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  1. Pragmaticism.Charles S. Peirce - 2024 - De Gruyter.
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  • A Stochastic Model of Mathematics and Science.David H. Wolpert & David B. Kinney - 2024 - Foundations of Physics 54 (2):1-67.
    We introduce a framework that can be used to model both mathematics and human reasoning about mathematics. This framework involves stochastic mathematical systems (SMSs), which are stochastic processes that generate pairs of questions and associated answers (with no explicit referents). We use the SMS framework to define normative conditions for mathematical reasoning, by defining a “calibration” relation between a pair of SMSs. The first SMS is the human reasoner, and the second is an “oracle” SMS that can be interpreted as (...)
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  • How to Recognize Artificial Mathematical Intelligence in Theorem Proving.Markus Pantsar - forthcoming - Topoi:1-14.
    One key question in the philosophy of artificial intelligence (AI) concerns how we can recognize artificial systems as intelligent. To make the general question more manageable, I focus on a particular type of AI, namely one that can prove mathematical theorems. The current generation of automated theorem provers are not understood to possess intelligence, but in my thought experiment an AI provides humanly interesting proofs of theorems and communicates them in human-like manner as scientific papers. I then ask what the (...)
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  • A human-like artificial intelligence for mathematics.Santiago Alonso-Diaz - 2024 - Mind and Society 23 (1):79-97.
    This paper provides a brief overview of findings in mathematical cognition and how a human-like AI in mathematics may look like. Then, it provides six reasons in favor of a human-like AI for mathematics: (1) human cognition, with all its limits, creates mathematics; (2) human mathematics is insightful, not merely deductive steps; (3) human cognition detects structure in the real world; (4) human cognition can tackle and detect complex problems; (5) human cognition is creative; (6) human cognition considers ethical issues. (...)
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