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Verisimilitude

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Refined Verisimilitude

Part of the book series: Synthese Library ((SYLI,volume 307))

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Abstract

In Chapter 1, I introduced Popper’s comparative content definition, which is based on truth-value and logical strength, and showed how it excludes the comparison of two different false theories. After the publication of this peculiarity in 1974,1 Miller and Kuipers searched independently for another way to formalize Popper’s intuitions about verisimilitude. Their endeavours resulted in comparative content definitions (Kuipers calls his version the naive comparative definition). Miller formulates a distance function which has as its codomain the original Boolean algebra instead of the real numbers. Both definitions are almost identical to the consequence definition also hinted at in the first chapter (subsection 1.4.1). Here we examine Miller’s and Kuipers’s content proposals.

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Notes

  1. Miller (1974) and Tichÿ (1974).

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  2. Miller (1978, p. 429).

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  3. This is in accordance with Miller (1994).

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  4. Ibid p. 416.

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  5. Miller (1978, p.423).

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  6. Note that Miller calls here A+B, what he calls A.B in Miller (1974a) and vice versa.

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  7. Miller (1978) p. 424. Further, the Brouwerian algebra is also known as the dual of the Heyting algebra. Curry calls it the subtractive lattice, and Popper the dual­intuitionistic calculus.

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  8. Miller (1974) p.168.

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  9. Ibid. p.169 note 1.

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  10. Miller (1978, p.427).

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  11. Miller (1974, p.174) second corollary of Theorem 5.

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  12. Ibid. Lemma on p.173.

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  13. Ibid.p.427.

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  14. Obviously, it H -’Tcp H T equals (yr A -t) y (-j, A t)(cp A ‘t) y (p A t). Consequently, [Mod(yr Ai) v Mod(--Air A t)] S [Mod(q) A --ti) v Mod(’cp A t)], which is abbreviated by: Mod(w) A Mod(t) Mod(cp) A Mod(t)].

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  15. See for more detailed information Bell and Slomson 1969.

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  16. However, the theory of densely ordered sets without end-points is complete and first order axiomatizable (see Bell and Slomson 1969 chapter 9 section 5).

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  17. See also Kuipers (2000).

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  18. The differences between the logicistic and structuralist theory representation emerge while using more sophisticated theory representations.

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  19. Kuipers (1992), p.300–301.

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  20. Ibid.p.301.

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  21. Ibidp.301. and Kuipers (1987) p.82.

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  22. Cf. Kuipers (1982), p.347.

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  23. Ibid.section 2.

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  24. Kuipers (1987a), p.82.

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  25. Ibid. p.83. Compare with the “potential falsifiers” in Popper (1963), p.385.

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  26. See for Kuipers’s version Kuipers (1982) and Kuipers (1992).

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  27. Kuipers (1982, p.347) gives the same list of the possible combinations of weak and strong, theoretical and descriptive truth.

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  28. Note that according to Popper (1963, fifth edition, p.232, and Addendum 1) the empirical content of a theory is proportional to its logical content.

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  29. Niiniluoto’s remarks (1987, p.381–382) seem to be inspired by the same observations.

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  30. See Kuipers (1982), p.353 and (1992), p.304.

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  31. Kuipers (1992), p.314.

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  32. See Miller (1978, last page) for the same assessment.

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  33. See for more properties of the A-definition van Benthem (1987).

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  34. Kuipers (1982), p.357. Although Kuipers (1992) refers to worlds on p. 301, the paper does not mention the incompleteness of the truth.

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  35. Niiniluoto (1987), p.381.

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  36. Kuipers (1982), the second section.

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  37. Although it cannot be denied that the descriptive theory of plate tectonics has been a big step in the right direction.

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  38. Niiniluoto (1987), p.381–382.

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  39. Actually, Niiniluoto proposes to replace first order constituents

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  40. Cohen (1980) and (1987).

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  41. Hughes and Cresswell (1984), p.7.

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  42. At least according to Kuipers (1982).

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  43. Here again we may restrict theories to be elements of SProp(2s5), but we leave the details to the reader.

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  44. In 2s5 [p,q] with i = q(p A q) the complete falsehood 4 is the most distinct constituent

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Authors and Affiliations

  1. Delft University of Technology and University of Amsterdam, The Netherlands

    Sjoerd D. Zwart

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  1. Sjoerd D. Zwart
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© 2001 Springer Science+Business Media Dordrecht

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Zwart, S.D. (2001). Verisimilitude. In: Refined Verisimilitude. Synthese Library, vol 307. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2870-6_2

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  • DOI: https://doi.org/10.1007/978-94-017-2870-6_2

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-5932-1

  • Online ISBN: 978-94-017-2870-6

  • eBook Packages: Springer Book Archive

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