Zwart and Franssen's impossibility theorem holds for possible-world-accounts but not for consequence-accounts to verisimilitude

Synthese 172 (3):415 - 436 (2010)
Zwart and Franssen’s impossibility theorem reveals a conflict between the possible-world-based content-definition and the possible-world-based likeness-definition of verisimilitude. In Sect. 2 we show that the possible-world-based content-definition violates four basic intuitions of Popper’s consequence-based content-account to verisimilitude, and therefore cannot be said to be in the spirit of Popper’s account, although this is the opinion of some prominent authors. In Sect. 3 we argue that in consequence-accounts , content-aspects and likeness-aspects of verisimilitude are not in conflict with each other, but in agreement . We explain this fact by pointing towards the deep difference between possible-world- and the consequence-accounts, which does not lie in the difference between syntactic (object-language) versus semantic (meta-language) formulations, but in the difference between ‘disjunction-of-possible-worlds’ versus ‘conjunction-of-parts’ representations of theories. Drawing on earlier work, we explain in Sect. 4 how the shortcomings of Popper’s original definition can be repaired by what we call the relevant element approach. We propose a quantitative likeness-definition of verisimilitude based on relevant elements which provably agrees with the qualitative relevant content-definition of verisimilitude on all pairs of comparable theories. We conclude the paper with a plea for consequence-accounts and a brief analysis of the problem of language-dependence (Sect. 6).
Keywords Verisimilitude  Truthlikeness  Content-definition of verisimilitude  Likeness-definition of verisimilitude  Possible-world-accounts to verisimilitude  Consequence-accounts to verisimilitude
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References found in this work BETA
K. R. Popper (1966). Conjectures and Refutations. Les Etudes Philosophiques 21 (3):431-434.
Ilkka Niiniluoto (1989). Truthlikeness. Journal of Symbolic Logic 54 (1):297-300.
David Miller (1974). Popper's Qualitative Theory of Verisimilitude. British Journal for the Philosophy of Science 25 (2):166-177.

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