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  1. Cognitive and Computational Complexity: Considerations from Mathematical Problem Solving.Markus Pantsar - 2021 - Erkenntnis 86 (4):961-997.
    Following Marr’s famous three-level distinction between explanations in cognitive science, it is often accepted that focus on modeling cognitive tasks should be on the computational level rather than the algorithmic level. When it comes to mathematical problem solving, this approach suggests that the complexity of the task of solving a problem can be characterized by the computational complexity of that problem. In this paper, I argue that human cognizers use heuristic and didactic tools and thus engage in cognitive processes that (...)
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  • Descriptive Complexity, Computational Tractability, and the Logical and Cognitive Foundations of Mathematics.Markus Pantsar - 2021 - 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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  • Bootstrapping of Integer Concepts: The Stronger Deviant-Interpretation Challenge.Markus Pantsar - forthcoming - Synthese:1-24.
    Beck presents an outline of the procedure of bootstrapping of integer concepts, with the purpose of explicating the account of Carey. According to that theory, integer concepts are acquired through a process of inductive and analogous reasoning based on the object tracking system, which allows individuating objects in a parallel fashion. Discussing the bootstrapping theory, Beck dismisses what he calls the "deviant-interpretation challenge"—the possibility that the bootstrapped integer sequence does not follow a linear progression after some point—as being general to (...)
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  • A Fresh Look at Research Strategies in Computational Cognitive Science: The Case of Enculturated Mathematical Problem Solving.Regina E. Fabry & Markus Pantsar - 2019 - Synthese 198 (4):3221-3263.
    Marr’s seminal distinction between computational, algorithmic, and implementational levels of analysis has inspired research in cognitive science for more than 30 years. According to a widely-used paradigm, the modelling of cognitive processes should mainly operate on the computational level and be targeted at the idealised competence, rather than the actual performance of cognisers in a specific domain. In this paper, we explore how this paradigm can be adopted and revised to understand mathematical problem solving. The computational-level approach applies methods from (...)
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  • Limiting the explanatory scope of extended active inference: the implications of a causal pattern analysis of selective niche construction, developmental niche construction, and organism-niche coordination dynamics.Regina E. Fabry - 2021 - Biology and Philosophy 36 (1):1-26.
    Research in evolutionary biology and philosophy of biology and cognition strongly suggests that human organisms modify their environment through active processes of niche construction. Recently, proponents of the free-energy principle and variational active inference have argued that their approach can deepen our understanding of the reciprocal causal relationship between organisms and their niche on various scales. This paper examines the feasibility and scope of variational formalisations and conceptualisations of the organism-niche nexus with a particular focus on the extended active inference (...)
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  • Mathematical Cognition and Enculturation: Introduction to the Synthese Special Issue.Markus Pantsar - 2020 - Synthese 197 (9):3647-3655.