This book develops Tennant's Natural Logicist account of the foundations of the natural, rational, and real numbers. Tennant uses this framework to distinguish the logical from the intuitive aspects of the basic elements of arithmetic. The aim of this book is to show how to introduce natural, rational, and real numbers in a redefined logicist manner...In addition to these topics, there are extensive passages about reverse mathematics, large cardinals, a conjecture by Harvey Friedman.