Das Unendliche in der Mathematik und seine Ausschaltung

Name: Das Unendliche in der Mathematik und seine Ausschaltung
Author: Kaufmann

1930

by Kaufmann

Mathematical EconomicsPhenomenologyEdmund HusserlEpistemologyLujo BrentanoImmanuel Kant

Table of Contents · 39 segments

Title Page and Publication Dataessay

Prefaceessay

Table of Contentschapter

Table of Contents: Decidability and Antinomieschapter

Introduction: The Actual Infinite and Misuse of Mathematical Symbolismessay

Basic Facts of Knowledge: Intentionality, Being, Generality, and Formal Logictheoretical

Conclusion of Logic, Identity, and Equalitytheoretical

Symptoms, Signs, Language, and Symbolic Conventiontheoretical

Objective Meaning, Hilbert’s Proof Theory, and Isomorphismtheoretical

Logistic Symbolism, Relation Calculus, and Symbolic Hypostatizationtheoretical

Mathematical Representation, Hilbertian Ideals, Brouwer’s Intuitionism, and Transition to Axiomaticstheoretical

Axiomatic Requirements, Completeness, and Geiger’s Essence Axiomaticstheoretical

Opening of Natural Number and Set: Counting as Modeltheoretical

Counting, Ordinal Invariance, and the Rejection of Sets as Prior to Numbertheoretical

One-to-One Correspondence, Equality of Number, and the Time Problemtheoretical

Natural Numbers as Logical Abstracts of the Unbounded Counting Processtheoretical

Peano’s Axioms, Complete Induction, and the Logical Structure of Arithmetictheoretical

Toward an Analysis of Sets, Manifolds, and Mathematical Generalitytheoretical

Reformulating Set Statements and Critiquing Iterated Setstheoretical

Power Set Totalities, Russell, and Sequences Without Transfinite Totalitiestheoretical

Number Extensions, Natural Numbers, and the Relation of Mathematics to Logictheoretical

Negative Numbers as Symbols for Subtraction and Counterrunning Relationstheoretical

Fractions, Rational Numbers, and Measurement as Relations Among Natural Numberstheoretical

Geometrical Intuition, Idealization, and the Illusion of the Transfinitetheoretical

Opening of the Epistemological Classification of Geometriestheoretical

Formal Geometry, Rational Sequences, and Inverse Operationstheoretical

Approximation, Square Root of Two, and Accumulation Intervalstheoretical

Critique of Dedekind, Cantor, and Russell on Irrational Numberstheoretical

Consequences for Analysis, Higher-Stage Irrationals, and Algebraic Rootstheoretical

Geometric Representation and the Conclusion of the Irrational-Number Analysistheoretical

Set Theory: Tools, Infinite Sets, Equivalence, and Countabilitychapter

Countability of Rationals and Cantor’s Diagonal Presentationtheoretical

Finite Meaning of Countable Correspondence and Critique of Uncountable Totalitiestheoretical

Power Sets, Belegungsmengen, and Transfinite Cardinal Arithmetictheoretical

Transition to Well-Ordered Sets and Ordinal Numberstheoretical

Cantorian Well-Ordering, Transfinite Ordinals, and the Critique of Uncountable Set Theorychapter

The Decidability of Arithmetic Questionschapter

The Antinomies of Logic and Set Theorychapter

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