CHAPTER V

THE FOURTH DIMENSION

The Ideal and the Representative Nature of Objects in the Sensible World--The Fluxional, the Basis of Mental Differences--Natural Symbols and Artificial Symbols--Use of Analogies to Prove the Existence of a Fourth Dimension--The Generation of a Hypercube or Tesseract--Possibilities in the World of the Fourth Dimension--Some Logical Difficulties Inhering in the Four-Space Conception--The Fallacy of the Plane-Rotation Hypothesis--C. H. Hinton and Major Ellis on the Fourth Dimension 118

_PART TWO_

SPATIALITY: AN INQUIRY INTO THE ESSENTIAL NATURE OF SPACE AS DISTINGUISHED FROM THE MATHEMATICAL INTERPRETATION