This open access book examines the many contributions of Paul Lorenzen, an outstanding philosopher from the latter half of the 20th century. It features papers focused on integrating Lorenzen's original approach into the history of logic and mathematics. The papers also explore how practitioners can implement Lorenzen's systematical ideas in today's debates on proof-theoretic semantics, databank management, and stochastics. Coverage details key contributions of Lorenzen to constructive mathematics, Lorenzen's work on lattice-groups and divisibility theory, and modern set theory and Lorenzen's critique of actual infinity. The contributors also look at the main problem of Grundlagenforschung and Lorenzen's consistency proof and Hilbert's larger program. In addition, the papers offer a constructive examination of a Russell-style Ramified Type Theory and a way out of the circularity puzzle within the operative justification of logic and mathematics. Paul Lorenzen's name is associated with the Erlangen School of Methodical Constructivism, of which the approach in linguistic philosophy and philosophy of science determined philosophical discussions especially in Germany in the 1960s and 1970s. This volume features 10 papers from a meeting that took place at the University of Konstanz.

In the last century, developments in mathematics, philosophy, physics, computer science, economics and linguistics have proven important for the development of logic. There has been an influx of new ideas, concerns, and logical systems reflecting a great variety of reasoning tasks in the sciences. This book embodies the multi-dimensional interplay between logic and science, presenting contributions from the world's leading scholars on new trends and possible developments for research.

Intuitionism is one of the main foundations for mathematics proposed in the twentieth century and its views on logic have also notably become important with the development of theoretical computer science. This book reviews and completes the historical account of intuitionism. It also presents recent philosophical work on intuitionism and gives examples of new technical advances and applications. It brings together 21 contributions from today's leading authors on intuitionism.

In the last century developments in mathematics, philosophy, physics, computer science, economics and linguistics have proven important for the development of logic. There has been an influx of new ideas, concerns, and logical systems reflecting a great variety of reasoning tasks in the sciences. This volume reflects the multi-dimensional nature of the interplay between logic and science. It presents contributions from the world's leading scholars under the following headings: - Proof, Knowledge and Computation;- Truth Values beyond Bivalence;- Category-Theoretic Structures;- Independence, Evaluation Games, and Imperfect Information;- Dialogue and Pragmatics