Abstract
I attempt to provide a general account of deontic context, equally applicable within and an intensional and a hyperintensional framework; I compare Rothschild's and Yablo's accounts of the semantics for deontic logic, deontic updating and denotic duality with my own accounts; and I conclude with some general remarks on negation
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Notes
- 1.
This is not necessarily a difficulty for the world-based approach, although if will be if, as is not uncommon, the worlds are themselves identified with sets of literals or truth-value assignments or the like.
- 2.
- 3.
A related issue concerning counterfactuals is discussed in Sect. 3.3 of Bacon’s contribution and in Sect. 2 of my response to his contribution
- 4.
I follow Rothschild and Yablo in using □ for obligation and ◊ for permission, rather than the notation in Fine (2018a, b).
- 5.
Similar definitions are given in Sect. 6 of my response to Giordani.
- 6.
Decomposition is also discussed in Sect. 6 of my response to Giordani and in Sects. 3–6 of my response to Jago.
- 7.
This is in line with the requirement-lists approach, which is considered, and criticized, in Sect. 4 of R/Y’s paper.
- 8.
I shall, like R/Y (fn. 68), be largely concerned with deontic statements of the form □A and ◊A in which the embedded statement A does not itself contain a deontic operator. These are the cases that are largely relevant to deontic revision even if not to the more general determination of deontic truth.
- 9.
Some related matters of formalization, and especially of axiomatization, are considered in Sects. 3 and 4 of my response to Krämer.
- 10.
Related principles concerning subject matter are considered in Sect. 2 of my response to Giordani. In the present context, we may understand ‘/’ as ⊃ and ‘//’ as ≡.
- 11.
The issue is discussed in Sects. 3.2, 15–17 of their paper. Failure of duality is also discussed in Sect. 6 of Fine (2018) (points 3 and 4 under the subheading ‘O/P inferences’).
- 12.
Some of R/Y’s clauses are in fact in violation of Positive Bias—one of the topics I shall take up in Sect. 28.5.
- 13.
- 14.
We should then note that treating ⊛ in this way will enable us to maintain the identities
under the possible worlds approach. - 15.
This is an infinitary version of the first mixture axiom from Sect. 7 of Fine (2018).
- 16.
This is an infinitary version of the second mixture axiom from Sect. 7 of Fine (2018).
- 17.
A further, somewhat curious, point of contact is that they take the context to consist of the truthmakers for the proposition ‘It’s all OK’ (Sect. 28.6), while I suggest, in discussing Andersonian constants under (5) of (Sect. 28.6), that ‘we might introduce a constant ‘A-OK’ for the imperative ‘do something completely alright … The actions in compliance with A-OK will then be the members of C [the deontic context].’
- 18.
Though I do suggest truth-maker conditions under (6) of §4, some of which appeal to only certain aspects of the deontic context. In the appendix, R/Y provide two-sided truth-makers (s, s) for hybrid statements, such as A ∧ □B, which are ‘exact on the s side, and inexact on the s side’, though my own inclination would be to treat both sides as exact but to take the fusion s ⊔ sʹ of two distinct contexts s and sʹ always to be the impossible state.
- 19.
I have here modified the formulation of their clauses by taking the states of a given context s to be the ideal states and by taking a deontic statement to be true or false according as to whether s is a truth-maker or falsity-maker for the statement.
- 20.
The paper says truth-maker but I think they mean falsity-maker.
- 21.
R/Y also consider some super-loose and super-strict clauses in Sect. 19 of their paper. It is worth noting, in this regard, that their super-loose clauses (+□) and (+◊) correspond to clauses (i)ʹʹ and (ii)ʹ from Sect. 4 of Fine (2018), although I have nothing corresponding to their super-strict clauses.
- 22.
One might also appeal to the failure of Conversion to defuse the earlier argument against combining Duality with Free Choice (Sect. 3, (1)–(7)).
- 23.
I have benefitted here from Moltmann (2019). The semantics of the ‘it is the case that’-operator is further discussed in Sect. 6 of my response to Jago.
- 24.
To put the point more carefully, it should be supposed that the operation neg denoted by ‘not’ has local application to the operation nec denoted by ‘required’, so that the application of neg(nec) to any proposition P can be determined by first applying nec to P and then applying the operation denoted by ‘¬’ to nec(P).
- 25.
This issue also infects the reading of the deontic operators, thereby adding a further layer of complication. For I might read ‘◊…’, for example, as ‘it is the case that it is permitted that …’ rather than as ‘it is permitted that ….’ The application of the same form of sentential negation to each might then result in different truth-conditions, with the one becoming equivalent to ‘it is not the case that it is permitted that …’ and the other to ‘it is not permitted that …’.
- 26.
I have here adopted R/Y’s notation for propositions and states rather than the notation that I have used elsewhere in this volume and some of my other work.
- 27.
The result may be established as follows. Given a transfinite cardinal κ, let Xκ = {Y ⊆ κ: card(Y) = κ and card (κ − Y) = κ}. We suppose that Xκ is ordered by the subset relation. We must then show that (i) Xκ satisfies the symmetry condition and (ii) for any partial ordering S, there exists a κ such that S is embeddable in Xκ. (i) is straightforward; and (ii) may be established by first showing that S is isomorphic to a partial ordering Sʹ on subsets of S and then showing that Sʹ is embeddable in a sufficiently large Xκ.
under the possible worlds approach.References
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Fine, K. (2023). ‘Truthmaker Foundations for Deontic Logic’: Response to Rothchild’s and Yablo’s ‘Permissive Updates’. In: Faroldi, F.L.G., Van De Putte, F. (eds) Kit Fine on Truthmakers, Relevance, and Non-classical Logic. Outstanding Contributions to Logic, vol 26. Springer, Cham. https://doi.org/10.1007/978-3-031-29415-0_28
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