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The Basic Laws of Arithmetic 1st Edition by Gottlob Frege, Montgomery Furth ISBN 0520312368 9780520312364

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The Basic Laws of Arithmetic Gottlob Frege (Editor) Digital Instant Download

Author(s): Gottlob Frege (editor); Montgomery Furth (editor)
ISBN(s): 9780520312364, 0520312368
Edition: Reprint 2020
File Details: PDF, 17.21 MB
Year: 1964
Language: english
SKU: EB-51818892 Category: Tags: ,

The Basic Laws of Arithmetic 1st Edition by Gottlob Frege, Montgomery Furth – Ebook PDF Instant Download/Delivery: 0520312368, 9780520312364
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ISBN 10: 0520312368 
ISBN 13: 9780520312364
Author: Gottlob Frege, Montgomery Furth

This title is part of UC Press’s Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1964.

The Basic Laws of Arithmetic 1st Table of contents:

1. Primitive Signs

i. Introduction: Function, Concept, Relation

  • §1. The function is unsaturated

  • §2. Truth-values. Denotation and sense. Thought. Object

  • §3. Course-of-values of a function. Concept. Extension of a concept

  • §4. Functions of two arguments

ii. Signs for Functions

  • §5. Judgment and thought. Judgment-stroke and horizontal

  • §6. Negation-stroke. Amalgamation of horizontals

  • §7. The identity-sign

  • §8. Generality. Gothic letters. Their scope. Amalgamation of horizontals

  • §9. Notation for the course-of-values. Small Greek vowels. Their scope

  • §10. The course-of-values of a function more exactly specified

  • §11. Substitute for the definite article: the function ξ

  • §12. Condition-stroke. And. Neither-nor. Or. Subcomponents. Main component

iii. Inferences and Consequences

  • §14. First method of inference

  • §15. Second method of inference. Contraposition

  • §16. Third method of inference

  • §17. Roman letters. Transition from Roman to Gothic letters

  • §18. Laws in symbols of Begriffsschrift (I. IV. VI.)

iv. Extension of the Notation for Generality

  • §19. Generality with respect to functions. Function-letters. Object-letters

  • §20. Laws in symbols of Begriffsschrift (II. III. V.)

  • §21. Functions and concepts of first and second level

  • §22. Examples of second-level functions. Unequal-leveled functions and relations

  • §23. Types of arguments and argument-places. Second-level functions of arguments of type 2 and type 3

  • §24. General explanation of the use of function-letters

  • §25. Generality with respect to second-level functions. Basic Law lib

2. Definitions

i. General Remarks

  • §26. Classification of signs. Names. Marks. Proposition of Begriffsschrift. Transition-sign

  • §27. The double-stroke of definition

  • §28. Correct formation of names

  • §29. When does a name denote something?

  • §30. Two ways to form a name

  • §31. Our simple names denote something

  • §32. Every proposition of Begriffsschrift expresses a thought

  • §33. Principles of definition

ii. Particular Definitions

  • §34. Definition of the function ξ-ζ

  • §35. Representation of second-level functions by first-level functions

  • §36. The double course-of-values. The extension of a relation

  • §37. Definition of the function 1 ξ

  • §38. Definition of the function ) ξ

  • §39. Definition of the function ξ

  • §40. Definition of the function ξ

  • §41. Definition of θ

  • §42. Definition of 1. Concept of Number

  • §43. Definition of f

  • §44. Some propositions of Begriffsschrift as examples

  • §45. Definition of the function – £ Following and preceding in a series

  • §46. Definition of the function u ξ

3. Derived Laws

  • §47. Summary of the Basic Laws

  • §48. Summary of the Rules

  • §49. Derivation of some propositions from (I)

  • §50. Derivation of the main principles of the function ξ = ζ

  • §51. Derivation of some propositions from (IV)

  • §52. Derivation of some propositions from (V) and (VI)

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Tags: Gottlob Frege, Montgomery Furth, Basic Laws