THE PHILOSOPHY OF SCIENCE.--In the last chapter we heard A. J. Balfour complaining of the absence of "a full and systematic attempt, first to enumerate, and then to justify, the presuppositions on which all science finally rests." And Mr. F. H. Bradley also drew attention to the absence of any critical philosophy of science in England. The need was for scientific standpoints to be investigated _de novo_; and the process had, as a matter of fact, already been begun on the Continent. MACH.--Ernst Mach, Professor of Physics at Prague, and subsequently Professor of Physics at Vienna (thus combining the roles of scientist and metaphysician--always a highly instructive and fruitful combination) had as early as 1863 laid it down as the task of science to give "an economic presentation of the facts." By which phrase he meant that science takes account only of the salient features of phenomena, selecting only those which seem strictly serviceable to its own purpose. SCIENCE "ABSTRACT" OR "SELECTIVE."--Mathematical science (which is the "pure" science _par excellence_) deals not--as is generally supposed--with "things," but with _certain selected aspects_ of things. For example, for purposes of arithmetic, every leaf on a tree is an "unit" (i.e. all are "identical"); but, in point of fact, there exist no two leaves that are alike, as Leibniz, long ago, pointed out. Again, for geometrical purposes two fields may be regarded as of like area; but no two fields are, or ever have been, so. Thus mathematics--where scientific method is seen at its purest--proceeds by deliberately disregarding individuality; it regards the differences between individuals as non-essential, and irrelevant to its purpose. ECONOMY OF THOUGHT.--And mathematical science is justified in acting in this way. This method, highly abstract as it is--in fact, just because it is highly abstract--leads to invaluable results. It's justification is that it is _economical of thought_; disregarding all irrelevant considerations, it is able, by using a short-cut, to reach its goal. Did the mathematician have to take into consideration all the manifold and complex aspects of each concrete "thing" (whether it be leaf, or field, or lever, or what not) with which he deals, he would never be able to cut his way through the jungle. His method of abstraction carries him at once to his goal. MACH ON THE "MECHANICAL VIEW."--Mach's criticism of the mechanical view of nature proceeded upon similar lines. He termed that view "analogical," by which he meant that mechanical "laws of nature" serve us as formal patterns to which the processes of nature may (for convenience sake) be represented as conforming. A clear account, though not a _complete_ account, of all physical processes may be given in terms of mechanical "law." And in fact it remains a question, Mach observed, "whether the mechanical view of things, instead of being the profoundest, is not in point of fact, the shallowest of all."[52]