Abstract
The variably strict analysis of conditionals does not only largely dominate the philosophical literature, since its invention by Stalnaker and Lewis, it also found its way into linguistics and psychology. Yet, the shortcomings of Lewis–Stalnaker’s account initiated a plethora of modifications, such as non-vacuist conditionals, presuppositional indicatives, perfect conditionals, or other conditional constructions, for example: reason relations, difference-making conditionals, counterfactual dependency, or probabilistic relevance. Many of these new connectives can be treated as strengthened or weakened conditionals. They are definable conditionals. This article develops a technique to infer the logic for such definable conditionals from the known logic of the underlying defining conditional. The technique is applied to central examples. The results show that a large part of the zoo of conditionals arises from a basic conditional—a constant nucleus of the different contextual and conceptual variations of variably strict conditionals.
Highlights
This section rehearses some known conditional logics and introduces the semantics used for the basic conditional >
For the sufficient reason’s translation and backtranslation to be well behaved axiomatically, we need to consider a classical conditional logic augmented by the proper axiom S0 for
This article laid out a general technique to transfer completeness results of a known basic conditional > to a definable conditional
Summary
A standard account has emerged, the so-called possible worlds account (Stalnaker 1968; Lewis 1973b) According to this account, a conditional A > C is true in the actual world (roughly) if and only if the closest A-worlds are C-worlds.. Different approaches argue for different conditions (Krzyzanowska et al 2013; Spohn 2015; Skovgaard-Olsen 2016; Raidl 2019; Rott 2019; Crupi and Iacona 2019) Some of these logics are not worked out yet, or only for specific semantics. The idea goes as follows: Redefine > in terms of This yields a formula α in the language for.
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