Intuitionistic Proof Versus Classical Truth

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-Loef.- 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.

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Informal Intuitionistic Proof;Creative Subject;Bar Theorem;Type Theory;Constructivism;Inductive Evidence;Semantical Groundedness;Impredicativity;Intuitionistic Choice Sequences;Beth-Models;Fallible Models;Brouwer realistic truth;Brouwer classical truth;Brouwer intuitionistic truth;Brouwer creative subject;Brouwer Michael Dummett;Brouwer Saul Kripke;Brouwer Per Martin-Loef;Brouwer Arend Heyting