Free Logic: Selected Essays

Free logic is an important field of philosophical logic that first appeared in the 1950s. J. Karel Lambert was one of its founders and coined the term itself. The essays in this collection (written over a period of 40 years) explore the philosophical foundations of free logic and its application to areas as diverse as the philosophy of religion and computer science. Amongst the applications on offer are those to the analysis of existence statements, to definite descriptions and to partial functions. The volume contains a proof that free logics of any kind are non-extensional and then uses that proof to show that Quine’s theory of predication and referential transparency must fail. The purpose of this collection is to bring an important body of work to the attention of a new generation of professional philosophers, computer scientists and mathematicians.

• Lambert is the founder of this field of logic: he is well known to philosophers and logicians • Cross-disciplinary potential for computer science

Introduction; 1. Russell’s version of the theory of definite descriptions; 2. Existential import, \'E!\' and \'the\'; 3. The reduction of two paradoxes and the significance thereof; 4. The Hilbert-Bernays theory of definite descriptions; 5. Foundations of the hierarchy of positive free definite description theories; 6. Predication and extensionality; 7. Nonextensionality; 8. The philosophical foundations of free logic; 9. Logical truth and microphysics.

‘Free logic is still very much a current concern both to logicians and to philosophical logicians and philosophers of language and mathematics … I cannot but believe that the proposed collection will have anything but a major impact and would be invaluable as a teaching aid at intermediate and advanced level as well as professional research interest.’

– Dr Peter Clark, University of St. Andrews

‘These essays will be seen to be even more important once mathematicians and software engineers realize that what they thought was new and novel to their fields (E-logic and E+-logic and the various other names that these logics go by in mathematics and computer science) are varieties of free logic and were first discovered 30-45 years ago.’

– Professor Raymond Gumb, University of Massachusetts, Lowell