Pure Mathematics

The science of mathematics presents the most brilliant example of how pure reason may successfully enlarge its domain without the aid of experience.

Pure Mathematics is the class of all propositions of the form “p implies q,” where p and q are propositions containing one or more variables, the same in the two propositions, and neither p nor q contains any constants except logical constants. And logical constants are all notions definable in terms of the following: Implication, the relation of a term to a class of which it is a member, the notion of such that, the notion of relation, and such further notions as may be involved in the general notion of propositions of the above form. In addition to these, mathematics uses a notion which is not a constituent of the propositions which it considers, namely the notion of truth.

“It’s magic,” the chief cook concluded, in awe.
“No, not magic,” the ship’s doctor replied. “It’s much more. It’s mathematics.”