Mysticism and Logic and Other Essays

This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1918 edition. Excerpt: ...say, contain the point. To secure a i,'definition giving this result, without previously assuming that physical objects are composed of points, is an agreeable problem in mathematical logic. The solution of 'this problem and the perception of its importance are due to my friend Dr. Whitehead. The oddity of regarding a point as a class of physical entrtieslveaiSuQrl-with--v l&miliarity, anoTbugEt: many case not to be felt by those who maintain, as practically every one does, that points are mathematical fictions. The word "fiction " is used glibly in such connexions by many men who seem not to feel the necessity of explaining how it can come about that a fiction can be so useful in the study of the actual world as the points of mathematical physics have been found to be. By our definition, which regards a point as a class of physical objects, it is explained both how the use of points can lead to important physical results, and how we can nevertheless avoid the assumption that points are themselves entities in the physical world. Many of the mathematically convenient properties of abstract logical spaces cannot be either known to belong or known not to belong to the space of physics. Such are all the properties connected with continuity. For to know that actual space has these properties would require an infinite exactness of sense-perception. If actual space is continuous, there are nevertheless many possible non-continuous spaces which will be empirically indistinguishable from it; and, conversely, actual space may be non-continuous and yet empirically indistinguishable from a possible continuous space. Continuity, therefore, though obtainable in the a priori region of arithmetic, is not with certainty obtainable in the...