Excerpt from Logic, Vol. 2
Mathematics is the best example of a Formal Deductive Science,; Mathematic treats of Quantity in the abstract, so far as definitely expressible, Notions of Mathematics.; Enumeration of the principal Notions, with a view to the propositions, Propositions of Mathematics.; Logically viewed these are of the nature of propria; the predicate is deducible from the subject, Definition in Mathematics.; Certain of the Notions are Ultimate; the rest are definable by derivation. Ultimate notions of Arithmetic; of Geometry, Axioms of Mathematics.; These should be (1) Real Propositions; (2) underived within the science, Euclid"s axioms tested. Postulates, Divisions of Mathematics :- Arithmetic.; Groundwork and Propositions of Arithmetic, Algebra.; Extension of Arithmetic by using symbols of numbers and signs of operation,; Algebra shows the equivalence of different operations, and renders them mutually resolvible,; The signs and rules of operation have to be adjusted by being verified,; The highest form of the Algebraical problem is the Resolution Of Equations,; Geometry.; Order of topics. Euclid"s proving the fourth proposition is a mistake; it should have been assumed on the basis of induction,; Ends served, in elementary Geometry, by the reference to Diagrams,
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