Kapitel in diesem Buch

1. Frontmatter I
2. EDITOR'S INTRODUCTION V
3. CONTENTS LXI
4. Introduction 1
5. § 0. Our task. Demands on the conduct of proof. Dedekind's system. Schroder's class 29
6. Exposition of the Begriffsschrift
7. 1. Primitive Signs
8. i. Introduction: Function, Concept, Relation
9. §1. The function is unsaturated 33
10. §2. Truth-values. Denotation and sense. Thought. Object 34
11. §3. Course-of-values of a function. Concept. Extension of a concept 36
12. §4. Functions of two arguments 36
13. ii. Signs for Functions
14. §5. Judgment and thought. Judgment-stroke and horizontal 37
15. §6. Negation-stroke. Amalgamation of horizontals 39
16. §7. The identity-sign 40
17. §8. Generality. Gothic letters. Their scope. Amalgamation of horizontals 40
18. §9. Notation for the course-of-values. Small Greek vowels. Their scope 43
19. §10. The course-of-values of a function more exactly specified 45
20. §11. Substitute for the definite article: the function \ξ 49
21. §12. Condition-stroke. And. Neither-nor. Or. Subcomponents. Main component 51
22. iii. Inferences and Consequences
23. §14. First method of inference 57
24. 15. Second method of inference. Contraposition 58
25. §16. Third method of inference 64
26. §17. Roman letters. Transition from Roman to Gothic letters 65
27. §18. Laws in symbols of Begriffsschrift (I. IV. VI.) 69
28. iv. Extension of the Notation for Generality
29. §19. Generality with respect to functions. Function-letters. Object-letters 70
30. §20. Laws in symbols of Begriffsschrift (lla. III. V.) 70
31. §21. Functions and concepts of first and second level 72
32. §22. Examples of second-level functions. Unequal-leveled functions and relations 74
33. §23. Types of arguments and argument-places. Second-level functions of arguments of type 2 and type 3 76
34. §24. General explanation of the use of function-letters 78
35. §25. Generality with respect to second-level functions. Basic Law lib 79
36. 2. Definitions
37. i. General Remarks
38. §26. Classification of signs. Names. Marks. Proposition of Begriffsschrift. Transition-sign 80
39. §27. The double-stroke of definition 82
40. §28. Correct formation of names 83
41. §29. When does a name denote something? 84
42. §30. Two ways to form a name 85
43. §31. Our simple names denote something 87
44. §32. Every proposition of Begriffsschrift expresses a thought 89
45. §33. Principles of definition 90
46. ii. Particular Definitions
47. §34. Definition of the function ξ-ζ 92
48. §35. Representation of second-level functions by first-level 54 functions 94
49. §36. The double course-of-values. The extension of a relation 94
50. §37. Definition of the function 1 ξ 96
51. §38. Definition of the function ) ξ 96
52. §39. Definition of the function ξ 98
53. §40. Definition of the function ξ 99
54. §41. Definition of θ 100
55. §42. Definition of 1. Concept of Number 100
56. §43. Definition of f 100
57. §44. Some propositions of Begriffsschrift as examples 101
58. §45. Definition of the function - £ Following and preceding in a series 102
59. §46. Definition of the function u ξ 104
60. 3. Derived Laws
61. §47. Summary of the Basic Laws 105
62. §48. Summary of the Rules 105
63. §49. Derivation of some propositions from (I) 110
64. §50. Derivation of the main principles of the function ξ = ζ 111
65. §51. Derivation of some propositions from (IV) 115
66. §52. Derivation of some propositions from (V) and (VI) 119
67. APPENDIX I 123
68. APPENDIX II 127