Abstract
Gustavo Cevolani et al. (Erkenntnis 75(2):183–202, 2011) have shown that their account of verisimilitude of ‘conjunctive theories’ of a finite propositional language can be nicely linked to a variant of AGM belief set revision, viz. belief base revision, in the sense that the latter kind of revision is functional for truth approximation according to the conjunctive account. In the present chapter I offer a generalization of these ideas to the case of approaching any divide of a (finite or infinite) universe, allowing several interpretations, besides true (false) atomic propositions, notably nomic states (not) in equilibrium, nomic (im-)possibilities, (non-)instantiated ‘Q-predicates’ of a monadic language. It shows how and why approximation of ‘the true boundary’ takes place by belief base revision guided by evidence.
In the nomic (im-)possibilities interpretation this chapter essentially deals with a belief base revision perspective on basic and quantitative nomic truth approximation of two-sided theories in the sense of Chaps. 4 and 5. The previous chapter dealt with a belief set revision (i.e., AGM-) perspective on basic and refined nomic truth approximation of (one-sided) exclusion theories. This chapter will leave the challenge open of a belief base revision perspective on refined nomic truth approximation of two-sided theories, and, more generally, a belief base perspective on refined approximation of ‘the true boundary’ belonging to whatever interpretation.
Revised version of: “Dovetailing belief base revision with (basic) truth approximation”, in E. Weber, D. Wouters, and J. Meheus , Logic, Reasoning, and Rationality, proceedings-conference in Ghent, 2010, Springer, 2014, pp. 77–93. Acknowledgements: I am very grateful for the stimulating interaction with Gustavo Cevolani and Roberto Festa , and for the comments I got at conferences in Gent (Logic, Reasoning, and Rationality) and Padua (Science, Truth, and Ontology) in September 2010. Finally, I am grateful to the two anonymous referees for their scrupulous remarks and a number of interesting suggestions.
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Notes
- 1.
We use the double symbols in T = «T +,T −» and later in e.g. X = «X+, X−» and R = «R+, R−» to clearly distinguish these ordered pairs from those in previous chapters, where the second set would correspond to its complement in the present notation, and vice versa. Hence, e.g. «X+, X−» and «R+, R−», typical of this chapter, formally correspond to <X+, cX−> and <R+, cR−>, respectively. Conversely, e.g. <M, P> and <R, S>, typical in previous chapters, formally correspond in this chapter to «M, cP» and «R, cS», respectively.
- 2.
Note that the two claims “X+ ⊆ T +” and “X− ⊆ T −” are compatible conjunctive claims, which means that the conjunction of these claims can be seen as a ‘conjunctive theory’ in the sense of Cevolani et al. (2011).
- 3.
As suggested before, note that the nomic interpretation, as represented in notably Chap. 4, with theory <M, P>, inclusion claim “M⊆T” and exclusion claim “T⊆P”, that is “cP⊆cT”, corresponds in the present representation to the theory <<M, cP>>and its claims, assuming T = T + = cT −.
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Kuipers, T.A.F. (2019). Dovetailing Belief Base Revision with Truth Approximation. In: Nomic Truth Approximation Revisited. Synthese Library, vol 399. Springer, Cham. https://doi.org/10.1007/978-3-319-98388-2_15
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