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

quarta-feira 23 de março de 2022, por

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

Ver online : Ernst Cassirer