Mass Nouns, Count Nouns, Sortals, and Identity
Gerhard Schaden
[email protected]
Université Lille 3, CNRS STL
11-04-2013
Paradox and Identity
Outline
Introduction
Linguistics and Philosophy
Sortals
Linguistics: The Bigger Picture
Mass-Count and Identity
Where does the Mass-Count Distinction Come From
There May Be Some Underlying Motivation, But it’s Arbitrary
Mass-Count Distinction is Semantic (All the Way Up and Down)
Conclusions
Outline
Introduction
Linguistics and Philosophy
Sortals
Linguistics: The Bigger Picture
Mass-Count and Identity
Where does the Mass-Count Distinction Come From
There May Be Some Underlying Motivation, But it’s Arbitrary
Mass-Count Distinction is Semantic (All the Way Up and Down)
Conclusions
Linguistics and Philosophy: Count and Sortals
I
Widespread intuition that there is something interesting in the
difference between table and water (and maybe also between
those and yellow)
I
Framed usually in linguistics as a distinction in noun (or noun
phrase) properties (i.e., mass vs. count)
I
Framed in philosophy as discussion about different sorts of
concepts (sortals vs. feature-concepts)
I
Discussion in the opposing field looks superficially familiar, but
has unexpected quirks about it.
Common Ground (Between some Philosophers and some
Linguists)
I
Countability has some relation with individuation (cf. Lowe
(2009), Moltmann (1998))
I
Mass nouns (NPs) have some properties that (typical) count
nouns lack: homogeneity, cumulativity
(1) [Yellow and red T-shirts were lying on the floor.]
Die Roten waren dreckig.
the reds were dirty.
(2) [The lawn was full of puddles, filled with water and mud.]
#Die Wasser waren aber häufiger.
the water.PL were though more frequent.
Intended: The water-puddles were more frequent.
Contrary to red, a mass noun like water cannot accomodate just any
kind of individuation-frame (by anaphora, for instance).
Sortals I
I
There is some tension in what is called a sortal, and crucially,
whether typical mass nouns are sortal or not:
I
I
mass not a sortal: Strawson (1959) (mass is a feature-universal or
a feature-concept)
(some) mass are a kind of sortal: Lowe (2009)
I
Sortals obligatorily come with a criterion for distinguishing
identity (what counts as a being the same entity under sort X)
I
Sortals (or a subgroup of them) come with some criterion on
enumerating or counting individual instances
I
Strange for linguists: thing is not a sortal (see ibid., 14f.)
Sortals II
I
According to Strawson: difference between sortals and
feature-concepts: reidentification/reidentificability
Operating with the idea of reidentifiable particular cats, we
distinguish between the case in which a particular cat appears,
departs and reappears, and the case in which a particular cat
appears and departs and a different cat appears. But one could
play the naming-game without making this distinction. Someone
playing the naming-game can correctly say ‘More cat’ or ‘Cat
again’ in both cases; but someone operating with the idea of
particular cats would be in error if he said ‘Another cat’ in the
first case, or ‘The same cat again’ in the second. The decisive
conceptual step to cat-particulars is taken when the case of ‘more
cat’ or ‘cat again’ is subdivided into the case of ‘another cat’ and
the case of ‘the same cat again’. (Strawson, 1959, p. 207)
I
Note that this discusses “fake mass nouns” (an imaginary one,
here), a category that will turn out to be important.
Mass and Count I
I
In languages like English, not all nouns combine felicitously with
indefinite articles, not all allow plurals, and not all allow for
combination with many:
(3) a. John owns a dog.
b. *John owns a money.
(4) a. John owns dogs.
b. *John owns moneys.
(5) a. John owns many dogs.
b. *John owns many money(s).
(6) a. ?John owns much dog.
b. John owns much money.
I
In languages like English, most (but: not all) nouns can have
both mass and count readings:
Mass and Count II
(7) a. A rabbit stole my suit.
b. There was rabbit all over my suit.
(8) a. I drank a lot of beer.
b. I ordered three beers.
I
The difference is not necessarily encoded in the lexicon (not even
in “number-marking languages”, such as English, cf. Pelletier
(2011))
I
The effects in (7) and (8) can be seen as the effect of some
covert operators, the universal grinder and the universal packager:
(9) a. There was [grinder(rabbit)] all over my suit.
b. I ordered three [packager(beer)]s.
I
It has been argued that in some languages (classifier languages,
e.g., Chinese) all nouns are lexically mass (Chierchia, 1998)
Mass and Count III
I
Mass nouns bear close ressemblance to count plurals
I
I
semantics: homogeneity
determiner choice
(10) a. I have seen *(a) dog.
b. I have seen (*a) water.
c. I have seen (*a) dogs.
I
Open question: is there any semantic property systematically
underlying the mass-count division?
The Paradox
I
There are (quite a few) examples of cases of translational
equivalence, where the mass-count feature (of whatever nature it
may be) is different:
(11) a. John eats fruit. [English: mass]
b. John mange des fruits. [French: count]
I
So, it appears that JfruitE K = JfruitsF K
But if countability has something to do with individuation (which
in many instances seems to be obvious), how could that possibly
be true?
I
Solution A: there is no general systematic meaning to (at least
one of either) mass or count
I
Solution B: Actually, JfruitE K 6= JfruitsF K
Number Marking and Animacy (Corbett 2000)
I
I
Mass nouns can be seen as nouns that do not mark number
obligatorily (a subset cannot mark it at all)
Many languages do not mark number consistently throughout
(pro)nouns, but there seems to be some regularity (cf. Corbett,
2000, p. 56): languages mark number (obligatorily) down to
some point in the animacy-hierarchy, and below only facultatively
(or not at all)
(12) speaker > hearer > 3rd person > kin > humans >
animates > inanimates
Languages like English may make the boundary of obligatory
number marking somewhere within the inanimates
⇒ This is not obligatorily at odds with the ideas that there is some
(semantic) substance to the count-mass distinction, or that it is
about individuation (animacy is in some sense also about
individuation)
I
Outline
Introduction
Linguistics and Philosophy
Sortals
Linguistics: The Bigger Picture
Mass-Count and Identity
Where does the Mass-Count Distinction Come From
There May Be Some Underlying Motivation, But it’s Arbitrary
Mass-Count Distinction is Semantic (All the Way Up and Down)
Conclusions
Shiftability and its Consequences
I
Most nouns can be shifted from mass to count, and vice-versa
I
Facts of translational equivalence and minimal pairs like the
following:
(13) shoe vs. footware
I
nouns shift freely, the denotations of mass and count are identical
(= Pelletier’s position as interpreted by Landman (2011))
You can count (nearly) anything, but not anyhow I
I
Observation by Landman (2011, p. 15): you can count
macro-packages, but not micro-packages
(14) a. I would like two coffees, two cognacs and two waters,
please.
b.#There are far more than a billion waters in this cup of
water.
I
Molecules of water might qualify as minimal water-packages, but
you cannot get that interpretation. That’s because they are too
small.
I
Glasses of water are about the right size, so you can count them
You can count (nearly) anything, but not anyhow II
My observation (in need of readjustment)
This is not about micro- vs. macro, but about a more general issue of
permissible individuation-frames:
I
(Stereotypical) mass individuates by type (or unit of
consumption)
I
Count individuates by tokens (i.e., individual instances)
I
Assume I took a bottle of water, emptying it onto the desk, and
creating two puddles with it
Result: 2 macro-units consisting of water. But: you cannot
describe them as two waters
I
I
I
I
Since they come from the same bottle, no type-distinction can
apply
Since we do not drink water from puddles, these are no valid
consumption units
Individuation fails, and it is not countable
You can count (nearly) anything, but not anyhow III
I
In some languages (German), there is a variety compatible only
with consumption units, showing signs of a covert classifier:
(15) Nach sieben Bier
und drei Schnaps
bin ich voll
After 7
beer.SG and 3 schnaps.SG am I full
in dich verliebt.
in you in love
a. After seven glasses/bottles of beer and 3 glasses of
Schnaps . . .
b.#After seven types of beer and 3 types of Schnaps . . .
(16) Der Angeklagte hatte drei Schnäpse getrunken.
The defendant had 3 schnaps.PL drunk
a. The defendant had drunk 3 glasses of Schnaps.
b. The defendant had drunk 3 types of Schnaps.
(17) Der Angeklagte trank 3 Liter Schnaps
| *Schnäpse.
The defendant drank 3 liters schnaps.SG | schnaps.PL
You can count (nearly) anything, but not anyhow IV
I
Size does not seem to matter (at least here):
(18) a. John ate three rices.
(i) John ate three dishes of rice. [consumption units]
(ii) John ate three types of rice. [subtypes]
(iii)#John ate three grains of rice. [rice-tokens]
b. John ate three lentils.
(i) #John ate three dishes of lentils. [consumption
units]
(ii) #John ate three types of lentils. [subtypes]
(iii) John ate three individual lentils. [lentil-tokens]
Lentils and grains of rice seem to have roughly equivalent sizes,
yet they behave very differently.
I
Rice has observable minimal parts, nevertheless, they do not
seem to be accessible to counting.
I
Is this valid for all mass nouns?
Fake Mass Nouns and Individuation I
I
Fake mass nouns have giant minimal units (cows, chicken, tables,
etc.), and are nevertheless mass.
I
Can they be individuated only by subtypes, and not by tokens?
I
The equivalents of cattle in French and my Southern German
dialect cannot take a plural:
(19) a. *Cunégonde possède 3 bétails.
C.
owns 3 cattle.PL
b. *da Hans hot 3 fea.
the H. has 3 cattle.PL
I
The infelicity of (19) can be interpreted (at least) in 2 ways:
I
I
bétail does not individuate at all its meaning (thus: infelicity is
somehow rooted in semantics)
Somehow, grammar disallows access to any kind of semantic
building block (yet, they are there, somehow).
Fake Mass Nouns and Individuation II
I
At least some of these mass nouns do allow for token-access,
e.g., volaille (poultry)
(20) Ferdinand possède trois volailles.
F.
owns 3
poultries.
I
I
(20) is judged true even if Ferdinand only owns 3 chickens (of a
single mother), so that we have token-access without
necessitating type-differences
Conclusion: fake mass is problematic
I
I
I
some behave like hard-core mass nouns, without any plural (even
though there should be atoms)
some pattern with respect to individuation (in some cases, at
least) with count nouns, rather than with mass nouns
There seems to be thus a class that is merely formally mass, and
so, it seems to be difficult to establish a stable meaning difference
between count and mass
Countability and Plurality
I
I
Does plurality presuppose countability?
At least some nominally plural nouns cannot be subjected to
counting:
(21) Trotz der Schließung der Banken sind Gelder
despite the closing
of the banks are money.PL
aus Zypern abgeflossen.
from Cyprus flown out
Despite the closing of the banks, funds have been
transferred out of Cyprus.
I
I
(21) would not be true if only one person had taken money from
only one account and transferred it out of Cyprus (contrary to
(21) with a singular “Geld”).
Yet you cannot count the funds. A cardinal cannot be applied to
“Gelder” in (21) (even if you knew exactly how many people
transferred money from how many accounts).
Outline
Introduction
Linguistics and Philosophy
Sortals
Linguistics: The Bigger Picture
Mass-Count and Identity
Where does the Mass-Count Distinction Come From
There May Be Some Underlying Motivation, But it’s Arbitrary
Mass-Count Distinction is Semantic (All the Way Up and Down)
Conclusions
The Stakes of an Account of the Mass-Count Distinction I
following Pelletier (2011, 35f.)
Theories of the Mass-Count Distinction face three different challenges:
I
say something reasonable about semantic content (in general)
I
say something reasonable about how language relates to reality
I
account for the linguistic facts of the mass-count distinction
I
If you ignore the second point (and especially, if you do not think about
it in terms of denotational semantics), things seem feasible much more
easily. This has been explicitely defended by Wierzbicka (1985, p. 327):
The Stakes of an Account of the Mass-Count Distinction II
If one agrees with Bloomfield’s idea of meaning (as something that
‘science’ can establish through a study of denotata) then indeed one
has to accept his conclusion: the formal difference between oats and
wheat is semantically arbitrary. If, however, one rejects that idea of
meaning and defines meaning, rather, as ‘what is meant’, i.e. as the
language-specific conceptualization of some part or aspect of the
reality, then Bloomfield’s conclusion is not warranted at all: water, too,
‘consists of particles’, but it is not conceived of as something consisting
of particles [. . . (Wierzbicka’s emphasis)]
I
This sounds nice, but there are some downsides to it:
I
I
If you think that languages — or at least supposedly simple
concepts like water, or horse — are conceptually grounded in
some kind of reality, Wierzbicka’s position may strike you as
suboptimal
More forceful objection by Pelletier (2011, p. 20):
The Stakes of an Account of the Mass-Count Distinction III
If water is divisive but water isn’t, then water can’t be the semantic
value of water (can it?). In turn this suggests a notion of semantics
that is divorced from “the world”, and so semantics would not be a
theory of the relation between language and the world. But it also
would seem not to be a relation between language and what a
speaker’s mental understanding is, since pretty much everyone
nowadays believes that water has smallest parts. Thus, the mental
construct that in some way corresponds to the word water can’t be the
meaning of water either. [Pelletier’s emphasis]
I
One of the advantages of Landman (2011) is that he takes all these
issues very seriously, and tries to work from the denotations.
I
One related important issue concerns the arbitrarity of the count-mass
distinction: could any word be in just any category?
I
Languages seem to agree on certain core-cases (e.g., substances tend
to be mass), but there is quite some variation on individual cases.
I
Assuming that arbitrariness is limited, and cross-linguistic consensus
the interesting point, where does this consensus come from?
The Stakes of an Account of the Mass-Count Distinction IV
I
I
Properties of the denotatum?
Of our way of seeing/conceiving the world surrounding us?
“Homeopathic Semantics”
I
I
One of the first, and best-known proposed formal accounts for
count vs. mass is Link (1983/2000)
He assumes two separate domains, one for mass, and one for
count, where
I
I
I
Landman’s reaction (to claim for mass): this is a homeopathic
semantics
I
I
I
count domain is an atomic lattice
mass domain is not atomic
postulates “arcane semantic structures solely to avoid counting”
plausible maybe at macro-level, but not at micro-level
Why can’t we count, then?
I
I
I
Rothstein, 2010: because some nouns come with built-in counter,
others don’t
Krifka (1989): because some have natural units, others don’t
in the end (according Landman): we cannot count because we
chose not to
Landman’s Proposal: Intuition
I
Mass noun denotations are overspecified: there are too many
building blocks which could make up the basic building blocks, so
counting must go wrong (picture from Landman (2011, p. 18)).
I
There are no priviledged pieces in the sense that you could make
out the real minimal pieces. You have 2 variants you might count
(SALT1 +SALT2 ) or (SALT3 +SALT4 ).
I
Count noun denotations are built from building blocks that are
non-overlapping, and that form a single variant.
More Formally
I
generating set (containing the basic semantic building blocks):
(22) A generating set for X is a set gen(X ) ⊆ X − {0} such
that:
∀x ∈ X : ∃Y ⊆ gen(X ) : x = tY
I
I
I
Minimal parts of X are part of the generating set
Sets can have more than one set of generators (namely if they
have variants)
generated set:
(23) A generated set is a pair X = hX , gen(X )i, with gen(X ) a
generating set for X
I
variant:
(24) V is a variant for a generated set X iff
a. V is a maximally disjoint subset of gen(X )
b. *V is a subset of X such that tX ∈ *V
Count and Mass, Neat and Mess
Landman separates countability from a second criterion, neatness
I Count vs. Mass:
(25) a. X is [+C], count, iff for every w: gen(Xw ) is disjoint
(i.e., the generators of Xw do not overlap)
b. X is [–C], mass, iff for every w: if |Xw > 1 then
gen(Xw ) is not disjoint (i.e., the generators of Xw
overlap).
I
Neat vs. Mess:
(26) a. X is [+N], neat, iff for every w: min(Xw ) is disjoint
(i.e., the minimal elements of Xw do not overlap)
b. X is [-N], mess, iff for every w: if |Xw |>1 then
min(Xw ) is not disjoint, i.e., the minimal elements of
Xw overlap.
I
count entails neat, and mess entails mass. But: the system
allows for neat mass nouns: [+N, -C]
Example 1: Neat Count
Diagram from Landman (2011, p. 30): disjoint generators and disjoint
minimal parts
Example 2: Mess Mass
Picture from Landman (2011, p. 31): overlapping generators,
overlapping minimal parts
Example 3: Neat Mass a.k.a “Fake” Mass
From Landman (2011, p. 34): the generators are not necessarily
disjoint; the minimal parts are disjoint
Why Can’t We Count? Because Generators Overlap
I
Counting presupposes that one should not count things twice,
which will happen when generators overlap.
I
Reinterpretation into consumption units and subtypes can be
seen as discretization-strategies
I
If Landman is right, neat mass should behave w.r.t.
individuation-frames like mass
I
There are exceptions to this (e.g., volaille), but let us assume
that these are isolated cases of homonymy.
I
Is fake mass really systematically neat mass in Landman’s sense?
Is all Fake Mass alike? Cattle: Escaping Countability
I
Should we really assume that the structure of the generating set
of cattle is any different from rabbit or sheep?
I
It does not seem to be more heterogeneous (like poultry), nor of
unclear minimal parts (like salt)
I
If not, then why can’t we (directly) count cattle?
Possible Solutions
If we want to keep the idea that the mass-count distinction is
meaningful (in a systematic way), we could . . .
I Do as Landman, but find other properties that account for the
difference between mass and count.
I
I
I
Sever link to denotata, work on how people conceive things
I
I
I
Doubts as to the feasibility of such an approach (especially for
“fake mass”)
Do we really want to go for his Bunsen burner semantics?
Risk of circularity, given that our principal evidence of how people
‘conceive things’ comes from language structure, which is what
we seek to explain
Will give rise to Pelletier’s puzzle: we will have a theory, but a
theory of what?
Find a formal analysis that accounts for the linguistic data, and
do not worry about psychological and/or denotational plausibility
What ‘Natural Language Metaphysics’ is the Theory of I
I
Recap: water is not divisive in reality (as far as science has
shown), nor do we believe it is (as far as we believe in science)
I
So it is neither a denotational theory nor a theory of mental
representations — which are the legitimate theories of linguistic
meanings, as Pelletier (2011) suggests
Not as self-evident as it may seem:
I
I
I
I
I
Should we assume that there is a big break in language meaning
of mass vs. plural since the development of modern chemistry
and science classes in obligatory education?
Should we assume that the atomists vs. non-atomists of old had
different meanings attached to water?
I may believe now that water is not infinitely divisible, but I
certainly did not know when I learned how to use water
More general question: How should we evaluate language
plasticity?
What ‘Natural Language Metaphysics’ is the Theory of II
I
Infinite divisibility of mass nouns (and other aspects of Natural
Language Metaphysics) may be correct as far as interaction
patterns of situated agents are concerned (and this is what
Wierzbicka (1985) and cognitive linguistics more in general
suggest)
I
Language needs to be transmitted from generation to generation;
Iterated Learning Models allow to give a representation of this
process:
I
Linguistic competence depends on actual linguistic behaviour of
preceding generations.
What ‘Natural Language Metaphysics’ is the Theory of III
I
Questions remaining:
I
I
I
How does the bootstrapping of elements like cattle as mass work
across generations (can be adressed by simulation).
Assuming that mental representations do change during the life
of an individual, how (and to which extent) is this process likely
to trigger changes in the (grammatical and lexical) structure of
the language?
If a divorce between interaction-patterns and (explicitely or
implicitely) held belief problematic?
Outline
Introduction
Linguistics and Philosophy
Sortals
Linguistics: The Bigger Picture
Mass-Count and Identity
Where does the Mass-Count Distinction Come From
There May Be Some Underlying Motivation, But it’s Arbitrary
Mass-Count Distinction is Semantic (All the Way Up and Down)
Conclusions
Conclusions
I
Some differences, but major points in common in literature on
mass-count and on sortals
I
Ambitious theories of mass-count distinctions have ontological
implications
I
Is it wise to be ambitious (in this area)?
Thank you!
References I
Chierchia, G. (1998). “Plurality of Mass Nouns and the Notion of
“Semantic Parameter””. In: Events and Grammar. Ed. by
S. Rothstein. Dordrecht: Kluwer: pp. 53–103.
Corbett, G. G. (2000). Number. Cambridge: Cambridge University
Press.
Landman, F. (2011). “Count Nouns — Mass Nouns. Neat Nouns —
Mess Nouns”. In: The Baltic International Yearbook of Cognition,
Logic and Communication 6: pp. 1–67.
Link, G. (1983/2000). “The Logical Analysis of Plurals and Mass
Terms: A Lattice-theoretical Approach”. In: Formal Semantics. The
Essential Readings. Ed. by P. Portner and B. H. Partee. Oxford:
Blackwell: pp. 127–146.
Lowe, E. J. (2009). More Kinds of Being. A Further Study of
Individuation, Identity, and the Logic of Sortal Terms. Oxford:
Wiley-Blackwell.
References II
Moltmann, F. (1998). “Part Structures, Integrity, and the
Mass-Count Distinction”. In: Synthese 116.1: pp. 75–111.
Pelletier, F. J. (2011). “Descriptive Metaphysics, Natural Language
Metaphysics, Sapir-Whorf, and all that Stuff: Evidence from the
Mass-Count Distinction”. In: The Baltic International Yearbook of
Cognition, Logic and Communication 6: pp. 1–46.
Rothstein, S. D. (2010). “Counting and the Mass–Count Distinction”.
In: Journal of Semantics: pp. 1–55.
Strawson, P. F. (1959). Individuals. An Essay in Descriptive
Metaphysics. London, New York: Routledge.
Wierzbicka, A. (1985). “Oats and Wheat: The Fallacy of
Arbitrariness”. In: Iconocity in Syntax. Ed. by J. Haiman. Amsterdam:
John Benjamins: pp. 311–342.