CHAPTER

PAGE

perception; its complex nature; its relations

to the conception of the straight line; empirical

nature of the straight line. The validity of

the Parallel Postulate not to be settled in ab-

solute fashion by any empirical investigation 79-123

V. THE NATURE AND VALIDITY OF THE PARALLEL

POSTULATE.

The number and variety of possible geometries.

Space parameter not necessarily constant to

accord with the space of experience. Distinc-

tion between the facts of experience and the

intellectual constructs formed on a basis of

this experience. Conditions imposed upon

these constructs. Non-Euclidean systems log-

ically possible. The Parallel Postulate not a

priori necessary. How judge the validity of

Euclid. Difficulties with Poincaré's doctrine

of convenience. Why is Euclid most con-

venient? Kant's Argument. It's failure to es-

tablish the necessary validity of Euclid. Must

appeal to experience. Methods of scientific

testing and the difficulties which attend them.

The experimental method suggested in Ladd's

A Theory of Reality

VI. RESULTING IMPLICATIONS AS TO THE NATURE

OF SPACE.

Distinctions drawn between conceptions of
space and of figures in space. The importance
of these distinctions pointed out. Varieties of
two-dimensional spaces and of tri-dimensional
spaces possible. Possibility of a fourth di-
mension. Euclidean and Non-Euclidean tri-
dimensional spaces independent of a fourth
dimension. What this implies. The space-
constant and what it means. The impossibility
of comparing different space-constants quan-
titatively in a strict geometrical sense. Log-

127-152

CHAPTER

ical difficulties of the conception of variable

curvature quantitatively considered. Diffi-

culties due to abstract conception. Geometry

must fit experience; not experience geometry.

Homogeneity does not mean mere logical any-

ness. Distinction between geometrical space

conceptions and the space category. The a

priori element. Summary and conclusion

VII. BIBLIOGRAPHY

PAGE

155-173

177-192

PRE-LOBATCHEWSKIAN

STRUGGLE

WITH THE

PARALLEL POSTULATE.