Intuitionistic Proof Versus Classical Truth

Enrico Martino was associated professor (now retired) of Logic and Philosophy of Mathematics in the department of Mathematics and, subsequently of FISPPA of the University of Padua. His main interests are Philosophy of Logic and Mathematics.

• Brouwer, Dummett and the bar theorem.-  Creative subject and bar theorem.- Natural intuitionistic semantics and generalized Beth semantics.-  Connection between the principle of inductive evidence and the bar theorem.- On the Brouwerian concept of negative continuity.- Classical and intuitionistic semantical groundedness.- Brouwer’s equivalence between virtual and inextensible order.- An intuitionistic notion of hypothetical truth for which strong completeness intuitionistically holds.- Propositions and judgements in Martin-Löf.-  Negationless Intuitionism.- Temporal and atemporal truth in intuitionistic mathematics.-  Arbitrary reference in mathematical reasoning.-  The priority of arithmetical truth over arithmetical provability.- The impredicativity of the intuitionistic meaning of logical constants.- The intuitionistic meaning of logical constants and fallible models.

“Anyone with an interest in the murkier aspects of intuitionism will find this book well worth reading.” (Peter Fletcher, Studia Logica, Vol. 107, 2019)