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IV.
explanation of the irrational numbers.--The problem of the
transfinite numbers.--The concept of "power."--The production
of transfinite numbers.--The second "principle of generation" of
numbers (Cantor) 		54
CHAPTER III

THE CONCEPT OF SPACE AND GEOMETRY
I. Concept and form.--The method of ancient geometry.--The con-
cept of space and the concept of number.--The fundamental
principle of analytic geometry.--The infinitesimal geometry.--
Magnitudes and functions 		68
II. Intuition and thought in the principles of the geometry of posi-
tion.--Steiner and Poncelet.--The concept of "correlation" and
the principle of continuity.--The transference of relations dis-
tinguished from induction and analogy.--Projection and the
imaginary in geometry.--Metrical and projective geometry, and
quadrilateral construction of Staudt.--Projective metric (Cayley
and Klein.--The concept of space and the concept of order.--
Geometry and the group theory.--The concepts of constancy
and change in geometry 		76
III. Characteristic (Kombinatorik) as pure "doctrine of forms" (Leib-
niz).--Geometry as pure "doctrine of relations" (Hilbert).--The
syntheses of generating relations.--Grassmann's Ausdehnungs-
lehre and its logical principles.--The forms of calculus, and the
concept of the Source 		91
IV. The problem of metageometry.--The attempt at an empirical
grounding of geometry (Pasch).--Ideal objects in empirical
geometry.--Veronese's modification of empiricism.--Rationalism
and empiricism.--Mathematical space and sensuous space.--Ob-
jections to the Kantian theory of geometry.--Real space and
experiment.--The conceptual principles of pure space.--Eu-
clidean space and the other forms of mathematical space.--
Geometry and reality 		100
CHAPTER IV

THE CONCEPTS OF NATURAL SCIENCE
I. The constructive concepts and the concepts of nature.--The con-
cept of traditional logic and the scientific ideal of pure descrip-
tion.--The apparent logical ideal of physics.--Is this the true
ideal of physics? 		112
II. Numbering and measuring as presuppositions.--Mechanism and the
concept of motion.--The "subject" of motion.--The "limiting
concept" and its significance for natural science (Karl Pearson).
--P. du Bois-Reymond's theory of the limiting concept.--The

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Publication Information: Book Title: Substance and Function and Einstein's Theory of Relativity. Contributors: Ernst Cassirer - author, Marie Collins Swabey - transltr, William Curtis Swabey - transltr. Publisher: Dover Publications. Place of Publication: New York. Publication Year: 1953. Page Number: viii.
    
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