Abstract
This is an essay on the understanding of disposition concepts, which exploits the Ramsey test semantics of conditionals for a refined conditional analysis of dispositions. I will show that this semantics allows for a more accurate account of disposition concepts than the standard semantics of conditionals by David Lewis. This includes dealing with the counterexamples to the conditional analysis, which are known as finks, antidotes, and mimics.
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Notes
There are multiple ways of striking and breaking, which respectively give rise to a distinct canonical disposition. For the purpose of the present investigation, however, the binary distinction between conventional and canonical dispositions is sufficiently fine-grained.
Writing down these axioms, I tacitly extend the system of Lewis (1973) to conditional predicate logic, as is done in many applications of this system.
Langton and Lewis (1998) have dismissed Kim’s original definition in view of subtle problems with disjunctive properties. It remains to be seen whether these problems carry over to the present analysis. At least apparently, they do not. For, the peculiar disjunctive properties used by Lewis to criticise the above explanation scheme are not relevant for the ascription of dispositions. For a criticism of the general approach used by Langton and Lewis (1998) to refine Kim’s original definition, see Marshall (2009).
Gärdenfors himself has viewed the Ramsey test, later on, with suspicion in light of a triviality theorem, according to which this test is inconsistent with a fundamental principle of the AGM theory called Consistency Preservation (Gärdenfors 1988, Ch. 7.4). (This principle says that, if \(\beta \) is accepted in K and \(\alpha \) consistent with K, then \(\beta \in K *\alpha \).) Recently, however, there have been various, apparently successful attempts at defending the Ramsey test. Leitgeb (2010) and Rott (2011) have shown, in different ways, that the Ramsey test is reconcilable with Preservation for “flat”, i.e., non-nested conditionals. Rott (2011) has shown, moreover, that Preservation is not a sensible requirement for nested conditionals. Bradley (2007) has devised a general argument against Consistency Preservation in the context of the Ramsey test.
The present introduction of negation of conditionals accords with Stalnaker (1968) and is endorsed by Bradley (2007). The more common alternative \(\lnot (\alpha> \gamma ) \in K_>(E) \text { if and only if } \gamma \notin K(E) *\alpha \) has counterintuitive consequences if used for the analysis of reasoning about dispositions. For, it implies that an object a does (determinately) not have a certain disposition D if we are indeterminate as to whether or not a exhibits the D-specific manifestation under the D-specific stimulus S.
Belief change models using belief bases or possible worlds typically work with such a definition of contractions.
In a similar vein, Lewis (1979) has argued that the semantics of counterfactuals should account for the vagueness and context-relativity of counterfactual statements.
There is a close connection between nonmonotonic and default reasoning. To keep technicalities to a minimum, we have not included a section on this type of reasoning. The reader interested in the connections between nonmonotonic and default reasoning, is referred to Brewka et al. (2008).
See Straßer (2014) for an introduction to adaptive logics.
See van Ditmarsch et al. (2008, Ch. 3) for an introduction.
I should clarify here that by the standard semantics of conditionals, I mean the formal framework of a system of spheres of possible worlds under its metaphysical interpretation by Lewis (1973). The formal framework of a possible worlds ordering by itself is consistent with the Ramsey test semantics, as is obvious from Stalnaker (1968) and Rott (2011).
Unlike the present account, the gradable approach does cover “soft” dispositions where the manifestation is exhibited in less than the majority of stimulus cases. Perhaps we should therefore distinguish between soft and hard dispositions, where the latter qualify as dispositions in the narrower, scientifically more respectable sense. The present approach does of course not exclude grades of dispositionality.
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Andreas, H. An analysis of disposition concepts by the Ramsey test. Synthese 198, 11379–11397 (2021). https://doi.org/10.1007/s11229-020-02794-x
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DOI: https://doi.org/10.1007/s11229-020-02794-x