348 PART V. WORKING STAGE. 



However, ultra-three-dimensional beings are usually thought 

 of as living entirely on one plane, in the fourth dimension. If 

 so, they must be conceived as entirely unconscious of the three 

 other planes. Besides, recent speculations hiave acquainted us 

 with hypothetical beings having two and three dimensions; but 

 not with beings living exclusively in the second or third dimen- 

 sion. No one, if we mistake not, has yet pretended that such 

 existed or could exist. We certainly are not cognisant of them. 

 Hence a being living exclusively in the fourth dimension, poses 

 a new problem, and raises the perplexing question of the 

 existence of beings living entirely in the second or third 

 dimension. 



Whatever way, then, we regard the dimensional problem, 

 it seems if our analysis is penetrating enough that nothing 

 but solids exist, and that we are wholly unconscious of the 

 existence of one or two-dimensional beings. Einstein's rigid 

 bodies and mollusks seem to fall both under the same definition. 

 Probably an analysis of the notions of curved spheroidal and 

 finite space would be equally non-confirmative of recent space 

 theories. 



176. In practical life, matters of degree are constantly 

 overlooked. For this reason one school will declare itself 

 ostentatiously for the upholding of authority and another of 

 freedom, when wise moderation suggests that the utmost liberty 

 of personal judgment is congruent with the deepest general 

 respect for authority. Similarly, this Conclusion urges the 

 advantage of increasingly more precise, refined, and powerful 

 instruments and methods, which have frequently revolutionised 

 a department of science and general activity, and the need of 

 observation being of the extremest delicacy, of experiments 

 being completely unequivocal, and of calculations disregarding 

 no factor however seemingly insignificant. Moreover, it com- 

 prehends all analogical reasoning both in respect of degree and 

 qualitative resemblance, as the analogy between food and fuel 

 or a gland and a lung, or the determination of the ponderable 

 nature of the air by noting that it can be warmed, cooled, 

 moved, compressed, dilated, even seen in certain circumstances, 

 that it rises in water, occupies space, exerts palpable pressure 

 when strongly agitated, behaves like smoke, is capable of pro- 

 ducing sound, etc. The Conclusion is also, as we have noted, 

 most especially applicable to the systematic testing of the 

 homogeneity of any content and of the reality of divisions, of 

 the comparative importance or position of two or more related 

 facts, as well as to terms involving degree, contrast, similarity, 

 and, in general, relativity. If Descartes and Malebranche had 

 applied this Conclusion, they would have probably abandoned 

 their favourite terms Clear and Distinct as terms normally 

 lacking absolute, and needing relative, determination, and 

 M. Henri Bergson would probably find himself left, perhaps, 



