ABSTRACT
The word ‘distance’ means of course length or extension. In that short single sentence the author uses three different words to describe real numbers: magnitude, measurement and quantity. Logical analysis is indispensable for an examination of the strength of a mathematical structure, but it is useless for its conception and design. G. Frege is correct that the two number systems are completely disjoint or different domains, but he cannot free himself of the concept of cardinal numbers because it is based on his whole concept of class logic, that is formal logic. The second edition of Hilbert’s Philosophy of Mathematics edited by Benacerraf and Putnan in 1983 has a comprehensive list of articles on the subject. Sir William Rowan Hamilton was born in Ireland in 1805. He had a brilliant career at Trinity College, Dublin, excelling in mathematics and languages. Hamilton published a long paper in the Transactions of the Royal Irish Academy in 1837.
