The Traditional Syntactic View
In the discussions of verisimilitude the so-called syntactic, or logico-linguistic, view to theories has been prevalent. This approach conceives the structure of empirical theories primarily as sets of statements in a formalized language (statements that, in the case of axiomatized theories, are logical consequences of a subset of axioms).
Therefore, most, if not all, of the attempts to estimate scientific progress in a realistic perspective move from a set of possible theories X1,..Xn exhaustive and disjoint, only one of which Xi, expressed in a given language L, is true. The idea is to apply the notion of truth for formalized languages proposed by Tarski, that is, one should not compare the best theory we have with reality, but with the true theory expressed in the language L (Zwart, 2001: 4). This whole approach, in our opinion, places too much emphasis on language. In fact, scientific progress almost always involves a change in language, so that such comparisons are often impossible, as noted by Kuhn.Furthermore, all traditional approaches undergo the objection (Miller 1974) that their verisimilitude definitions are not linguistically invariant. You can see this quite easily. Consider a very simple language with three sentences A, B, C. Truth is A A B A C. Let us consider the theories: Ti = ~ A A B A C, T2 = ~ A A~ B A C, T3 = ~ A A~ B A~ C. Therefore T1 has one mistake, T2 two mistakes and T3 three mistakes. Hence it is reasonable to say that, although all three theories are false, T1 is more verisimilar than T2, and T2 more than T3. Let us introduce new sentences D = dfA = B and E = DfA = C. It is easy to show that T1, T2 and T3 could be expressed through the three sentences A, D, E as well.
In particular, we have Ti = ~ Aa ~ Da ~ E, T2 = ~ A A Da ~ E, T3 = ~ A A D A E. But now T1 has three mistakes, T2 two mistakes and T3 one mistake. This means that the order of verisimilitude in the new language is inverted.There are two possible answers to this objection (Oddie, 2014): either arguing that predicates A, B and C are in some ways the right ones, while D and E are wrong, or accepting that the definition of verisimilitude is language-dependent. The former (defined by Kuipers 2000 as “essentialistic realism”) is implausible, especially if we are dealing with the epistemological problem of the estimation of verisimilitude without knowing the truth[76]; the latter is the one followed by the majority of scholars. As stated by Niiniluoto (1998), the request that the notion of verisimilitude be independent of a change of language, though inter-translatable, is too strong. In fact, the whole approach to the problem of verisimilitude is built on Popper’s attempt to implement Tarski’s notion of truth in the analysis of truth in scientific theories. So, from the outset, a given language is assumed as well as the existence of a true theory in that language.[77] These approaches, therefore, are interesting from the logical point of view, but actually they are only partly appropriate responses to the problem of establishing a way to compare the verisimilitude of two theories which do not share the same language; the latter is a very common situation in science.
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