Realism and the logic of conceivability
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Realism and the logic of conceivability Dominik Kauss1,2
Springer Nature B.V. 2020
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. Keywords Conceivability Thinkability Apriority Epistemic modality Realism Non-normal logics
& Dominik Kauss [email protected] 1
Goethe University Frankfurt, Norbert Wollheim Platz 1, 60629 Frankfurt am Main, Germany
2
Massachusetts Institute of Technology, 77 Massachusetts Avenue, 32-d808, Cambridge, MA 02139-4307, USA
123
D. Kauss
1 Introduction If you’re interested in the logic of conceivability, chances are that at some point you’ll be wondering which of the principles that we know to hold for alethic possibility also hold for conceivability, and what kind of philosophical commitment one incurs by accepting any of those principles for conceivability. Among the most basic platitudes shaping our notion of alethic modality are the duality principle, stating that necessity equals impossibility of the opposite: hP $ ::P; the (T) principle, stating that necessity entails truth: hP ! P; the (D) principle, stating that necessity entails possibility: hP ! P; and the (K) principle, stating that necessity distributes over the conditional: hðP ! QÞ ! ðhP ! hQÞ. Here, h and abbreviate ‘it’s necessary that’ and ‘it’s possible that’, respectively, pertaining not to what is necessary or possible relative to our knowledge or imaginative capacities, say, but to what is necessary or possible tout court. Deviating from this alethic interpretation, we will discuss (T), (D), and (K) on a broadly epistemic reading— call it the conceivability interpretation—which I will flag by painting box and diamond black. In a nutshell, we will use to abbreviate ‘it’s conceivable that’, defining as short for ::, thus validating the corresponding duality principle P $ ::P by f
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