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  1. Theorem proving in artificial neural networks: new frontiers in mathematical AI.Markus Pantsar - 2024 - European Journal for Philosophy of Science 14 (1):1-22.
    Computer assisted theorem proving is an increasingly important part of mathematical methodology, as well as a long-standing topic in artificial intelligence (AI) research. However, the current generation of theorem proving software have limited functioning in terms of providing new proofs. Importantly, they are not able to discriminate interesting theorems and proofs from trivial ones. In order for computers to develop further in theorem proving, there would need to be a radical change in how the software functions. Recently, machine learning results (...)
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  • Metaphor and the Philosophical Implications of Embodied Mathematics.Bodo Winter & Jeff Yoshimi - 2020 - Frontiers in Psychology 11.
    Embodied approaches to cognition see abstract thought and language as grounded in interactions between mind, body, and world. A particularly important challenge for embodied approaches to cognition is mathematics, perhaps the most abstract domain of human knowledge. Conceptual metaphor theory, a branch of cognitive linguistics, describes how abstract mathematical concepts are grounded in concrete physical representations. In this paper, we consider the implications of this research for the metaphysics and epistemology of mathematics. In the case of metaphysics, we argue that (...)
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  • The Enculturated Move From Proto-Arithmetic to Arithmetic.Markus Pantsar - 2019 - Frontiers in Psychology 10.
    The basic human ability to treat quantitative information can be divided into two parts. With proto-arithmetical ability, based on the core cognitive abilities for subitizing and estimation, numerosities can be treated in a limited and/or approximate manner. With arithmetical ability, numerosities are processed (counted, operated on) systematically in a discrete, linear, and unbounded manner. In this paper, I study the theory of enculturation as presented by Menary (2015) as a possible explanation of how we make the move from the proto-arithmetical (...)
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  • On Radical Enactivist Accounts of Arithmetical Cognition.Markus Pantsar - 2022 - Ergo: An Open Access Journal of Philosophy 9.
    Hutto and Myin have proposed an account of radically enactive (or embodied) cognition (REC) as an explanation of cognitive phenomena, one that does not include mental representations or mental content in basic minds. Recently, Zahidi and Myin have presented an account of arithmetical cognition that is consistent with the REC view. In this paper, I first evaluate the feasibility of that account by focusing on the evolutionarily developed proto-arithmetical abilities and whether empirical data on them support the radical enactivist view. (...)
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  • On the development of geometric cognition: Beyond nature vs. nurture.Markus Pantsar - 2022 - Philosophical Psychology 35 (4):595-616.
    How is knowledge of geometry developed and acquired? This central question in the philosophy of mathematics has received very different answers. Spelke and colleagues argue for a “core cognitivist”, nativist, view according to which geometric cognition is in an important way shaped by genetically determined abilities for shape recognition and orientation. Against the nativist position, Ferreirós and García-Pérez have argued for a “culturalist” account that takes geometric cognition to be fundamentally a culturally developed phenomenon. In this paper, I argue that (...)
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  • Descriptive Complexity, Computational Tractability, and the Logical and Cognitive Foundations of Mathematics.Markus Pantsar - 2020 - Minds and Machines 31 (1):75-98.
    In computational complexity theory, decision problems are divided into complexity classes based on the amount of computational resources it takes for algorithms to solve them. In theoretical computer science, it is commonly accepted that only functions for solving problems in the complexity class P, solvable by a deterministic Turing machine in polynomial time, are considered to be tractable. In cognitive science and philosophy, this tractability result has been used to argue that only functions in P can feasibly work as computational (...)
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  • Developing Artificial Human-Like Arithmetical Intelligence (and Why).Markus Pantsar - 2023 - Minds and Machines 33 (3):379-396.
    Why would we want to develop artificial human-like arithmetical intelligence, when computers already outperform humans in arithmetical calculations? Aside from arithmetic consisting of much more than mere calculations, one suggested reason is that AI research can help us explain the development of human arithmetical cognition. Here I argue that this question needs to be studied already in the context of basic, non-symbolic, numerical cognition. Analyzing recent machine learning research on artificial neural networks, I show how AI studies could potentially shed (...)
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  • A Pattern Theory of Scaffolding.Albert Newen & Regina E. Fabry - forthcoming - Review of Philosophy and Psychology:1-26.
    In recent years, philosophers have developed accounts of cognitive and affective scaffolding to describe the contribution of environmental resources to the realization of mental abilities. However, an integrative account, which captures scaffolding relations in general terms and across domains, is currently lacking. To close this gap, this paper proposes a pattern theory of scaffolding. According to this theory, the functional and causal role of an environmental resource for an individual agent or a group of agents concerning a mental ability in (...)
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  • The Tools of Enculturation.Richard Menary & Alexander Gillett - 2022 - Topics in Cognitive Science 14 (2):363-387.
    Topics in Cognitive Science, Volume 14, Issue 2, Page 363-387, April 2022.
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