Mathematical Intuitionism and Intersubjectivity

the long version

This book is the first modern examination of the philosophical foundations of intuitionism since Oscar Becker's (1927) Mathematische Existenz. Placek examines the three most widely-known arguments for mathematical intuitionism: Brouwer's, Heyting's and Dummett's. The examination centres on the questions of the intersubjectivity of mathematics and is concerned with understanding and evaluating the arguments. An unprejudiced stance leads to refreshing conclusions concerning Brouwer: the philosophical side of Brouwer's doctrine cannot be accused of such sins as psychologism, solipsism or the advocacy of private meaning. Similarly, examination of the Husserlian grounds of Heyting's explanation of the meaning of logical constants shows that this view of language should not be accused of violating the requirement of intersubjectivity of meaning. The approach of the work is philosophical, rather than mathematical or logico-technical.