Rethinking Logic

Rethinking Logic

This volume examines the limitations of mathematical logic and proposes a new approach to logic intended to overcome them. To this end, the book compares mathematical logic with earlier views of logic, both in the ancient and in the modern age, including those of Plato, Aristotle, Bacon, Descartes, Leibniz, and Kant. From the comparison it is apparent that a basic limitation of mathematical logic is that it narrows down the scope of logic confining it to the study of deduction, without providing tools for discovering anything new. As a result, mathematical logic has had little impact on scientific practice. Therefore, this volume proposes a view of logic according to which logic is intended, first of all, to provide rules of discovery, that is, non-deductive rules for finding hypotheses to solve problems. This is essential if logic is to play any relevant role in mathematics, science and even philosophy. To comply with this view of logic, this volume formulates several rules of discovery, such as induction, analogy, generalization, specialization, metaphor, metonymy, definition, and diagrams. A logic based on such rules is basically a logic of discovery, and involves a new view of the relation of logic to evolution, language, reason, method and knowledge, particularly mathematical knowledge. It also involves a new view of the relation of philosophy to knowledge. This book puts forward such new views, trying to open again many doors that the founding fathers of mathematical logic had closed historically.

Rethinking Logic

Transcendental Ontology

Transcendental Ontology

Transcendental Ontology in German Idealism: Schelling and Hegel sheds remarkable light on a question central to post-Kantian philosophy: after the Copernican Revolution in philosophy, what can philosophy say about the world or reality as such? What remains of ontology’s task after Kant? This is a question often overlooked in contemporary scholarship on German Idealism.

Transcendental Ontology

Wittgenstein, Comparisons and Context

Wittgenstein, Comparisons and Context

Wittgenstein: Comparisons and Context is a collection of P. M. S. Hacker’s papers on Wittgenstein and Wittgensteinian themes written over the last decade. It presents Hacker’s own (Wittgensteinian) conception of philosophy, and defends it against criticisms. Two essays compare Wittgenstein with Kant on transcendental arguments, and offer a Wittgensteinian critique of Kant’s transcendental deduction. Two further essays trace the development of Wittgenstein’s philosophy of psychology, and examine his anthropological and ethnological approach to philosophical problems. This leads naturally to a synoptic comparison of Wittgenstein’s later philosophy of language with formal, truth-conditional conceptions of language. A further two clarificatory essays follow these comparative ones: the first concerns Wittgenstein’s conception of grammar, and his exclusion of theses, doctrines, dogmas, and opinions in philosophy; the second concerns his treatment of intentionality. The penultimate essay examines Quine’s epistemological naturalism, which is often presented as a more scientific approach to philosophical problems than Wittgenstein’s. The final essay offers a synoptic view of analytic philosophy and its history, in which Wittgenstein played so notable a part. The volume complements Hacker’s previous collection, Wittgenstein: Connections and Controversies (OUP, 2001), but stands as an independent contribution to work in the field.

Wittgenstein, Comparisons and Context