Semantic Minimalism and Nonindexical Contextualism

John MacFarlane (University of California, Berkeley)

Abstract: According to Semantic Minimalism, every use of "Chiara is tall"

(fixing the girl and the time) semantically expresses the same proposition,

the proposition that Chiara is (just plain) tall. Given standard assumptions,

this proposition ought to have an intension (a function from possible worlds

to truth values). However, speakers tend to reject questions that

presuppose that it does. I suggest that semantic minimalists might address

this problem by adopting a form of "nonindexical contextualism," according

to which the proposition invariantly expressed by "Chiara is tall" does not

have a context-invariant intension. Nonindexical contextualism provides an

elegant explanation of what is wrong with "context-shifting arguments" and

can be seen as a synthesis of the (partial) insights of semantic minimalists

and radical contextualists.

1. Introduction

My niece is four and a half feet tall—significantly taller than the average

seven-year old. With this in mind, I might say "Chiara is tall," and, it seems,

I would be speaking truly. Yet it also seems that if her basketball coach

were to say "Chiara is tall" while discussing who should play which position

on the team, he would not be speaking truly. What can we conclude about

the meaning of "tall"?

Moderate Contextualists conclude that the sentence must be contextsensitive,

in a way that goes beyond the context sensitivity of "Chiara" and

"is" (which we may presume are being used in reference to the same girl

and time). They reason as follows: If I am speaking truly and the coach is

speaking falsely, we must be saying different things. Since we are using

the same sentence, and using it "literally," this sentence must be contextsensitive.

Used at my context, it expresses the proposition that Chiara has

significantly greater height than the average seven-year old; used at the

coach's context, it expresses the proposition that she has significantly

greater height than the average member of team he coaches.

Cappelen and Lepore (2005) reject this reasoning, but only at the last step.

They agree that different things are said in the two contexts I have

described, but they deny that anything interesting follows from this about

the meaning of "Chiara is tall." They can do this because they are Speech

Act Pluralists: they hold that indefinitely many different things can be said

in a single utterance. So, although I have said that Chiara is tall for a

seven-year old, and the coach has said that she is tall for a member of the

basketball team, that is consistent with there also being something that we

have both said—namely, that she is (just plain) tall. It is this that Cappelen

and Lepore take to be the invariant semantic content of the sentence we

have used. Thus they can concede to the Moderate Contextualist that

different things have been said in the two contexts, while resisting the

conclusion that the sentence used is context-sensitive.

This deployment of Speech Act Pluralism helps deflect one argument

against the view that there is a single proposition that is semantically

expressed by every use of "Chiara is tall" (fixing the girl and the time). But

it does nothing to make it plausible that there is such a proposition. Indeed,

most contextualists, including some who accept Speech Act Pluralism,

take it to be obvious that there cannot be any such proposition, on the

grounds that there is no such thing as being just plain tall (as opposed to

tall for a seven-year old, or tall for a team member, or tall compared to a

skyscraper, or …). That there is in fact such a proposition—a bona fide,

truth-evaluable proposition, not a "proposition radical" or anything

schematic—is the central tenet of what Cappelen and Lepore call

Semantic Minimalism. It is this, chiefly, that distinguishes them from the

philosophers they call Radical Contextualists. If it should turn out that there

is no such "minimal" or (borrowing a phrase from Ken Taylor)

"modificationally neutral" proposition, then Cappelen and Lepore will have

no choice but to embrace the Radical Contextualists' conclusion that there

is no hope for systematic theorizing about the propositions expressed by

sentences in contexts.1 After all, they accept all of the Radicals' arguments

against the Moderates.

Our first order of business, then, should be asking what might be thought

1 Note that this is not at all the same as the claim that systematic

semantics is impossible. What Radical Contextualists reject is only a

certain conception of what semantics must accomplish.

to be problematic about such propositions—since Moderate and Radical

Contextualists are united in rejecting them—and considering whether

Cappelen and Lepore have said enough to dispel these worries. I am

going to argue that although Cappelen and Lepore misidentify the real

source of resistance to minimal propositions, and so do not address it, this

worry can be addressed. However, the strategy I will describe for making

sense of Semantic Minimalism is not one that Cappelen and Lepore can

take on board without cost. For my way of "making sense" of Cappelen

and Lepore's view can, with a slight shift of perspective, be regarded as a

way of making sense of Radical Contextualism, a position they regard as

incompatible with their own (and indeed as hopeless).2

2. The intension problem

Let's call the proposition putatively expressed in every context of use by

the sentence "Chiara is tall" (fixing girl and time) the proposition that Chiara

is (just plain) tall (at time t—I will henceforth omit this qualification).

According to Cappelen and Lepore, "[t]his proposition is not a 'skeleton'; it

is not fragmentary; it's a full-blooded proposition with truth conditions and a

truth value" (181). What they mean, presumably, is that it has a truth value

at every circumstance of evaluation (since propositions may, in general,

have different truth values at different circumstances of evaluation).

I believe that most philosophers' worries about minimal propositions are

rooted in puzzlement over the question this claim naturally provokes: At

which circumstances of evaluation is the proposition that Chiara is (just

plain) tall true? Here I'm using the technical term "circumstance of

evaluation" the way David Kaplan taught us to use it in Demonstratives

(1989). A circumstance of evaluation includes all the parameters to which

propositional truth must be relativized for semantic purposes. Though

Kaplan himself included times in his circumstances of evaluation (and

contemplated other parameters as well), the current orthodoxy is that

2 Because my concern here is with the coherence of Semantic

Minimalism, I will not address the arguments Cappelen and Lepore

muster in favor of that doctrine (most of them arguments against the

contextualist alternative).

circumstances of evaluation are just possible worlds.3 In this setting, our

question becomes: At which possible worlds is the minimal proposition that

Chiara is (just plain) tall true? I'll call this the intension problem for minimal

propositions (using the term "intension" for a function from possible worlds

to truth values for propositions, or to extensions for properties and

relations).

It's easy to feel pressure to make this intension very, very weak. After all,

being tall for a seven year old does seem to be a way of being tall. So it is

natural to think that the proposition that Chiara is (just plain) tall must be

true at every world at which the proposition that Chiara is tall for a seven

year old is true. Similar reasoning will move us inexorably towards the

conclusion that, no matter what reference class F we pick, the proposition

that Chiara is (just plain) tall is weaker than the proposition that she is tall

for an F. After all, even being tall compared to an ant is a way of being tall.

We are left with the surprising conclusion that the minimal proposition that

Chiara is (just plain) tall is true at every world at which Chiara has any

degree of height at all.

That's odd enough. It gets even odder when we run the same argument

with "short" and conclude that the proposition that Chiara is (just plain)

short is true at every possible world in which she is not absolutely gigantic.

It follows that at all but a few very odd worlds, Chiara has both the property

of being (just plain) tall and the property of being (just plain) short. And that

does not sit well with our feeling that being tall and being short are

incompatible properties.

Cappelen and Lepore do not themselves embrace this view about the

3 Kaplan included times because he thought the tenses were best

understood as propositional operators, which need a parameter to shift

(1989: 502-3). This view of tenses is now rejected by most

semanticists, so there is no longer a compelling reason to include a

time parameter in circumstances of evaluation (see King 2003). But

everything I say in this paper about the orthodox framework could be

said (with minimal modifications) about a Kaplan-style framework as

well.

intension of tall. They do not reject it either. They present it as one of

several possible views one might adopt about the metaphysics of tallness

(171):

• A thing is tall if there is some comparison class with respect to which

it is tall.

• A thing is tall if it is tall with respect to its privileged comparison

class.

• A thing is tall (at time t) if it is tall with respect to the comparison

class that is appropriate to its situation (at t).

• A thing is tall if it is taller than the average of all objects with height.

All of these views are problematic; indeed, Cappelen and Lepore point out

many of the problems themselves. But they don't think that solving these

problems, or deciding between these options, is part of their job as

semanticists. Their charge is language, not the metaphysics of properties.

Having argued to their satisfaction that "tall" is not context sensitive, they

are content to leave it to the metaphysicians to sort out just what an object

has to be like in order to have the property that "tall" invariantly expresses.

This response is fine, as far as it goes. Semanticists should not be

required to be metaphysicians (or physicists or biologists or ethicists).

They need not give informative answers to questions about the intensions

of properties.4 However, in taking resistance to minimal propositions to be

grounded in a misguided demand for an informative specification of their

intensions, Cappelen and Lepore have missed what is most troubling

about their doctrine. Semantic Minimalism is problematic not because it

does not provide an answer to questions about the intensions of its

minimal properties and propositions, but because it requires that there be

answers to such questions.

4 It is not difficult for the Semantic Minimalist to give uninformative

answers: for example, "a thing has the property of being tall (in some

world w) just in case it is tall in w."

Suppose that you are examining some ants on the sidewalk. Most of the

ants are tiny, but one is significantly bigger than the rest. "That's a big

one," you say. After a while, the ants begin to disappear though a barely

perceptible crack in the concrete. When the last ant, the bigger one,

squeezes through, you say, "Boy, that ant is small." At this point a

Semantic Minimalist appears and begins to question you in a most

annoying way:

"Wait a second. You just said that that ant was big. Now you say it's

small. I didn't notice it changing size. So which is it, big or small?"

"Well, it's big for an ant, but small compared to most of the other things

we can see."

"Fine, but I'm not asking about these properties; I'm asking about plain

old bigness and smallness. You said (among many other things) that the

ant was (just plain) big, and then that it was (just plain) small. Do you

suppose it could have had both properties, bigness and smallness?"

"No..."

"So which is it, then? Or don't you know?"

The question seems completely inappropriate. But why should it, if the

Semantic Minimalist is right that there is a property of being (just plain) big

which is always expressed by "big", and a property of being (just plain)

small which is always expressed by "small"? Why shouldn't we be able to

entertain questions about which things have these properties? It is not

enough to point out that semanticists need not answer metaphysical

questions. For even the answer "I have no idea" seems out of place here.5

5 It should be clear that the problem does not stem from the vagueness

of "big" and "small". It would not help the Semantic Minimalist here if

we allowed the intensions of bigness and smallness to be functions

from possible worlds to fuzzy extensions (mappings of objects to

degrees of truth) or partial functions from possible worlds to

extensions.

It might be suggested that we reject such questions because we aren't

aware of the minimal propositions that are semantically expressed by our

sentences, but only of the more determinate contents of our speech acts.

But such a line would be incompatible with what Cappelen and Lepore say

about the cognitive role of the minimal content. They say that "the

proposition semantically expressed is that content the audience can expect

the speaker to grasp (and expect the speaker to expect the audience to

grasp, etc.) even if she has such mistaken or incomplete information"

about the context (184-5). Explaining how a speaker could use the

(presumably quite weak) proposition that A is red in order to make a much

more determinate claim about A's color, they say: "The audience can

assume that the speaker knew that this [the proposition semantically

expressed] was trivial and was not interested in conveying such trivialities

with his utterance and can, therefore, infer that there's work to be done in

order to figure out exactly what the speaker was trying to communicate"

(185-6). All of this assumes that both speaker and audience are aware of

the proposition semantically expressed. (Indeed, the second claim

assumes some mutual knowledge about the intension of this proposition.)

If Cappelen and Lepore were to abandon this assumption, they would

open themselves up to the objection that their minimal propositions play no

real cognitive role in communication.

Alternatively, the Minimalist might say that the reason speakers find the

question in our dialogue inappropriate is that they have mistaken views

about the semantics of terms like "big" and "small." They implicitly take

these words to be context sensitive, when in fact they invariantly express

the properties of being (just plain) big and (just plain) small.

It should be obvious, however, that this response would completely

undermine the positive case for Semantic Minimalism. For the contextualist

can use exactly the same trick—attributing confusion or error about the

semantics of these terms to ordinary speakers—to dismiss the evidence

Cappelen and Lepore have mustered that terms like "red," "tall," and

"know" do not behave like context-sensitive expressions. For example,

Cappelen and Lepore make much of the fact that we report others who

utter the sentence "Chiara is tall" as having said that Chiara is tall, without

much regard to differences in our contexts. The practice of making such

"intercontextual disquotational indirect reports" only makes sense, they

say, if "tall" semantically expresses the same property in every context. But

the contextualist can accept this conditional and conclude that the practice

doesn't make sense—that it embodies a fundamental mistake people

implicitly make about the semantics of their own terms, a mistake that the

contextualist hopes to correct. (This is, in fact, a common line for

contextualists to take, although they sometimes also question the

uniformity or the relevance of the data about intercontextual indirect

reports: see DeRose, forthcoming.) Cappelen and Lepore need to say

something to block this kind of move. Whatever they say, it will presumably

also block them from appealing to massive speaker error or confusion in

explaining our rejection of the question in the dialogue above as somehow

absurd or inappropriate.

To recap: The intension problem is the problem of saying just what a world

must be like if the proposition that Chiara is (just plain) tall is to be true at

that world. Cappelen and Lepore rightly put this aside as a metaphysical

question, not a semantic one. But they fail to see that there is a semantic

problem lurking in the immediate vicinity. If Semantic Minimalism is true,

then the intension problem should have a solution (even if the solution is

not known to us). But we do not treat it as having a solution at all. We

reject as inappropriate questions that ought to have perfectly definite

answers if there is such a property as being (just plain) tall and that

property has an intension.

3. Minimal propositions without intensions?

In view of this problem, it is worth asking whether a Semantic Minimalist

can coherently deny that minimal propositions, like the proposition that

Chiara is (just plain) tall, have intensions.

In orthodox frameworks of the kind favored by most Moderate

Contextualists, this option is not open. For propositions have truth values

relative to circumstances of evaluation. If circumstances of evaluation are

just possible worlds, then propositions have truth values relative to worlds:

in other words, they have intensions. So if there is a proposition that is

semantically expressed by "Chiara is tall" at every context of use, it must

have an intension. At this point, contextualists conclude modo tollente that

there is no such proposition, while Cappelen and Lepore conclude modo

ponente that, since there is such a proposition, it must have an intension.

We can go beyond these two alternatives by thinking a bit differently about

circumstances of evaluation. Possible worlds will presumably be one

component of our circumstances of evaluation (otherwise, what will our

modal operators shift?), but nothing stops us from introducing other

components as well. (Indeed, semanticists have for various reasons

suggested adding times, "standards of precision," and other parameters.)

So let's think of a circumstance of evaluation as an ordered pair consisting

of a world and a "counts-as" parameter, which we can model as a function

from properties to intensions (functions from worlds to extensions). The

"counts-as" parameter is so called because it fixes what things have to be

like in order to count as having the property of tallness (or any other

property) at a circumstance of evaluation.6

As before, we say that propositions have truth values at circumstances of

evaluation. But now our circumstances are not just worlds, so it no longer

follows that propositions have truth values at worlds. This is why it is not

appropriate to ask about the truth value of the proposition that Chiara is

(just plain) tall at a possible world (including the actual world). For there will

in general be many circumstances of evaluation that have a given world as

their world parameter but differ in their "counts-as" parameter. Our

proposition will be true at some of these circumstances and false at others.

So it does not have an intension (a function from possible worlds to truth

values).7 This should be a welcome result for the Semantic Minimalist, who

no longer has to say that there is a (context-invariant) answer to the

question: Does Chiara have the property of being (just plain) tall, in the

actual world, or not?

Following Kaplan, we say that an occurrence of a sentence is true just in

6 Note that the function assigns an intension to every property, not just

"minimal" properties. This is important because, as Cappelen and

Lepore point out (172-5), the same kinds of arguments that may lead

one to doubt that the property of being tall has an intension can also be

run for the property of being tall for a giraffe.

7 Of course it has an "intension" in a broader sense: a function from

circumstances of evaluation to truth values.

case the proposition expressed is true at the circumstance of the context.8

Which circumstance of evaluation is the "circumstance of the context," in

this framework? The world parameter of the circumstance of the context is,

of course, just the world of the context. But the counts-as parameter will be

determined in complex ways by other features of the context, including the

topic of conversation and the speaker's intentions. In a context C1 where

I'm talking about seven-year olds, the counts-as function might assign to

the property of being (just plain) tall the same intension it assigns to the

property of being tall-for-a-seven-year-old. In a context C2 where I'm

talking about members of the basketball team, the counts-as function

might assign to the property of being tall the same intension it assigns to

the property of being tall-for-team-member. Thus the circumstance of C1

can differ from the circumstance of C2 even if the two contexts are situated

in the same world (say, the actual world). And as a result, an occurrence of

"Chiara is tall" in C1 can differ in truth value from an occurrence of "Chiara

is tall" in C2, even if the same proposition is expressed by both.

We can now say precisely what goes wrong in the story about the ants

(above). The problem is not that there is no such proposition as the

proposition that the ant is (just plain) big. The present view concedes that

there is such a proposition, and that this proposition is perfectly suitable, in

general, for use in questions and answers. In general, we look to

contextual factors to determine a counts-as parameter that (together with

the world of utterance) can settle a truth value for the proposition in

8 "If c is a context, then an occurrence of in c is true iff the content

expressed by in this context is true when evaluated with respect to

the circumstance of the context" (Kaplan 1989: 522). Semanticists

sometimes ascribe truth to utterances rather than to occurrences of

sentences in contexts, but as Kaplan notes, the notion of an utterance

is proper to pragmatics, not semantics. It is especially odd to find

Speech Act Pluralists like Cappelen and Lepore ascribing truth and

falsity to utterances (e.g. in their "intercontextual disquotational test,"

105), since on their view an utterance can express indefinitely many

propositions, which (one assumes) need not all have the same truth

value at the circumstance of the context.

context. In the ant story, however, the context fails to determine a single

counts-as parameter, because the questioner has deliberately made

salient two incompatible counts-as parameters: the one that was in play

when the ant was first described as big and the one that was in play when

it was later described as small. The question "which is it, big or small?"

presupposes that the context determines sufficiently what counts as having

the properties of bigness and smallness. But the questioner in this case

has ensured that this presupposition cannot be met. That is why we

(rightly) reject the question and find every answer (even "I don’t know") to

be inappropriate.

As far as I can see, the view I have just described is consistent with

Semantic Minimalism, as Cappelen and Lepore describe it. It allows that

"Chiara is tall" expresses the same proposition at every context of use

(fixing girl and time). This proposition is not a "schema," but "a full-blooded

proposition with truth conditions and a truth value," that is, a truth value at

each circumstance of evaluation. Granted, the proposition does not have a

truth value at each possible world, but that is just what we should expect in

a framework where there is more to circumstances of evaluation than just

worlds.9

On this picture, the sentence "Chiara is tall" is not context-sensitive in the

sense that it expresses different propositions at different contexts. But it is

context-sensitive in the sense that the truth of an occurrence of it depends

on features of the context—not just the world of the context, but the

speaker's intentions, the conversational common ground, and other such

things.10 Accordingly, this brand of Semantic Minimalism might also be

9 "Temporalists" who take circumstances of evaluation to be world/time

pairs do not think that propositions have truth values relative to worlds,

either.

10 Interestingly, Cappelen and Lepore give two distinct definitions of

"context-sensitive," corresponding roughly to these two senses (146).

According to the first, "To say that e is context sensitive is to say that

its contribution to the proposition expressed by utterances of sentences

containing e varies from context to context." According to the second,

"To say that e is context sensitive is to say that its contribution to the

described as a kind of contextualism: what I have elsewhere called

Nonindexical Contextualism.11 This way of describing it brings out how

close it is to Radical Contextualism. Too close, Cappelen and Lepore may

feel! However, it is immune to their best arguments against Radical

Contextualism, so if they are going to reject it, they need fresh reasons.

truth conditions of utterances u of a sentence S containing e (in some

way or other) references various aspects of the context of u." In the

framework I have described, these two definitions are not equivalent.

11 See my "Nonindexical Contextualism" (in preparation). See also

MacFarlane 2005a and 2005b, where I describe nonindexical

contextualist views in order to distinguish them from views I regard as

genuinely "relativist." I take it that the account developed by Predelli

2005, to which I am much indebted, is also a form of nonindexical

contextualism. Instead of countenancing an extra parameter of

circumstances of evaluation, as I do here, Predelli conceives of points

of evaluation as something like state descriptions (which fix the

extension of every property and relation expressible in the language).

There are state descriptions according to which Chiara falls into the

extension of both "four and a half feet tall" and "tall", and others

according to which she falls into the extension of the former but not the

latter. Which state description is "the circumstance of the context" will

depend not just on the world of the context, but on other features of

context as well. I think that the differences between these two versions

of nonindexical contextualism are largely notational. I prefer to "factor

out" my circumstances of evaluation into a world component and a

catch-all counts-as parameter, because it is convenient to have a

separate "world" parameter of circumstances for modal operators to

shift. If we let them shift state descriptions wholesale, then "That could

have been red" could come out true just because what counts as red

might have been different, even if the color of the object demonstrated

could not have been different—surely an undesirable result. But this is

not a fatal objection to Predelli's approach: as Kenny Easwaran has

pointed out to me, Predelli could allow his modal operators to shift

state descriptions "retail," the way quantifiers shift assignments.

4. Context Shifting Arguments reconsidered

An advantage of the framework I have just sketched is that it offers a

different (and perhaps deeper) diagnosis than Cappelen and Lepore's of

what goes wrong in Moderate Contextualists' uses of Context Shifting

Arguments (CSAs). Unlike Cappelen and Lepore's diagnosis, this one

does not require Speech Act Pluralism, though it is consistent with it.

Let's consider again the general form of a Context Shifting Argument. We

describe two occurrences of the same sentence, S, one in context C1, the

other in context C2. We then observe that intuitively the former is true,

while the latter is false. Assuming these intuitions are accurate, we can

conclude the following:

(1) At C1, S expresses a proposition that is true at the circumstance of

C1.

(2) At C2, S expresses a proposition that is false at the circumstance of

C2.

We cannot conclude, however, that the proposition S expresses at C1 is

different from the proposition S expresses at C2. For if the circumstance of

C1 is different from the circumstance of C2, our two occurrences of S can

diverge in truth value even while expressing the same proposition.

Nothing about the general point I am making here depends on

circumstances of evaluations being anything other than just worlds.

Suppose S is the sentence "Bush won the US Presidential election in

2000," and suppose that the world of C1 is different from the world of C2.

Then an occurrence of S in C1 could diverge in truth value from an

occurrence of S in C2, not because different propositions are expressed,

but simply because the circumstances of the two contexts are different.

(Say, Bush won in the world of C1, but lost in the world of C2.)

Thus, a CSA establishes that the propositions expressed are different only

given an additional premise:

(3) The circumstance of C1 = the circumstance of C2.

Normally users of CSAs do not even mention (or perhaps see the need for)

this premise, because in orthodox frameworks it is relatively easy to

secure. In these frameworks, a circumstance of evaluation is just a

possible world, so (3) amounts to

(4) The world of C1 = the world of C2.

So the user of a CSA has only to describe contexts that take place at the

same world and differ only in other ways—in the topic of conversation, for

example—and the CSA will establish that what is said at C1 is different

from what is said at C2.

Cappelen and Lepore seem to accept all of this reasoning. They accept

that the CSAs used by contextualists show that something different is said

at the two contexts described. Their point is that this does not show that

the proposition semantically expressed is different, because (given Speech

Act Pluralism) the proposition semantically expressed is only one of many

things said.

If we adopt the framework described in the last section, however, we can

reject the contextualists' reasoning in a more fundamental way. For in this

framework it is no longer true that a circumstance of evaluation is just a

world. This makes it much more difficult to construct a CSA for which (3)

holds. It is no longer sufficient to ensure that C1 and C2 are situated at the

same world; we must also make sure that these contexts determine the

same counts-as function. This is relatively easy to do when we are making

up CSAs to demonstrate the indexicality of "I", "here", or "now", but difficult

or impossible when we are making up CSAs to demonstrate the

indexicality of "knows", "tall", and other such terms. That is why CSAs work

in the former cases but not in the latter.

5. Conclusion

I have offered up this version of Nonindexical Contextualism as a way of

making sense of Semantic Minimalism. If Cappelen and Lepore accept my

exegesis, then they can block Context Shifting Arguments in a different

way than they do in Insensitive Semantics, and without invoking Speech

Act Pluralism. If they do not accept it, then they must find another way to

explain why speakers reject questions that should admit of answers (if only

"I don't know") if minimal propositions have determinate intensions.

In closing, a Hegelian thought. In a recent paper, Stefano Predelli (2005)

has offered up his own version of Nonindexical Contextualism as a way of

making sense of Radical Contextualism. It is striking, I think, that a

plausible interpretation of Semantic Minimalism and a plausible

interpretation of Radical Contextualism should come out looking very

similar! This suggests that, far from being fundamentally opposed, the two

positions are just the two one-sided ways of grasping the truth about

context sensitivity that are available when one supposes that propositions

have truth values at possible worlds. Thesis: Semantic Minimalism.

Antithesis: Radical Contextualism. Synthesis: Nonindexical Contextualism.

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