On Similative Reduplication in Vietnamese

Abstract

Vietnamese has a productive reduplication strategy where the reduplicant appears to the right of the base and is segmentally identical to the base except that its last rime is iếc (pronounced [ɪək]). In this note, I attempt to account for some observations about iếc, including the fact that it gives rise to ignorance inferences and is incompatible with classifiers. I propose that the semantics of iếc parallel the pragmatics of disjunctions and that the notion of similarity underlying the interpretation of iếc is contextual while that underlying the interpretation of classifiers is grammatical. The proposal makes use of some tools of predicate logic and formal semantics.

1. Introduction

Vietnamese has a productive reduplication strategy where the reduplicant appears to the right of the base and is segmentally identical to the base except that its last rime is iếc [ɪək] (Maspero, 1912, p. 109; Emeneau, 1951, p. 186; Thompson, 1987, p. 173; Nguyễn Đình Hoà, 1997, pp. 53–59; Vu, 1998, pp. 172–174; Đoàn Thiện Thuật, 2007, p. 71; Ngo, 2021, p. 135). Some examples are given in (1):1

(1)	sách ‘book’	→	sách siếc
	[sɛk]		[sɛk.sɪək]
	cam ‘orange’	→	cam kiếc
	[kam]		[kam.kɪək]
	thuyền ‘boat’	→	thuyền thiếc
	[thwɪən]		[thwɪən.thɪək]
	sinh viên ‘student’	→	sinh viên sinh viếc
	[sɪŋ.vɪən]		[sɪŋ.vɪən.sɪŋ.vɪək]
	mỳ Ý ‘spaghetti’	→	mỳ Ý mỳ iếc
	[mi.i]		[mi.i.mi.ɪək]
	sinh viên ‘student’	→	sinh viên sinh viếc
	[sɪŋ.vɪən]		[sɪŋ.vɪən.sɪŋ.vɪək]
	ca-mê-ra ‘camera’	→	ca-mê-ra ca-mê-riếc
	[ka.me.ra]		[ka.me.ra ka.me.rɪək]
	philosophy	→	philosophy philosophiếc
	[fi.lo.so.fi]		[fi.lo.so.fi.fi.lo.so.fɪək]

For present purposes, I will assume that the Vietnamese lexicon contains a morpheme, and I will call it red, which is mnemonic for “reduplication”. The rule in (2) captures how this morpheme is phonologically realized:

(2)	Morpho-phonemic rule
	Let [w ___X] be a word whose last rime is X
	[w ___X] + red → $\underset{base}{\underbrace{{[}_w \_\mathrm{X}]}}$ + $\underset{reduplicant}{\underbrace{{[}_w \_ɪə\mathrm{k}]}}$

The application of this rule is exemplified in (3) for cam ‘orange’ and sinh viên ‘student’. The rimes targeted by the rule are underlined:

(3)	a.	[kam]+red → [kam]+[kɪək]
	b.	[sɪŋ.vɪən]+red → [sɪŋ.vɪən]+[sɪŋ.vɪək]

As we can see, there is no constraint on the number of syllables in the base: sách ‘book’ and cam ‘orange’ have one syllable, sinh viên ‘student’ has two, ca-mê-ra ‘camera’ has three, and philosophy has four syllables. Note, also, that (2) does not distinguish between words of different origins. Among the examples in (1), sách ‘book’ and cam ‘orange’ are “native” Vietnamese words. With the possible exception of historical linguists, no-one can say where these words came from. In contrast, most speakers will be able to recognize that sinh viên ‘student’ is “Sino-Vietnamese” (“Hán Việt”), i.e., that it was “imported” from Chinese. However, it has undergone complete Vietnamization: both of its syllables occur independently as syllables in native Vietnamese words, and there is no native counterpart which expresses the same meaning. The tri-syllabic ca-mê-ra is transparently a loan word. It is quite often written with hyphens between the syllables. This fact is instructive. Vietnamese is a “monosyllabic” language, in the sense that every morpheme is a syllable.2 Empty spaces are inserted into Vietnamese texts following the same rule that holds for European languages like German: namely, between the smallest linguistic units that are guaranteed to be a sequence of syllables (Trinh, 2014). In German, these are words, but in Vietnamese these are morphemes.3 The fact that Vietnamese speakers (often) write <ca-mê-ra>, not <ca mê ra>, indicates their intuition that these three syllables are not morphemes, i.e., that this word is not a “regular” word in their language.4 Also, the last syllable, [ra], is perceived by speakers of the standard dialect as “exotic”, as [r] is not a possible onset in this dialect. As for philosophy, it is clearly a foreign word. The Vietnamese word for ‘philosophy’ is triết học. However, if philosophy is used as a foreign word in conversation then the option of reduplicating it as philosophy philosophiếc is available, together with all of its concomitant semantic effects.

What are these effects? The most prominent one is that iếc-reduplication licenses the inference of “uncertainty” on the part of the speaker. Consider the conversation below:5

(4)	A:	John đang ăn gì thế?
		John is eating what?
	B:	Nó đang ăn cam+kiếc        gì đó
		He is eating an orange+red demwh

B’s answer in (4) conveys the message that B is not sure whether John is eating an orange or just something “similar” to an orange. In other words, B does not rule out the possibility that John is in fact eating an orange, but nor does she rule out the possibility that John is eating, say, a tangerine. This intuition is corroborated by the fact that it is odd for someone to contest B’s answer with the statement that John is actually eating a tangerine. In the same way, it is odd to contest it with the statement that John is eating an orange:6

(6)	A:	John đang ăn gì thế?
		John is eating what?
	B:	Nó đang ăn cam+kiếc        gì đó
		He is eating an orange+red demwh
	C:	#Không đúng.   Nó đang ăn   quýt   / cam
		That’s not true. He is eating a tangerine / orange.

I will call iếc-reduplication in Vietnamese “similative reduplication”, borrowing a term from works on phenomena in other languages that share some family resemblance to what we are now describing.7 Note that if B had used the plain and not the reduplicated form of cam ‘orange’, such a follow-up as C’s would be totally natural. This shows that red does make an interpretive difference:

(7)	A:	John đang ăn gì thế?
		John is eating what?
	B:	Nó đang ăn cam.
		He is eating an orange.
	C:	Không đúng. Nó đang ăn quýt.
		That’s not true. He is eating a tangerine.

Before we go on, a remark about the bounds of this note should be made. The reader will have seen that in the examples above, the reduplicated form of cam, namely, cam+kiếc, co-occurs with the expression gì đó, which I gloss as dem_wh. The reason for this gloss is that gì has a life of its own as a question word, and đó is also the demonstrative article.8

(8)	a.	John đang ăn gì?
		John is eating what?
		‘What is Nam eating?’
	b.	John đã mua quyển sách đó.
		John bought that CL book
		‘Nam bought that book.’

Intuitively, the reduplication form is more natural with than without gì đó. I will put aside the question as to what underlies the preference for this co-occurrence. The semantic effects of red together with dem_wh will be analyzed as arising from red alone. A more detailed account of the construction that derives such effects compositionally from its subconstituents—i.e., red, gì, and đó—will have to be left for future research.9

I will end this introduction by stressing that iếc-reduplication is just one among many reduplication strategies of Vietnamese. My gloss of it as red should not mislead the reader into thinking that this is the reduplication process in Vietnamese. Given the bound of this note, I will not present an overview of reduplication in Vietnamese. I refer the reader to Hoàng Văn Hành (2008) for such an overview.

Let us now analyze the uncertainty inference associated with red.

2. Uncertainty

I propose that the reduplication morpheme red weakens the meaning of the base word. Specifically, red maps a predicate P to another predicate $sim\left(P\right)$, where $sim\left(P\right)$ is defined as in (9):

(9)	$sim\left(P\right){=}_{\mathrm{def}}\{x\mid x \mathrm{is} \mathrm{something} \mathrm{similar} \mathrm{to} \mathrm{a} P\}$

Assuming that identity is the limiting case of similarity, i.e., that everything is maximally similar to itself, applying the $sim$ function to a predicate P amounts to disjoining P with predicates similar to P.10 Thus, $sim\left(P\right)$ means $P\vee P^{\prime }\vee P^{″}\dots$, where $P^{\prime }$, $P^{″}$, …are similar to P.11 Let us consider an example, supposing that quýt ‘tangerine’ and bưởi ‘grapefruit’ are the predicates similar to cam ‘orange’:12

(10)	a.	〚cam〛 = 〚orange〛 = {x | x is an orange};
	b.	〚cam hoặc quýt hoặc bưởi〛
		= 〚orange or tangerine or grapefruit〛
		= {x | x is an orange} ∪ {x | x is a tangerine} ∪ {x | x is a grapefruit};
	c.	〚cam kiếc〛 = 〚cam+red〛 = sim(〚cam〛) = sim(〚orange〛)
		= {x | x is similar to an orange}
		= {x | x is an orange} ∪ {x | x is a tangerine} ∪ {x | x is a grapefruit}.

We see that orange+red ends up meaning the same as orange or tangerine or grapefruit. Now, a disjunction is logically weaker than any individual disjunct: if it is true that John is eating an orange then it is also true that John is eating an orange or a tangerine. Given that $sim\left(P\right)$ is $P\vee Q$, we have (11-a) and (11-b):13

(11)	a.	P ⇒ sim(P);
	b.	$\underset{p}{\underbrace{\mathrm{John} \mathrm{is} \mathrm{eating} \mathrm{an} \mathrm{orange}}}$ ⇒ $\underset{p\vee q}{\underbrace{\mathrm{John} \mathrm{is} \mathrm{eating} \mathrm{an} \mathrm{orange}+\mathrm{RED}}}$

We are now in a position to make a first attempt at explaining the uncertainty inference associated with red. Consider the disjunctive statement in (12):14

(12)	John ate an orange or a tangerine
	⇝$\neg K_S($John ate an orange)

A clear intuition about (12) is that it conveys the message that the speaker is not certain that John ate an orange.15 This fact, as we know, can be accounted for in terms of Gricean reasoning. Grice (1967) proposes the following “maxims of conversations”, i.e., rules that discourse participants are mutually assumed to be following when they talk:

(13)	a.	Q̇uality: Say only what you believe to be true!
	b.	Quantity: Be informative!

Two things should be noted about these maxims. Firstly, they are ranked. Specifically, Quality takes precedence over Quantity, which means that one should never sacrifice truthfulness for informativity: one should try to convey as much information as possible, provided one is not lying. It follows, then, that what is more informative than what one says is also what one does not believe to be true. Secondly, informativity respects logical strength: if p is logically stronger than q then p is more informative than q.16 As John ate an orange is logically stronger than John ate an orange or a tangerine it is also more informative, and the fact that the speaker asserts the latter proposition but not the former means, given the maxims, that she does not believe the former, i.e., that she is not certain that John ate an orange.17

Are we done? Well, no. It turns out that there is a problem in my account of the facts. It is based on the claim that assertion of a proposition p licenses the inference that $\neg K_S\left(q\right)$, where q is stronger than p. This claim, I argued, can be derived from the Gricean maxims of Quality and Quantity. However, there is good reason to believe that the claim is false. Consider the following conversation:

(14)	A:	Where does John live?
	B:	He lives in France.
		$\cancel{⇝}$$\neg K_S($John lives in Paris)

Suppose we happen to hear this exchange out of the blue, say between two people on the subway, we would not conclude that B is not sure John lives in Paris. B may very well know the particular street address in France at which John lives, but simply does not feel the need to be that specific. Given that John lives in Paris is more informative than John lives in France, this intuition we have about (14) conflicts with what I said above, namely, that utterance of a weaker proposition p gives rise to the inference that the speaker is not sure about a stronger proposition q. Here is another example:

(15)	A:	Who did John talk to?
	B:	He talked to a student
		$\cancel{⇝}$$\neg K_S($John talked to a male student)

Given that every male student is a student but not vice versa, a more informative statement that B could have made is that John talked to a male student. However, B’s answer in (15), out of the blue, clearly does not imply that she is not sure that John talked to a male student.

Here is, then, the dialectical situation. I have proposed that John is eating an orange+red implies that the speaker is not certain John is eating an orange, because the former is less informative than the latter, and the Gricean maxims, Quality and Quantity, together tell us that the speaker asserts the most informative proposition of which she is certain. We then saw examples that challenge this analysis, i.e., the conversations in (14) and (15), where the assertion of a less informative proposition does not imply the speaker’s uncertainty about a more informative proposition. How do we resolve this conflict? Quality and Quantity seem to be virtual truisms of language use, so we do not want to tinker with these principles. And we cannot tinker with logic either: if John talked to a male student then he talked to a student. There is no way out of that. What we could do is either (i) revise our semantics of red, withdrawing the claim that orange+red is weaker than orange, or (ii) add auxiliary hypotheses to the account. I propose we take the latter course.

One addition we need turns out to be another Gricean maxim, namely, that of Relation. What the maxim of Relation tells us is that we should be “relevant” (Lewis, 1988), i.e., answer the “question under discussion” (Roberts, 1996). Recall that Quality and Quantity together derive the claim that the speaker asserts the most informative proposition of which she is certain. With Relation added to the mix, we derive something weaker: the speaker asserts the most informative relevant proposition of which she is certain. This means that the assertion of a weaker proposition p would imply the speaker’s uncertainty about a stronger proposition q only if q is relevant, i.e., only if there is interest in knowing whether q is true. That this result is empirically correct can be seen from reflecting on our intuition about a slight modification of the scenarios in (14) and (15). Consider (16):

(16)	A:	Does John live in Paris?
	B:	He lives in France.
		⇝$\neg K_S($John lives in Paris)

Changing A’s question from where does John live? to does John live in Paris?, we made it clear that the proposition John lives in Paris is relevant, i.e., that we are interested in knowing whether it is true. Given this set up, B’s assertion of the proposition that John lives in France, which is less informative than the proposition that he lives in Paris, is predicted to license the inference that the speaker is not certain that John lives in Paris. This prediction is confirmed by our intuition. The same holds for the modified version of (15), which is (17):

(17)	A:	Did John talk to a male student?
	B:	He talked to a student.
		$⇝\neg K_S($John talked to a male student)

A’s question makes sure that the proposition that John talked to a male student is relevant. Given this background, assertion of a less informative proposition—in this case, he talked to a student—leads to the inference that the speaker is not certain John talked to a male student.

Is the addition of the maxim of Relation enough to derive the fact that red implies the speaker’s uncertainty? No. What I have said about the semantics of red is only that it weakens the meaning of the base. In order to generate speaker uncertainty about this meaning, I also need to say that red makes the base relevant. Thus, there are two components to the interpretation of John is eating an orange+red. Firstly, it is weaker than John is eating an orange. Secondly, it makes John is eating an orange relevant.18

(18)	Interpretation of red (first version, to be revised):
	a.	P ⇒ P$+\mathrm{RED};$
	b.	P$+\mathrm{RED} \mathrm{makes}$ P $\mathrm{relevant}.$

Let us recap. Consider, again, the sentence in (19):

(19)	John đang ăn	cam+kiếc	gì đó.
	John is eating an	orange+red	demwh
	$⇝\neg K_S($John is eating an orange)

Given (18), this sentence is weaker than John is eating an orange and, at the same time, makes John is eating an orange relevant. From Quality, Quantity, and Relation we conclude that the speaker is not certain John is eating an orange.

Are we done? As it turns out, no. Let us see why not.

3. Ignorance

There is a crucial difference between the speaker’s uncertainty in (16) and the speaker’s uncertainty in (19) that we have not discussed.

(20)	A:	Does John live in Paris?
	B:	He lives in France.
		Possible inference: $K_S\neg ($John lives in Paris)

It is, intuitively, possible to understand B’s answer in (20) as conveying the message that B knows that John does not live in Paris. Specifically, B knows that John lives in some city in France, and while she is not sure which city it is, she knows that it is not Paris. Note that this inference is stronger than but consistent with the uncertainty inference that we claim is associated with B’s answer in (20), namely, $\neg K_S($John lives in Paris). Now, consider (19), reproduced below as (21):

(21)	John đang ăn	cam+kiếc	gì đó.
	John is eating an	orange+red	demwh
	Not a possible inference: $K_S\neg ($John is eating an orange)

A clear intuition about (21) is that it does not convey the message that the speaker knows John is not eating an orange. The speaker does not rule out the possibility that John is eating, say, a tangerine instead of an orange, but neither does she rule out the possibility that John is, in fact, eating an orange. Thus, the uncertainty inference we have associated with (21), namely, $\neg K_S($John is eating an orange), is too weak. It must be strengthened into a claim that is inconsistent with $K_S\neg ($John is eating an orange). One obvious way to do this is to conjoin the uncertainty about John eating an orange with the uncertainty about John not eating an orange. Here is our empirical claim:

(22)	John đang ăn	cam+kiếc	gì đó.
	John is eating an	orange+red	demwh
	⇝$\neg K_S($John is eating an orange) ∧ $\neg K_S\neg ($John is eating an orange)

Inferences of the form $\neg K_{S}p\wedge \neg K_S\neg p$ are “ignorance inferences”. We say that speaker S is “ignorant” about proposition p if S is not certain that p and is not certain that $\neg p$. Ignorance about p is stronger than uncertainty about p: it is uncertainty about p conjoined with uncertainty about $\neg p$.

How do we explain the ignorance inference associated with red? Specifically, what do we need to say about the meaning of orange+red so that the sentence John is eating an orange+red conveys the message that the speaker is not certain that John is eating an orange and is not certain that John is not eating an orange? A good starting point, again, is to look to disjunction. It is well-known that disjunction licenses ignorance inferences: the speaker is understood to be uncommitted to the truth and uncommitted to the falsehood of the individual disjuncts. This makes a disjunction different from an apparently equivalent vague term. Compare (20) with (23):

(23)	A:	Does John lives in Paris?
	B:	He lives in Paris or Nice or Toulouse or Lyon or Marseille …
		Not a possible inference: $K_S\neg$ John lives in Paris

Suppose B listed all locations in France. In that case, what B says in (23) would be logically equivalent to what B says in (20). But, as we have seen, B’s answer in (20) allows for the possibility that B knows John does not live in Paris. B’s answer in (23), however, clearly implies that B does not know whether John lives in Paris or not. The crucial difference between a vague term and a disjunction of specific terms is this: the disjunction necessarily makes all the disjuncts relevant (Chemla, 2008; Sauerland, 2004), while a vague term does not necessarily make the more specific terms relevant. B’s utterance in (23), i.e., Paris ∨ Nice ∨ Toulouse …, is weaker than Paris, and at the same time makes Paris relevant. Therefore, it implies that B is ignorant about Paris, i.e., that she is committed neither to the claim that John lives in Paris nor to the claim that he does not live in Paris. B’s utterance in (20), on the other hand, does not (necessarily) make Paris relevant, so no conclusion about Paris is drawn, and the utterance is consistent with B’s knowing that John does not live in Paris.

What we can say to explain the ignorance inferences associated with P+red, then, is that P+red makes P relevant and all other alternatives relevant. In other words, $sim\left(P\right)$ is not only interpreted as $P\vee P^{\prime }\vee P^{″}\dots$, i.e., as a logically more inclusive concept, but also as P or $P^{\prime }$ or $P^{″}\dots$, i.e., as an expression of this more inclusive concept in the form of a syntactic disjunction. Another way to say this is that P+red has not only the semantics but also the pragmatics of a disjunction:

(24)	A:	What is John eating?
	B:	He is eating an orange+red
		$\cancel{\approx }$ ‘he is eating something similar to an orange’
		≈ ‘he is eating an orange or a tangerine or a grapefruit …’
(25)	Interpretation of red (final version)
	a.	P$+\mathrm{RED} \mathrm{is} \mathrm{interpreted} \mathrm{as}$ P ∨ P′ P″ …, $\mathrm{where}$ P′, P″…⇒sim(P);
	b.	P$+\mathrm{RED} \mathrm{makes}$ P, P′, …P″, $\mathrm{relevant}.$

4. Classifiers

Vietnamese is a “classifier language”. The combination of nouns and numerals must be mediated by a function word, i.e., the so-called “classifier”:

(26)	a.	John	ăn	một	*(quả)	cam
		John	ate	one	CL	orange
	b.	John	mua	hai	*(quyển)	sách
		John	ate	two	CL	book

For present purposes, I will assume the account proposed by Trinh (2011) of this fact.19 Specifically, I will assume that nouns in classifier languages such as Chinese and Vietnamese differ from their counterparts in non-classifier languages such as English and German in being “number neutral”: whereas English book denotes the set of singular (i.e., atomic) books, Vietnamese sách ‘book’ denotes the set containing both singular books and pluralities of books. I will write “a+b” for the plurality consisting of a and b, etc.

(27)	a.	$〚\mathrm{book}〛=\{x\mid x \mathrm{is} \mathrm{a} \mathrm{singular} \mathrm{book}\}$$=\{a,b,c,\dots \}$
	b.	〚sách〛 $=\{x\mid x \mathrm{is} \mathrm{a} \mathrm{singular} \mathrm{book} \mathrm{or} \mathrm{a} \mathrm{plurality} \mathrm{of} \mathrm{books}\}$
		$=\{a,b,c,\dots ,a$+$b,a$+$c,b$+$c,a$+b+$c,\dots \}$

As counting books means counting atomic books,20 the noun sách must be “atomized” before it can compose with a numeral. This task of atomization is carried out by the classifier. Specifically, the classifier maps a predicate P to the set of entities that are singular Ps, i.e., atoms of P.

(28)	Interpretation of CL:
	$〚\mathrm{CL}〛=\lambda P.$ $\lambda x.$ x is a singular P.

Applying CL to sách ‘book’ yields the following set:

(29)	〚quyển sách〛 $=\{x\mid x \mathrm{is} \mathrm{a} \mathrm{singular} \mathrm{book}\}$ $=\{a,b,c,\dots \}$

I have been speaking of “the classifier”, as if there is a unique classifier for all nouns in Vietnamese. The reader will have seen from the example sentences in (26) that this is not the case. The classifier for cam ‘orange’ is quả, while that for sách ‘book’ is quyển. Exchanging the classifiers will result in severe deviance:

(30)	a.	*J̣ohn ăn một quyển cam;
	b.	*John mua hai quả sách.

A selectional relationship, then, obtains between the classifier and the noun. The relationship is not purely syntactic. One can say that the classifier imposes a semantic requirement on the noun it combines with. In fact, the requirement seems to be that the noun must belong to a class of predicates that are “similar” in some sense. Take quyển, for example. It selects not only sách ‘book’ but also sổ ‘logbook’, vở ‘notebook’, lịch ‘calendar’, tạp chí ‘magazine’, etc. There is certainly some similarity between these concepts: they all denote things that have pages. As for quả, it selects not only cam ‘orange’ but also other fruits, such as quýt ‘tangerine’, bưởi ‘grapefruit’, táo ‘apple’, etc. The similarity in this case is quite obvious. This means we should revise our view on classifier semantics. Firstly, we should not speak of “the classifier”. There are many classifiers, each selecting nouns of a certain “similarity class”. Secondly, (28) is not the interpretation of any particular expression but an interpretation scheme for many expressions: it is what underlies the semantics of all classifiers. The interpretation of each individual classifier will have to come with presuppositions about the class of predicates that it selects. We will consider quyển as a representative case. Here is the entry for it:

(31)	Interpretation of quyển (first version, to be revised):
	〚quyển〛 $=\lambda P$: $P\Rightarrow sim\left(book\right).$ $\lambda x.$ x is a singular P.

The reader can see that for the semantics of quyển I am making use of the same $sim$ function that I used for the semantics of red. This move is motivated by the hope that the same notion of similarity is operative in both cases. What (37) is intended to say is that quyển selects for predicates that are “similar” to book in the same way that the predicates falling under book+red are, e.g., notebook, logbook, magazine, etc. It would, of course, be an interesting result if the hope turns out to be actualized, as that would show that we have found independent evidence for $sim$ from another corner of grammar.

The hope, unfortunately, is not actualized. Consider the following data point:

(32)	A:	John đang đọc gì?
		John is reading what?
		‘What is John reading?’
	B:	Nó đang đọc sách+siếc gì đó.
		he is reading a book+red demwh
		‘He’s reading a book+red’
	C:	#Không đúng. Nó đang đọc báo.
		not true he is reading a newspaper
		‘That’s not true. He’s reading a newspaper.’

The crucial observation here is that C’s utterance is infelicitous. The intuition is that C objects to what B has said but then goes on to say something that does not contradict what B has said. What this suggests is that newspapers are considered similar to books as far as red is concerned. In other words, the claim that John is reading something that falls under book+red is consistent with the claim that John is reading a newspaper. Now, consider the following data point:

(33)	a.	John đang đọc một quyển sách / *báo
		John is reading one ${\mathrm{CL}}_{quyen}$ book / newspaper;
	b.	John đang đọc một tờ *sách / báo
		John is reading one ${\mathrm{CL}}_{to}$ book / newspaper.

As we can see, the classifier for sách ‘book’ is quyển and the classifier for báo ‘newspaper’ is tờ. Switching the classifiers gives rise to deviance. This means that, as far as the classifiers are concerned, books and newspapers are not similar.

What about the other classifier that I have mentioned, quả, which, as I have said, combines with nouns for fruits? Can we also argue that it refers to a different notion of similarity as compared to red? The answer is yes. Consider (34):

(34)	A:	John đang mua cam+kiếc gì đó.
		John is buying orange+red demwh
		‘John is buying orange+red’;
	B:	Không đúng. Nó đang mua bóng.
		not true. He is buying balloons
		‘That’s not true. He’s buying balloons.’

The fact that B’s response to A in (34) is perfectly felicitous suggests that as far as red is concerned balloons are not similar to oranges: the claim that John is buying balloons can be used to negate the claim that John is buying orange+red. Now, as it turns out, the classifier for bóng ‘balloon’ is also quả, i.e., the same one as for cam ‘orange’:

(35)	John đang mua một quả cam / bóng.
	John is buying one ${\mathrm{CL}}_{qua}$ orange / balloon.

This means that as far as the classifier quả is concerned, oranges and balloons are similar. The conclusion, then, is that quả and red, and more generally classifiers and red, refer to two different notions of similarity. The question now is how we are to characterize this difference? I propose that we appeal to the semantics–pragmatics divide. Specifically, I propose that the notion of similarity underlying the interpretation of red is contextual, notationally represented by the function $si{m}_c$, while that underlying the interpretation of classifiers is grammatical, notationally represented by the function $si{m}_g$. What I mean by this is simply that the selectional property of a classifier such as quyển is lexically specified: we can, in principle, list all nouns that can combine with quyển, i.e., all predicates in $si{m}_g\left(book\right)$, and we know that this list does not contain báo ‘newspaper’. On the other hand, book-red is a predicate whose extension varies from context to context: it may include things that fall under báo ‘newspapers’ in some but not all situations:21

(36)	Interpretation of red (final version)
	a.	P$+\mathrm{RED} \mathrm{is} \mathrm{interpreted} \mathrm{as}$ P ∨ P′ ∨ P″ …, $\mathrm{where}$ P′, P″ ⇒ simc(P);
	b.	P$+\mathrm{RED} \mathrm{makes}$ P, P′, P″, …$\mathrm{relevant}.$
(37)	Interpretation of quyển (final version):
	〚quyển〛 $=\lambda P$: $P\Rightarrow si{m}_g\left(book\right).$ $\lambda x.$ x is a singular P.

Note that, given (36) and (37), we predict that red makes the noun it combines with incompatible with classifiers. This prediction is borne out, as it is certainly not the case that book+red ⇒$si{m}_g\left(book\right)$, (38) is a presupposition failure.

(38)	*John đang đọc một quyển sách-siếc gì đó
	John is reading one ${\mathrm{CL}}_{quyen}$ book+reddemwh

Now, there is an interesting prediction that we make. We have considered the case where N+red combines with a classifier. What about the case where red combines with the classifier+noun complex, i.e., the case of [CL+N]-red. The account just proposed actually predicts that such construction should be acceptable. Let us assume, following several works on the semantics of classifiers, that the classifier maps a noun’s meaning, which in languages like Vietnamese would be a cumulative predicate, to an atomic predicate. Thus, whereas sách denotes a set that contains both singular books and pluralities of books, quyển sách denotes a set that contains only singular books. This means that quyển sách-red would just denote the set containing things that are similar to singular books. This set is practically just the set of things similar to books. What is different now is that there should be no presupposition failure due to the selectional requirement of quyển, because what it combines with is just sách, not sách-red. This prediction is borne out, as evidenced by the acceptability of (39).22

(39)	Nam đang đọc quyển sách-quyển siếc gì đó
	Nam is reading a singular book-red DEMwh
	‘Nam is reading a (singular) book or something like that’

Similarly, (40) is acceptable:

(40)	Nam đang ăn quả cam-quả kiếc gì đó
	Nam is eating a singular orange-red DEMwh
	‘Nam is eating a (singular) orange or something like that’

Excursus on encapsulation—What I have just said amounts to claiming that grammar is “blind” to the fact that newspapers are similar to books (in the sense that they are both reading materials which have pages) or, in the same way, blind to the fact that balloons are not similar to oranges in the same way that tangerines are. More generally, my description of similative reduplication in Vietnamese subscribes to the view that grammatical knowledge is, to some extent, “encapsulated” from contextual, i.e., encyclopedic, knowledge. This view has been defended elsewhere (cf. Fox, 2000; Fox & Hackl, 2006; Magri, 2009). However, it is not clear to what extent it has become consensus in the field, so I will end this section with a brief illustration of encapsulation, using two examples from the literature.

The first is taken from (Fox & Hackl, 2006). These authors address the puzzle that John has three children implies John does not have four children, while John has more than three children does not imply John does not have more than four children.23 Their explanation is based on the hypothesis that the scale underlying measurement in natural language is dense, not discreet. This means that, as far as grammar is concerned, counting is carried out in terms of rational, not natural, numbers, and that the quantity implicatures that are potentially associated with (41-a) and (42-a) are (41-b) and (42-b), respectively:

(41)	a.	John has three children.
	b.	¬John has n children, for each rational number n greater than 3.
(42)	a.	John has more than three children.
	b.	¬John has more than n children, for each rational number n greater than 3.

A sentence $\varphi$ is associated with an implicature $\psi$ only if $\varphi \wedge \psi$ is consistent, i.e., non-contradictory. Since (41-a) ∧ (41-b) is consistent, (41-a) ends up meaning John has three but not four children. In contrast, (42-a) ∧ (42-b) is contradictory: if (42-a) is true, then it must be the case that John has $3+ϵ$ children, which means John has more than $3+ϵ/2$ children, which means there is a rational number n greater than 3, namely, $3+ϵ/2$, such that John has more than n children, which means (42-b) is false. Thus, the implicature in (42-b) is not associated with the sentence (42-a), and more than three just means more than three. The claim needed for (Fox & Hackl, 2006)’s account, which is relevant to our discussion, is this: grammar does not know that one cannot count children with non-natural numbers. The computation of quantity implicatures, which (Fox & Hackl, 2006) claim takes place in grammar, is encapsulated from the encyclopedic knowledge that John cannot have 3.5 children.

The second example is taken from Magri (2009), and it has to do with the fact that (43) is an odd sentence:

(43)	#Some Italians come from a warm country.

Magri (2009) attributes the oddness of (43) to the fact that it licenses the quantity implicature that not all Italians come from a warm country, which (in conjunction with the literal meaning of the sentence) conflicts with our common knowledge that all Italians come from the same country. Now, in order for the implicature not all to be associated with some, all has to be more informative than some, but all is not more informative than some in this case. If we know, and we do, that all Italians come from the same country, saying that some of them come from a warm country should convey the same amount of information as saying that all of them do. This means that for the grammar to associate the implicature not all Italians come from a warm country with the sentence some Italians come from a warm country, it must not know that all Italians come from the same country. Again, we see that a computation that is carried out in grammar is blind to contextual knowledge. End of excursus.

5. Open Questions and Conclusions

The discussion above has concerned iec-reduplication of nouns. An anonymous reviewer points out that the same process can apply to verbs also. The example they provide is (44):

(44)	Giờ này mà còn tắm tiếc gì nữa

The sentence, spoken by A to B, means something like ‘why would you do something like washing at this time of day?’.24 The word to pay attention to here is tắm tiếc, which is the reduplicated form of tắm, which means ‘wash’. My intuition is that tắm tiếc describes activities that are similar to washing. If this intuition is correct, an extension of the theory I proposed above that can deal with verbs seems to be in sight. I leave the task of working out its details for future research.

Another open question is the following puzzle: when there is no ignorance inference, red conveys dismissiveness on the part of the speaker:

(45)	A:	Nam làm gì?
		Nam do   what
	B:	Giáo sư+giáo siếc gì đó
		professor+red        demwh

B’s response to A’s question in (45) suggests that B does not think very highly of professors, i.e., that she is “dismissive” towards them. The account I gave does not explain this fact. An issue to ponder here is how much of this interpretation is to be derived from ‘purely pragmatic’ considerations.25 Again, I leave this problem to future research.

To conclude, I have argued for the following claims about similative reduplication in Vietnamese: (i) it gives rise to ignorance inferences in the same way disjunctions do; (ii) it refers to a notion of similarity that is different from the one referred to by classifiers. The second claim implies that (aspects of) grammatical knowledge can be encapsulated from encyclopedic knowledge.