Brouwer's Cambridge Lectures on IntuitionismLuitzen Egburtus Jan Brouwer founded a school of thought whose aim was to include mathematics within the framework of intuitionistic philosophy; mathematics was to be regarded as an essentially free development of the human mind. What emerged diverged considerably at some points from tradition, but intuitionism has survived well the struggle between contending schools in the foundations of mathematics and exact philosophy. Originally published in 1981, this monograph contains a series of lectures dealing with most of the fundamental topics such as choice sequences, the continuum, the fan theorem, order and well-order. Brouwer's own powerful style is evident throughout the work. |
Contents
HISTORICAL INTRODUCTION AND FUNDAMENTAL | 1 |
GENERAL PROPERTIES OF SPECIES SPREAD | 21 |
ORDER | 40 |
PRECISION ANALYSIS OF THE CONTINUUM | 57 |
THE BUNCH THEOREM | 77 |
Appendix | 90 |
References | 103 |
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Common terms and phrases
absurdity of absurdity arrow containing assigned belongs binary fractions Brouwer bunch theorem Cambridge lectures Cartesian plane Cartesian space choice sequence classical logic closed interval coincide compact complete principle conjugate removable subspecies constructional subspecies core of Q critical number crude block Dedekind cut deduce define denote element of 2Nm excluded third existence finite number fleeing property free arrow fundamental sequence Heine-Borel theorem Hence indicated infinite sequence initial sequence intercalation subdivision intuitionism intuitionist full continuum intuitionist reduced continuum intuitive lawlike Let us suppose locally compact marked well-ordered species mathematical assertions mathematical entities N₁ natural number node of order non-contradictory non-sterilized node notion ordinal connectedness ordinal sum overlap p₁ point core species point spread possess predeterminate principle proved rational numbers real number relations right subspecies row of nodes species F species of point spread clue spread direction spread key spread law square sterilized node stump sector up-number v₁