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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
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