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i, ii, iii, iv, v, vi, vii, viii, ix, x, xi, xii, 1, 3, 4, 5, 6, 27, 68, 112, 235, 237, 271, 309, 326, 347, 349, 351, 367, 387, 394, 409, 430, 445, 457, 461

• Ernst Cassirer
• Theory of Relativity

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Substance and Function and Einstein's Theory of Relativity

by Ernst Cassirer, Marie Collins Swabey, William Curtis Swabey. 484 pgs.

Contributors:

   Ernst Cassirer, Marie Collins Swabey, William Curtis Swabey

Publisher:

   Dover Publications

Place of Publication:

  New York  

Publication Year:

  1953

Subjects:

Knowledge, Theory Of, Relativity (Physics), Substance (Philosophy)

	CONTENTS
	PART I
	CHAPTER I
I.	New developments in logic.--The concept in Aristotelian logic.-- Purpose and nature of the generic concept.--The problem of abstraction.--The metaphysical presuppositions of Aristotelian logic.--The concept of substance in logic and metaphysics	3
II.	The psychological criticism of the concept ().--The psychology of abstraction.--Mill's analysis of mathematical concepts. --The defect of the psychological theory of abstraction.--The forms of series.--The place of the thing-concept in the system of logical relations	9
III.	The negative process of "abstraction."--The mathematical concept and its "concrete universality."--The criticism of the theories of abstraction.--Objects of the "first" and "second" orders.--The variety of objective "intentions."--The serial form and the members of the series	18
	CHAPTER II
I.	The sensationalistic deduction of number.--Frege's foundations of arithmetic.--The system of arithmetic.--Number and presentation.--The content of presentation and the act of presentation	27
II.	The logical foundations of the pure concept of number (Dedekind). --The logic of relations.--The concept of progression.--Number as ordinal number.--The theories of Helmholtz and Kronecker.-- Criticism of the nominalistic deduction	35
III.	Number and the concept of class.--Russell's theory of cardinal numbers.--Criticism of "class theories."--The logical definition of the zero and of unity.--The presupposition of the class concept.--The generic concept and the relational concept	44
IV.	Extension of the concept of number.--' theory of the negative and imaginary numbers.--The irrational numbers.--Dedekind's
	CHAPTER III
I.	Concept and form.--The method of ancient geometry.--The concept 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 position.--Steiner and Poncelet.--The concept of "correlation" and the principle of continuity.--The transference of relations distinguished 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" (Leibniz).--Geometry as pure "doctrine of relations" (Hilbert).--The syntheses of generating relations.--Grassmann's Ausdehnungslehre 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.--Objections to the Kantian theory of geometry.--Real space and experiment.--The conceptual principles of pure space.--Euclidean space and the other forms of mathematical space.-- Geometry and reality	100
	CHAPTER IV
I.	The constructive concepts and the concepts of nature.--The concept of traditional logic and the scientific ideal of pure description.--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
III.	The problem of the physical method and its history.--The problem of knowledge (Plato).--The sceptical theory of knowledge (Protagoras, etc.).--The concepts of nature and purpose (Plato).-- Mathematics and teleology (Plato, Aristotle, Kepler).--The concept of hypothesis (Kepler and Newton).--The logical and ontological "hypotheses."	130
IV.	Robert Mayer's methodology of natural science.--Hypotheses and natural laws.--The presuppositions of physical "measurement." --The physical "fact" and the physical "theory."--Units of measurement.--The verification of physical hypotheses.--The motive of serial construction.--The physical concepts of series	139
V.	The concept of substance in the Ionian philosophy of nature.--The hypostatization of sensuous qualities (Anaxagoras).--The hypostatization of sensuous qualities (Aristotle).--Atomism and number.--The impact of atoms.--The postulate of continuity, and the "simple" atom of Boscovich and Fechner.--The concept of the atom and the application of differential equations.--The changes in the concept of the atom.--The concept of the ether.--The logical form of the concept of the physical object.--"Real" and "not real" elements in the concepts of the physical object.--The concept of non-being.--Matter and idea and Galileo's concept of inertia	151
VI.	The concepts of space and time.--Newton's concepts of absolute space and absolute time.--The system of reference of pure mechanics.--The substitution of the fixed stare for absolute space.--The "intellectual experiment" and the law of inertia.-- Streintz's concept of the "fundamental body."--The theory of C. Neumann: the body alpha.--Space and time as mathematical ideals.--Hertz's system of mechanics.--Construction and convention	170
VII.	The concept of energy.--Energy and the sense qualities.--Energy and the concept of number.--The concept of the measure of work.--The formal presuppositions of energism.--Rankine's deductions of energetics.--Criticism of the method of physical "abstraction."--The problem of abstraction in modern logic.-- Energy as a relational concept.--Energetics and mechanics.-- Physics as a science of qualities	187
VIII.	The problem of the construction of concepts in chemistry.--The chemistry of sensuous qualities and Richter's law of definite proportions.--Dalton's law of multiple proportions.--The atom as a relational concept.--The "regulative" use of the concept of the atom.--The concept of valency and the theory of types.--Logical aspects of the concept of type.--The chemical concept as a rele­
	tional concept.--The concept of the "radical" and the theories of "composite radicals."--The reconstruction of the systematic form of chemistry.--The periodic system of the elements.-- Chemistry and mathematics	203
	IX. The concept of natural science and "reality."--Rickert's theory of the scientific construction of concepts.--Criticism of Rickert's theory.--Word-meanings and mathematical concepts.--Rickert's confusion of "meanings" and "presentations."--The concept as the expression of individual relations.--The problem of the constants of natural science.--Magnitudes and other forms of relations	220
	PART II
	CHAPTER V ON THE PROBLEM OF INDUCTION
I.	The metaphysical tendency in induction and deduction.--The empirical theory of judgment.--Mach's "thought-experiment."-- Criticism of Mach's theory.--Locke's theory of empirical judgment.--The "element of eternity" in all empirical judgment.-- The postulate of necessary determinateness.--Judgments of perception and judgments of experience.--Experience as aggregate and as system.--Discrete and continuous "wholes."--Induction and the theory of invariants.--Induction and analogy	237
II.	Induction and analysis, "compositive" and "resolutive" methods. --Experiment as the means of analysis.--The relation of "universa!" and "particular" relations.--" Isolation" and "superposition."--Laws and rules.--The concept of the "fundamental" relation and the relation of mathematical necessity.--The two fundamental types of knowledge	252
III.	The problem of laws of nature.--Laws and constants.--The general form of experience.--The concept of the a priori and the "invariants of experience."	265
	CHAPTER VI
I.	The separation of "subjective" and "objective" reality.--The development of the concepts of objectivity and subjectivity.-- Changing and constant elements of experience.--The subjectivity of the sensuous qualities.--The series of degrees of objectivity. The logical gradations of the contents of experience.--The prob­lem of transcendence.--The meaning of judgment.--The "transcending" of sensuous experience.--The concept of "representation."--Transformation of the concept of representation and progress to the "whole of experience."--Association as a principle of explanation
II.	The concept of objectivity and the problem of space.--The theory of projection and its defects.--Concept and perception distinguished (Helmholtz).--The division into circles of objectivity.-- "Projection" and "selection."	286
III.	The function of judgment; permanence and repetition.--The problem of the "transsubjective."--The correlation of the consciousness of the ego and the consciousness of the object.--The separation of thought and experience.--The concept of the object in critical idealism.--The objectivity within pure mathematics.-- The unity of the physical world	293
IV.	The historical transformation of the "thing."--Helmholtz' theory of signs.--The logical and the ontological conceptions of relativity.--The unity of the scientific views of the world	302
	CHAPTER VII
I.	The problem of the subjectivity and objectivity of relational concepts.--The universal functions of rational and empirical knowledge.--The reciprocal relation of the "form" and "matter" of knowledge.--The existence of the "eternal truths."--The concept of truth of modern mathematics	309
II.	The relational concepts and the activity of the ego.--Constancy and change in knowledge.--The independence of logical truths of the thinking subject.--The problem of pragmatism.--Truth and the "practical."--The critical concept of truth.--The reconciliation of permanence and change.--The double form of the concept	314
	CHAPTER VIII
I.	Logical relations and the problem of self-consciousness.--Plato's psychology of relations.--Aristotle's Doctrine of the Kοινονó-- "Thoughts of relation" in modern psychology.--The concept of substance.--The doctrine of the "form-quality" in modern psychology.--Ebbinghaus's physiological account of relations.-- Criticism of the physiological explanation of relational concepts	326
II.	Meinong's theory of "founded contents."--"Objects of a higher order."--The conflict between empiricism and nativism.--The psychology of the idea of space.--The psychology of thought	337
	SUPPLEMENT
I.	Concepts of measure and concepts of things	351
II.	The empirical and conceptual foundations of the theory of relativity	367
III.	The philosophical concept of truth and the theory of relativity	387
IV.	Matter, ether and space	394
V.	The concepts of space and time of critical idealism and the theory of relativity	409
VI.	Euclidean and non-Euclidean geometry	430
VII.	The theory of relativity and the problem of reality	445
	Bibliography	457
	Index	461

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