1. Fallibilism, Verisimilitude, and the Preface Paradox.Gustavo Cevolani - 2017 - Erkenntnis 82 (1):169-183.
    The Preface Paradox apparently shows that it is sometimes rational to believe logically incompatible propositions. In this paper, I propose a way out of the paradox based on the ideas of fallibilism and verisimilitude. More precisely, I defend the view that a rational inquirer can fallibly believe or accept a proposition which is false, or likely false, but verisimilar; and I argue that this view makes the Preface Paradox disappear. Some possible objections to my proposal, and an alternative view of (...)
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Definition of verisimilitude I suggest
Some words in my paper:

T(hj|ei)--fuzzy truth function of a predicate hj.

T(hj)--logical probability or  average thue-value of a predicate hj.

Popper defined Testing severity and Verisimilitude (1963/2005, 526, 534). Since Logical Probability and Statistical Probability are not well distinguished by him, his definitions are not satisfactory. The author suggests defining log [1/T(hj)] as testing severity, and T(hj|ei)/T(hj) as verisimilitude. In terms of Likelihood method, P(ei| hi is true)/P(ei) =T(hj|ei)/T(hj) is also called standard likelihood. So, we may say Semantic information = log (Standard likelihood) = log (Verisimilitude)=Testing severity - Relative deviation
 If negative verisimilitude for lies or wrong predictions is expected, one may also define verisimilitude by log [T(hj|ei)/T(hj)]. 

The figure 8 in the paper shows how positive and negative degrees of believe affect thruthlikeness. 

Definition of verisimilitude I suggest
Reply to Chenguang Lu
Logical probability T(hj)=sum i P(xi)T(hj|ei).1/ T(hj) indicates Fallibility or testing severity.

Definition of verisimilitude I suggest
Reply to Chenguang Lu
Don't worry about anything Popper said. As far as epistemology goes, his work may be considered pseudoscience. Better look into how physicists use Bayesian methods. That's going to tell you a lot more about actual science.


Definition of verisimilitude I suggest
Reply to Chenguang Lu
Chenguang Lu, since Popper's original two proposals for defining verisimilitude a lot has been written on the topic. It would benefit your work to catch up with the reasons for which Popper's original ideas were dismissed and also the motivations for (at least) the next two generations of this notion. You could start with simply reading a Stanford entry on it [1] and proceed with what you find in the references, especially the following papers and books:
  • Tichý, P., 1974, “On Popper's definitions of verisimilitude”, The British Journal for the Philosophy of Science, 25: 155–160.
  • Psillos, S., 1999, Scientific Realism: How Science Tracks Truth, London: Routledge.
  • Zwart, S. D., 2001, Refined Verisimilitude, Dordrecht: Kluwer.
  • Zwart, S. D., and M. Franssen, 2007, “An impossibility theorem for verisimilitude”, Synthese, 158(1): 75–92.
  • Schurz, G., and Weingartner, P., 1987, “Verisimilitude defined by relevant consequence-elements”, in Kuipers 1987a, 47-77.
  • Niiniluoto, I., 2011, “Revising beliefs towards the truth”, in Erkenntnis, 75: 165–181.
[1] https://plato.stanford.edu/entries/truthlikeness/