ABSTRACT

This book is meant as a part of the larger contemporary philosophical project of naturalizing logico-mathematical knowledge, and addresses the key question that motivates most of the work in this field: What is philosophically relevant about the nature of logico-mathematical knowledge in recent research in psychology and cognitive science? The question about this distinctive kind of knowledge is rooted in Plato’s dialogues, and virtually all major philosophers have expressed interest in it. The essays in this collection tackle this important philosophical query from the perspective of the modern sciences of cognition, namely cognitive psychology and neuroscience. Naturalizing Logico-Mathematical Knowledge contributes to consolidating a new, emerging direction in the philosophy of mathematics, which, while keeping the traditional concerns of this sub-discipline in sight, aims to engage with them in a scientifically-informed manner. A subsequent aim is to signal the philosophers’ willingness to enter into a fruitful dialogue with the community of cognitive scientists and psychologists by examining their methods and interpretive strategies.

chapter 1|14 pages

Introduction

A Naturalist Landscape
BySorin Bangu

chapter 2|15 pages

Psychology and the A Priori Sciences

ByPenelope Maddy

chapter 3|22 pages

Reasoning, Rules, and Representation

ByPaul D. Robinson, Richard Samuels

chapter 4|37 pages

Numerical Cognition and Mathematical Knowledge

The Plural Property View
ByByeong-uk Yi

chapter 5|17 pages

Intuitions, Naturalism, and Benacerraf’s Problem

ByMark Fedyk

chapter 6|25 pages

Origins of Numerical Knowledge

ByKaren Wynn

chapter 7|17 pages

What Happens When a Child Learns to Count?

The Development of the Number Concept
ByKristy vanMarle

chapter 8|16 pages

Seeing Numbers as Affordances

ByMax Jones

chapter 9|15 pages

Testimony and Children’s Acquisition of Number Concepts

ByHelen De Cruz

chapter 10|16 pages

Which Came First, the Number or the Numeral?

ByJean-Charles Pelland

chapter 11|23 pages

Numbers Through Numerals

The Constitutive Role of External Representations
ByDirk Schlimm

chapter 12|16 pages

Making Sense of Numbers Without a Number Sense

ByKarim Zahidi, Erik Myin

chapter 13|18 pages

Beyond Peano

Looking Into the Unnaturalness of Natural Numbers
ByJosephine Relaford-Doyle, Rafael Núñez

chapter 14|16 pages

Beauty and Truth in Mathematics

Evidence From Cognitive Psychology
ByRolf Reber

chapter 15|26 pages

Mathematical Knowledge, the Analytic Method, and Naturalism

ByFabio Sterpetti