attributes and abstract mass nouns

Attributes and Abstract Mass Nouns*

Byeong-uk Yi

1)

Abstract singular nouns (e.g., ‘whiteness’, ‘humanhood’), on the standard account, refer to attributes. But many of them (e.g., ‘whiteness’) are mass nouns. Like concrete mass nouns (e.g., ‘water’), they can combine with determiners relating to amounts of stuff (e.g., ‘a little’, ‘much’, ‘less’). Levinson (1978; 1980) argues that this means that a large group of attributes are stuffs of some kind, abstract stuffs. This view, the stuff view, is widely

considered indefensible. But it would be hard to resist the view without rejecting the usual

account of determiners that combine with mass nouns, the quantity account, according

to which such determiners relate to amounts of stuff. This paper argues against both

the stuff view and quantity account, and presents an account of abstract mass nouns

based on an adequate account of determiners that combine with them.

Subject metaphysics, philosophy of language

Key words mass noun, abstract, attribute, stuff, number, quantity, gradable adjective,

comparative marker, degree adverb, Plato, form

* Received: 26. Nov, 2016 Revised: 16. Jun, 2017 Accepted: 17. Jun, 2017

철학 분석 37 (2017) pp.1-37

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Qualifications admit of a more or a less; for one thing is called more pale or less pale than another ― Aristotle, the Categories1)

. . . mass-words are quantified by such words as much, little, less. ― Otto Jespersen, The Philosophy of Grammar

Abstract singular nouns (e.g., ‘whiteness’, ‘humanhood’), on the standard account, refer to attributes.2) But many of them (e.g., ‘whiteness’) are mass nouns. Like concrete mass nouns (e.g., ‘water’), they can combine with determiners3) relating to amounts of stuff: ‘a little’, ‘much’, ‘less’, etc. Jerrold Levinson (1978; 1980) argues that this means that a large group of attributes are stuffs of some kind, abstract stuffs. This view, the stuff view, is widely considered indefensible. But it is interesting and important, I think, to see why it is not viable. And it would be hard to resist the view without rejecting the usual account of determiners that combine with mass nouns, the quantity account, according to which such determiners relate to amounts of stuff. In this paper, I argue against both the stuff view and quantity account. And I present an account of abstract mass nouns based on an adequate account of determiners that combine with them.

1) Aristotle (Cat./1963, 10b26). He adds that “not all qualifications admit a more and a less” (ibid., 11a5). See note 38.

2) This assumes the existence of attributes. See, e.g., my (2014; forthcoming) for arguments against the view that attributes do not exist.

3) Determiners, which modify common nouns, include articles, demonstratives, and quantifiers, and are distinguished from adjectives. (The determiners discussed in this paper, M-determiners, might be considered quantifiers.) In contemporary linguistics, determiners are taken to form a closed word class. See Bloomfield (1933, 203-5), where he distinguishes determiners from adjectives. In English, determiners usually precede both the nouns they modify and the adjectives modifying nouns. For an account of the English determiner system, see, e.g., Quirk et al. (1985, 253-265).

Attributes and Abstract Mass Nouns 3

1. Are attributes abstract stuffs?

Many languages have devices for constructing abstract nouns. For example, English uses some suffixes (e.g., ‘-ness’, ‘-ity’, ‘-itude’, ‘-cy’, ‘-tion’, ‘-ment’, ‘-hood’, ‘-ship’) to construct them: ‘whiteness’, ‘vivacity’, ‘exactitude’, ‘vibrancy’, ‘appreciation’, ‘refinement’, ‘humanhood’, ‘leadership’, etc.4) What do these nouns mean? It is usual to take them to relate to attributes.5) For example, J. S. Mill (1891/2002), who distinguishes between singular and general nouns, divides singular nouns into two kinds:

(a) the concrete: ‘John’, ‘London’, etc.(b) the abstract: ‘whiteness’, ‘triangularity’, etc.6)

And he says, “A concrete name is a name which stands for a thing; an abstract name is a name which stands for an attribute of a thing” (ibid., Bk. I, Ch. II, §4). On this account, the abstract noun ‘whiteness’, for example, refers to an attribute (viz., whiteness) that any white particular

4) Not all English abstract singular nouns result from adding suffixes. Consider, e.g., ‘courage’, ‘patience’, ‘mercy’, and ‘red’ (as used in, e.g., ‘Red is a color’).

5) Attributes include properties (i.e., one-place attributes) and relations (i.e., multi-place attributes). Properties correspond to one-place predicates (e.g., ‘be white’, ‘be lively’) or the abstract nouns related to them (e.g., ‘whiteness’, ‘liveliness’), and relations to multi-place predicates (e.g., ‘be close to’, ‘give ... to’) or the related abstract nouns (e.g., ‘closeness’, ‘proximity’, ‘perpendicularity’, ‘identity’, ‘similarity’). Levinson (who divides properties into two kinds) does not discuss relations, and the stuff view has serious difficulties in handling relations (e.g., perpendicularity). In this paper, I ignore this problem to focus on the nature of properties, and use ‘attribute’ primarily for them. But I argue that one cannot give a proper account of properties or attributes that abstract nouns refer to (e.g., liveliness) without invoking relations (e.g., being more lively) (see §4).

6) General nouns are also divided into the concrete (e.g., ‘horse’) and the abstract (e.g., ‘virtue’).

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has or instantiates. And instantiating the attribute is what makes white things white: a snowflake, for example, is white because it instantiates whiteness.

The account of abstract nouns sketched above dates back to Plato, who holds in his theory of forms that there are attributes or what he calls forms (e.g., largeness, justice, beauty) as well as particulars (e.g., things that are large, just, or beautiful). Particulars are large, just, beautiful, and so on, on the theory, because they instantiate the matching forms (or attributes), which abstract nouns relate to. In the Parmenides, a dialogue in which he presents difficulties of the theory, he formulates this view as follows:

. . . there are certain forms from which these other things, by getting a share of them, derive their names―for instance, they come to be like by getting a share of likeness, large by getting a share of largeness, and just and beautiful by getting a share of justice and beauty . . . . (Parm./1996, 130e-131a)

In this statement, he uses ‘get a share of’ for the instantiation relation, which seems to suggest the view that particulars instantiate a form by having parts of the form. And he examines this view as a potential view about the relation between particulars and forms. According to the view, he says, “the forms themselves are divisible . . . and the things that partake of them would partake of a part; no longer would a whole form, but only a part of it, be in each thing” (ibid., 131c). This states what I call the stuff view of attributes, the view that an attribute (or form) is something divisible, a kind of stuff that has parts inside some particulars, and its existence in the particulars is what makes them have the character associated with the attribute―largeness, for example, is a kind of stuff whose parts are inside large particulars, and these are large because some


parts of the stuff are in them.7)

While Plato (ibid.) examines this view to raise problems with it, Levinson (1978; 1980) presents an interesting defense of the view.8) He holds that a large group of attributes (e.g., whiteness, vivacity) are stuffs that differ from the usual, material stuffs (e.g., water) in that they are abstract.9) His argument for this view appeals to the fact that a variety of abstract singular nouns are mass nouns.10)

Otto Jespersen (1924) divides common nouns of English and related languages into mass and count nouns.11) The count noun ‘cow’, for example, (a) has the singular and plural forms, and (b) combines directly

7) I say that A is (or exists) in B, if A is wholly or partly in B; but I say that A is inside B, only if A exists wholly (or completely) in B.

8) Levinson (1980, 110ff) also argues that the stuff view is compatible with the platonist thesis that attributes are immune to change, and Gail Fine (1986, 78) draws on his version of the stuff view to propose the interpretation that Plato regards forms as stuffs in his earlier dialogues (e.g., the Phaedo). Bae (1996, 69–80; 1999), I think rightly, argues against Levinson’s thesis and Fine’s interpretation. See Appendices 1 and 2.

9) He divides attributes into two kinds: (a) whiteness, vivacity, etc. and (b) being white, being vivacious, etc. And he holds that the former, unlike the latter, are abstract stuffs. (They are, roughly, attributes abstract mass nouns can refer to (i.e., what I call M-attributes below). See note 18.)

10) In his later article (Levinson 2006), he rejects the stuff view. But he does not explain what is wrong with his earlier argument for the view, and holds that the view is “coherent” (ibid., 565). I think both the view and the argument have serious problems. See the last paragraph of §2.1.

11) Jespersen calls count nouns “thing-words” or “countables”, and mass nouns “mass-words” or “uncountables” (1924, 198f). For contemporary formulations of the distinction, see, e.g., Quirk et al. (1972, 247) and Pelletier and Schubert (2003). The so-called classifier languages, which include many East Asian languages (e.g., Chinese, Japanese, Korean), do not have as overt a distinction between mass and count nouns as most Indo-European languages (e.g., English) do, and many linguists and philosophers hold that all common nouns of classifier languages are mass nouns (the mass noun thesis). But I think classifier languages have subtle devices for distinguishing count nouns from mass nouns (the count noun thesis). See, e.g., my (2009; 2011a; 2011b).

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with numerals as in, e.g., ‘one cow’ and ‘two cows’ (where it takes the singular and plural forms, respectively). Mass nouns (e.g., ‘water’, ‘gold’), by contrast, do not have singular and plural forms; nor can they combine directly with numerals. Now, mass nouns are often taken to relate to some stuff, mass, or substance in the chemist’s sense (e.g., water, gold).12) But they include many nouns that do not seem to relate to stuff: ‘justice’, ‘liveliness’, ‘patience’, ‘refinement’, ‘mercy’ etc. These are abstract nouns and yet satisfy criteria for mass nouns: they do not have singular and plural forms, nor can they combine directly with numerals.13) So it is usual to distinguish between two kinds of mass nouns:

(a) concrete mass nouns: ‘water’, ‘gold’, etc.14)

(b) abstract mass nouns: ‘justice’, ‘liveliness’, ‘refinement’, etc.15)

12) See Quine (1960, Ch. 3). See also Jespersen (1924). He says that while count nouns “call up the idea of some definite thing with a certain shape or precise limit”, concrete (or “material”) mass nouns “denote some substance in itself independent of form” (where he uses ‘substance’ in the chemist’s sense, not in the Aristotelian sense); but he thinks that there is another group of mass nouns, the abstract (or “immaterial”) mass nouns, as noted below (ibid., 198).

13) They also satisfy other usual criteria for mass noun, including the determiner criterion discussed below (they can combine with, e.g., ‘much’, ‘little’).

14) Jespersen does not discuss a substantial group of concrete mass nouns: ‘furniture’, ‘silverware’, ‘jewelry’, ‘clothing’, ‘infantry’, ‘footwear’, etc. Barner and Snedeker (2005) call these “object-mass nouns” to contrast them with the usual concrete mass nouns, which they call “substance-mass nouns” (ibid., 45). Their study suggests that English speaking children understand that the two kinds of concrete mass nouns have different kinds of meanings. In this paper, I focus on how abstract mass nouns contrast with substance-mass nouns, and ignore the further complexity arising from the existence of object-mass nouns (I think these are quasi-mass nouns that do not relate to stuff).

15) See, e.g., Jespersen (1924, 198) and Quirk et al. (1972, 247). Jespersen calls concrete mass nouns “material”, and abstract mass nouns “immaterial” (1924, 198), but his distinction between material and immaterial nouns more or less


If so, what do abstract mass nouns mean?One might take them to refer to attributes, for they are abstract singular

nouns. Some might hold that this means that they (unlike concrete mass nouns) are proper nouns: ‘justice’, for example, is a proper noun for an attribute (viz., justice), as ‘Socrates’ is one for a concrete particular (viz., Socrates). This would help to explain why ‘justice’ neither has singular and plural forms nor combines directly with numerals―it is the same with proper nouns. Unlike proper nouns, however, abstract mass nouns share an important additional feature with concrete mass nouns. They can combine with some determiners: ‘some’, ‘no’, ‘little’, ‘a little’, ‘much’, ‘more’, ‘less’, etc. (call these M-determiners). And these are determiners that can combine with concrete mass nouns.16) So one can talk of ‘some justice’, ‘much admiration’, ‘more liveliness’, ‘a little refinement’, ‘less constancy’, etc., just as one can talk of ‘some water’, ‘much milk’, ‘more gold’, etc. This distinguishes abstract mass nouns from proper nouns and places them, like concrete mass nouns, under the category of common nouns.

If so, what do M-determiners mean when they combine with abstract mass nouns? When they combine with a concrete mass noun (e.g., ‘water’), they seem to relate to amounts of the stuff it refers to (e.g., water). For example, ‘A watermelon has more (or less) water than another’ is equivalent to ‘A watermelon has a larger (or smaller) amount of water than another.’ Levinson (1978; 1980) assumes that M-determiners have the

coincides with Mill’s distinction between concrete and abstract nouns.16) Most of the M-determiners can combine only with mass nouns, but some of them

(e.g., ‘some’, ‘more’, ‘no’) can combine with count nouns as well. Jespersen (1924, 198) notes that ‘some’ and ‘more’ have different meanings because their translations into some languages (e.g., German, Danish) when they combine with mass and count nouns yield different words. I think all M-determiners are ambiguous with some of them (e.g., ‘more’) having multiple ambiguities (see §3).

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same meanings when they combine with abstract mass nouns, and concludes that the attributes they refer to are stuffs of a special kind, abstract stuffs. In this view, the attribute that ‘whiteness’ refers to (i.e., whiteness), for example, is a stuff that has parts inside white particulars as water is a stuff that has parts inside, e.g., watermelons, and white particulars (e.g., snowflakes) are white because parts of the stuff are inside the particulars. He argues that this explains why the abstract noun ‘whiteness’ is like ‘water’ in combining with M-determiners: ‘A snowflake has more (or less) whiteness than another’ is equivalent to ‘A snowflake has a larger (or smaller) amount of whiteness than another.’

This argument has an obvious limitation in establishing the stuff view of attributes. Its conclusion would be that attributes that abstract mass nouns refer to are stuffs, but this does not mean that all attributes are stuffs. One reason for this is that not all abstract singular nouns are mass nouns. For example, ‘humanhood’ is not a mass noun; it cannot combine with M-determiners.17) But some might take the argument to establish a restriction of the stuff view. Call attributes abstract mass nouns refer to M-attributes. Then we can formulate the conclusion of the argument as follows:

The stuff view of M-attributes: M-attributes are stuffs.

If so, does the argument give a good reason to hold this view?I think the answer is no. There are serious problems with the view.

And the argument rests on a wrong assumption about M-determiners:

The quantity account: M-determiners relate to quantities (viz., amounts) of stuffs.

17) Neither can ‘trilaterality’ and ‘three-sidedness’. See §3.


On this account, the M-determiners have the same meanings when they combine with mass nouns (whether concrete or abstract), and relate to amounts of their referents. For example, ‘more’ and ‘less’ equally mean a larger amount of and a smaller amount of, respectively, on the account, whether they combine with concrete or abstract nouns. This account results from generalizing the meanings the determiners have when they combine with concrete nouns (e.g., ‘water’) to the cases in which they combine with abstract nouns (e.g., ‘whiteness’) by assuming that they have the same meanings in both cases. But I think this assumption of univocity is incorrect. I do not think ‘more’ has the same meaning in ‘more whiteness’ and ‘more water’.

In the next section, I argue against both the stuff view and quantity account.

2. The stuff view and quantity account

The stuff view, we have seen, has two versions:

[A] The stuff view of attributes: Attributes are stuffs.[B] The stuff view of M-attributes: M-attributes are stuffs.

Levinson (1978; 1980) rejects the first view, [A]. He holds that some attributes (e.g., being white, being vivacious) are not stuffs. Those are attributes “standardly designated by gerundive expressions”: ‘being white’, ‘being vivacious’, etc. (1980, 106). But he holds the second view, [B]. He thinks that there are attributes of another kind, those that are “standardly designated by abstract nouns”, such as “redness, vivacity, fluidity, contentment” (ibid., 106).18) And he argues that these attributes

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are stuffs because they can combine with M-determiners, which he takes to relate to amounts of stuffs. I think both the stuff view of M-attributes and the key assumption of this argument, the quantity account of M-determiners, have serious problems.

2.1. The stuff view

On the stuff view, an attribute (or M-attribute) is a kind of stuff that has parts inside some particulars, and its existence in the particulars is what makes them have the character associated with the attribute. For example, whiteness is a stuff (viz., the whiteness-stuff) that has parts inside all the white particulars, and these particulars are white because some parts of the stuff are in them. So we can formulate the main thesis of the stuff view of M-attributes as follows:

[S] A particular instantiates an M-attribute (e.g., φ-ness) if and only if a part of the stuff identified as the attribute (e.g., the φ-ness-stuff) is inside the particular.19)

This implies the expansivity thesis:

18) He calls attributes of the first kind “properties” and those of the second “qualities”, and holds that the former are conditions while the latter are stuffs (ibid., 106). (In his view, “corresponding properties and qualities” (e.g., being white and whiteness) “are, as a rule, co-instantiated” but “remain ontologically distinct” (ibid., 106).) For the purposes of this paper, the so-called qualities might be identified with M-attributes (but see note 40).

19) So Levinson proposes the stuff view of M-attributes (or “qualities”) by saying “having a quality (e.g., whiteness) amounts to partaking of a certain stuff” (1980, 106; original italics).


[E] Expansivity of M-attributes: Any particular that has a part that instantiates an M-attribute must also instantiate the attribute.

For [E] follows from [S] together with its stuff cousin:

[Eʹ] Expansivity of stuffs: Any object that has a part that has a part of some stuff (e.g., a portion of water) in it must also have a part of the same stuff in it.20)

[Eʹ] is unexceptionable, but it is straightforward to see that [E] is false. This means that both versions of the stuff view are false.

Say that an attribute is expansive, if it is instantiated by anything that has a part that instantiates it.21) Then [E] states that all M-attributes are expansive. While some attributes (e.g., largeness) are expansive, however, there are many non-expansive attributes: smallness, triangularity, whiteness, rigidity, etc. Consider, for example, a rectangular plane figure, R, composed of two triangular parts, T1 and T2. Although R has parts instantiating triangularity, it does not itself instantiate the attribute (it is not triangular but rectangular). Similarly, a large object, L, composed of many small parts does not instantiate smallness.22)

Some might object that although this shows that the stuff view of attribute is false, this does not mean that the stuff view of M-attributes is false. To defend this view, they might argue that triangularity, for example,

20) Suppose that a particular, A, is a part of a particular, B, and instantiates an M-attribute, φ. Then a part of the φ-stuff must be inside A (by [S]), and thus inside B as well (by [Eʹ]). If so, B must instantiate the attribute φ (by [S]).

21) See Goodman (1951), who says “A one-place predicate is expansive if it is satisfied by everything . . . that has a part satisfying it” (ibid., 49). He gives ‘is large’ and ‘is populated’ as examples of expansive predicates.

22) As Quine (1960, 104) in effect notes, color attributes are non-expansive: red apples might have white interiors.

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is not a genuine M-attribute because ‘triangularity’ is not (properly speaking) a mass noun, one that can combine with M-determiners.23) I think they might disqualify many non-expansive attributes as M-attributes. But this does not help to defend the view. There is no denying that ‘rigidity’, for example, can combine with M-determiners. For example, ‘some rigidity’, ‘more rigidity’, and ‘less rigidity’ are as well-formed as ‘some refinement’, ‘more vivacity’, and ‘less fluidity’. Like smallness and triangularity, however, rigidity is non-expansive. Consider, for example, the fluid water in a bucket. While all the molecules composing the water are rigid, the water itself is not. So the water does not instantiate rigidity but has parts instantiating the property.

To avoid this problem, defenders of the stuff view might attempt to replace [S] with a suitable alternative. To do so, they might reject the ‘if’ part of [S] (in short, [S1]).24) That is, they might deny that the existence in a particular of the stuff identified as an attribute is a sufficient condition for its instantiating the attribute. If so, how does the existence of the stuff in some particulars relate to whether or not they instantiate the attribute? To answer this question, some might propose a modification of [S1]:

[Sʹ] A particular instantiates an M-attribute (e.g., φ-ness), if it has a part of the stuff identified as the attribute (e.g., the φ-ness-stuff) that is not confined

to a proper part of that particular.

23) They might hold that ‘more triangularity’, for example, is not well-formed, and argue that smallness, for example, also fails to be an M-attribute because ‘more smallness’ is not quite well-formed. (This phrase is a bit awkward and unusual, but I do not think this means that it is ill-formed. I think it is related to ‘smaller’. See note 37. See also notes 39 and 40.)

24) One cannot reject the other part of [S] while holding a version of the stuff view; it is essential to the view that the stuff responsible for a particular having an attribute is in the particular.


This thesis seems to have a good motivation,25) and it helps to avoid the non-expansive attribute problem. The thesis (even with the other part of [S]) does not imply the expansivity thesis, [E]. So proponents of [Sʹ] might argue that none of the parts of the smallness-stuff inside the small parts of a large particular, L, can make L itself small because they are all confined to proper parts of L. But this gives only a temporary relief. Consider the sum of all the parts of the smallness-stuff inside the small parts of L. The sum itself is also a part of the stuff, but it is not confined to any proper part of L. So [Sʹ], too, yields the wrong conclusion that L instantiates smallness. And the fluid water case gives rise to the same problem for [Sʹ].26)

In his later article (Levinson 2006), Levinson rejects the stuff view. He holds that his version of the view is “ultimately incredible” (ibid., 565) because “the supposition of . . . abstract stuffs” as conceived in the

25) It is based on the idea that an attribute of something is to be attributed to the thing itself, not to one of its proper parts: parts of a whole that has an attribute might not themselves have the attribute; and even when a part of the whole does, the grounds for this must be different from the grounds for the whole itself having the attribute; but if the part of the attribute that is responsible for something’s having the attribute is confined to a proper part of the thing, it would be responsible for that part of the thing (not the thing itself) having the attribute. Incidentally, note that both this idea and [Sʹ] conflict with Levinson’s treatment of the sharpness that a knife has on account of the sharpness of its edge. He holds that the part of the sharpness-stuff that a knife has can be the same as the part thereof that its edge has (1980, 114f). But this view (given [S]) has a serious problem. We may assume that the part of the knife complementing its edge has bluntness, which in the stuff view must have a part in the knife itself as well. If so, the knife itself must be blunt as well as sharp (by [S]). Levinson might reject [S] to avoid this problem. But he has yet to explain why the sharpness-stuff inside the edge makes the knife itself sharp while the bluntness-stuff inside the rest of it does not make the knife itself blunt.

26) For the sum of all the parts of the rigidity-stuff in the molecules in the water in a bucket would not be confined to a proper part of the water.

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version “is ontologically extravagant and conceptually outlandish” (ibid., 564). But he fails to point out any problem with his earlier argument for the view, and holds that the stuff view is “coherent” (ibid., 565). This, we have seen, is not correct: the stuff view is not coherent at all. And I think the argument has a serious problem. It rests on the quantity account of M-determiners, but this account has a fundamental problem, as I argue next.27)

2.2. The quantity account

The quantity account holds that M-determiners relate to quantities (viz., amounts) of stuffs. Usual accounts of mass nouns suggest this account. Jespersen might seem to do so when he says that mass nouns are “quantified by means of such words as much, little, less” (1924, 198).28) And Levinson, as noted above (§1), assumes the quantity account to argue for the stuff view: he takes the account to imply that M-attributes “admit of quantization”, namely, that they are “somewhat substance-like, in that varying amounts of them can be doled or parcelled out in a particular instance” (1978, 10).29) I think the quantity account, like the

27) The argument has another problem. The quantity account implies that an M-attribute has parts (that particulars can have), but this does not mean that the parts (or some of them) must be in its instances (i.e., the particulars that instantiate it): Alice and Bob, for example, may instantiate liveliness by having different parts of it without having the parts in them. Incidentally, this means that the above objections to the stuff view do not refute the quantity account. By contrast, the objection to the quantity account given below (§2.2) applies to the stuff view as well, for it would be hard to accept the view without holding the account.

28) I do not think Jespersen himself would hold the quantity account. His remark on concrete mass nouns suggests that he does not take abstract mass nouns to relate to stuff (see note 12).

29) In other words, they have “variable quantifiability” (Levinson 1980, 106).


stuff view, is mistaken. The account assumes that M-determiners have the same meanings whether they combine with concrete or abstract mass nouns. But I do not think ‘more’, for example, has the same meaning in ‘more water’ and ‘more liveliness’. Although the determiner relates to amounts of water in ‘more water’, it does not relate to amounts at all in ‘more liveliness’.

To see this, compare two groups of sentences:

(1) a. Alice has no patience (at all).b. Alice has more patience than Bob.c. Bob has less patience than Ali.

(2) a. Ali has no water (at all).b. Ali has more water than Baba.c. Baba has less water than Ali.

Clearly, (2a) is compatible with neither (2b) nor (2c). The same does not hold for (1a)-(1c). (1a) is compatible with both (1b) and (1c). Suppose that Alice is not patient at all while Bob is even less patient (for example, Alice cannot wait in line for 1 minute while Bob cannot wait even for 30 seconds). If so, one can correctly say, “Alice has no patience at all, but Bob has even less patience.” And one might as well say, “Alice has no patience at all. Still, she has more patience than Bob.” Similarly, a boy might have even less liveliness than one who has no liveliness at all, for a boy might not be lively at all and yet be more lively than someone who is even more apathetic.30)

30) It is the same with mercy (which is also an M-attribute). One might consistently say, e.g., “Rorschach . . . [who] has clear lines divided between right and wrong . . . carries it out to the point of no mercy . . . . Another hero . . . is even more merciless than Rorschach” (Jesky 2009). If this is true, one can correctly say

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There is a significant logical difference, we have seen, between (1a)-(1c), on the one hand, and (2a)-(2c), on the other. The difference arises because the M-determiners in the former do not relate to amounts of stuff. So applying the quantity account to them yields incorrect results about their logical relations. The account takes ‘no’, ‘more’, and ‘less’ to be equivalent to ‘no amount of’, ‘a larger amount of’, and ‘a smaller amount of’, respectively. So (1a)-(1c) can be paraphrased on the account as follows:

(1ʹ) a. Alice has no amount (whatsoever) of patience.b. Alice has a larger amount of patience than Bob.c. Bob has a smaller amount of patience than Ali.

But these cannot be considered correct paraphrases. While (1a)-(1b) are compatible, (1ʹa)-(1ʹb) are not. Similarly, (1ʹa) and (1ʹc), unlike (1a) and (1c), are incompatible.31)

3. M-determiners

M-determiners, we have seen, cannot be taken to relate to amounts of stuff when they combine with abstract mass nouns. If so, what do they mean when they combine with such nouns?

Consider various uses of ‘more’:

“Rorschach has no mercy at all, but the other hero has even less mercy.”31) Note that the same problem does not arise for the quantity account paraphrases

of (2a)-(2c) because (2a) is incompatible with both (2b) and (2c).


(3) a. Alice has more1 patience than Bob. (=(1b))b. Ali has morea water than Baba. (=(2b))c. Alice has moren books than Bob.d. Alice has morec patient than Bob.

While the quantity account takes ‘more1’ (i.e., the ‘more’ in ‘more patience’) to mean the same as ‘morea’ (i.e., the ‘more’ in ‘more water’), I think it has essentially the same meaning or function as ‘morec’, namely, the comparative marker that figures in ‘more patient’. In this view, it derives from ‘morec’ much as the abstract noun ‘patience’ derives from its adjectival base, ‘patient’ (so ‘more patience’ can be considered the noun version of ‘more patient’). Let me explain.

It is usual to take ‘more’ to be ambiguous in (3b) and (3c). It relates to numbers of books in (3c), and amounts or quantities of water in (3b). That is, ‘moren’ is the comparative form of ‘many’, and ‘morea’ that of ‘much’. If so, it is an accidental feature of English that it uses the same word as the comparatives of both ‘many’ and ‘much’, as it is an accidental feature of English that it uses ‘bank’ for both the so-called money banks and river banks, and ‘warm’ and ‘cold’ for both physical features and personality traits.32) Some languages, as Jespersen (1924, 198) notes, have different words corresponding to ‘more’ in their translations of ‘more books’ and ‘more water’. English itself has two contraries of ‘more’: ‘fewer’ and ‘less’ (which are contraries of ‘moren’

32) Many, if not all, languages use some adjectives (e.g., ‘warm’, ‘cold’) for both physical features and personality traits. This might have to do with the fact that humans develop a close mental association between tactile temperature sensation and feelings of interpersonal warmth and trust, as some studies (e.g.,Williams and Bargh 2008) suggest. Needless to say, this does not mean that the warm personality trait rests on the warm body, let alone that the adjectives have the same meanings in both cases.

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and ‘morea’, respectively). Moreover, English has different phrases that are interchangeable with ‘moren’ and ‘morea’: ‘a larger number of’ and ‘a larger amount of’.

(3d) has another use of ‘more’: ‘morec’. This can be identified with neither ‘moren’ nor ‘morea’, for it does not relate at all to numbers or amounts. It figures in periphrastic comparatives (e.g., ‘more patient’, ‘more lively’) as a device for constructing comparative forms of adjectives. So it has the same semantic function as the comparative morpheme ‘-er’ that figures in inflectional comparatives, such as ‘whiter’ and ‘taller’.33) Clearly, however, neither ‘moren’ nor ‘morea’ can be taken to have the same meaning or function as this morpheme. They are by themselves comparatives of ‘many’ and ‘much’, and the irregular comparatives might be taken to have a latent comparative marker, namely, the counterpart of the morpheme ‘-er’ in ‘a larger number of’ and ‘a larger amount of’.34) So one might imagine a language that is like English except that it has ‘much-er’ or ‘morec much’ instead of ‘morea’.35) These

33) Some adjectives (e.g., ‘lively’) have both inflectional and periphrastic comparatives (e.g., ‘livelier’ and ‘more lively’), and the two kinds of comparatives have no difference in meaning.

34) Some might regard ‘more1’ as the comparative form of the ‘much’ in ‘much liveliness’, but this does not help to explain its connection to the comparative marker in ‘more lively’, which cannot be taken to have the comparative form of the ‘much’ in ‘much liveliness’. And translations of ‘more liveliness’ and ‘much liveliness’ into Korean, for example, do not preserve the apparent relation between ‘much’ and ‘more’ in the English phrases. I think the ‘much’ in ‘much liveliness’ relates to the adverb ‘very’ in ‘very lively’ (see below).

35) So one might take the comparative marker to figure implicitly in ‘morea’ because this is the comparative form of the ‘much’ in ‘much water’. But this does not mean that the marker, like ‘morea’, relates to amounts. The reason that ‘morea’ relates to amounts is not that it has a covert comparative marker, but that it has another covert component (which amounts to the ‘much’ in ‘much water’) that relates to amounts.


quasi-English comparatives have the same composition as the translations of ‘morea’ into some languages (e.g., Korean). The Korean translations of ‘morea’ and ‘more lively’ (or ‘livelier’) have a common component: the comparative marker te.36) Like the Korean te, the English ‘morec’ relates to neither numbers nor amounts.

Now, we can consider the ‘more’ in ‘more patience’ and ‘more liveliness’: ‘more1’. Although it figures as a determiner to combine with common nouns, as in (3a), it cannot be taken to have the same meaning as its determiner cousins: ‘moren’ and ‘morea’. If it means the same as either of these (which are interchangeable with ‘a larger number of’ and ‘a larger amount of’, respectively), (3a) (i.e., (1b)) must be incompatible with (1a): ‘Alice has no patience (at all).’ But it is not (see §2.2). I think ‘more1’ derives from the comparative marker ‘morec’. The abstract noun ‘liveliness’, for example, derives from the adjective ‘lively’, and something has (or instantiates) liveliness if and only if it is lively. Similarly, ‘more liveliness’ derives from ‘more lively’, and something has more1 liveliness if and only if it is morec lively. So ‘more1’ might be considered the determiner version of the comparative marker ‘morec’ that figures in the abstract noun form of ‘morec lively’.

This identification of the determiner as a version of the comparative marker is facilitated by the fact that they figure as homonyms in ‘more lively’ and ‘more liveliness’, but it does not depend on this. The inflectional morpheme ‘-er’ has the same function as the periphrastic marker ‘morec’,

36) They are te man(h)un (‘morea’) and te hwualpalhan (‘more lively’), which result from combining te with man(h)un ‘many, much, a lot of’ and hwualpalhan ‘lively’, respectively. So Korean distinguishes between the uses of ‘more’ in ‘more water’ and ‘more lively’. By contrast, Korean uses the same particle, te, for ‘more’ in the translations of both ‘more lively’ and ‘more liveliness’ (the Korean translation of ‘more liveliness’ is the same as that of ‘being more lively’). For more about the Korean comparative marker, see, e.g., Sohn (1999, 340).

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and they can be considered different manifestations of the same underlying comparative marker. So the determiner ‘more1’ in ‘more1 liveliness’ can be equally considered a version of the comparative morpheme in ‘livelier’, which is a mere inflectional variant of ‘more lively’.37)

We can extend the above account of ‘more1’ to other M-determiners. Like ‘more’, ‘less’ figures both as a determiner and as a comparative marker (as in ‘less lively’), and the determiner ‘less’, on my account, derives from the comparative marker ‘less’. And the other determiners (e.g., ‘some’, ‘much’, ‘little’, ‘a little’, ‘no’) stem from the matching adverbs: ‘somewhat’, ‘very’, ‘not very’ (or ‘not quite’), ‘a (little) bit’, ‘not (at all)’, etc. So to say that Alice has some, much, little, a little, and less liveliness is to say that she is somewhat, very, not very, a little bit, and less lively, respectively, and to say that she has no liveliness (whatsoever) is to say that she is not lively at all.

M-determiners stem from comparative markers (e.g., ‘more’, ‘less’) or degree adverbs (e.g., ‘very’). (Call both M-adverbs for convenience of exposition.) And adjectives that can combine with M-adverbs are called gradable adjectives.38) On the account of M-determiners presented above,

37) So I think one might use, e.g., ‘more smallness’ as the abstract noun form of ‘smaller’. Incidentally, it would be interesting to compare wateriness with water. Having water is different from having wateriness; although ‘watery’ is an adjective deriving from ‘water’, it does not mean having some water but having too much water. Moreover, having more1 wateriness is also different from having morea water. The former is the same as being morec watery, and an area (e.g., Britain) might have more water (in total) but be less watery (or drier) than a smaller area (e.g., Glasgow).

38) Gradable adjectives (e.g., ‘lively’) are adjectives that can take comparative and superlative forms (e.g., ‘more lively’, ‘less lively’, ‘the most lively’) and that can combine with degree adjectives (e.g., ‘very’, ‘too’, ‘so’, ‘quite’, ‘enough’). See, e.g., Quirk et al. (1972, 385). Although Quirk et al. (ibid.) lists ‘as’ with degree adjectives, they also discuss it together with the comparative markers ‘more’ and ‘less’. I think it is closer to these than to degree adjectives. (The superlative


abstract mass nouns can combine with M-determiners because they are based on gradable adjectives. Call it the gradability account.

On this account, it is straightforward to explain the logic of (1a)-(1c). In (1a)-(1b), on the account, the determiners ‘no’ and ‘more’ do not relate to amounts of stuff but figure as versions of the particles ‘not (at all)’ and ‘more’ that figure in (4a) and (4b), respectively:

(4) a. Alice is not patient (at all).b. Alice is more patient than Bob.

And the account analyzes (1a)-(1b) as (4a)-(4b). Now, we can see that (1a)-(1b) are compatible because (4a)-(4b) are. Just as someone might be very short but taller than someone else, so might a girl who is not patient at all still be more patient than an even less patient boy. Similarly, we can explain how ‘Alice has no liveliness whatsoever’ and ‘Alice has more liveliness than Bob’ are compatible: one might not be lively at all and yet be more lively than someone even less lively.

And the gradability account gives a good explanation of why some abstract nouns, unlike others, are mass nouns. Abstract nouns deriving from gradable adjectives (e.g., ‘lively’, ‘vivacious’, ‘vibrant’) can take M-determiners. By contrast, those deriving from non-gradable adjectives (e.g., ‘male’, ‘trilateral’, ‘four-sided’, ‘finite’, ‘infinite’) cannot.39) Neither can abstract nouns with the

forms of gradable adjectives do not directly concern us because the superlative ‘most’ in them does not have an adjective or determiner form that combines with abstract mass nouns.)

39) I think ‘triangular’ is ambiguous. It can mean either (a) having three angles (or sides) or (b) being shaped like a triangle (see, e.g., Online Oxford English Dictionary). (One might take the second sense to derive from the first: being close to having three angles (or sides).) The adjective is not gradable if used in the strict sense, (a), but gradable if used in the loose sense, (b). (In this paper,

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suffix ‘-hood’ (e.g., ‘humanhood’, ‘motherhood’), which derive from other nouns (e.g., ‘human’, ‘mother’). We can explain this difference in terms of the origin of M-determiners: they stem from M-adverbs (e.g., ‘more’, ‘very’).40) M-determiners cannot combine with nouns deriving from other nouns or non-gradable adjectives, for these cannot combine with M-adverbs.

Now, most M-adverbs41) can combine not only with gradable adjectives but also with some verbs: ‘admire’, ‘refine’, ‘satisfy’, etc. Such verbs yield abstract nouns that can combine with M-determiners, as in ‘some admiration’, ‘much refinement’, ‘more satisfaction’, etc. The use of M-determiners when they combine with verb-based abstract nouns can also be analyzed in terms of the matching adverbs: to have some, more, or less admiration for someone is to admire her somewhat, more, or less.42)

I use it in the strict sense, and take the noun ‘triangularity’ not to be a mass noun because the adjective ‘triangular’ (as used for (a)) is not gradable.) Similarly, ‘unique’ can be used as a gradable adjective with a loose sense: being close to being unique. (Thanks are due to an anonymous referee for Philosophical Analysis for noting the complexity of ‘triangular’.)

40) By contrast, the quantity account provides no resources for explaining the difference. So Levinson just classifies abstract nouns according to their suffixes. He in effect identifies abstract mass nouns with “expressions formed from adjectives by appending certain suffixes” (e.g., ‘-ness’, ‘-ity’, ‘-itude’, ‘-cy’) (1978, 11), and holds that such abstract nouns refer to stuffs whether they can combine with M-determiners or not. He holds that those among such nouns that cannot combine with M-determiners (e.g., ‘triangularity’, ‘trilaterality’, ‘three-sidedness’) refer to “quantum” stuffs, which “come in only one ‘size’ package” (ibid., 13). His idea is that triangularity (or trilaterality) is composed of some units, atomic parts of the same size and amount, and that all triangular (or trilateral) figures have exactly one of those units. But this is an incoherent idea. A big triangle composed of several small triangles would have to have in it more than one unit of the triangularity-stuff (or trilaterality-stuff).

41) Or their variants, such as ‘very much’ and ‘not very much’ (which are related to ‘very’ and ‘not very’, respectively). Note that it is an accidental feature of English that ‘very’ can combine with adjectives but not with verbs while ‘a little’ and ‘a bit’ can combine with both. The Korean translation of ‘very’, for example, can combine with verbs as well as adjectives.


Because M-adverbs can combine with verbs as well, it is useful to extend the term ‘gradable’ for them. Then ‘admire’ and ‘refine’, for example, are gradable verbs while ‘believe’ is not. We can then see that abstract mass nouns (e.g., ‘liveliness’, ‘admiration’) derive from gradable adjectives or verbs. So they can combine with M-determiners (e.g., ‘more’), which have abstract uses (e.g., ‘more1’) that differ from their concrete uses (e.g., ‘morea’) because they stem from M-adverbs (e.g., ‘morec’). When they combine with abstract mass nouns, M-determiners figure with semantic functions they inherit from the matching M-adverbs. For example, the determiner ‘more1’ has the semantic function that relates to that of the comparative marker as the meanings of ‘liveliness’ (or ‘refinement’) relate to those of ‘lively’ (or ‘refine’).

4. Abstract mass nouns and comparative relations

Consider (5a)-(5b):

(5) a. Alice has more1 liveliness than Bob.b. Alice is morec lively than Bob.

On the gradability account, (5a) can be analyzed as (5b) because ‘more liveliness’ can be considered the noun form of ‘more lively’ as ‘liveliness’

42) Some nouns deriving from verbs (e.g., ‘satisfaction’, ‘refinement’) have close ties to the adjectives related to the verbs (e.g., ‘satisfied’, ‘refined’) as well. To give a proper analysis of the combination of such nouns with M-determiners, it is necessary to consider their ties to those adjectives as well. For example, to have more satisfaction is to be more satisfied while to give more satisfaction to some people is to satisfy them more. Similarly, to have more refinement is to be more refined, while to make more refinement of something is to refine it more. This phenomenon yields another addition to the variety of uses of M-determiners.

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can be considered the noun form of ‘lively’. If so, one can give a full account of the determiner ‘more1’ by analyzing the semantics of the comparative marker ‘morec’. What is then the semantic function of this?

In English, comparative forms have a complex structure. The periphrastic comparative ‘more lively’ results from adding ‘more’ to ‘lively’. Similarly, the inflectional comparative ‘livelier’ results from adding the suffix ‘-er’ to the adjective. So one might take the meaning of the comparative form of the adjective to reflect its morphosyntactic complexity: it results from combining the semantic function of ‘morec’ (or ‘-er’) with that of ‘lively’. Similarly, one might take comparative relations (i.e., relations comparative forms of gradable adjectives refer to) to be based on the properties gradable adjectives refer to. For example, the relation of being more lively, in this view, can be analyzed in terms of the property of being lively.

I think both views are incorrect. One cannot analyze the comparative relation in terms of a property that only distinguishes the things that instantiate it from those that do not. Neither can one take the meaning of ‘more lively’ to be based on the function of ‘lively’ for distinguishing the things it denotes from those it does not. I think the adjective ‘lively’ has a richer semantic profile not exhausted by its reference to a property. It refers to the property of being lively by way of relating to an underlying relation: being more lively. In this view, the comparative marker ‘morec’ is semantically impotent. It does not make a semantic contribution to the comparative ‘morec lively’; the full semantic profile of the adverb ‘lively’ includes reference to the relation its comparative form refers to.43)

43) In this connection, note that English is rather exceptional in having an overt marking in positive comparative forms (e.g., ‘livelier’, ‘more lively’). Strassen says that “the vast majority of languages” have no overt comparative marking in their counterparts (2013, §3). In Korean, which has the (positive) comparative marker te, it is optional in the translation of ‘A is more lively than B’ (so the


This, to be sure, does not mean that other M-adverbs (e.g., ‘less’, ‘very’), too, lack semantic significance. The comparative ‘less lively’ relates to the converse of being more lively, and ‘very lively’ does not denote something simply because ‘lively’ denotes it. I think the semantics of phrases resulting from combining ‘lively’ with other M-adverbs (e.g., ‘very lively’) can be analyzed in terms of the semantic profile of the adverb, including reference to the comparative relation: ‘very lively’, for example, denotes the things that are more lively than most of the things that are lively (in the relevant domain). Moreover, I think we can analyze the property the adverb relates to (i.e., being lively), too, in terms of the comparative relation: roughly, something is lively if and only if it is more lively than most of the things (in the relevant domain). On this account, the comparative relation lies under the property of being lively, not vice versa.

The account sketched above of gradable adjectives gives a central role to comparative relations. So I call it the relational account. I leave it for another occasion to develop it.44) In the rest of this section, let me elaborate on a key motivation for the account by explaining why the morphosyntactic composition of comparative forms of gradable adjectives cannot be taken to reflect their semantic composition.

Note that the adjective ‘lively’, for example, can figure either (a) with M-adverbs (as in ‘more lively’ and ‘very lively’) or (b) without M-adverb (as in ‘Alice is lively’ and ‘being lively’). So the full semantic profile of ‘lively’, for example, must include not only (a*) semantic features sufficient for its absolute use (i.e., its use without M-adverb) but also (b*) those relevant for its non-absolute uses (i.e., its uses with M-adverbs),

Korean translation has the same structure as ‘A is (more) lively than B’), although it is not optional in the translation of ‘A is more lively.’

44) See my (unpublished).

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including its use in the comparative form ‘more lively’. I think one cannot explain the latter semantic features, (b*), in terms of the former, (a*). For the adjective ‘lively’ figures with much richer semantic features in its comparative forms (e.g., ‘more lively’) than in its absolute use. One might take its semantic features as used in, e.g., ‘Alice is lively’ to be exhausted by reference to the property of being lively, while its semantic features as used in ‘more lively’ must be sufficient to enable the comparative form to attain reference to the relation of being more lively. But the ‘lively’ in ‘more lively’ cannot help to attain reference to this relation if its semantic features are exhausted by reference to the property of being lively, for the relation has a richer profile of instantiation than the property. The instantiation profile of the property just includes which objects instantiate it, and which do not. But that of the relation yields more fine-grained distinctions: among those who are lively, some are more lively than others; among those who are not, too, some are more lively than others. So one cannot construct the instantiation profile of the comparative relation on the basis of the semantic features relevant to the absolute use of the adjective.

Some might attempt to avoid this problem by enriching semantic profiles of gradable adjectives in their absolute use. The attributes they refer to, they might hold, differ from those that non-gradable adjectives relate to in that they admit degrees of instantiation. Unlike being trilateral, being lively is not just instantiated by some things but instantiated by them in different degrees. For example, Alice instantiates the property in a high degree (she is very lively), and Bob in a low

degree (he is just a little bit lively). One might argue that this explains why one can modify gradable adjectives with degree adjectives (e.g., ‘very’, ‘a bit’), which one might take to relate to degrees of instantiation


of M-attributes. And one might argue that gradable adjectives admit comparative markers because these, too, relate to degrees of instantiation of M-attributes. Quirk et al. (1972) give this account when they say that the dual comparative forms (e.g., ‘more lively’, ‘less lively’) relate to “comparison in relation to a higher degree” and “comparison in relation to a lower degree” (ibid., 458). The comparative ‘more lively’, on the account, relates to a relation that holds between two things when one of them is lively in a higher degree than the other. Call it the degree

account.Some might accept this account but supplement it with a further

analysis of the notion of degree of instantiation. The quantity account of M-determiners can be seen to result from combining the degree account with an analysis of this notion: to instantiate an attribute in a higher

degree is to have a larger amount of the attribute (so to be lively in a

higher degree, for example, is to have a larger amount of liveliness). This analysis requires that an M-attribute is something with parts. Price (1953, 36f) gives an analysis of degrees of instantiation that does not require M-attributes to have parts. He analyzes them in terms of determinable and determinate attributes. White (or whiteness), for example, is a determinable (roughly, less definite) property under which fall many determinate (roughly, more definite) properties: pure white, nearly pure white, farther from pure white, farther still from pure white, etc. M-attributes, on his analysis, are determinable attributes the determinates of which are “serially ordered” (ibid., 37). For example, white is an M-attribute because it has determinates that are serially ordered with pure white having the highest rank. Suppose that A is a pure white object and B a nearly pure white object. Then A is white in a higher degree than B, on Price’s account, because (i) they have color properties that are

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determinates of white (i.e., pure white and nearly pure white), and (ii) the determinate color property of A has a higher rank than that of B in the serial order among the determinates of white.

The quantity account, we have seen (§2.2), has a serious problem. And we can see that Price’s account has the same problem. The reason is that the problem arises for their common root: the degree account.

Consider (6a)–(6c):

(6) a. Alice is more lively than Bob. (=(5b))b. Alice is lively (or instantiates liveliness) in a higher degree than Bob.c. Alice is lively.

The degree account analyzes (6a) as (6b). But this is not correct. (6b) implies (6c), for someone who is lively (or instantiates liveliness) in a higher degree than someone else must be lively (or instantiate liveliness). But (6a) does not imply (6c), for someone who is not lively at all, we have noted, might still be more lively than someone who is even more apathetic.45)

We can now see that the quantity account and Price’s have the same problem. They replace (6b) with their analyses of the sentence:

(6) bʹ. Alice has a larger amount of liveliness (or being lively) than Bob. (Cf., (1ʹb))bʺ. Alice instantiates a determinate of liveliness (or being lively) that has

a higher rank than its determinate that Bob instantiates.

Both of these, like (6b), imply (6c).

45) Similarly, someone who is not tall (large, or heavy) at all might be taller (larger, or heavier) than someone who is even less tall (large, or heavy). This raises the same problem for the degree account.


Appendix 1: Stuff and change

On the stuff view about an attribute, the attribute is a stuff so that a particular instantiates the attribute if and only if a part of the stuff identified as the attribute exists inside the particular. A standard objection to this view is that it conflicts with the platonist thesis that attributes are immune to change (the immutability thesis).46) Levinson (1980), who holds the stuff view for a large group of attributes (e.g., whiteness), argues that the view is compatible with this thesis (ibid., 110ff). I do not think this is correct. If whiteness, for example, is a stuff whose existence in particulars are responsible for their being white, the attribute must be subject to change in location.

On the immutability thesis, attributes are not subject to genuine change (i.e., change in the proper sense) although they might undergo putative change, what Peter Geach (1972, 90-92) calls Cambridge change.47) If Alice was white yesterday but black today, we can correctly say “Whiteness was instantiated by Alice yesterday but not today.” This might suggest that whiteness went through change while Alice changed in color. But platonists would hold that the truth of the above statement is not due to a change that whiteness went through, but just to the change in color that Alice went through to have a different relation to the attribute. Whiteness’s ceasing to be instantiated by Alice, in this view, is

46) The objection dates back to Aristotle. See Denyer (1983, 325).47) Geach says that an object O undergoes Cambridge change if “there are two

propositions about O, differing only in that one mentions an earlier and the other a later time, and one is true, the other false” (ibid., 90f). See also Russell (1903/1937, 468), who defines change as Geach’s Cambridge change. As Geach points out, an object that undergoes Cambridge change (e.g., Alice, who remains the same in size while Bob becomes larger than her) might not undergo genuine change. Such an object is said to undergo mere Cambridge change.

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similar to Alice’s becoming smaller than Bob without herself changing in size because Bob changes to become larger than before. We can use the notion of Cambridge change to state the platonist view about Alice’s change in color: when she ceases to be white, she undergoes genuine change in color, but whiteness does not undergo genuine change but only Cambridge change.

If whiteness is a stuff, however, it seems that the attribute would be subject to genuine change. If all white particulars cease to be white, the whiteness-stuff will no longer have a part inside a particular. If so, it seems that whiteness would cease to exist in the stuff view. And the view, it seems, must take the attribute to be subject to change in amount, for the amount of the whiteness-stuff must decrease or increase if some white particulars cease to be white or some black particulars become white

To reconcile the stuff view with the immutability thesis, Levinson (1980, 110ff) proposes that whiteness, for example, is an abstract stuff that is not exhausted by its immanent parts (i.e., the parts inside its instances). In addition to these, he holds, the attribute has a transcendent part: “an infinite, non-depletable amount” of stuff outside its instances (ibid., 111).48) Because this part exists independently of any particulars, he argues, whiteness will continue to exist even if all white particulars get destroyed. And its amount does not change no matter how many particulars come or cease to instantiate it; its total amount is always infinite because of the transcendent part.

But this does not mean that stuffs with transcendent parts can be immune to change. Such stuffs, too, must be subject to change in location because

48) He calls the transcendent part “the quality-pool”, and suggests that it exists in space although it has no definite spatial location (ibid., 111).


their immanent parts have spatial locations, as Bae (1996, 69-80; 1999) argues.49)

Suppose that Alice is presently white and exists in a place, p. Then whiteness, W, must have a part, Wa, inside Alice in the stuff view. If so, the immanent part Wa is inside the place p.50) Now, suppose that Alice becomes black. Then she cannot continue to have Wa inside her and this must cease to exist in p.51) This means that W itself goes through change in location. It exists (partly) in p but will no longer do so. Some might object that W might still exist in p because another white particular might move into p while Alice moves out while becoming black. This is correct, but it does not help to reconcile the stuff view with the immutability thesis. W must move, if it continues to exist in p because one part of it, Wa, withdraws from p while another part, Wb, moves into p (imagine a rotating disk that continues to occupy the same area). Moreover, we might suppose that Alice becomes black while staying in p. In that case, W must completely move out of p.52)

We can reach the same conclusion about the case in which Alice simply moves out of p while no white object moves in. In this case, too,

49) The argument presented below is based on arguments Bae (1996, 69-80; 1999) presents against Fine’s interpretation of Plato’s theory of forms that draws on Levinson’s view of attributes.

50) Levinson holds that M-attributes are “in their possessors” in “the spatial” sense―“one thing being in another if the region occupied by the first is wholly included in the region occupied by the second” (1980, 108; original italics).

51) Levinson proposes two possibilities for Wa when Alice ceases to be white: (i) it ceases to exist; and (ii) it “rejoins” the transcendent part of W (1980, 112). In either case, Wa must cease to be in p.

52) W might continue to exist in p while Alice becomes black (without moving out of p), because some part of Alice might remain white. But we might suppose that no part of Alice remains white while she becomes black. (Note also that the possibility of Alice being black while having white parts raises problems for the main thesis of the stuff view, [S]. See §2.1.)

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W must completely withdraw from p in the stuff view.Note that proponents of the stuff view cannot hold that W undergoes

mere Cambridge changes in location as Alice undergoes real changes in color or location. In their view, unlike in the platonist view, the attribute (which they identify as the whiteness-stuff) has spatial locations―it has immanent parts (e.g., Wa) that exist in the places its instances occupy (e.g., p).53) If so, as we have seen, the attribute must undergo genuine changes in location while its instances undergo certain changes in color or location: it must move out of the place Alice is in, if she either ceases to be white without moving out of the place or moves out of the place without leaving anything white in it.

We can now see a connection between two key components of the platonist doctrine about attributes:

[P1] Attributes are immune to change.[P2] Attributes do not exist (wholly or partly) in particulars.

If whiteness is wholly or partly in Alice when she instantiates it, we have seen, the attribute must be subject to change in location. So those who hold [P1] cannot locate attributes even partly in the places occupied by their changeable instances. They have no choice but to take attributes to be “nowhere”, as Bertrand Russell (1912/1973, 56) does.

53) This does not mean that they must take all parts of the attribute to have spatial locations. Levinson suggests that its transcendent part, too, is in space (see note 48), but some might deny this while accepting the existence of the transcendent part. But the problem arises as long as one holds that the immanent parts have (definite) spatial locations.


Appendix 2: The stuff interpretation of Plato’s forms

Some Plato scholars propose the stuff interpretation of Plato’s forms, the view that Plato conceives of forms as stuffs in his earlier dialogues, including the Phaedo. Denyer (1983) argues that Plato’s theory of forms is not a theory of universals but a theory of “elemental stuffs”, such as gold (ibid., 315), and holds that this interpretation is compatible with the immutability thesis about forms, the thesis that they are immune to change (ibid., 325). Fine (1986), who also takes Plato to regard forms as stuffs in his earlier dialogues, draws on Levinson’s notion of abstract stuff to hold that her interpretation is compatible with the immutability thesis. As Bae (1996; 1999) argues, however, I think their interpretations have serious problems.

In the Phaedo, Plato postulates entities of a third kind, those intermediate between forms and particulars: they (e.g., “the largeness in us”) exist inside the particulars that instantiate the matching forms (e.g., “largeness itself”), and are subject to change―they can either perish or withdraw from the particulars they are in when the particulars cease to instantiate the forms (Phdo./1975, 102d-e). Fine takes Plato to regard the largeness itself as a whole whose parts include a transcendent part as well as intermediate entities (e.g., the largeness in Simmias). On this interpretation, as we have seen (Appendix 1), Plato must take the largeness itself to be subject to change in location.

Denyer explains his interpretation by contrasting the element gold with the gold in a ring as Plato contrasts largeness itself with the largeness in Simmias. Unlike Fine, however, he suggests that Plato denies that the largeness in Simmias is a part of largeness itself. After asserting “The gold in an object is not . . . identical with the element gold as a whole”, he raises a rhetorical question: “need we suppose it as a part of that

34 Byeong-uk Yi

element?” (1983, 325). He suggests that Plato would give a negative answer, and holds that this answer is compatible with the immutability thesis (ibid., 325). If Plato denies that the largeness in Simmias is a part of largeness itself, however, there is no reason to take him to regard this form as a “whole” (with proper parts). I think Denyer might confuse the notion of gold as chemical element and that of gold as stuff. One might regard gold as a non-divisible chemical element. This view (in which the gold in a ring is not a part of the element) is different from the view that the element is some stuff (i.e., a whole divisible into parts). Those who hold the second view must answer Denyer’s question in the affirmative, and conclude that gold is divisible and subject to change in location. The same holds for largeness itself. Incidentally, Denyer argues that given the discovery of gold atoms in modern chemistry, one would have to identify the element gold with some stuff, viz., the mereological sum of gold atoms (ibid., 326). I see no reason that those who consider gold an indivisible element would have to do so. They might well hold that the element is a universal instantiated by gold atoms, aggregates thereof, etc.

5. Acknowledgments

The work for this paper was supported in part by a SSHRC Insight Grant [Grant No. 435-2014-0592], which is hereby gratefully acknowledged. I wish to thank E. Bae, M. Durand, A. Harmer, B. Linsky, T. McKay, A. Morton, J. Pelletier and three anonymous referees for Philosophical

Analysis for useful discussions and comments on previous versions. Needless to say, they are not responsible for any errors or infelicities in this paper.


References

Aristotle (Cat./1963) Categories and De Interpretatione, translated with notes and glossary by J. L. Ackrill, Oxford: Oxford University Press.

Bae, E. (1996) Soul and Intermediates in Plato’s Phaedo, Ph.D. Dissertation, UCLA.

. (1999) “Are Plato’s forms stuffs”, paper presented in the Eastern Division Meeting of The American Philosophical Association, April 2, 1999.

Barner, D. and J. Snedeker (2005) “Quantity judgments and individuation: evidence that mass nouns count”, Cognition 97, pp. 41-66.

Bloomfield, L. (1933/1984) Language, New York, NY: Holt, Rinehart and Winston; reprinted, Chicago, IL: University of Chicago Press, 1984.

Denyer, N. (1983) “Plato’s theory of stuffs”, Philosophy 58, pp. 315-327.Fine, G. (1986) “Immanence”, Oxford Studies in Ancient Philosophy 4,

pp. 71-97.Geach, P. T. (1979) Truth, Love and Immortality, London: Hutchinson.Goodman, N. (1951) The Structure of Appearance, Cambridge, MA:

Harvard University Press.Jesky, D. (2009) “Watchman”, http://www.theamerican-guardian.com/

2009_07_01_archive.html, July 26, 2009 [retrieved on 2010-04-08].Jespersen, O. (1924) The Philosophy of Grammar, London: George Allen

& Unwin Ltd.Kim, Y.-W. et al. (eds.) (2011) Plurality in Classifier Languages, Seoul:

Hankookmunhwasa.Levinson, J. (1978) “Properties and related entities”, Philosophy and

Phenomenological Research 39, pp. 1-22.

36 Byeong-uk Yi

. (1980) “The particularization of attributes”, Australasian

Journal of Philosophy 58, pp. 102-115. . (2006) “Why there are no tropes”, Philosophy 81, pp. 563-

579.Mill, J. S. (1891/2002). A System of Logic: Ratiocinative and Inductive,

reprinted from the 1891 edition, Honolulu, HI: University Press of the Pacific, 2002.

Pelletier, F. J. and L. K. Schubert (2003) “Mass expressions”, in D. Gabbay and F. Guenthner (eds.), Handbook of Philosophical Logic, 2nd ed., Vol. 10, Dordrecht: Reidel, pp. 249-336.

Plato (Phdo./1975) Phaedo, translated with notes by D. Gallop, Oxford: Oxford University Press.

. (Parm./1996) Parmenides, translated by M. L. Gill and P. Ryan, Indianapolis: Hackett.

Price, H. H. (1953) “Universals and resemblance”, Chapter 1 of his Thinking and Experience, London: Hutchinson’s University Library, 1953; reprinted in M. J. Loux (ed.), Metaphysics: Contemporary

Readings, London: RKP, 2001, pp. 20-41.Quine, W. V. (1960) Word and Object, Cambridge, MA: The MIT Press.Quirk, R. et al. (eds.) (1972) A Grammar of Contemporary English, New

York, NY: Seminar Press.Russell, B. (1903/1937) The Principles of Mathematics, Cambridge:

Cambridge University Press; 2nd ed., London: Allen & Unwin, 1937.

. (1912/1973) The Problems of Philosophy, Home University Library; reprinted, Oxford: Oxford University Press, 1973.

Sohn, H.-M. (1999) The Korean Language, Cambridge: Cambridge University Press.


Strassen, L. (2013) “Comparative constructions”, in Dryer, M. S. and, Haspelmath, M. (eds.), The World Atlas of Language Structures Online, Leipzig: Max Planck Institute for Evolutionary Anthropology, Chapter

121 [Available online at http://wals.info/chapter/121, Accessed on

2017-06-10]. Williams, L. E. and J. A. Bargh (2008) “Experiencing physical warmth

promotes interpersonal warmth”, Science 322, pp. 606-607.Yi, B.-U. (2009) “Chinese classifiers and count nouns”, Journal of Cognitive

Science 10, pp. 209-225; reprinted in Kim et al. (2011), pp. 245-264. . (2011a) “What is a numeral classifier?”, Philosophical Analysis

23, pp. 195-258; partially reprinted in Kim et al. (2011), pp. 1-51. . (2011b) “Afterthoughts on Chinese classifiers and count nouns”,

in Kim et al. (2011), pp. 265-282. . (2014) “Abstract nouns and resemblance nominalism”, Analysis

74, pp. 622-629. . (forthcoming) “Nominalism and comparative similarity”, Erkenntnis,

forthcoming. . (unpublished) “Mass nouns, gradable attributes, and comparative

relations”, unpublished manuscript, Department of Philosophy, University of Toronto.

Department of Philosophy, University of TorontoDepartment of Philosophy, Kyung Hee UniversityEmail: [email protected]

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