The Logic of Number

The Logic of Number – Ebook Instant Download/Delivery ISBN(s): 9780192846679,0192846671,9780192661982, 0192661981

Product details:

• ISBN-10 ‏ : ‎ 0192661981
• ISBN-13 ‏ : ‎9780192661982
• Author: Neil Tennant

In The Logic of Number, Neil Tennant defines and develops his Natural Logicist account of the foundations of the natural, rational, and real numbers. Based on the logical system free Core Logic, the central method is to formulate rules of natural deduction governing variable-binding number-abstraction operators and other logico-mathematical expressions such as zero and successor. These enable ‘single-barreled’ abstraction, in contrast with the ‘double-barreled’ abstraction effected by principles such as Frege’s Basic Law V, or Hume’s Principle.

Table contents:

I Natural Logicism
1. What is Natural Logicism?
2. Before and after Frege
3. After Gentzen
4. Foundations after Gödel
5. Logico-Genetic Theorizing
II Natural Logicism and the Naturals 65
6. Introduction, with Some Historical Background
7. Denoting Numbers
8. Exact Numerosity
9. The Adequacy Condition Involving Schema N
10. The Rules of Constructive Logicism
11. Formal Results of Constructive Logicism
12. Reflections on Counting
13. Formal Results about the Inductively Defined Numerically Exact Quantifiers
III Natural Logicism and the Rationals
14. What Would a Gifted Child Need in order to Grasp Fractions? The Case of Edwin
15. Past Accounts of the Rationals as Ratios
16. Mereology and Fraction Abstraction
17. Taking Stock and Glimpsing Beyond
IV Natural Logicism and the Reals
18. The Trend towards Arithmetization
19. Resisting the Trend towards Arithmetization
20. Impurities and Incompletenesses
21. The Concept of Real Number
22. Geometric Concepts and Axioms
23. Bicimals
24. Uncountability
25. Back to Bicimals

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