Hempel's Raven Paradox, Hume's Problem of Induction, Goodman's
Research Report KSTS/RR-19/002 September 12, 2019 (Revised November 1, 2019) Hempel’s raven paradox, Hume’s problem of induction, Goodman’s grue paradox, Peirce’s abduction, Flagpole problem are clarified in quantum language by Shiro Ishikawa Shiro Ishikawa Department of Mathematics Keio University Department of Mathematics Faculty of Science and Technology Keio University c 2019 KSTS 3-14-1 Hiyoshi, Kohoku-ku, Yokohama, 223-8522 Japan KSTS/RR-19/002 September 12, 2019 (Revised November 1, 2019) Hempel's raven paradox, Hume's problem of induction, Goodman's grue paradox, Peirce's abduction, Flagpole problem are clarified in quantum language Shiro Ishikawa *1 Abstract Recently we proposed \quantum language" (or, \the linguistic Copenhagen interpretation of quantum me- chanics", \measurement theory") as the language of science. This theory asserts the probabilistic inter- pretation of science (= the linguistic quantum mechanical worldview), which is a kind of mathematical generalization of Born's probabilistic interpretation of quantum mechanics. In this preprint, we consider the most fundamental problems in philosophy of science such as Hempel's raven paradox, Hume's problem of induction, Goodman's grue paradox, Peirce's abduction, flagpole problem, which are closely related to measurement. We believe that these problems can never be solved without the basic theory of science with axioms. Since our worldview has the axiom concerning measurement, these problems can be solved easily. Hence there is a reason to assert that quantum language gives the mathematical foundations to science.*2 Contents 1 Introduction 1 2 Review: Quantum language (= Measurement theory (=MT) ) 2 3 Hempel's raven paradox in the linguistic quantum mechanical worldview 12 4 Hume's problem of induction 19 5 The measurement theoretical representation of abduction 23 6 Flagpole problem 25 7 Conclusion; To do science is to describe phenomena by quantum language 27 1 Introduction This preprint is prepared in order to reconsider ref.
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