Abstract
On their alethic reading, formulas (T), (D), and (K) codify three of the most basic principles of possibility and its dual (necessity). This paper discusses these formulas on a broadly epistemic reading, and in particular as candidate principles about conceivability and its dual (inconceivability of the opposite). As will be shown, the question whether (T) and its classical dual equivalent, as well as (D) and (K) hold on this reading is not only a logical one but involves a distinctively metaphysical controversy between realist and antirealist views on the relation between truth on the one hand and various cognitive conditions such as knowability, conceivability, and thinkability on the other. It will be argued that the stance we take with regard to the metaphysical dispute has consequences for our assessment of the plausibility not only of (T) and its classical equivalent, but also of (D) and—when that stance is combined with a structural account of propositions—potentially of (K) as well; with all four taken in the above epistemic sense. A second upshot will be that the same sensitivity to metaphysical background commitment also applies to our view as to whether or not inconceivability of the opposite coincides with, or even entails, apriority.
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Notes
Here and in the following, by ‘interpretation’ I don’t mean anything more technical than simply the vernacular counterparts which box and diamond are used to abbreviate in a given application of modal logic.
I will use ‘it’s inconceivable that P’ as synonymous with ‘it’s not conceivable that P’. This use differs from other legitimate uses, such as Yablo’s (1993: 11f, 29ff.), on which the former phrase is strictly stronger by way of entailing without being entailed by the latter.
As words are being used here, in order for it to be rationally feasible to imagine a scenario in which P, there is no requirement that it be feasible to visually imagine such a scenario. For instance, in the intended general sense, we can imagine a scenario featuring an invisible man performing such and such deeds, even though it may not be feasible to visually imagine such a scenario.
The example is of course Evans’ (1979), although he uses it to illustrate a slightly different claim.
The claim that ‘it’s a priori that P’ is factive may not be obvious, especially if that locution is read as short for ‘it’s a priori justifiable to believe that P’. For a discussion of fallibilist accounts of a priori justification, see Casullo (2003: 56ff.) However, here ‘it’s a priori that P’ is understood as short for ‘it’s a priori knowable that P’. While many philosophers have assumed knowability to be non-factive—e.g. Williamson (2000: 292)—Brogaard and Salerno (2008) and Fuhrmann (2014) argue quite plausibly that our ordinary notion of knowability is factive. If so, apriority in the intended sense is factive due to the factivity of knowability.
Antirealists are known for their resistance to interdefining box and diamond as duals. Presumably, this resistance partially flows from their having in mind a certain preformal interpretation of box and diamond as necessity and possibility, taken in some epistemic sense. But recall that our abbreviative definition of \(\blacksquare\) as inconceivability of the opposite does not presuppose this notion to be equivalent to any sort of necessity, epistemic or alethic, so antirealists should have no reservations about accepting that definition.
It is not uncommon to see philosophers define or introduce the term ‘proposition’ in terms of something along the lines of ‘potential content of thought’. This definition makes it trivially false that there are or may be unthinkable propositions, and thus is unacceptable to realists who want to claim the latter. Moreover, paired with the idea/heuristic that quantification into sentence position is tantamount to quantification over propositions, that definition is bound to strike the realist as having the effect of restricting the domain of such quantification to the thinkable. Faced with this complication, realists may either reject the definition or rephrase their point, as well as the mentioned idea/heuristic about sentential quantification, in terms of ‘state of affairs’ in place of ‘proposition’. That said, I will continue to use ‘proposition’, without of course assuming the above definition.
For simplicity, I’m ignoring the fact that the rule is standardly put in terms of sentences rather than in terms of the propositions expressed by those sentences.
Perhaps we can indirectly—i.e. without thinking them—“rule out” inconsistent unthinkable propositions, based on some general principle; but that still leaves all the consistent unthinkable propositions, if there are such.
In contrast, realism does not rule out either of the (IV) formula: \(\blacklozenge \blacklozenge P \rightarrow \blacklozenge P\), the (B) formula: \(P \rightarrow \blacksquare \blacklozenge P\), or the (V) formula: \(\blacklozenge P \rightarrow \blacksquare \blacklozenge P\), which correspond, respectively, to transitivity, symmetry, and the Euclidean property.
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Acknowledgements
Versions of this paper were presented at the workshop Logics for Imagination, Ruhr-University Bochum (March 2018), at the University of Konstanz (May 2018), at the Massachusetts Institute of Technology (May 2019), and at the University of California, Irvine (June 2019). My thanks to all four audiences, in particular to Christopher Badura, Lisa Benossi, Francesco Berto, Daniel Dohrn, Sophia Gilbert, Caspar Hare, Vann McGee, Toby Meadows, Thomas Müller, Eric Raidl, Pierre Saint-Germier, Mattias Skipper, Jack Spencer, Will Stafford, Kai Wehmeier, and Roger White. Special thanks to Ali Esmi, Stephen Yablo, and an anonymous referee for Philosophical Studies.
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Kauss, D. Realism and the logic of conceivability. Philos Stud 177, 3885–3902 (2020). https://doi.org/10.1007/s11098-020-01413-2
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DOI: https://doi.org/10.1007/s11098-020-01413-2