Determinations, geometrical, the necessity of, inheres in logical deductions, 78 -- the factors of conscious, 162 Determinative period of mental development, 31 Development of the intuitive faculty, future, 188 Diacritics of life, 286 Diameter, the ratio of, to the circumference, 311-2 Difference between concept and thing, 121-2 -- between mathematical and perceptual space, 120 -- between the ideal and the actual is dynamic, 108 Differential, among minds, 124 Difficulty of imagining the fourth dimension, 90 -- of propagating an intuition, 315 Difficulties in the acquisition of real knowledge, 325 -- of hyperspace, the logical, 139-41 Dilemma of metageometricians, 97-8 Dimension, a distinct stage in psychogenesis, 27 -- -- system of space measurement, 5 -- and analysis, 163 -- -- D'Alembert, _note_, 51 -- -- the action of a tartrate in, 156 -- as an arbitrary contrivance, 262 -- -- -- assemblage of elements, 93 -- -- direction, 140 -- -- extent, 98 -- -- lying near the surface of things, 159-60 -- -- space, 96 -- current definitions of, 98-100 -- denied legitimate anchorage, 265 -- determined by consciousness, 145 -- does not explain spiritualism, 155 -- evolution of the fourth, 44 -- fourth, direction of, 134 -- as "jack of all trades," 156 -- impossible to actualize, 124 -- key, to non-Euclidean geometry, 90 -- movement of a plane into, 147-8 -- no motion of material masses into, 125 -- not _a priori_, 116 -- proof of the existence of the fourth, 136 Dimensionality, and the intellect, 200 -- as dependent upon the will of the investigator, 95 Dimensionality, conception of, purely conventional, 92 -- logical difficulties which beset, 97 -- of perceptual space, 72 -- -- space, the four, 142-3 Dimensions, four, no basis in consciousness for, 172 -- piled upon one another, 300 -- vanity, the, of segmenting space into many, 299 Direction as dimension, 99 Disappointment with the sensible world, 120-1 Discoveries, metageometrical, as excrescences of mental unfoldment, 131 -- never the result of methodic reflection, 29-30 Disorder, the edict of, and space, 230 Disorderliness, the fringe of, 277 Dispossessal of the intellect by the intuition, 195 Dissimilarities, besetment of, 291 Distinctions, between conceptual and perceptual space, fundamental, 73-5 Diversity, a result of the fragmentative tendency of life, 6 -- as transfinite quantity, 42 Divinity, prize of, won by the intellect, 43 Duadic phase of evolution, 210-1 Duodim, defined, 6; 128, 129, 134, 177 -- consciousness, 163 Duopyknon, 212, 213 -- the meaning of, 6 Duopyknosis, 208-10, 218 -- as a stage in the evolution of space, 6 Duration and space, 224 -- eternal, 234 Dynamic appearance, space as, 104, 107 Dynamism, of the intellect, functional, 303 E