This book examines three connected aspects of Frege's logicism: the differences between
Dedekind's and Frege's interpretation of the term 'logic' and related terms and reflects on
Frege's notion of function comparing its understanding and the role it played in Frege's and
Lagrange's foundational programs. It concludes with an examination of the notion of arbitrary
function taking into account Frege's Ramsey's and Russell's view on the subject. Composed of
three chapters this book sheds light on important aspects of Dedekind's and Frege's logicisms.
The first chapter explains how although he shares Frege's aim at substituting logical
standards of rigor to intuitive imports from spatio-temporal experience into the deductive
presentation of arithmetic Dedekind had a different goal and used or invented different tools.
The chapter highlights basic dissimilarities between Dedekind's and Frege's actual ways of
doing and thinking. The second chapter reflects on Frege's notion of a function in comparison
with the notions endorsed by Lagrange and the followers of the program of arithmetization of
analysis. It remarks that the foundational programs pursued by Lagrange and Frege are crucially
different and based on a different idea of what the foundations of mathematics should be like.
However despite this contrast the notion of function plays similar roles in the two programs
and this chapter emphasizes the similarities. The third chapter traces the development of
thinking about Frege's program in the foundations of mathematics and includes comparisons of
Frege's Russell's and Ramsey's views. The chapter discusses earlier papers written by Hintikka
Sandu Demopoulos and Trueman. Although the chapter's main focus is on the notion of arbitrary
correlation it starts out by discussing some aspects of the connection between this notion and
Dedekind Theorem.
