MATHEMATICS (MS 1-278)
The nature of mathematics, pure and applied. In general, mathematics is concerned with the substance of hypotheses, drawing necessary conclusions from them; pure mathematics is concerned only with those hypotheses which contain nothing not relevant to the forms of deduction. The nature of quantity (real, rational, and imaginary). System of quaternions as an enlargement of the system of imaginary quantity. Possible grades of multitude. Spatial and temporal continuity. Common sense notions of continua, especially with regard to the flow of time. "Continuum" defined as "a whole composed of parts, with the parts of the whole comprising a series, such that, taking any multitude whatever, a collection of those parts can be discovered the multitude of which is greater than the given multitude." Lastly, reasons are given for thinking that continuity exists beyond the evidence afforded by our natural beliefs in the continuity of space and time.
common sense notions of Continuity, existence of and feeling Continuity, spatial Continuity, temporal Continuity (see also Continuum; Synechism; Thirdness), Continuum, Mathematics, pure Mathematics, Multitude, logic of Quantity, Quaternions
MATHEMATICS / THE SIMPLEST MATHEMATICS