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.
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.
Brouwer and Brouwerian intuitionism.- Another look at Brouwers
dissertation.- Brouwerian infinity.- The new intuitionism.- Truth and
experience of truth.- The proper explanation of intuitionistic logic: on
Brouwers demonstration of the Bar Theorem.- The intersection of intuitionism
(Brouwer) and phenomenology (Husserl).- Brouwer on hypotheses and the
middle Wittgenstein.- Brouwers notion of intuition and theory of knowledge
by presence.- Buddhist models of the mind and the common core thesis on
mysticism.- Kindred spirits.- Remarks on the supposed french semi- or
pre-intuitionism.- Poincaré: intuitionism, intuition, and convention.- Some
of Julius Königs mathematical dreams in his New Foundations of Logic,
Arithmetic, and Set Theory.- Gödel, constructivity, impredicativity, and
feasibility.- Lorenzens operative justification of intuitionistic logic.-
Mathematical perspectives.- The Hilbert-Brouwer controversy resolved?.- Proof
theory and Martin-Löf Type Theory.- Some remarkson linear logic.- Two
applications of dynamic constructivism: Brouwers continuity principle and
choice sequences in formal topology.- A reverse look at Brouwers Fan
Theorem.- Some applications of Brouwers Thesis on Bars.- Concluding remarks
at the Cerisy conference.- A bibliography of L.E.J. Brouwer.
