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Modelling the Psychological Structure of Reasoning

Winstanley, M. A. (2022) Modelling the Psychological Structure of Reasoning. [Preprint]

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Abstract

Mathematics and logic are indispensable in science, yet how they are deployed and why they
are so effective, especially in the natural sciences, is poorly understood. In this paper, I focus
on the how by analysing Jean Piaget’s application of mathematics to the empirical content of
psychological experiment; however, I do not lose sight of the application’s wider
implications on the why. In a case study, I set out how Piaget drew on the stock of
mathematical structures to model psychological content, namely, the operations of thought
involved in reasoning. In particular, I show how operations of thought form structured wholes
that initially resisted modelling by either lattices or groups but could be modelled adequately
by modifications of these mathematical structures. Piaget coined the term ‘grouping’ for the
modified structure, I conclude that it represents a non-canonical application of mathematics
to the empirical content of experimental psychology. I also touch on the role external factors
played in Piaget’s development of the grouping.
According to the genetic epistemology conceived by Piaget, the origin of intelligence lies in
the biological organism and develops in stages over time, and, via the grouping, Piaget
established a genetic relationship between two stages of reasoning. I show how this
relationship explains why mathematics and logic fit the psychological content of reasoning
whilst simultaneously making their successful deployment in the natural sciences more
mysterious. Finally, I turn to the explanation Piaget envisaged for the unreasonable
effectiveness of mathematics in the natural sciences and consider some consequences for
naturalism and Pythagoreanism.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Winstanley, M. A.218maw@gmail.com0000-0003-0036-1060
Keywords: applicability of mathematics; psychology of reasoning; genetic epistemology; constructivism; structuralism; grouping; naturalism; Pythagorean strategy; Jean Piaget
Subjects: Specific Sciences > Mathematics > Applicability
Specific Sciences > Psychology > Developmental Psychology
General Issues > History of Science Case Studies
General Issues > Models and Idealization
General Issues > Structure of Theories
Depositing User: Dr Mark Winstanley
Date Deposited: 06 Mar 2022 20:24
Last Modified: 06 Mar 2022 20:24
Item ID: 20193
Subjects: Specific Sciences > Mathematics > Applicability
Specific Sciences > Psychology > Developmental Psychology
General Issues > History of Science Case Studies
General Issues > Models and Idealization
General Issues > Structure of Theories
Date: 2022
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/20193

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