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Dual-Process Theories of Numerical Cognition

  • Book
  • © 2018

Overview

Authors:
  1. Mario Graziano

    1. Department of Cognitive Sciences, University of Messina, Messina, Italy

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  • Presents a philosophical interpretation to numerical cognition based on dual process theories
  • Shows how cognitive science can shed light on issues traditionally raised by philosophers of mathematics
  • Offers new insights into the acquisition of mathematical concepts

Part of the book series: SpringerBriefs in Philosophy (BRIEFSPHILOSOPH)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-x
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  2. Introduction

    • Mario Graziano
    Pages 1-5

  3. The Cognitive Science of Numbers

    1. Front Matter

      Pages 7-7
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    2. The System 1

      • Mario Graziano
      Pages 9-37

    3. The System 2

      • Mario Graziano
      Pages 39-60

    4. Dissociations Between System 1 and System 2

      • Mario Graziano
      Pages 61-86

  4. The Transition from System 1 to System 2

    1. Front Matter

      Pages 87-87
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    2. Possible Explanations

      • Mario Graziano
      Pages 89-121

    3. Dual Process Theories for Calculus

      • Mario Graziano
      Pages 123-147
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Keywords

About this book

This book presents a philosophical interpretation to numerical cognition based on dual process theories and heuristics. It shows how investigations in cognitive science can shed light on issues traditionally raised by philosophers of mathematics. The analysis will also help readers to better understand the relationship between current neuroscientific research and the philosophical reflection on mathematics.

The author seeks to explain the acquisition of mathematical concepts. To accomplish this, he needs to answer two questions. How can the concepts of approximate numerosity become an object of thought that is so accessible to our consciousness? How are these concepts refined and specified in such a way as to become numbers? Unfortunately, there is currently no model that can truly demonstrate the role of language in the development of numerical skills starting from approximate pre-verbal skills.

However, the author details a solution to this problem: dual process theories. It is an approach widely used by theorists focusing on reasoning, decision making, social cognition, and consciousness. Here, he applies this approach to the studies on mathematical knowledge. He details the results brought about by psychological and neuroscientific studies conducted on numerical cognition by key neuroscientists. In the process, he develops the foundations of a new, potential philosophical explanation on mathematical knowledge.

Authors and Affiliations

  • Department of Cognitive Sciences, University of Messina, Messina, Italy

    Mario Graziano

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