Ideas from 'Nature and Meaning of Numbers' by Richard Dedekind [1888], by Theme Structure
[found in 'Essays on the Theory of Numbers' by Dedekind,Richard [Dover 1963,0486210103]].
Click on the Idea Number for the full details 
back to texts

expand these ideas
4. Formal Logic / F. Set Theory ST / 3. Types of Set / d. Infinite Sets
10183

An infinite set maps into its own proper subset

4. Formal Logic / G. Formal Mereology / 1. Mereology
10706

Dedekind originally thought more in terms of mereology than of sets

6. Mathematics / A. Nature of Mathematics / 3. Numbers / a. Numbers
9823

Numbers are free creations of the human mind, to understand differences

6. Mathematics / A. Nature of Mathematics / 3. Numbers / c. Priority of numbers
7524

Order, not quantity, is central to defining numbers

10090

Dedekind defined the integers, rationals and reals in terms of just the natural numbers

6. Mathematics / A. Nature of Mathematics / 3. Numbers / p. Counting
9824

In counting we see the human ability to relate, correspond and represent

6. Mathematics / A. Nature of Mathematics / 4. The Infinite / b. Mark of the infinite
9826

A system S is said to be infinite when it is similar to a proper part of itself

6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Number / a. Axioms for numbers
13508

Dedekind gives a base number which isn't a successor, then adds successors and induction

6. Mathematics / B. Foundations for Mathematics / 6. Mathematical Structuralism / a. Structuralism
8924

Dedekind originated the structuralist conception of mathematics

9. Objects / A. Existence of Objects / 3. Objects in Thought
9825

A thing is completely determined by all that can be thought concerning it

18. Thought / D. Concepts / 6. Abstract Concepts / c. Abstracta by ignoring
9189

Dedekind said numbers were abstracted from systems of objects, leaving only their position

9827

We derive the natural numbers, by neglecting everything of a system except distinctness and order
