Introduction

There has been little overt discussion of the experimental philosophy of logic or mathematics. So it may be tempting to assume that application of the methods of experimental philosophy to these areas is impractical or unavailing. This assumption is undercut by three trends in recent research: a renewed interest in historical antecedents of experimental philosophy in philosophical logic; a “practice turn” in the philosophies of mathematics and logic; and philosophical interest in a substantial body of work in adjacent disciplines, such as the psychology of reasoning and mathematics education. This introduction offers a snapshot of each trend and addresses how they intersect with some of the standard criticisms of experimental philosophy. It also briefly summarizes the specific contribution of the other chapters of this book

Connecting With Fundamental Mathematical Knowledge Directly: The Organizational Features of Good Mathematical Cognitive Structure

This paper reported on the study of a good mathematical cognitive structure (GMCS) based on 43 top university students and 82 concepts of Calculus materials, using the social network analysis method. The results indicated that the GMCS has the following organizational features: (1) The mathematical knowledge (MK) in GMCS interconnected widely, especially in MK with a higher connection tightness; (2) Most connections between MK were direct; (3) MK of the basic and higher inclusive level had a greater impact; and (4) There were multiple MK accumulation points connecting others to form subsets. These new findings enrich the results of previous GMCS studies and promotes further exploration of GMCS. In view of this, teachers should pay closer attention to basic and abstract MK and help their students construct various direct connections of the MK in their mind