Charlow on Grice on strength ("Post the letter or burn it! -- less strong than "Burn it!")

http://www-personal.umich.edu/~ncharlo/work/imperative_statics_and_dynamics.pdfLogics of Content

Charlow writes:

"A different approach to the logic of imperatives is what I will term the “logic of content.”"

"There
is undoubtedly a sense in which a logic of imperative fulfillment is a logic of content."

"Logics
of fulfillment pay attention to what is required or commanded by an imperative sentence, and
construe an imperative conclusion as following from a set 􀀀 of formulas just in case the content
of the conclusion (what the conclusion requires) follows from what the imperatives in 􀀀 require
(together with the facts that the non-imperatives in 􀀀 describe)."

"But I wish to identify the content
of an imperative sentence with something other than what the sentence requires."

"What precisely
imperative content amounts to will depend on the specific sort of semantic theory one endorses."

"But what I have in mind generally is the denotation assigned by a semantic theory to an arbitrary
imperative formula ! of LPI .

"Logics of content may (and do) di er significantly from one another."

"Some (e.g., those
that identify the denotation of ! with that of O , where O is a species of deontic necessity
operator), will endorse the statement of conditions on given in (11)."

"Others will not."

"What
distinguishes logics of content as a class is a particular conceptualization of imperative logic."

"As normative for commanding (or, more precisely, the endorsement of commands). Ordinary

4: This is not to say that such an authority will view as impermissible. Only that she might reserve positive
endorsement (of the sort expressed by an imperative ! ) for those ways of fulfilling the original command that are, by her
lights, both permissible and best. We say much more about the issues raised here in the next section.
8

imperative statics and dynamics 9

propositional logic is often held to be normative, in some nebulous sense, for assertion and
belief: if 1; :::; n , then asserting (or believing) that 1; :::; n commits an agent to endorsing
an assertion (or belief) that .

Similarly, logics of content conceptualize imperative logic as
normative for endorsement of commands: if f! 1; :::; ! ng[f 1; :::; mg ! , then endorsing
each member of f! 1; :::; ! ng[f 1; :::; mg commits an agent to endorsing ! .5

Logics of content
generally implement this conceptualization of imperative logic by developing novel theories of
the semantic content of imperative formulae (hence their name).

This is, of course, a rather
crude sketch.

Although we could say a good deal more by way of filling it in (and illustrating
with example accounts), we will save those words now. Logics of content will be a focus of our
attention in this paper.

Instead, we turn to applications.
Endorsing a logic of content gives one a foothold in resisting the arguments in (12) and
(13) that troubled the logic of fulfillment. Indeed, it is easy to see that the deontic logic-inspired
argument against their validity assumes the conceptualization of imperative logic characteristic of
logics of content.6 It is, of course, only a foothold. Genuine leverage over these arguments comes
only with the development of a bona fide semantics.

-------------------

"More interestingly, logics of content are
well-positioned to handle the famous “paradox” about imperative logic of Ross (1941)."

"Indeed, doing so seems to inspire most examples of logics of content in the literature on imperatives."

(16)

! 6 !( _ )

Post the letter! 6

Post or burn the letter!


"It is well-known that the way logics of fulfillment conceptualize imperative entailment is incompatible with the felt invalidity of the Ross inference—indeed, this point goes back to Ross himself."

"Since any valuation fulfilling ! also fulfills !( _ ), any reasonable implementation of a logic of fulfillment will have it that ! !( _ )."

"By contrast, conceptualizing imperative
logic as a logic of content supplies a rationale for formulating a logic (and theory of imperative
content) in which the Ross inference is predicted invalid."


-------------- or 'unhappy' or conversationally queer.

----

"Intuitively, endorsing ! (e.g., issuing a
command to post a letter) does not per se commit an agent to endorsing !( _ )."

"It is worth refining this point further."

"We can do so by comparing the Ross inference to the
following argument."

(17)

See to it that if you read the book, you come see me. [!( ! )]

Read the book! [! ]

) Come see me! [! ]

"Castaneda (1958)—applying apparently the same sort of conception of

IMPERATIVE ENTAILMENT

we take to characterize logics of content—argues that the argument form illustrated in (17) is invalid."

"[A] teacher who [issues the premise commands in (17)] has not thereby ordered
or told his student to come to see him, regardless of the student’s reading of the
book"

(Castaneda 1958: 43-44).

Similar reasoning might be thought to explain why logics of content should not endorse the
inference of !( _ ) from ! : if teacher commands student to post the letter, teacher has not
thereby committed herself to endorsing the command to post or burn it, regardless of the student’s
posting it.

5: Endorsement is conceived as a generic pro-attitude. Endorsement of non-imperative formulas is something like
belief in them. We leave the notion of imperative formula endorsement vague for now, but take up the issue again below.
6: This isn’t to say that logics of content must invalidate (12) and (13), only that they supply a rationale for doing so.
See the end of x3.2 for some discussion.
9
10 nate charlow

There are two things to note here. First, if Castaneda’s argument against the argument form
in (17) succeeds, it appears to rule out an entire class of proposals about the semantic content of
imperatives—namely, any analysis of the imperative operator as a species of deontic necessity
modal—as possible implementations of the conceptualization of imperative entailment that is
characteristic of logics of content. Consider the deontic version of the K axiom.
(18) O( ! )!(O !O )
K is valid in the class of all frames for Standard Deontic Logic. The following is an easily proved
metatheorem of SDL.
(19) 􀀀[f g i 􀀀 !

Together with K, this implies that O( ! );O O .

If Castaneda is right about the invalidity
of (17), and we aim to analyze the imperative operator as the deontic necessity operator O of
SDL, we are saddled with an obvious contradiction. (Noticing that O !O( _ ) is valid in the
class of all frames for deontic modal logic, if Castaneda-esque reasoning about the Ross Paradox
is correct, we have an even more direct argument to the same conclusion.)

Second, and more interestingly, Castaneda’s argument involves a tacit commitment to a
definite view about the content of imperatives.

The order regardless of locution is most
naturally interpreted as expressing that both ^ and ^: are permitted (when possible), and
at least one required. The reason that the conclusion imperative of (17) is held not to follow from
the premise imperatives is that the content of the imperative, according to Castaneda, is given,
roughly, by a command to come see teacher regardless of the student’s reading of the book. In
other words, Castaneda seems to think that the conclusion imperative expresses a requirement
to come see teacher and a permission to do so with or without having read the book.

Since a
speaker who endorses the premise imperatives of (17) in no way commits herself to permitting
her addressee not to read the book (indeed, quite the opposite), a logic of content ought to dictate
that the argument is invalid.

"The adaptation of Castaneda’s argument to the Ross inference holds
that


a

DISJUNCTIVE IMPERATIVE


!( _ ) expresses a requirement to make it the case that _ and
a permission to do so without making it the case that (assuming this to be possible).

Since a
speaker who issues the command ! in no way commits herself to endorsing such a permission, a
logic of content should dictate that the Ross inference is invalid.)


The notion that imperatives bear permissions as part of their content has a significant degree
of historical (see, e.g., Bernard A. O. Williams 1963; R. M. Hare 1967 -- relying on Grice 1966, "Logic and Conversation", Oxford lectures -- also earlier Grice 1961, On "My wife is in the kitchen OR in the garden" -- "Causal theory of perception", Aristotelian Society) and contemporary (see, e.g., Aloni 2007)
appeal, and there is undoubtedly something right about it.

"It is impossible to consistently endorse
a command without being disposed to endorse some sort of permission—minimally, a permission
that the command be fulfilled.7

What sort of permissions should be written into the content of
imperatives (consistent with the conceptualization of imperative logic characteristic of logics of
content) is, however, a di erent matter.

I want to suggest that there are ways of integrating the
notion of permission into a theory of imperative content that sanction the validity of the inference
in (17) and which are consistent with the shared motivations of logics of content.


"There are ways of integrating the notion of permission which sanction the
validity of the Ross inference, but they involve commitments to questionable assumptions about
the permissive content of choice-o ering disjunctive imperatives.

From the vantage of a logic of content, it is clear that inferring an order to see teacher,
regardless of your reading, from the premises of (17) is fallacious. Here we are in agreement with
7: This requirement is the imperative logic analogue of the D axiom of SDL: O !:O: .
10
imperative statics and dynamics 11
Castaneda. But glossing the conclusion of (17) with the locution come see me regardless of your
reading of the book involves badly misrepresenting its content: whatever its permissive content, it
is obvious that the conclusion is silent about whether failing to read the book is permitted. On
the minimal assumption that an imperative formula ! expresses a permission that it be fulfilled,
Castaneda appears to predict that the conclusion of imperative of (17) expresses a permission that
is, loosely speaking, inconsistent with the requirement of the premise imperative Read the book!.

"This is problematic ground for a logic of content to occupy."

Consider the following imperative
argument, which any logic of content ought to rule valid.
(20) Read the book! [! ]
Come see me! [! ]
) Read the book and come see me! [!( ^ )]

If the command Come see me! expresses a permission to do so without having read the book,
then no logic of content could sanction (in view of its conceptualization of imperative entailment)
the validity of this argument: agents are never committed to endorsing a command which requires
that while permitting that : . And yet it is clear that any agent who endorses the premise
commands in this argument is committed to endorsing the conclusion.

There is a better way of presenting a worry about (17)—one which is actually consonant
with the motivation for logics of content.

An agent who endorses the premise imperatives of (17)
might reasonably refrain from endorsing its conclusion. In, for example, a situation where her
addressee fails to read the book, an agent who endorses both premise commands might reasonably
demur about issuing the further command Come see me!. This is a reasonable thing to say, but
note that it is tied to a particular understanding of endorsement—one concerned with an agent’s
communicative dispositions: roughly, an agent endorses an imperative ! at time t if she would
have no complaint, in view of her desires and beliefs at t, about issuing ! at t.8

Although this is a natural way of understanding endorsement (and presumably will characterize
a reasonable subclass of imperative logics of content—e.g., that endorsed by Castaneda),

I want to employ a rather di erent sense of endorsement. The reason is simple: the logics of
content we consider in this paper appear to be exploiting this di erent sense of endorsement, in
that they all predict the inference in (17) valid. The relevant sense of endorsement is this: an
agent endorses an imperative ! at time t if the content of ! is a suitable expression of her desires
at t. Distinguish the state of a airs required by an imperative ! (its command content, i.e., the
state of a airs expressed by ) from the states of a airs permitted by ! (its permissive content).
Then, very roughly, ! is a suitable expression of an agent’s desires at t i the agent desires its
command content at t and its permissive content is compatible with what she desires at t.
This is, as it stands, so abstract as to be almost useless. We clarify with examples. Suppose it
is important to an agent that you read the book, and she desires that you do so. Such an agent will
not endorse a command whose content is glossed as Come see me, regardless of your reading of
the book. Such a command expresses a permission that conflicts with her desire that you read
the book, and, so, does not count as a suitable expression of her desires. An agent who utters
the premise commands in (17), on the other hand, desires (or at least is committed to desiring)
a future in which her addressee comes to see her (indeed, if she is rational, strictly prefers one
such future—the one where her addressee reads the book—to any future in which the addressee

8: The complaint would have to concern the content of ! , as opposed to, say, the logistics of performing the utterance.

This is a good time to note that much of what’s going on in this section is quite rough, but generally, I hope, precise
enough to enable us to draw the relevant distinctions. We’re not doing conceptual analysis here—only trying to roughly
taxonomize imperative logic.
11
12 nate charlow

does not come to see her). So the content of the conclusion imperative of (17) counts as a suitable
expression of her desires, although tokening that content in an utterance might not.9 Supposing an
agent endorses the premise imperatives in (17), then, it follows that she is committed to endorsing
the conclusion imperative. Which is to say: pairing this conception of endorsement with a logic
of content means endorsing the validity of the argument form illustrated in (17).

"What about the Ross inference?"

"Here we have options, depending on how we understand
the permissive content of disjunctive imperatives."

"If we hold that the imperative

Post or burn the letter!

semantically expresses a permission to burn the letter (and more generally that an
imperative of the form !( _ ) expresses a permission to bring it about that and to bring it about
that ), the class of logics of content we are considering will rule the Ross inference invalid."

"This
is because the content of an imperative ! being a suitable expression of an agent’s desires fails to
imply that the content of an imperative !( _ ) is as well."

"The latter will express a permission (to
bring it about that ) that may fail to be compatible with the desires of the agent.
So endorsing !
does not commit an agent to endorsing !( _ ).
Alternatively, we may hold that !( _ ) somehow conveys, without semantically expressing,
a permission to bring it about that and that . If that is the case, then both the permissive and
command contents of !( _ ) are exhausted by _ , and the content of !( _ ) will count as
a suitable expression of the desires of an agent who endorses ! . An agent who desires that
desires, inter alia, that _ , in which case the permissive content of !( _ ) is compatible with
her desires. It follows that the content of !( _ ) will count as a suitable expression of her desires
whenever ! does. Endorsing ! will commit an agent to endorsing !( _ ).
It seems to me overwhelmingly plausible that a permission to burn the letter is part of the
permissive content of

Post or burn the letter!.

So, an adequate theory of the semantic content
of disjunctive imperatives should predict their free choice readings

by appeal to

non-pragmatic mechanisms.

"I will not spend a great deal of time arguing for this position in this essay, although
it would be possible to.10"

"I will only try to provide some basic motivation for the semantic tack."

"In response to the claim of Bernard A. O. Williams (1963) that the felt permissions of disjunctive imperatives are part of their semantic content (Williams suggests treating them as presuppositions), R. M. Hare (1967) argued they are in fact

conversational implicatures

—apparently (although he is not explicit about the point) something rather like quantity implicatures."

----- The terminology is Griceian. But the example of 'or' had been used by Grice before coining 'implicature'. Grice coined implicature in 1966 -- OXFORD lectures on Logic and Conversation. In 1961 he speaks of a requirement of "STRENGTH" in terms of entailment. The jargon of "Quantitas" in 1967 (only -- not in the Oxford lectures) is a pun on Kant, and so not to be taken too seriously. Nobody in philosophy did. Some in linguistics did.

---


"The reasoning by which the

conversational
implicature

is derived is presumably something like this."


i.

If an agent desires some such that _ but _ 2 (and it is reasonable to expect that may be fulfilled by her addressee), then, if

U is cooperative, she will not endorse
the imperative !( _ ).

Practical analogue of the Maxim of Quantity (Grice 1989):

be neither more nor less action-restrictive than required.)

----- This is a good point, since, while Hare cannot be quoting from Grice's full lectures, he knew of them. Especially, the Oxonian variants of the "Logic and Conversation" lectures. Grice refers to strength and informativeness generally, rather than anything related to his pun on Kant (quantitas, qualitas, relatio, modus).


ii. Suppose the agent endorses !( _ ). Then, assuming cooperativity (and that _ 2
and _ 2 ), she desires _ and it is not the case that: she desires or desires .

iii. If the agent desires : , then her desires are inconsistent unless she desires .

But she
does not desire , so she does not desire : . Similarly, she does not desire : . So, both
and are compatible with what she desires.

9: Green (1997) draws a similar distinction, although to a di erent purpose.

10: There exist a number of sophisticated accounts whose sole purpose is to explain free choice e ects (in particuar,
free choice permissions) using exclusively non-semantic (pragmatic) mechanisms. See, e.g., Kratzer & Shimoyama
(2002); Schulz (2003, 2005) for sophisticated recent examples. The predominant view in the semantics literature is that a free choice permissions is an

ENTAILMENT

(see, e.g., Aloni 2007; Geurts 2005; Zimmermann 2000), and presumably that
view will extend to cover free choice interpretations of imperatives with disjunctive complements.

12

imperative statics and dynamics 13

iv. So the agent desires _ , but does not desire any particular way of fulfilling !( _ ).

So both bringing it about that and bringing it about that are acceptable ways of
fulfilling !( _ ).

"The reasoning isn’t either precise or airtight, but it seems plausible enough -- even, dare I say, Griceian in spirit."

----- Yes. Various analogues of the maxims can be postulated. Harnish/Bach's being the most popular. And seeing all that Grice wrote about mood operators ("Probability, desirability, and mood operators" -- and "Aspects of reason" where indeed Harman criticises him for allowing for Ross-type paradoxes -- "Mail those letters or burn them!") this seems to be alright.

"But there are reasons for worrying about a conversational-implicature account of
a free-choice readings of a disjunctive imperatives."

"Note, e.g., the badness of (21a) (and the “dual”
command (21b)).

(21) a. ?

Post or burn the letter. But you may not burn it!

b. ?

Post or burn the letter. But do not burn it!

"These sorts of constructions are nearly always marked."

CANCELLABLE IMPLICATUM?

"This is surprising if the permission to burn the letter is merely a conversational implicature of the imperative."

For, as Grice notes, conversational
implicatures may, in general, be felicitously cancelled."

"A proponent of the conversational
implicature account of a free choice permission in a disjunctive imperative owes us an explanation of why permission implicatures of disjunctive imperatives are not generally felicitously cancelable."

They are; it goes without saying. Similarly, Megarian Grice does not need (or does not owe you) an account of the queerness of uttering some of the oddest conditionals the Greeks ever utterered!

---

11

As we see below, accommodating the sort of permissive content we are defending here need not require explicitly building permissions into the imperative logic and semantics (although it is
far preferable, I will argue, to do so).

"Permissive content can, in principle, serve as a rationale for
a logic that invalidates the Ross inference, but that does so without giving any sort of account of
or making any explicit commitments to the permissive dimension of imperatives. (See x3.5 for
further discussion in connection with a Montague-Scott-style resolution of the Ross Paradox.)

2.4 Logics of Planning

"R. M. Hare (1967) attempts to characterize the motivations of those who reject the statement of conditions
on given in (11), for reasons having to do with the Ross Paradox."

---- and Hare relies HEAVILY ON GRICE. (On his left shoulder).

"Although Hare’s
project is to reveal the rejection as without basis, it is clear enough that he is presupposing the conceptualization of imperative entailment that is characteristic of a logic of fulfillment, and
noting that the motivations of his envisioned target diverge from it."

"What is interesting about
Hare’s argument is that the motivations he attributes to his opponents might be used to characterize
an alternative conception of imperative logic—a conception common to what I will term “logics
of planning.”"

"Hare takes it that dissatisfaction with the Ross inference stems from the (he thinks mistaken)
assumption that in saying that an imperative conclusion ! follows from a series of imperative
premises ! 1; :::; ! n, we say that fulfilling ! is a necessarily


satisfactory

way of fulfilling the
obligations issued by the premise imperatives."

"According to Hare and other proponents of logics
of fulfillment, of course, this gets things exactly backward."

"On this conception of imperative
entailment, it makes sense to reject the Ross inference as invalid: since fulfilling !( _ ) is not

11:

"In fact, in very much Griceian vein, Hare (1967: 315) appears to give a dialogue in which the permission IS felicitously _canceled_. But it can be argued that the case is artificial—designed to bring out the no choice interpretation of the imperative, on which the permissive content of the
imperative is exhausted by _ ."

"I am not claiming that no choice interpretations do not exist."

"Rather, I claim, with
Aloni (2007), that (i) there is a semantic di erence between no choice and free choice interpretations;

(ii)

"Disjunctive imperatives are sometiems ambiguous between free choice and no choice interpretations."

(iii) no choice interpretations
of !( _ ) are entailed by ! , while free choice interpretations are not.

"No-choice readings are generally dispreferred, probably for Griceian (i.e. rational) reasons."

"As such, they will not occupy a central place in our discussion."

"Dealing with the ambiguity will,
however, require complicating the semantics and/or object language. See x3.5.
13
14 nate charlow
necessarily a

satisfactory way of fulfilling ! , we should endorse a logic in which ! 6 !( _ ).
More generally, conditions on imperative entailment should receive the following statement:

(22) ! 1; :::; ! n ! i 1 and ... and n

"The primary proponent of this sort of view in the literature is A. J. P. Kenny (see, e.g., Kenny
1966 -- and used in the Griceian literature by Atlas and Altas-Levinson, on weighed desirability reasoning, extrinsically weighed -- Grice quotes from Kenny in Grice 1971, Intention and uncertanty, so he recognised the value of Kenny's explorations in Aristotelian practical reasoning).12

(Like Hare, Williams, and Grice, Kenny is an Oxford philosopher).

----

"The properties of the logic associated with the statements of conditions on in (22) are
not particularly interesting (as is the case with the conditions given in (11) and (15)).13

The logic
will, of course, be non-monotonic—in that 􀀀 ! will not generally imply 􀀀[f! g ! —but
not so in any interesting way.

"Non-monotonicity is just the natural consequence of reversing the
direction of the entailment relation, which is essentially all that has been done here."


More interesting, for our purposes, are the intuitions that might be used to animate this
approach.

"Kenny’s general perspective on imperative logic—one common to logics of planning
as a class—is essentially agent-oriented, in that it regards imperatives as primarily encoding
information that agents use to structure their practical reasoning (planning)."

"Compare logics
of content, which are essentially issuer-oriented: they treat imperatives as primarily encoding
information about the desires of agents who issue them."

"There are a variety of ways to implement
this general perspective."

"Kenny does so as follows."

"The logic of

satisfactoriness

consists of the rules which ensure that in practical
reasoning we never pass from a fiat [i.e., plan] which is satisfactory for a
particular purpose to a fiat which is unsatisfactory for that purpose (Kenny
1966: 72)."

"According to Kenny, a proper logic of imperatives allows drawing an imperative conclusion !
from a set 􀀀 of imperative premises just in case the plan associated with ! (roughly, the plan to
bring it about that ) is a satisfactory implementation of the plans associated with 􀀀."

"Intuitively,
what we have here is a logic designed to model the implementation of general, higher-order plans
by way of specific, lower-order plans in a rational agent."

"It is clear enough why we would want
such a logic to be non-monotonic: some plan may be a satisfactory implementation of a plan
0, although strengthening (i.e., adding requirements to) 0 might easily destroy this.

"There is, however, a class of natural agent- and planning-oriented logics that (i) do not
focus their attention on the implementation of plans and (ii) preserve the monotonicity of .
What I have in mind are conceptions of imperative logic that characterize it as in the business
of expressing or generating higher-order constraints (and freedoms) on planning activities—or
on the mathematical structures we use to model such activities—of rational agents.14

On such
conceptions, the fundamental semantic relation is something like requirement (or being in force)
in view of constraints in force on an agent’s planning.

An imperative conclusion ! may be drawn
from a set 􀀀 of imperative premises just in case, roughly, 􀀀 contains at least as much practical
planning content as ! . Just in case, that is to say, whenever the constraints on planning expressed
by the premise imperatives are required or in force, the constraints on planning expressed by !
are required or in force.

"This is a vague sketch and all of the key notions remain undefined."

"But, since we develop an
account along these lines in the second half of the paper, we will save precision for later. Three

12: Geach (1966) also voices his support.

13: The matter of integrating non-imperatives into the logic remains, but we will not pursue it here.

14: In particular, I have in mind the dynamic approaches of Mastop (2005); Charlow (2008a); Veltman (2008). I will
present such an account in x5 of this essay.
14
imperative statics and dynamics 15
brief notes, however.

"First, how such an account handles the Ross Paradox will obviously depend
on how the notion of practical content gets cashed out."

"An account which builds free choice
permissions into practical content will make di erent predictions about the (in)validity of the
Ross inference than one which does not."

"Second, I think it is clear enough that the entailment
relation characterized by such a logic will be monotonic."

"Third, and most interestingly, although it is clear that logics of planning and logics of content
(as I have characterized them) have divergent motivations, it is not clear that a concrete example
of a logic of planning would have to be distinct, in any deep sense, from a concrete example of
a logic of content."

"Di erences in motivation need not manifest as di erences in the semantic
analysis of imperative formulae, and the class of argument forms predicted valid by a logic of
content might coincide perfectly with the class predicted valid by a logic of planning. Di erences
will tend to depend on two factors: how the logical formalisms of the respective classes ultimately
(i) cash out the notions of content that figure in their motivations (command/permissive content
for logics of content; practical content for logics of planning) and (ii) characterize the behavior of
non-imperative formulas in imperative inference.

Concerning (i): the logics of planning we develop in this paper will be dynamic, in one of
two senses: they focus on planning behavior in time or on the changes that updating a cognitive
state with a series of formulas (imperative and otherwise) induces. Insofar as these incarnations
of logics of planning direct their focus at the planning behavior of the imperative “addressee”
(either the constraints that “in force” commands impose on planning behavior or the changes
that imperatives have the capacity to induce in an agent’s cognitive state), they may appear
to be essentially planning-oriented. Nevertheless, I shall argue (x4.13) that there are ways of
e ecting a rapprochement between the conception of imperative logic as a logic of content and
the conception of imperative logic as a logic of planning (although things get a bit trickier when
we shift our attention to update semantics, on account of the peculiarities of imperative inference
in an update logic). Command/permissive content and practical planning content can be seen as
two sides of the same coin. Because the formalism we develop in the course stating a logic of
planning is rather more sophisticated than the formalism we develop in the course of stating a
logic of content (capable of representing ordered commands, accounting for the contrast between
stable/ephemeral commands, giving a semi-realistic treatment of action and planning in time),
rapprochement will appear to recommend using the more sophisticated formalism in stating a
logic of content.
Concerning (ii): it is natural in certain logics of planning—those concerned with modeling
cognitive update in accordance with commands—to treat the argument forms of (12), (13), and
(17) as valid. Consider (12): updating a cognitive state with a command to bring it about that
! and the information that constrains the plans of the agent. To obey the command, in
view of what she knows, the agent will have to bring it about that . But this is not an inference
a logic of content is necessarily comfortable with: as argued above, endorsing !( ! ) and
does not necessarily commit an agent, qua issuer of imperatives, to endorsing ! . While subjects
are constrained to obey, authorities are not constrained to prefer obedience. Or consider (17):
updating a cognitive state with !( ! ) and ! also constrains the agent’s plans. If she fails to
see to it that , she violates at least one of her obligations. While there are conceivable logics of
content that validate all of these argument patterns (see the end of x3.2), the primary examples of
such do not. Nevertheless, this is not, I shall suggest, a di erence to be accounted for by appeal to
the distinction between logics of content and logics of planning. Certain logics of planning—those
which are dynamic in the sense of focusing on planning behavior in time, rather than on modeling
cognitive update—fail to validate precisely these argument patterns. The di erence is more
15
16 nate charlow
naturally accounted for by the special properties of update-semantic treatments of the imperative.
What the di erence means, if anything, is that it may not be possible to construe the logic that
arises from the update-semantic treatment of the imperative as anything but a logic of planning.
2.5 Conclusion
We have spent a large amount of time taxonomizing imperative logics according to their understandings
of the subject matter of imperative logic and the nature of imperative entailment. We
did so informally (and at times with a good deal of imprecision). Nevertheless, we were able
to draw out some interesting logical properties shared by certain classes of imperative logics.
There is a fairly clear menu of options for the imperative logician to choose from. The remainder
of this paper is devoted to examining concrete logics that implement the motivations we have
been detailing (with the exception of those that characterize logics of fulfillment). We begin by
considering a group of logics of content, the primary examples of which give a semantics for the
imperative operator in terms of a semantics for a deontic modal operator.