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``Platonism and intuitionism are rival philosophies of Mathematics, the former holding that the subject matter of mathematics consists of abstract objects whose existence is independent of the mathematician, the latter that the subject matter consists of mental construction... both views are implicitly opposed to materialistic accounts of mathematics which take the subject matter of mathematics to consist (in a direct way) of material objects...'' FROM THE INTRODUCTION
Among the aims of this book are:
- The discussion of some important philosophical issues using the precision of mathematics.
- The development of formal systems that contain both classical and constructive components. This allows the study of constructivity in otherwise classical contexts and represents the formalization of important intensional aspects of mathematical practice.
- The direct formalization of intensional concepts (such as computability) in a mixed constructive/classical context.
Subject categories
- Academic > Mathematics > General > Logic, Symbolic and mathematical
- Academic > Mathematics > General > Nonclassical mathematical logic
- Academic > Mathematics > General > Modality (Logic)
- Academic > Mathematics > Instruments and machines
- Academic > Mathematics > Analytic mechanics
- Academic > Logic > Nonclassical mathematical logic
- Academic > Logic > Modality (Logic)
- Academic > Computer Science
- Mathematics
ISBNs
9780444876324
9780080880044
0080880045