Haverkamp, Nick Intuitionism vs. classicism. A mathematical attack on classical logic. (English) Zbl 1358.03004 Studies in Theoretical Philosophy 2. Frankfurt am Main: Vittorio Klostermann (ISBN 978-3-465-03906-8/pbk). xvi, 269 p. (2015). This book carefully examines the conflict between classical logic (stemming from Frege) and intuitionist logic (stemming from Brouwer). The arguments fall into four classes. (i) McCarty’s uniformity principle, de Swart’s continuity principle, and the like. Against these is the lack of any reason to accept the underlying existential claims. (ii) Prawitz’s theory of grounds, which can be modified to permit the provability of disjunctions that instantiate the law of excluded middle. (iii) Dummett’s manifestation argument, which needs to take into account that meaning and understanding are compositional. It is then shown that compositional manifestation of understanding is consistent with classical truth-conditional semantics. (iv) Proof-theoretic arguments, undermined by the presentation of harmonious collections of rules of inference for classical calculi. The findings suggest that Dummett’s hope for a meaning-theoretic resolution to the conflict is ill-founded, and that it may be that there can be no non-question-begging resolution. Reviewer: Jim Mackenzie (Sydney) Cited in 1 Document MSC: 03-03 History of mathematical logic and foundations 01A60 History of mathematics in the 20th century 03B20 Subsystems of classical logic (including intuitionistic logic) 03B05 Classical propositional logic 03B10 Classical first-order logic Keywords:intuitionist logic; classical logic; excluded middle; manifestation; principle of charity PDF BibTeX XML Cite \textit{N. Haverkamp}, Intuitionism vs. classicism. A mathematical attack on classical logic. Frankfurt am Main: Vittorio Klostermann (2015; Zbl 1358.03004)