We present an approach in which ancient Greek mathematical proofs by Hippocrates of Chios and Euclid are addressed as a form of (guided) intentional reasoning. Schematically, in a proof, we start with a sentence that works as a premise; this sentence is followed by another, the conclusion of what we might take to be an inferential step. That goes on until the last conclusion is reached. Guided by the text, we go through small inferential steps; in each one, we (...) go through an autonomous reasoning process linking the premise to the conclusion. The reasoning process is accompanied by a metareasoning process. Metareasoning gives rise to a feeling-knowing of correctness. In each step/cycle of the proof, we have a feeling-knowing of correctness. Overall, we reach a feeling of correctness for the whole proof. We suggest that this approach allows us to address the issues of how a proof functions, for us, as an enabler to ascertain the correctness of its argument and how we ascertain this correctness. (shrink)

Book synopsis: This is the first volume of a two-volume introduction to and guide through philosophy. It is intended to orientate, assist, and stimulate the reader at every stage in the study of the subject. Eleven extended essays have been specially commissioned from leading philosophers; each surveys a major area of the subject and offers an accessible but sophisticated account of the main debates. An extended introduction maps out the philosophical terrain and explains how the different subjects relate to each (...) other. The first part of the book deals with the foundations of philosophical enquiry: epistemology; philosophical logic; methodology; metaphysics; and the philosophy of mind. The second part offers four historical chapters, two on ancient and two on modern philosophy, introducing great thinkers from the past, explaining and discussing their ideas, and showing the value of studying them today. The third part comprises two chapters devoted to questions of value, in ethics and aesthetics. Full annotated bibliographies are provided at the ends of chapters to serve as guides to further reading. This is real philosophy, not simplified philosophy; it will be accessible for the beginner but equally valuable for the third-year student. Deep and challenging questions are not shirked; the reader will be given a sense of involvement in the practice of philosophy today. (shrink)

An introductory text dealing with the Pre-Socratic philosophers and central aspects of Plato.