ABSTRACT
This chapter describes the most fundamental differences between the experimental and the historical sciences. It has already been pointed out that the sciences are orderly branches of knowledge. The chapter examines that mathematics differs from all other sciences in that the nature of mathematical facts is such that they can be ordered in an exact way. In mathematics, and in mathematics alone, demonstration is possible. Thus mathematics is a pure science to be contrasted with all other sciences which are empirical in that they are based upon the observation of sensible fact. The chapter is concerned with the conditions essential to any branch of science capable of formulating abstract functional laws. The experimental sciences, especially physics and physical chemistry are frequently spoken of as 'the most advanced sciences'. Unless there be advance of this kind the science is at a standstill, as was long the case with the science of logic.
