AN ENQUIRY CONCERNING THE PRINCIPLES OF NATURAL KNOWLEDGE BY A. N. WHITEHEAD, Sc.D., F.R.S. Fellow of Trinity College, Cambridge, Professor of Philosophy in Harvard University, and sometime Professor of Applied Mathematics in the Imperial College of Science and Technology "PHILONOUS. I am not for imposing any sense on your words: you are at liberty to explain them as you please. Only, I beseech you, make me understand something by them." BERKELEY, The First Dialogue between Hylas and Philonous. CAMBRIDGE AT THE UNIVERSITY PRESS 1925 TO ERIC ALFRED WHITEHEAD ROYAL FLYING CORPS November 27, 1898 to March 13, 1918 Killed in action over the Forêt de Gobain giving himself that the city of his vision may not perish. The music of his life was without discord, perfect in its beauty. First Edition 1919 Second Edition 1925 PRINTED IN GREAT BRITAIN PREFACE THERE are three main streams of thought which are relevant to the theme of this enquiry; they may, with sufficient accuracy, be termed the scientific, the mathematical, and the philosophical movements. Modern speculative physics with its revolutionary theories concerning the natures of matter and of electricity has made urgent the question, What are the ultimate data of science? It is in accordance with the nature of things that mankind should find itself acting and should then proceed to discuss the rationale of its activities. Thus the creation of science precedes the analysis of its data and can even be accompanied by the acceptance of faulty analyses, though such errors end by warping scientific imagination. The contributions of mathematics to natural science consist in the elaboration of the general art of deductive reasoning, the theory of quantitative measurement by the use of number, the theory of serial order, of geometry, of the exact measurement of time, and of rates of change. The critical studies of the nineteenth century and after have thrown light on the nature of mathematics and in particular on the foundations of geometry. We now know many alternative sets of axioms from which geometry can be deduced by the strictest deductive reasoning. But these investigations concern geometry as an abstract science deduced from hypothetical premisses. In this enquiry we are concerned with geometry as a physical science. How is space rooted in experience?