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Introduction and Terminology

  • Sjoerd D. Zwart
Chapter
Part of the Synthese Library book series (SYLI, volume 307)

Abstract

The approach-to-the-truth project started with the publication of Popper’s Conjectures and Refutations in 1963, which contains the first formal explication of the “verisimilitude” notion. Eleven years after this publication, the twenty-fifth volume of the British Journal for the Philosophy of Science gave the project a significant incentive. In their contributions, Miller, Tichý, and Harris, proved the inadequacy of Popper’s definition. In this chapter the rise and fall of Popper’s proposal is sketched, and a technical framework is developed to compare the alternatives to Popper’s proposal. I deal with the general philosophical background of the verisimilitude notion, Popper’s definition and its failure in Sections 1.1–1.2. An explanation of how I shall compare the various proposals presented in Chapters 2–3 is given in Section 1.3. I shall base this comparison on the most elementary mathematical applications of the definitions: propositional languages. The two different ways to paraphrase theories and data in the algebra foreshadow the paramount distinction between two kinds of approach-to-the-truth proposals: the content and likeness definitions. This distinction is reconstructed in Section 1.4 in terms of two different strategies to revise Popper’s original explication. It leads to a formal definition of the contrast between content and likeness definitions. Finally, in the fifth section, I introduce further metatheoretical properties used in later chapters.

Keywords

Atomic Proposition Atomic Sentence False Proposition Propositional Language False Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Notes

  1. 1.
    Peirce (1965) fifth volume section 565.Google Scholar
  2. 2.
    See for instance Niiniluoto (1984), p.76–77.Google Scholar
  3. 3.
    Whether the scientific claims about these different fields are, or should be, reducible is still a question of debate.Google Scholar
  4. 4.
    Laudan (1981).Google Scholar
  5. 5.
    Kuipers (1987), p.7.Google Scholar
  6. 6.
    also relates to the cognitive problem that is to be solved. I elaborate on this in Chapter 5.Google Scholar
  7. 7.
    In the sequel, the term “proposition cp of a language 2” (cp E Sent(2)) refers to the set of equivalent 2-sentences, [cp]=, and has nothing to do with intentional objects. Often, we refer to such a set by one representative of it, and occasionally will use proposition, sentence and statements almost as synonyms. In the same vain, we use the logical connectives of propositions. The set of 2 propositions is designated by Prop(2):= [cp]_ I cp E Sent(2)).Google Scholar
  8. 8.
    Niiniluoto (1987), p.256.Google Scholar
  9. 9.
    The empirical sentences are the non-tautological, and non-contradictory sentences of a language.Google Scholar
  10. 10.
    Popper (1963), p 234.Google Scholar
  11. 11.
    Popper (1963), p.233.Google Scholar
  12. 12.
    Rescher (1967, chap. vi) gives a nice introduction to Kleene’s three-valued logic.Google Scholar
  13. 13.
    Weston (1992).Google Scholar
  14. 14.
    See Kuipers (1987), p. 88. Not surprisingly, the explication of such a general idea of progress has a wider scope than only Popper’s methodology. There are also implications for instrumentalistic and technological progress.Google Scholar
  15. 15.
    Popper (1963), p.233.Google Scholar
  16. 16.
  17. 17.
    Popper (1963), chapter X, section xi.Google Scholar
  18. 18.
    Compare with the dual consequences of Jan Wolenski (1990), p. 619.Google Scholar
  19. 19.
    The Miller-Tichÿ result has also consequence for followers of Popper. For example, Lakatos (1970), p.116 “follows Popper” and defines “sophisticated falsification”. According to Lakatos’s proposal T is falsified if there new theory T’ such that there is a true novel fact e,such that T’ I- e I- - ’T,and T’ F- Tv T (T is the truth); consequence is that T can only be falsified using a true theory T’(else T’= 1); which is at least improbable.Google Scholar
  20. 20.
    Hattiangadi (1983), note 10; Miller (1974).Google Scholar
  21. 21.
    See Tichÿ (1974) and Miller (1974).Google Scholar
  22. 22.
    si, x] has a intermediate if 3 t E Sent(2): w [pA a cP pAq X.Google Scholar
  23. 23.
    See Tichÿ (1974), p.157, note 2; Harris (1974), p.165; Miller (1978), p.415 and Niiniluoto (1987), p. 190.Google Scholar
  24. 24.
    McCarthy (1980) on circumscription was an important starting point of non-monotonic reasoning, see also Makinson (1994). Brewka, Dix and Kolonige (1997) is a comprehensive and readable introduction on non-monotonic reasoning.Google Scholar
  25. 25.
    There is an increasing interest in the relation between verisimilitude and standard concepts in philosophical logic. See e.g. van Benthem (1987), Ryan and Schobbens (1995).Google Scholar
  26. 26.
    Schurz and Weingartner’s (1987) revision of Popper’s definition drops the assumption that all consequences of theories are equally important. The definition only takes the “relevant consequences” of theories into account. According to their analysis, however, one consequence cp may be relevant whereas an equivalent reformulation of cp is not. For instance, (p A - q) -] - ’p is a relevant implication, and it is equivalent to the irrelevant p -+ (p y q) (see Schurz and Weingartner (1987, p.54)).Google Scholar
  27. 27.
    Some of the definitions presented in Chapter 3–4 are to be found in Kuipers (1987); among the most recent proposals are Wolenski (1990), Gerla (1992), Zamora Bonilla (1992/6), Volpe (1995), and Kieseppä (1996). Niiniluoto (1998) gives an excellent overview of the third period“ in the approach-to-the-truth research.Google Scholar
  28. 28.
    E.g. see van Benthem (1987).Google Scholar
  29. 29.
    Although Popper used the content and similarity notions in his original presentation, Hilpinen (1976, p. 38) stressed the difference between the content and likeness approach. Finally, it was Oddie who has claimed that the content and likeness distinction obtains for almost all definitions. See e.g. Oddie (1990).Google Scholar
  30. 30.
    Niiniluoto (1987), p.459.Google Scholar
  31. 31.
    Popper (1963), p.391–398.Google Scholar
  32. 32.
    Popper (1972), p. 56.Google Scholar
  33. 33.
    See also footnote 24a in Popper (1972), p. 56.Google Scholar
  34. 34.
    Miller (1978).Google Scholar
  35. 35.
    Oddie (1986), sect.1.3.Google Scholar
  36. 36.
    See Hilpinen (1975).Google Scholar
  37. 37.
    From Niiniluoto (1987b), p. 13–15.Google Scholar
  38. 38.
    Kuipers (1992), p.317–319.Google Scholar
  39. 39.
    Kuipers (1992b) applies the idealization concretization ideas ofNowak (1980).Google Scholar
  40. 40.
    Brink and Heidema (1987).Google Scholar
  41. 41.
    For a more elaborate introduction see the Section 2.6.Google Scholar
  42. 42.
    See e.g. Suppe (1977), the introduction.Google Scholar
  43. 43.
    The example is also to be found in Oddie (1987).Google Scholar
  44. 44.
    In the next chapter, we shall show that if the language 2 will be extended into a modal language 2s5, then Popper’s revision can be interpreted as “more correct permissions and prohibitions”.Google Scholar
  45. 45.
    Of course, weak theories do not need to imply literals at all. Real likeness definitions are all equipped with technical devices that also measure the distance to the truth of weak theories.Google Scholar
  46. 46.
    Miller (1974b).Google Scholar
  47. 47.
    See Miller (1978) and Kuipers (1992), respectively.Google Scholar
  48. 48.
    Popper (1963), p.233, first paragraph.Google Scholar
  49. 49.
    Tichÿ (1974), p158, p.159.Google Scholar
  50. 50.
    Oddie (1986), p 13.Google Scholar
  51. 51.
    Hilpinen (1976), p.38.Google Scholar
  52. 52.
    The complete falsehood notion is not restricted to propositional languages. Regarding more sophisticated languages the complete falsehood is the proposition that contradicts the truth in all restrictions of the language.Google Scholar
  53. 53.
    Tichÿ (1974, p.157 note 2).Google Scholar
  54. 54.
    The reason for this phenomenon will become clear in Chapter 2.Google Scholar
  55. 55.
    In Miller (1994) the author has changed his mind and dismisses the argument.Google Scholar
  56. 56.
    The Chapter 2 shows that it is the descriptive nature of the content approaches that causes the trouble; our modal content proposal blocks the child’s-play argument.Google Scholar
  57. 57.
    Our analysis seems to agree with that of Miller (1994).Google Scholar
  58. 58.
    Although Miller uses three propositions, two suffice to formulate the argument.Google Scholar
  59. 59.
    Neither does Miller’s (1975) argument against quantitative estimation.Google Scholar
  60. 60.
    Miller (1978, p. 431, last paragraph) clearly uses this meta-interpretation.Google Scholar
  61. 61.
    For numerous other examples see Niiniluoto (1987), chapter 1.Google Scholar
  62. 62.
    Niiniluoto (1987), p.2.Google Scholar
  63. 63.
    Miller (1994), p.207–208.Google Scholar
  64. 64.
    Niiniluoto (1987) sections 6.4 and 6.5 present and assess quite a number.Google Scholar
  65. 65.
    See also Niiniluoto (1987), p.233 (M10).Google Scholar
  66. 66.
    The term is Roberto Festa’s, see Kuipers (1987a), p.85.Google Scholar
  67. 67.
    Miller (1976) and Niiniluoto (1987), section 6.2.Google Scholar
  68. 68.
    E.g. Chang and Keisler (1973), p.19.Google Scholar
  69. 69.
    See van Benthem (1996).Google Scholar
  70. 70.
    Kuipers (1982), p.352–353.Google Scholar
  71. 71.
    Niiniluoto (1987), p.380–382.Google Scholar
  72. 72.
    Niiniluoto (1987), sec. 6.8.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2001

Authors and Affiliations

  • Sjoerd D. Zwart
    • 1
  1. 1.Delft University of Technology and University of AmsterdamThe Netherlands

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