Introduction -- Part I. The nature of philosophy -- The heuristic view -- The foundationalist view -- The limits of scepticism -- Philosophy and the humanistic disciplines -- Part II. The nature of knowledge -- Knowledge and naturalism -- Knowledge and reality -- Knowledge and truth -- Knowledge, plausibility, and common sense -- Other questions about knowledge -- Part III. The methods to acquire knowledge -- A discourse on method -- The methods of knowledge -- Modelling scientific knowledge -- Knowledge as problem solving -- Perceptual knowledge -- Knowledge and error -- Knowledge and mind -- Part IV. The nature of mathematical knowledge -- Mathematics as problem solving -- Mathematical objects, definitions, diagrams -- Mathematics: problem solving or theorem proving? -- Concepts of demonstration -- Mathematical explanations -- Mathematical beauty -- Mathematics and the world -- Part V. Coda -- Knowledge and the meaning of human life -- Conclusion.
This monograph addresses the question of the increasing irrelevance of philosophy, which has seen scientists as well as philosophers concluding that philosophy is dead and has dissolved into the sciences. It seeks to answer the question of whether or not philosophy can still be fruitful and what kind of philosophy can be such. The author argues that from its very beginning philosophy has focused on knowledge and methods for acquiring knowledge. This view, however, has generally been abandoned in the last century with the belief that, unlike the sciences, philosophy makes no observations or experiments and requires only thought. Thus, in order for philosophy to once again be relevant, it needs to return to its roots and focus on knowledge as well as methods for acquiring knowledge. Accordingly, this book deals with several questions about knowledge that are essential to this view of philosophy, including mathematical knowledge. Coverage examines such issues as the nature of knowledge; plausibility and common sense; knowledge as problem solving; modeling scientific knowledge; mathematical objects, definitions, diagrams; mathematics and reality; and more. This monograph presents a new approach to philosophy, epistemology, and the philosophy of mathematics. It will appeal to graduate students and researchers with interests in the role of knowledge, the analytic method, models of science, and mathematics and reality.