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  1. #401
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    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."

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    https://plato.stanford.edu/entries/induction-problem/

    "Popper’s account appears to be incomplete in an important way. There are always many hypotheses which have not yet been refuted by the evidence, and these may contradict one another. According to the strictly deductive framework, since none are yet falsified, they are all on an equal footing. Yet, scientists will typically want to say that one is better supported by the evidence than the others. We seem to need more than just deductive reasoning to support practical decision-making (Salmon 1981). Popper did indeed appeal to a notion of one hypothesis being better or worse “corroborated” by the evidence. But arguably, this took him away from a strictly deductive view of science. It appears doubtful then that pure deductivism can give an adequate account of scientific method."

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    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.

    inductive deductive 1.jpg

    inductive deductive 3.jpg

  4. #404
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    "Popper’s account appears to be incomplete in an important way. There are always many hypotheses which have not yet been refuted by the evidence, and these may contradict one another. According to the strictly deductive framework, since none are yet falsified, they are all on an equal footing. Yet, scientists will typically want to say that one is better supported by the evidence than the others. We seem to need more than just deductive reasoning to support practical decision-making (Salmon 1981). Popper did indeed appeal to a notion of one hypothesis being better or worse “corroborated” by the evidence. But arguably, this took him away from a strictly deductive view of science. It appears doubtful then that pure deductivism can give an adequate account of scientific method."
    https://en.wikipedia.org/wiki/Inductive_reasoning

    In 1963, Karl Popper wrote, "Induction, i.e. inference based on many observations, is a myth. It is neither a psychological fact, nor a fact of ordinary life, nor one of scientific procedure." Popper's 1972 book Objective Knowledge—whose first chapter is devoted to the problem of induction—opens, "I think I have solved a major philosophical problem: the problem of induction". In Popper's schema, enumerative induction is "a kind of optical illusion" cast by the steps of conjecture and refutation during a problem shift. An imaginative leap, the tentative solution is improvised, lacking inductive rules to guide it. The resulting, unrestricted generalization is deductive, an entailed consequence of all explanatory considerations. Controversy continued, however, with Popper's putative solution not generally accepted.

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    https://en.wikipedia.org/wiki/Poincaré_conjecture

    Conjectures are inductive processes, but deductive logic is much more important in mathematics and philosophy.

    The process of solving mathematical problems/theorems includes analogy and categorization (i.e. shared structure), which do not try to achieve general conclusions.

    ------

    mathematics and philosophy: deductive reasoning is hard, inductive reasoning is easy

    science: inductive reasoning is hard, deductive reasoning is easy
    Last edited by Petter; Today at 06:35 AM.

  6. #406
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    https://en.wikipedia.org/wiki/Poincaré_conjecture

    Conjectures are inductive processes, but deductive logic is much more important in mathematics and philosophy.

    The process of solving mathematical problems/theorems includes analogy and categorization (i.e. shared structure), which do not try to achieve general conclusions.

    ------

    mathematics and philosophy: deductive reasoning is hard, inductive reasoning is easy

    science: inductive reasoning is hard, deductive reasoning is easy
    Finding patterns (analogy etc) is hard in both mathematics/philosophy and science.

    Deductive reasoning and inductive reasoning are (relatively) easy in both mathematics/philosophy and science.

    The patterns are fuzzy/incomplete in science so heuristic methods are needed.
    Last edited by Petter; Today at 07:43 AM.

  7. #407
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    https://www.youtube.com/watch?v=eYfpSAxGakI (The Dehn Invariant - Numberphile)

    Daniel Litt's type is "the ​mathematician".
    introvert, not a planner, primary PFA/PFS, leading Se, the right hemisphere, analytic



    https://www.youtube.com/watch?v=u8VdPW8tCWY (Closer To Truth ... Seth Lloyd - What is Information?)

    introvert, not a planner, primary PFA/PFS, leading Se, the right hemisphere, heuristic

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