Cassirer: Substance And Function And Einsteins Theory Of Relativity (1923)

Part I THE CONCEPT OF THING AND THE CONCEPT OF RELATION
Chapter I ON THE THEORY OP THE FORMATION OP CONCEPTS
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
II. The psychological criticism of the concept (Berkeley  )
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
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
Chapter II THE CONCEPT OP NUMBER
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
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
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
IV. Extension of the concept of number
Gauss’ theory of the negative and imaginary numbers
The irrational numbers
Dedekind’s explanation of the irrational numbers
The problem of the transfmite numbers
The concept of "power.
The production of transfmite numbers
The second "principle of generation" of numbers (Cantor)
Chapter III THE CONCEPT OF SPACE AND GEOMETRY
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
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
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
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
Chapter IV THE CONCEPTS OP NATURAL SCIENCE
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?
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 problem of existence
The existence of the limiting point
Logical idealism on the problem of existence
Consequences of the confusion of truth and reality
The "idealization" of presentations
The relation of the ideal and reality
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."
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
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
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 stars 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
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
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 relational 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
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
Part II THE SYSTEM OF RELATIONAL CONCEPTS AND THE PROBLEM OF REALITY
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
II. Induction and analysis, "compositive" and "resolutive" methods.
Experiment as the means of analysis
The relation of "universal" 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
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."
Chapter VI THE CONCEPT OF REALITY
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."
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
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
Chapter VII SUBJECTIVITY AND OBJECTIVITY OF THE RELATIONAL CONCEPTS
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
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
Chapter VIII ON THE PSYCHOLOGY OF RELATIONS
I. Logical relations and the problem of self-consciousness
Plato’s psychology of relations
Aristotle’s Doctrine of the HLoivov
"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
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
Supplement: EINSTEIN’S THEORY OF RELATIVITY CONSIDERED FROM THE EPISTEMOLOGICAL STANDPOINT OF RELATIVITY
I. Concepts of measure and concepts of things
II. The empirical and conceptual foundations of the theory of relativity
III. The philosophical concept of truth and the theory of relativity
IV. Matter, ether and space
V. The concepts of space and time of critical idealism and the theory
VI. Euclidean and non-Euclidean geometry
VII. The theory of relativity and the problem of reality