Refined Verisimilitude pp 191-226 | Cite as

# Refined Verisimilitude

## Abstract

The difference between verisimilitude and truthlikeness definitions is presented in Chapter 1; I then expounded on this difference in Chapters 2–3. Together, the first three chapters constitute the expository part of this book. In Chapters 4–5, I discussed the epistemic problem of approach-to-the-truth, and Miller’s extensional substitution argument. Putting forward the solution to Miller’s puzzle, in the preceding chapter, I paved the way for my refined verisimilitude proposal, which is the subject of this chapter. In a way, Chapters 1–5 can be viewed as preparatory steps leading up to my new approach-to-the-truth proposal presented in Section 6.4. As a prelude I first introduce the refined Δ-verisimilitude definition that merges the Δ-distances on the Lindenbaum and constituent algebra of a language. Then we will see that the ≤^{+} ordering of the ℒ-propositions can be combined with the total preorder on the constituents of the language. I shall partition the Lindenbaum algebra in equivalence classes of propositions of the same distance to the truth, and I shall prove that the merger of the two orderings is compatible with this partition and orders the equivalence classes. I call the resulting ordering the *refined verisimilitude* proposal. A more detailed summary of this chapter can be found at the end of Section 6.1.

## Keywords

Equivalence Class Partial Order Boolean Algebra Transitive Closure Atomic Proposition## Preview

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## References

- 1.Interestingly, in private conversation, Niiniluoto contended that his two dimensional truthlikeness continuum does not subsume my refined verisimilitude proposal.Google Scholar
- 3.E.g. Chang and Keisler (1973), p.46–47.Google Scholar
- 4.Although T, yr E Sent(2)/H are equivalence classes of sentences in the sequel, I will use them as if they are a single sentence and write ç wGoogle Scholar
- 5.Clearly, as the constituent and Lindenbaum algebra both are Boolean algebras, the more abstract version of our proposals only uses set algebras; it disregards the identity of the atomic propositions.Google Scholar
- 8.See Davey and Priestley (1990), p. 25.Google Scholar
- 9.In case the language is finite and the truth T is complete, the truth ideal consists of the contradiction and T. The truth ideal is less trivial if T is incomplete or unaxiomatizable.Google Scholar
- 10.See e.g. Davey and Priestley (1990), p.145.Google Scholar
- 11.For more details see Davey and Priestley (1990), p.145).Google Scholar
- 12.See e.g. Davey and Priestley (1990), p.18–19.Google Scholar
- 13.See e.g. Stoll (1961), p.263.Google Scholar
- 14.Intuitively, the verisimilitude of a theory is the similarity between that theory and the true theory regarding
*empirical*content. Consequently, it make no sense to contribute verisimilitude to the tautology and the contradiction, which lack empirical content.Google Scholar - 15.Counterbalancing logical strength and false consequences is less counter intuitive if the truth is complete; it might even be helpful in language dynamics, where the choice of conceptual frameworks is at stake.Google Scholar
- 16.This might be the beginning of a compound definition if the truth is incomplete.Google Scholar
- 19.A relation
*R*is a*weak ordering of the set A*iff*R*is transitive and stongly connected in*A.“*Google Scholar - 20.See e.g. Suppes (1960), p.84.Google Scholar
- 21.Niiniluoto (1987), p 192.Google Scholar