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