BROUWERIAN INTUITIONISM

The focal question of this essay is what if any role logical inference should be taken to play in mathematical reasoning. Special attention is given to the idea of Brouwer and Poincaré that, by its very topic-neutral character, logical inference is unsuitable for use in mathematical reasoning, and t...

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Bibliographic Details
Published inProof and Knowledge in Mathematics pp. 137 - 163
Format Book Chapter
LanguageEnglish
Published United Kingdom Routledge 1992
Taylor & Francis Group
Subjects
Mathematical logic
Philosophy of mathematics
Genuinely Mathematical
Logical Extrapolation
Ordinary Counting
Mental Proof
Constructional Activity
Mathematical Reasoning
Compound Propositions
Direct Sensory Experience
Brouwerian Intuitionism
Cognitive Mode
Credential Effect
Superb
Natural Kind
Arena Seats
Inferential Justification
Logical Relations
Mathematical Epistemology
Classical Epistemology
Soundness Question
Epistemic Growth
Mathematical Knowledge
Intuitionistic Conjunction
Intuitionistic Constructions
Epistemic Condition
Intuitionist Logic
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ISBN9780415068055
0415068053
DOI10.4324/9780203979105-15

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Summary:The focal question of this essay is what if any role logical inference should be taken to play in mathematical reasoning. Special attention is given to the idea of Brouwer and Poincaré that, by its very topic-neutral character, logical inference is unsuitable for use in mathematical reasoning, and the epistemology standing behind this idea is partially developed. According to this epistemology, intuition is needed not only to supply axioms, but also to power inference.
ISBN:9780415068055
0415068053
DOI:10.4324/9780203979105-15