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  1. Enculturation and the historical origins of number words and concepts.César Frederico dos Santos - 2021 - Synthese 199 (3-4):9257-9287.
    In the literature on enculturation—the thesis according to which higher cognitive capacities result from transformations in the brain driven by culture—numerical cognition is often cited as an example. A consequence of the enculturation account for numerical cognition is that individuals cannot acquire numerical competence if a symbolic system for numbers is not available in their cultural environment. This poses a problem for the explanation of the historical origins of numerical concepts and symbols. When a numeral system had not been created (...)
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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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  • Objectivity in Mathematics, Without Mathematical Objects†.Markus Pantsar - 2021 - Philosophia Mathematica 29 (3):318-352.
    I identify two reasons for believing in the objectivity of mathematical knowledge: apparent objectivity and applications in science. Focusing on arithmetic, I analyze platonism and cognitive nativism in terms of explaining these two reasons. After establishing that both theories run into difficulties, I present an alternative epistemological account that combines the theoretical frameworks of enculturation and cumulative cultural evolution. I show that this account can explain why arithmetical knowledge appears to be objective and has scientific applications. Finally, I will argue (...)
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  • On the development of geometric cognition: Beyond nature vs. nurture.Markus Pantsar - 2022 - Philosophical Psychology 35 (4):595-616.
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  • From Maximal Intersubjectivity to Objectivity: An Argument from the Development of Arithmetical Cognition.Markus Pantsar - forthcoming - Topoi:1-11.
    One main challenge of non-platonist philosophy of mathematics is to account for the apparent objectivity of mathematical knowledge. Cole and Feferman have proposed accounts that aim to explain objectivity through the intersubjectivity of mathematical knowledge. In this paper, focusing on arithmetic, I will argue that these accounts as such cannot explain the apparent objectivity of mathematical knowledge. However, with support from recent progress in the empirical study of the development of arithmetical cognition, a stronger argument can be provided. I will (...)
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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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  • 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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  • 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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  • Re-establishing the distinction between numerosity, numerousness, and number in numerical cognition.César Frederico Dos Santos - 2022 - Philosophical Psychology 35 (8):1152-1180.
    In 1939, the influential psychophysicist S. S. Stevens proposed definitional distinctions between the terms ‘number,’ ‘numerosity,’ and ‘numerousness.’ Although the definitions he proposed were adopted by syeveral psychophysicists and experimental psychologists in the 1940s and 1950s, they were almost forgotten in the subsequent decades, making room for what has been described as a “terminological chaos” in the field of numerical cognition. In this paper, I review Stevens’s distinctions to help bring order to this alleged chaos and to shed light on (...)
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