The Paradox of the Heap, from John L. Bell’s Oppositions and Paradoxes
In Oppositions and Paradoxes John L. Bell explores a variety of mathematical and scientific paradoxes with philosophical precision, while retaining a great sense of humour in his investigations. In this excerpt, Bell formulates and works through “The Problem of the Heap,” asking: how many grains of sand does one need to make a heap, exactly?…
Oppositions and Paradoxes
Since antiquity, opposed concepts such as the One and the Many, the Finite and the Infinite, and the Absolute and the Relative, have been a driving force in philosophical, scientific, and mathematical thought. Yet they have also given rise to perplexing problems and conceptual paradoxes which continue to haunt scientists and philosophers. In Oppositions and…
Logical Options
Logical Options introduces the extensions and alternatives to classical logic which are most discussed in the philosophical literature: many-sorted logic, second-order logic, modal logics, intuitionistic logic, three-valued logic, fuzzy logic, and free logic. Each logic is introduced with a brief description of some aspect of its philosophical significance, and wherever possible semantic and proof methods…