Thursday, October 12, 2017

Evening Note for Thursday, October 12

Thought for the Evening: Of the Logic of Imperatives

Inference is often assumed to be a matter of assertions; but there are good reasons for thinking that you can infer with imperatives. Consider, for instance, these arguments:

Don't brake while accelerating. (A little later) You are accelerating; therefore, don't brake.

A: Drive to Cleveland to see your mother.
B: I cannot drive to Cleveland unless I rent a car.
A: So rent a car!

Act only according to that maxim that you can at the same time will to be universal law. The maxim to lie to get money is not such a maxim. Therefore do not act according to it.

A: You have to go to town, either by bus or by car.
B: I can't go by car; my car's in the shop.
A: Then go by bus.

A: Take all of Joe's things to the station.
B: Does this belong to Joe?
A: Yes, so take that.

All of these seem to be reasoning involving imperatives, with imperatives in either the premises or the conclusions. Because of the assumption that inference is tied to assertion, though, there was a big dispute, as far as a logical dispute can be big, a few decades back, over whether you could have a logic involving imperatives, in the proper sense. Héctor-Neri Castañeda (who is still absurdly underappreciated) was probably the most influential voice arguing that you could indeed have such a logic. In the course of the dispute it became clear that the two major arguments against were (1) the fact that imperatives have no truth values; and (2) that trying to do an imperative logic on analogy with that for assertions creates some anomalies.

The first of these is certainly the major obstacle for most people; it has become common to associate logic so much with truth values and truth conditions that the prejudice against a non-truth-value logic is quite strong. But it's clear enough that you can have things that are analogous to truth values -- the one that I think is usually most useful is concerned with whether a command or imperative is 'in force', but there are others. I, of course, am on record saying that you can be interested in many other things beside truth values and truth conditions (possibility values and possibility conditions, for instance), so I am utterly unimpressed with this line of argument. But it also, I think, serves to distract from another, more important point, which is that you can obviously give rules governing reasoning with imperatives.

We can identify rule-governed phenomena involving imperatives. For instance, we can identify contradictories:

Go to the store. Don't go to the store.

Obviously, this is because we have some form of negation. We can find imperatives that are equivalent:

Go to Canada. Go to the country that is second largest by land area.

That means that we can substitute imperatives for another. Some imperatives include each other. For instance, 'Do this' and 'Do something' are related in that if you have conform to the former, you have also conformed to the latter, although the reverse is not true. This is at least something like an implication. We can have conjunctions (Talk to Bob and talk to Jane), disjunctions (Talk to Bob or talk to Jane); we can eliminate the conjunction by taking one of the conjuncts, and we can eliminate the disjunction by something that looks very like disjunctive syllogism. These are not arbitrary moves; they are rule-governed, and so there should be some logic to them.

The second major reason used by doubters is that we get puzzles if we take a logic of imperatives to be very like a logic of assertions. To some extent, this objection only gets its force by assuming that a logic of imperatives and a logic of assertions would have to be isomorphic, which was a common supposition in the attempt to build a logic of imperatives, but I see no reason to assume such a thing farther than the evidence requires. (It should be noted, that some anomalies are arguably not. For instance, one of the most common examples makes use of disjunction addition: 'Post this letter; therefore, post this letter or burn it.' But this is not a problem. Because disjunction addition is not standard for natural language assertions, either; it is a rule that is proposed not because it fits the way we talk -- it very much does not -- but because it simplifies the organization of the formal logical system. Thus some of these problems are due to the complications that come from trying to translate between natural languages and artificial languages, and are not actually unique to imperatives.) But there do seem to be some differences. The most obvious one, of course, is that you can't understand arguments based on imperatives to have validity in the sense of truth-preservation. Rather, there needs to be an analogous kind of validity -- in-force-preservation, perhaps.

I think there's another big issue that hasn't been considered at all in the literature. Every attempt at formulating a logic of imperatives that I have seen has focused on building the logic on the model of propositional logic. But there seems good reason to think that this will inevitably give us some odd results. Many imperatives seem to work not like unitary propositions but like predications. We have a subject (usually You), and what we do is apply the imperative to the subject: (You) -- go to the store. This is perhaps not true of all imperatives (if I say, 'This shall be done' as a command, it seems like the imperative is being treated more like a proposition and than like a predication), but it does seem true of enough that we should consider that a propositional-logic model might sometimes not fit things very well.

Various Links of Interest

* Thony Christie discusses the logician Christine Ladd-Franklin.

* Ralph C. Wood, J. R. R. Tolkien's Vision of Sorrowful Joy

* Razib Khan, The 100 Million Killed Under Communist Regimes Matter

* Clare Coffey, Addictions flourish when people are left to manage pain

Currently Reading

Giuseppe di Lampedusa, The Leopard
Maximos the Confessor, On Difficulties in the Church Fathers: The Ambigua, Volume II
Cajetan, Commentary on St. Thomas Aquinas' On Being & Essence
Edith Stein, The Hidden Life: Essays, Meditations, Spiritual Texts

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