Rethinking Logic: Logic in Relation to Mathematics, Evolution, and Method

The book develops an alternative to current mathematical logic, capable of overcoming the limitations of the latter. On the basis of it, logic is a logic of discovery. Despite strenuous efforts by its proponents, mathematical logic has generally failed to convince mathematicians, natural scientists and human scientists of its relevance to their work, increasingly so in the last few decades. This raises the question: Why does this come about and how to remedy it? This skeptical attitude contrasts with the reputation logic enjoyed in antiquity, not only as one of the main parts of philosophy, but especially as a supplier of instruments for the sciences. At that time, almost no one disputed that such instruments could be beneficial to their potential users, so much so that logic was a standard part of the school curriculum. The aim of this book is to deal with this question. To this purpose, the book first gives an overview of how logic and its relation with the scientific method have been conceived in antiquity and in the modern age, because this provides indications for a new approach to the subject. Then the book proposes a new view of logic and its relation with evolution, language, reason, method and knowledge, as well as a new view of philosophy and its relation with knowledge, since seeing logic in a wider perspective helps to place the subject on a more satisfactory basis. According to the new view, logic is primarily a logic of discovery. Finally, the book deals with the rules of discovery.