ‘relevant’, and analytic processes which operate on the selected items to generate inferences or judgements. These two stages are illustrated in a selective review of work on both deductive and statistical reasoning. Factors identified as contributing to heuristic selection include perceptual salience, linguistic suppositions and semantic associations. Analytic processes are considered to be context dependent: people reason from experience, not from inference rules. The paper includes discussion of the theory in comparison with other contemporary theories of human inference, and in relation to the current debate about human rationality."
It is possible that "the scientist" is a heuristic type/subtype and "the philosopher" is an analytic type/subtype.
https://en.wikipedia.org/wiki/Problem_of_induction
"In contrast, Karl Popper's critical rationalism claimed that inductive justifications are never used in science and proposed instead that science is based on the procedure of conjecturing hypotheses, deductively calculating consequences, and then empirically attempting to falsify them."
I think "conjecturing hypotheses" is inductive reasoning.
https://en.wikipedia.org/wiki/Problem_of_induction
"In contrast, Karl Popper's critical rationalism claimed that inductive justifications are never used in science and proposed instead that science is based on the procedure of conjecturing hypotheses, deductively calculating consequences, and then empirically attempting to falsify them."
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