Modals for Imperative Logic
This is pretty underdeveloped, but bear with me.
Modal logic is the study of logics that include modalities. For propositional logics, a modality is a way of being true. Normally when we teach propositional logic we assign truth values to propositions like “True” or “False” via a valuation function. The truth values that get assigned in a non-modal logic are, in some sense, truth values simpliciter. A proposition simply has a truth value, whatever that truth value happens to be. (Whether propositions are the only things that get assigned truth values is another question.) A modal logic is a logic that adds at least one modal operator (e.g. ◻) to describe a way that a proposition could be true.
Consider the proposition “Two plus three equals five.” and call it P. If P is true, then it seems like a candidate for being a necessary truth of mathematics. That is, P→◻P.
Necessity and possibility (in the logical or mathematical sense) are one modality that we could consider when building a modal logic. Other modalities include:
metaphysical modalities: metaphysically possible and necessary;
deontic modalities: obligatory, permissible, forbidden;
epistemic modalities: known by S, believed by S, doubted by S;
temporal modalities: before, simultaneous with, after
and so on.
So now I want to suggest the following. Non-propositional logics such as imperative logics don’t have a truth-based semantics. The typical ways to evaluate an imperative are as either satisfied/violated or binding/nonbinding. Peter Vranas, for instance, is developing a trivalent imperative logic with satisfaction, avoidance, and violation as the three semantic assignments.
An alternative way of evaluating command-like sentences is by appealing to a deontic modal logic, but what if we instead apply modal operators to imperatives? What are the modalities of imperative such that we could represent the ways in which an imperative can be satisfied, violated, and so on? Here are a few ideas:
Standard Modality
An imperative can be necessarily or possibly satisfied or violated in virtue of its analyticity or other properties, in a way very similar to standard propositional cases. Consider the imperative: “Be yourself!” This imperative (on a perhaps flat-footed interpretation of this command) is necessarily satisfied if satisfied. One can’t do otherwise but be self-identical, and so one can’t help but satisfy this command.
Intentionality & Goal-Directedness
Another approach to modalities for satisfaction is whether or not imperatives are satisfied by an agent intentionally or with respect to a specific goal or reason. These intentions, goals, or reasons can be represented as modal operations on imperatives: “Do your duty (for the good of the realm)!” or “Do your duty (to avoid punishment)!” are distinct modals on the same imperative.
Alternatively, one could introduce an imperative modal that represents the kind of sentence expressed by the modality. I think this is a version of the intentionality & goal-directedness modal, but expressed in a way that focuses on the speaker rather than the actor. For example, an imperative to “Close the door!” might be a command, a suggestion, an instruction, or a request. These different speech acts all express the same imperative but with different modes of importance or urgency.
Anyway, I’ll be working on developing more formal approaches to modal imperative logics as a way of exploring the ways in which modals, imperatives, counterfactuals, and causal structure intersect.
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