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Early Analytic Philosophy - New Perspectives on the Tradition pp 283–300Cite as

The Concept of “Essential” General Validity in Wittgenstein’s Tractatus

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Part of the book series: The Western Ontario Series in Philosophy of Science ((WONS,volume 80))

Abstract

In the Tractatus, Wittgenstein describes the general validity of logical truths as being “essential,” as opposed to merely “accidental” general truths. He does not say much more, and little has been said about it by commentators. How to make sense of the essential general validity by which Wittgenstein characterizes logic? This chapter aims to clarify this crucial concept.

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Notes

  1. 1.

    Wittgenstein (1974, p. 63).

  2. 2.

    Fogelin (1976, Chap. vii, pp. 78–83).

  3. 3.

    Morris (2008, pp. 237–240).

  4. 4.

    See Hacker (1989, pp. 38 and 47).

  5. 5.

    Anscombe (1959, p. 158).

  6. 6.

    As an example, see Stenius (1960, p. 201).

  7. 7.

    Black (1964, p. 326).

  8. 8.

    Frascolla (1994, pp. 38–39).

  9. 9.

    “What is peculiar about a truth of logic is that you can tell that it is true from the symbol alone, so that the proposition is true regardless of the way the world is, i.e., necessarily true.” (White 2006, p. 106).

  10. 10.

    Cora Diamond (“Throwing Away the Ladder: How to Read the Tractatus”, Chap. 6 of Diamond 1991) rightly insists against Hacker that logical necessity has nothing to do with “features of reality” whatsoever, but pertains to linguistic constructions. She writes, about 6.37 and 6.375: “Logical necessity is that of tautologies. It is not that they are true because their truth conditions are met in all possible worlds, but because they have none. ‘True in all possible worlds’ does not describe one special case of truth conditions being met but specifies the logical character of certain sentence-like constructions formulable from sentences.” (Diamond 1991, p. 198) However, she adds: “But the remark that there is only logical necessity is itself ironically self-destructive. […] In so far as we grasp what Wittgenstein aims at, we see that the sentence-form he uses comes apart from his philosophical aim. If he succeeds, we shall not imagine necessities as states of affairs at all. We throw away the sentences about necessity; they really are, at the end, entirely empty.” (ibid.) If one were to follow Diamond’s reading, one should conclude, not only that logical necessity is not descriptive, but that it is indescribable. Yet it entirely remains to understand what the necessity of tautologies consists in exactly.

  11. 11.

    McGinn (2006, p. 59).

  12. 12.

    Russell (1992a, pp. 518–519).

  13. 13.

    Gregory Landini (see Landini 2007, Appendix B) holds that Russell defines as necessary any true fully generalized proposition in the sense of its first-order and second-order universal generalization. For instance, \( \varphi x \supset_{x} \psi x \,.\, \varphi a\,: \, \supset \,.\, \psi a \enspace\left({1_{R} } \right) \) is Russell-necessarily true because its full universal generalization \( \left( \varphi \right)\left( \psi \right)\left( y \right): \,.\, \varphi x \supset_{x} \psi x \,.\, \varphi y:\, \supset \,.\, \psi y \enspace\left( {2_{R} } \right) \) is true. One possible objection is that necessity then becomes the feature of a sentence, i.e., of the particular linguistic expression of a proposition. For suppose \( Px \) is \( \varphi x \supset \psi x \). Then \( \left( {1_{R} } \right) \) is equivalent with \( \left( x \right)Px \,. \,\varphi a: \,\supset \,.\, \psi \enspace\left( {1_{R}^{\prime } } \right) \), whereas \( \left( {2_{R} } \right) \), which is true, is not equivalent with the full universal generalization of \( \left( {1_{R} ^{\prime }}\right),\, \) \( \left( P \right)\left( \varphi \right)\left( \psi \right)\left( y \right): \,.\, \left( x \right)Px \,.\,\varphi y: \,\supset \,. \,\psi y \enspace\left( {2_{R}^{\prime } } \right) \), which is false.

  14. 14.

    Kant (1992), “The Jäsche logic,” p. 528 (I, Ak. ix, 12).

  15. 15.

    Kant (1929, p. 592; A737/B765).

  16. 16.

    Russell (1992a, p. 508).

  17. 17.

    About Russell’s wariness about modal notions, which does not amount to “wholesale eliminativism,” see Shieh (2011, pp. 3–4).

  18. 18.

    Wittgenstein (1974, p. 49).

  19. 19.

    “[…] every propositional function has a certain range of significance, within which lie the arguments for which the function has values.” (Russell 1956, pp. 72–73)

  20. 20.

    Wittgenstein (1974, p. 51).

  21. 21.

    It should be noted that the phrase “propositional function” occurs only once in the whole Tractatus, at 5.521.

  22. 22.

    Cf. Wittgenstein (1978, p. 453).

  23. 23.

    Ricketts (2013, p. 136).

  24. 24.

    Wittgenstein (1961, 13.10.14, p. 11).

  25. 25.

    Wittgenstein (1967, pp. 216–217).

  26. 26.

    See, in particular, 4.0411, 5.1311, and 5.52.

  27. 27.

    See Wittgenstein (2001, pp. 125–127 and 171–175). On this point, see Sackur (2005, pp. 133–141).

  28. 28.

    Wittgenstein (1961, 13.10.14, p. 11): “But let us remember that it is the variables and not the sign of generality that are characteristic of logic.”

  29. 29.

    Wittgenstein (1974, p. 53).

  30. 30.

    This is actually, in a way, Tarski's conclusion: The interpretation of a variable changes as one shifts from one “universe of discourse” to another.

  31. 31.

    Wittgenstein (1974, p. 17).

  32. 32.

    Wittgenstein (1961, 23.10.14, p. 17): “If the completely generalized proposition is not completely dematerialized, then a proposition does not get dematerialized at all through generalization, as I used to think.”

  33. 33.

    On this topic, see Marion (1998, p. 98 sq.).

  34. 34.

    Wittgenstein (1978, pp. 458–459): “How a proposition is verified is what it says. Compare generality in arithmetic with the generality of non-arithmetical propositions. It is differently verified and so is of a different kind.”

  35. 35.

    Wittgenstein (1978, p. 457): “What is general is the repetition of an operation.”

  36. 36.

    Fogelin (1976, particularly pp. 78–79).

  37. 37.

    See Geach (1981, pp. 169–170), Soames (1983, p. 578), McGray (2006), Landini (2007 pp. 136–138), and Rogers and Wehmeier (2012).

  38. 38.

    On this question specifically, see McGray (2006, pp. 161–168).

  39. 39.

    This point is well brought out in Sackur (2005, pp. 129–137). See also McGinn (2006, pp. 231 and 235–236).

  40. 40.

    McGinn (2006, p. 60. See also p. 248): “A particular instance of a proposition of this form [namely, \( (p \vee - p) \)] is not a logical truth in virtue of being a substitution instance of a general logical law, \( (p)(p \vee - p) \), but simply in virtue of the way it is constructed, that is, simply in virtue of its having the form \( (p \vee - p) \).” Ricketts (2013, p. 127) also insists on the distinction to be made between a relation between entities on the one hand, and the construction of a logical structure such as a material conditional on the other. Consequently, logical generality cannot consist in the substitutability of entities, but only in the generality of a construction, i.e., in the iterative generativity of a truth-operation.

  41. 41.

    Kaplan (1989, p. 493).

  42. 42.

    Kaplan (1989, p. 569).

  43. 43.

    This point dovetails with Diamond’s remarks quoted in Footnote 10. As Sanford Shieh summarizes: The reason why a tautology is true in a special way “is not because it describes a special type of invariably obtaining situations. […] it is the nature of linguistic representation, rather than features of the world or of all possible worlds, that makes tautologies true.” (Shieh 2011, p. 3)

  44. 44.

    As Wittgenstein puts it in his Notebooks: “The logic of the world is prior to all truth and falsehood.” (Wittgenstein 1961, 18.10.14, p. 14)

  45. 45.

    Potter (2009, pp. 160–164).

  46. 46.

    Anscombe (1959, p. 132).

  47. 47.

    Landini (2007, p. 143). See also Ricketts (2013, p. 140): “[…] the general form of sentences has an intrinsically schematic character. […] The general sentence-form is rather a scheme for the construction of any sentence: it is the most general form for the construction of truth-functions of elementary sentences.”

  48. 48.

    In the series \( [\bar{p},\;\bar{\xi },\;{\kern 1pt} {\text{N}}{\kern 1pt} (\bar{\xi })] \), contrary to what McGinn claims (McGinn 2006, p. 234), \( \bar{p} \) does not have to be the totality of all elementary propositions.

  49. 49.

    This point is recalled by Landini (2007, p. 142).

  50. 50.

    Wittgenstein (1974, p. 63).

  51. 51.

    Frege (1972, p. 183).

  52. 52.

    See Russell (1992b, pp. 360 ff).

  53. 53.

    See Russell (1973, pp. 200–201).

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  1. Université Paris Ouest Nanterre La Défense (IREPH) & SPHERE, Paris, France

    Brice Halimi

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  1. Philosophy Department, University of Bucharest, Bucharest, Romania

    Sorin Costreie

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Halimi, B. (2016). The Concept of “Essential” General Validity in Wittgenstein’s Tractatus . In: Costreie, S. (eds) Early Analytic Philosophy - New Perspectives on the Tradition. The Western Ontario Series in Philosophy of Science, vol 80. Springer, Cham. https://doi.org/10.1007/978-3-319-24214-9_11

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