The Place of the Begriffsschrift

  • E.-H. W. Kluge
Chapter
Part of the Martinus Nijhoff Philosophy Library book series (MNPL, volume 5)

Abstract

Probably the first of Frege’s works to attract attention1 — certainly the first to be noted on an international scale2 — was his Begriffsschrift.3 This little book of some eighty-eight pages constituted his first public attempt to fulfil a programme that was to concern him for the rest of his academic career and as such was fundamental to all of his later efforts. In a letter to Jourdain, he expressed himself about it as follows:4

I had been thinking about the plan of a Begriffsschrift for a long time before it assumed definite shape. The desire to exclude with certainty the assumptions tacitly introduced into the foundations of arithmetic led me to the Begriffsschrift of the year 1897. Occu?pation with the latter then led me to a more precise formulation of the basic concepts of arithmetic, although I can no longer give the precise details [of this]. The recognition that the bearer of a number is not a heap, an aggregate, a system of things but a concept was, I dare say, inevitably facilitated by the Begriffssch?rift. Instead of a concept we may also take its extension — or, as I also call it, the class that belongs to it. I believe I owe the distinc?tion between a heap (aggregate, system) and a class — which probably was not drawn sharply before me — to my Begriffsschrift, although perhaps you cannot detect any trace of this when reading my little book.

Keywords

Logical Structure Function Expression Predicative Expression Argument Expression Argument Place 
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Notes to Chapter I

  1. 1.
    Although by no means his first publication. For a complete bibliography of Frege’s published works, see the bibliography, pp. 305ff. in Nachgelassene Schriften Google Scholar
  2. 2.
    Cf the reactions of Peano, Russell, Couturat, etc.Google Scholar
  3. 3.
    Published in 1879.Google Scholar
  4. 4.
    BW p. 111 (23.9.1902)Google Scholar
  5. 5.
    N, p. 200 (August, 1906)Google Scholar
  6. 6.
    N p. 16, Beg pp. 6 ff.Google Scholar
  7. 7.
  8. 8.
    Angelelli, p. 270 note 5.Google Scholar
  9. 9.
    The topic might well be the subject of a separate monograph on the role of the notion of an ideal language in the development of philosophy.Google Scholar
  10. 10.
    I omit the obvious: `Begriffschrift’ as an abbreviation for the whole title.Google Scholar
  11. 11.
    Cf. N, pp. 9 ff. Beg pp. XI f. On the use of the phrase itself see Patzig “Frege, Leibniz, u.d. sogenannte `lingua characteristica universalis”’ in Studia Leibnitiana, suppl. vol. III, no. 3, 1969 pp. 102–112 and my reply “Frege, Leibniz et alii” in Studia Leibnitiana, vol. IX, no. 2, 1977 pp. 266–274.Google Scholar
  12. 12.
    Ibid pp. 14–15.Google Scholar
  13. 13.
    Beg, p. X.Google Scholar
  14. 14.
    Cf. N, pp. 9 ff; see also Chapter V below.Google Scholar
  15. 15.
    Ibid, p. 13; Beg pp. X ff.Google Scholar
  16. 16.
    N pp. 14 f.Google Scholar
  17. 17.
    See notes 11 and 12 above.Google Scholar
  18. 18.
    N, p. 227.Google Scholar
  19. 19.
    N p. 7 (dated about 1879)Google Scholar
  20. 20.
    N p. 289 (dated 1924–25)Google Scholar
  21. 21.
    N pp. 160–161Google Scholar
  22. 22.
    N p. 13. These passages appear to be the conceptual and historical basis for Wittgenstein’s later characterization of philosophy as a fight against the bewitchment of language. Cf. N pp. 182, 285, 292, 155, 192, f., etc.Google Scholar
  23. 23.
    See Chapter V below. See also Gottfried Gabriel, Definitionen u, Interessen - Über die praktischen Grundlagen der Definitionslehre (Stuttgart-Bad Cannstatt, 1972, 2.4)Google Scholar
  24. 24.
    GGA pp. XV f.Google Scholar
  25. 25.
    Ibid, p. XVI; see also N p. 168 etc.Google Scholar
  26. 26.
    Cf. N, p. 160.Google Scholar
  27. 27.
    Cf. GGA, XVIGoogle Scholar
  28. 28.
  29. 29.
  30. 30.
  31. 31.
    E.g Bolzano, Leibniz, Lotze. Some of Frege’s formulations approximate certain of Lotze’s statements particularly closely. But see below, Chapter V.Google Scholar
  32. 32.
    Cf. N 2 ff., pp. 138 ff; “Negation”, p. 151 etc.Google Scholar
  33. 33.
    Cf. N p. 160 et pass Google Scholar
  34. 34.
    GGA, p. XVIGoogle Scholar
  35. 35.
    Cf C.L. Stevenson, Ethics and Language (Yale, 1944).Google Scholar
  36. 36.
    Cf. N pp. 4, 139, 156, etc.Google Scholar
  37. 37.
    GGA, p. XVIIGoogle Scholar
  38. 38.
  39. 39.
    L.C. Cf. N. pp. 4 ff.Google Scholar
  40. 40.
    Cf N p. 160 f.Google Scholar
  41. 41.
    N p. 155.Google Scholar
  42. 42.
    L.C See also “The Thought”. I substitute an English idiom for the German, which contains an intranslatable allusion to a tale by Münchhausen.Google Scholar
  43. 43.
    Cf. N p. 159 f.Google Scholar
  44. 44.
    L.C. Cf “The Thought”Google Scholar
  45. 45.
    N pp. 160 ff., et pass Google Scholar
  46. 46.
    N p. 159.Google Scholar
  47. 47.
    N pp. 2, 262, 183 f, 139, 134.Google Scholar
  48. 48.
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  49. 49.
    N p. 160. Cf Ang. pp. 343 ff, et pass Google Scholar
  50. 50.
  51. 51.
    N pp. 160–161Google Scholar
  52. 52.
    Ibid p. 13.Google Scholar
  53. 53.
    Cf ibid, p. 13.Google Scholar
  54. 54.
    On the objective nature of thoughts, see Ang. pp. 353–362 passim Google Scholar
  55. 55.
    Loc. cit “And when we call a sentence true, we really mean its sense.”Google Scholar
  56. 57.
    For more on this see Chapter V below.Google Scholar
  57. 58.
    BW pp. 96 f.Google Scholar
  58. 59.
    Beg p. 2 et pass, GGA, p. X, etc.Google Scholar
  59. 60.
    Cf Ang., p. 144, et pass Google Scholar
  60. 61.
    GGA pp. 45 f., N pp. 128, 133, 168, 259 ff. pass, p. 192 ff.: Ang. p. 135. See also Eike-Henner W. Kluge, “Frege et les termes…”, Dialogue vol. XIX no. 2 (June ‘75) pp. 254–280.Google Scholar
  61. 62.
    Ang. p. 289 (Kluge, p. 60)Google Scholar
  62. 63.
    Ang. p. 150.Google Scholar
  63. 64.
    BW p. 128.Google Scholar
  64. 65.
    N pp. 191 ff, GGA, I, p. 43–6, etc.Google Scholar
  65. 66.
    Ang., p. 149.Google Scholar
  66. 67.
    See BW pp. 126 ff.; SR p. 27–9; Ang., pp. 344 ff, 353 ff, 362, 371, etc.; N p. 7, etc.Google Scholar
  67. 68.
    Ang. p. 359; For more on thoughts see N pp. 148 ff, 214, 222 f; BW, p. 102; etc.Google Scholar
  68. 69.
    Cf. N p. 135 f, 232.Google Scholar
  69. 70.
    N pp. 207, 227; BW pp. 127 f, etc.Google Scholar
  70. 71.
    Ang. p. 144 f.; N pp. 208, 210, etc.Google Scholar
  71. 72.
    Ang. l.c.; BW p. 96, N p. 136, 224.Google Scholar
  72. 73.
    Ang. p. 144. See also Ang. p. 143, BW p. 128, etc.Google Scholar
  73. 74.
  74. 75.
    This follows from Frege’s rejection of multiple definitions in an ideal language. For more on this, see the discussion of Frege’s theory of definitions below.Google Scholar
  75. 76.
    Ang. p. 169, N p. 106, etc.Google Scholar
  76. 77.
    Cf Ang. p. 269 f (Kluge, pp. 33 ff.); N pp. 107 ff., 120, 129 ff., 133, 192 f., 246, 247 f., etc.Google Scholar
  77. 78.
    Ang., p. 269 (Kluge, p. 33)Google Scholar
  78. 79.
    GGA, I #2; Cf. N pp. 166 f.Google Scholar
  79. 80.
    Ang. pp. 167–171 et pass.; N pp. 167, 258.Google Scholar
  80. 81.
    GGA I §1.Google Scholar
  81. 82.
  82. 83.
    Kluge, Functions and Things, (diss. Ann Arbor, 1968) p. 44.Google Scholar
  83. 84.
    GGA I §§29 f.; Ang. pp. 141 f., 271 f., etc.Google Scholar
  84. 85.
  85. 86.
    Ang., p. 140Google Scholar
  86. 87.
    GG 1903 II p. 374Google Scholar
  87. 88.
    Ang. pp. 416 f.; Cf Kluge, pp. XXIV, 32, 47, 76 f.; N. p. 111; BW p. 73 f., etc.Google Scholar
  88. 89.
    I here forego all discussion of unequal-levelled functional expressions and functions; e.g. Ang. p. 141. For our purposes, these differences are not important.Google Scholar
  89. 90.
    Cf GGA I§§1–4; N p. 258 ff.; Beg, p. 16, etc.Google Scholar
  90. 91.
    N p. 259.Google Scholar
  91. 92.
    Frege located the reason for this in the universality of the law of the excluded middle. For more on this, see the discussion of Frege’s theory of definition below.Google Scholar
  92. 93.
    Ang. pp. 269 f., et pass Google Scholar
  93. 94.
    To be sure, the distinctions just indicated are not exhaustive; however, they suffice for our present purposes.Google Scholar
  94. 95.
    Kluge, pp. 60 f. (Ang., pp. 289 f.)Google Scholar
  95. 96.
    GGA, I §66, Cf Ang. p. 288 f., N, p. 55, etc.Google Scholar
  96. 97.
    Cf Ang. p. 288; GGA I § 30.Google Scholar
  97. 98.
    GGA I §§3–4, II §147; Cf Ang. pp. 167 ff., 287 ff., 301, etc; N pp. 6, 19, 98, etc.Google Scholar
  98. 99.
    Cf. N pp. 227 ff. et pass Google Scholar
  99. 100.
    Ang. pp. 287 ff. (Kluge, pp. 59–61)Google Scholar
  100. 101.
    N pp. 227 f.; Ang., pp. 287 f. (Kluge, pp. 60–61)Google Scholar
  101. 102.
    N p. 227; Cf Ang., l.c (Kluge, pp. 60 ff.)Google Scholar
  102. 103.
    Cf. Ang., pp. 263, 287 f., etc. (Kluge, pp. 24, 61); BW p. 61 f.Google Scholar
  103. 104.
    N pp. 227.Google Scholar
  104. 105.
  105. 106.
    Kluge, p. 60, Ang., p. 289)Google Scholar
  106. 107.
    L.C.; Cf. N. pp. 227 ff.Google Scholar
  107. 108.
    N p. 227; Cf. BW pp. 61 ff.Google Scholar
  108. 109.
    Lest the conjunction `sense and reference’ occasion unease, let us point out that this conjunction follows by an elementary logical mode of inference from what Frege said in “Logic Mathematics” and GGA, the relevant passages from which were quoted above.Google Scholar
  109. 110.
    GGA, I §§26 ff.; Kluge, pp. XVII ff.Google Scholar
  110. 111.
    See my paper “Frege et les Termes sans Référence”Google Scholar
  111. 112.
    Cf. GGA, II §§60 f.Google Scholar
  112. 113.
    Cf. BW p. 80; See also Kambartel “Frege and die axiomatische Methode’. pass in Frege and die moderne Grundlagenforschung,C Thiel, ed. (1975).Google Scholar
  113. 114.
    Cf. GGA, II §66.Google Scholar
  114. 115.
    Cf Kluge pp. XI, XXII, XXX-XXXII; Kambartel, op cit Google Scholar
  115. 116.
    Cf. GGA. II §§60 ff.; BW pp. 182–5; N, pp. 261 f.; Kluge, pp. XXVI-XXIX.Google Scholar
  116. 117.
    GGA II §57.Google Scholar
  117. 118.
    Ang. pp. 235–7; N pp. 168, 212.Google Scholar
  118. 119.
    Ang. pp. 287–8, (Kluge, pp. 58)Google Scholar
  119. 120.
    Ang. pp. 167–8.Google Scholar
  120. 121.
    Ang. p. 288 (Kluge, p. 59)Google Scholar
  121. 122.
  122. 123.
    GGA I p. 45; Ang. pp. 167 f.Google Scholar
  123. 124.
    Cf. GGA II §§56 ff.; Ang. pp. 224, 235 f., 289 f. (Kluge, pp. 61–9); N pp. 168, 259 ff., 262, etc.Google Scholar
  124. 125.
    GGA I pp. 45 f.Google Scholar
  125. 126.
    See note 124.Google Scholar
  126. 127.
    Cf Ang. p. 148; N p. 288, etc.Google Scholar
  127. 128.
    Sentences, being a particular kind of nominative expression (Cf BW p. 127) would be included in this.Google Scholar
  128. 129.
    GGA I, p. 45.Google Scholar
  129. 130.
    L.C As we shall see a little later, in the light of Frege’s further pronouncements about sense and reference this entails that they will also have a sense. However, care should be taken not to conflate the two. Although the one may imply the other, the other need not imply the one. See below.Google Scholar
  130. 131.
    GGA I pp. 45 f.Google Scholar
  131. 132.
    Strictly speaking, condition (2) is redundant. Also, the conditions placed on proper names are actually more complicated. For present purposes, however, this will do.Google Scholar
  132. 133.
    Cf. GGA I §11, N. p. 168.Google Scholar
  133. 134.
    Grundlagen, §74, GGA I p. 18, B.W. p. 177, etc.Google Scholar
  134. 135.
    Axioms could also be involved here. Cf Ang. pp. 108 ff. (Kluge, pp. 148 ff.)Google Scholar
  135. 136.
  136. 137.
    Ibid, p. 133.Google Scholar
  137. 138.
    On our tacit equating of properties and functions see below, Chapters II and III.Google Scholar
  138. 139.
    Ang., p. 123.Google Scholar
  139. 140.
    N pp. 193–4.Google Scholar
  140. 141.
    Cf. N pp. 247 et pass Kluge, pp. 4–5 (Ang. pp. 405 f.), 35–6; GA §53; GGA I p. 3; etc.Google Scholar
  141. 142.
    Cf Ang. pp. 404 ff., 269 ff. (Kluge, pp. 4–5, 35 ff.); N p. 113; Geach and Black, pp. 59 ff. Theoretically this would introduce a further distinction; between subsumption and subordination (Cf. Kluge, pp. XVII f.) However, since it is of an essentially metaphysical and logical import, we shall reserve discussion of it until the next chapter.Google Scholar
  142. 143.
    Cf his controversy with Thomae, Ang. pp. 324–333 (Kluge, pp. 121–38).Google Scholar
  143. 144.
    The sign-symbol distinction is not stated in those terms by Frege, but it is a clear implication of his theory of definition and his stance on the difference between simplicity qua logico-syntactic and qua physical phenomenon. In this context “On Formal Theories of Arithmetic” Ang. pp. 103–111 (Kluge, pp. 140–153) is also of some interest, in particular pp. 105–6 (p. 145) where Frege distinguishes between a sign and a figure, where the former corresponds to what we have called “Expression qua symbol” and the latter to what we have called “sign”. The similarity between this and what Wittgenstein says in the Tractatus will be apparent.Google Scholar
  144. 145.
    I.e that each term will be defined completely, precisely and only once; and that there not be distinct definitions for one and the same complex.Google Scholar
  145. 146.
    Ang., p. 289 (Kluge, p. 61).Google Scholar
  146. 147.
  147. 148.
    This is the import of repeated assertions like those at N p. 227, to the effect that only a sign that does not yet have a sense and a reference can be defined.Google Scholar
  148. 149.
    Cf. N pp. 229, 261, etc.Google Scholar
  149. 150.
    N p. 225.Google Scholar
  150. 151.
  151. 152.
    Ang., p. 289 (Kluge, p. 61).Google Scholar
  152. 153.
    N p. 225.Google Scholar
  153. 154.
    Cf. ibid, p. 226.Google Scholar
  154. 155.
    N p. 226.Google Scholar
  155. 156.
    Although these two questions are similar, they are distinct because they are raised on different levels.Google Scholar
  156. 157.
    See my article “Frege et les Termes…”Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1980

Authors and Affiliations

  • E.-H. W. Kluge
    • 1
  1. 1.The University of VictoriaCanada

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