The Carleton University 

Student Journal of Philosophy 
 

Vol. 16, No. 1, Fall 1994

Helen Cartwright, Mass Nouns, and Individuation

Leslie Elliott

Queen's University
 
Copyright1994 The Carleton University Student Journal of Philosophy


 Contents

 The works by Helen Morris Cartwright that I will be examining span 19 years, from 1965 to 1984. The articles clearly demonstrate one of Cartwright's contributions to metaphysics and the philosophy of language: her theory that mass terms individuate. Cartwright argues that the grammar of a mass noun indicates an individuating standard much like a count noun does; the grammar of a mass noun indicates a kind of measure indicated by Cartwright's notion of quantity.
    I will begin by providing a brief background concerning count and mass nouns: their syntactical differences, and the semantic issues that arise from their use. From here I will explore Cartwright's own project, beginning with her 1965 article, "Heraclitus and the Bath Water." Then I will look more closely at Cartwright's use of the term 'quantity' to designate the individuating nature of mass nouns. Cartwright relies on an analogy with sets to demonstrate how mass nouns individuate, which I hope to show is untenable. I will then compare Cartwright's quantities with plural reference, and again hope to show that an analogy with pluralities cannot suffice to demonstrate the individuating nature of mass nouns, although the move to plural reference likely has its advantages outside of Cartwright's theory. Ultimately Cartwright seems to rely on reference as a means for mass nouns to individuate; a position which I hope to show is indefensible.
    To begin, it may be helpful to describe some of the primary differences between mass nouns and count nouns. Syntactical differences are the most obvious and the least controversial: count nouns (like apple, ring, or dog) can occur in a phrase preceded by a number, while mass nouns (like gold, water, or coffee: "matter" generally speaking) normally cannot. Thus it is grammatical to say "five apples" but "five waters" will not do. Further, count nouns can take the plural modifiers 'many,' 'few,' and so forth, and singular modifiers like 'an', while mass nouns cannot. On the whole, mass nouns do not have different forms in the singular and the plural, while count nouns often do. Although there are exceptions to the above cases, they generally serve to mark the syntactic distinctions between count and mass nouns.1
    Although the syntactical differences between mass and count nouns may seem relatively straightforward, semantic differences concerning mass and count nouns are not so obvious. In particular, whether mass terms individuate "objects" in the same way that count nouns do is much contested. Cartwright argues, in the articles that will be discussed below, that in fact mass terms are semantically equivalent with logical terms involving variables. These terms, she argues, have values, and individuate particulars through their use. Importantly, Cartwright is making an ontological claim concerning what is denoted by mass terms: the objects of mass terms occur in the world as particulars.
    Concerning Cartwright's use of mass nouns, she notes:
...I shall say that a word or phrase has the syntax of a mass noun only if, in addition to its appearance in applied amount terms, it regularly occurs where 'water' appears in sentences like
(1) I'll have some (Sm) more water,

(2) This is as much water as that,
(3) That water is some of this,
(4) This is the same water as that.2 
It is from this base that Cartwright begins her project and attempts to demonstrate the individuating nature of mass terms.
    In her 1965 article, "Heraclitus and the Bath Water," Cartwright tries to show, as mentioned, that there are values for mass terms, and that these values ultimately result in the individuation of such things as gold or water. To demonstrate this thesis, Cartwright begins by analyzing some common sentences which contain mass nouns. On the first page of "Heraclitus and the Bathwater," Cartwright quotes P.T. Geach and notes that, according to the received view:
(1) Heraclitus bathed in some river yesterday, and
bathed in the same river today;
is equivalent to:
(2) Something (or other) is a river, and
Heraclitus bathed in it yesterday, and
Heraclitus bathed in it today;
which is also equivalent to:
(3) For some x, x is a river, and
Heraclitus bathed in x yesterday, and
Heraclitus bathed in x today.
By "parity of reasoning," Cartwright notes,
(4) Heraclitus bathed in some water yesterday and
bathed in the same water today;
is equivalent to:
(5) Something (or other) is water, and
Heraclitus bathed in it yesterday, and
Heraclitus bathed in it today;
which is equivalent to:
(6) For some x, x is water, and
Heraclitus bathed in x yesterday, and
Heraclitus bathed in x today.3
    In a discussion concerning the ontological basis of mass nouns, Cartwright's choice of words and variables in the above sentences is telling. First, the equivocation of a singular entity (of sorts) -- a river -- with a mass term -- water -- is not yet obvious, although the sentences are grammatically correct. Second and correlatively, in (5) we see: Something or other is water, and Heraclitus bathed in it yesterday, and Heraclitus bathed in it today. It is not clear at this stage what Cartwright means by "it" in this sentence; that is, what she means when she designates a mass term by the singular "it". This idea will be more fully developed through a closer look at Cartwright's work, and it will soon become obvious that Cartwright is not simply employing a term common to everyday speech to denote mass terms; her use of "it" here belies a more fundamental belief about the ontology of such concepts.
    Cartwright notes an immediate problem with using statements (5) and (6) as equivalent to (4): because of the ambiguity of the phrases, it is not clear that Heraclitus bathed in exactly the same water today as yesterday.4  She proposes the use of the word 'some' as an article, and is careful to note that she is not advocating the use of the unstressed 'some' (Sm). In this way we have:
(5) Something (or other) is some water, and
Heraclitus bathed in it yesterday, and
Heraclitus bathed in it today.5 
    In (5), 'some' is not to be understood as it is used in the phrase, "Some people are friendlier than others." Instead, "some" in (5) is stressed, resulting in the "it" in the sentence to be understood as "the same water"; 'some' is to be used as an indefinite article, akin to 'a' or 'an'. In this way, the phrase "some water" is grammatically equivalent to the phrase "an apple". This use of 'some' Cartwright notes, is particular to mass nouns and plural count nouns.6  Cartwright's later reliance on pluralities to describe what is referred to by mass nouns is alluded to here, and will be discussed later. For now, it is useful to ask just what 'some' individuates, such that x as some water may be different from y as some water.
    Cartwright attempts to answer this question by using a count noun to individuate terms like 'water' and 'gold'.
    We can suppose that "some special individuating standard" is some standard according to which an ordinary count noun applies -- or an ordinary phrase with a count noun as head -- or, at any rate, some word or phrase which is no more extraordinary than the language of chemistry...7 
    Cartwright notes that a count noun of this sort will be something on the order of "amount" which, she notes, "...applies with all the stability and precision of the phrase 'some water'."8 Again ambiguity creeps in: two glasses of water may be the same amount of water, but may fail to be the same water. Cartwright recognizes this, and notes that
...just as the same number of people might not be the same people, so the same amount of water might not be the same water; just as in the former case two things then bear a certain relation to one another, so in the latter case two things bear that relation to one another in virtue of which they may be said to be one amount of water.9
    In her 1979 article, "Quantities," Cartwright strives to clarify just what these 'amounts' of water must be.
    In "Quantities," Cartwright explores the difference between count nouns and mass nouns and whether, in particular, mass nouns can be said to individuate. This paper is a logical extension of "Heraclitus and the Bath Water," where Cartwright introduces an individuating phrase for mass nouns ('amount') without fully exploring this concept.
    Cartwright begins "Quantities" by rejecting Strawson's statement that
[t]he general question of the criteria of distinctness and identity of individual instances of snow or gold cannot be raised or, if raised, be satisfactorily answered.10
    Cartwright looks to count nouns to demonstrate what she feels is a truth about mass nouns: that they do individuate. While a term like 'cat' necessarily denotes one cat, and 'cats' denotes a plurality of cats, so too does 'gold' individuate gold. Obviously count and mass terms do not individuate in quite the same way; while 'cat' individuates one specific, whole, cat, "...the grammar of a mass noun indicates...measure."11 In this way the term 'bronze' provides a measure, which is why we can understand the sentence, "The bronze that comprises the statue," without prefacing 'bronze' with an adjunct like 'piece'. However, the individuating nature of mass nouns is not simply found in measurements of stuff, according to Cartwright; she thus introduces the term "quantity" and distinguishes this sense of quantity from mere amounts.
    Cartwright notes, "...since you and I might have the same amount of gold though not the same gold, the gold in my ring is not in this sense a quantity."12 Here the individuating nature of quantities can be seen. Quantities are more than mere measurements since they individuate specific instances of water, gold, flour and the like. Thus,
x is a quantity of ß if and only if, for some y, x and y are comparable with respect to the amount of ß each contains, and x contains nothing other than ß. Further, with respect to the amount of stuff x and y contain, they are identical or one is greater and the other less.13
    Cartwright explicates her notion of quantities through a discussion of sets. Sets, she notes, allow us to say what there is one of: a plurality of individual entities. What is needed, she argues, is such a device for mass nouns; hence
A set of cats contains so many cats; that gold is so much gold. It is a certain quantity -- that is, amount -- of gold in the sense in which our cats are a certain number of cats. We need not suppose it is a piece, lump, globule, or any other such thing...the general criteria of distinctness and identity of quantities of gold are those of gold...14
As a cat in a set of cats cannot, for instance, be cut in half and still be that cat, so too quantities cannot grow or shrink and still remain the same quantity. What is left is, nonetheless, a quantity of something, but not the original quantity. As sets can have subsets, Cartwright argues, so quantities can have subquantities. For example, we can consider the fairly large set that contains all Homo Sapiens, and within it examine the subset of Homo Sapiens living in Kingston, Ontario. We can subdivide the set even further still, to consider the subset of Homo Sapiens in this room. In regards to quantities, Cartwright notes, they too can be subdivided:
[m]y claim is that there is a non-empty set Q, of quantities of coffee, each of which contains some of the coffee in my cup and one of which contains all of it.15
    Cartwright notes an obvious disanalogy between sets and quantities; namely, that quantities of stuff have no unique measurement for each subquantity, while sets do. In the case of sets, it is necessary that there be a number of singular entities of some sort to comprise the set: five cats, for instance, to comprise a set of cats, or ten apples to comprise a set of apples. In the case of Cartwright's 'quantities,' it is not clear what comprises this 'set'. Recall that Cartwright wants to allow for subquantities as we allow for subsets; however, if quantities are more than mere measurements, what comprises a quantity at all, in order that it may be divided into subquantities? What, that is, is the singular entity that is multiplied in some sense to make a quantity? Using the example of water, for instance, it is not at all clear how Cartwright's reliance on the set analogy pertains: unlike individual cats comprising a set of cats, we don't seem to have similar mass-term entities -- waters, for instance -- to comprise a quantity of water.
    The identity of a cat is relatively clear-cut; the identity of a quantity of water is less so, if at all. Moreover, even accepted units of measurement cannot be counted on to distinguish quantities from one another: weight, mass and volume are relative to the location (so to speak) of the measurements. In this way, it is unclear how we can understand Cartwright's notion of quantity which is, she notes, an instance of an amount, when there are discrepancies between amounts and measurements. Is there one amount for measuring quantities? A notion like this seems necessary for understanding, for example, the overall set of quantities of water. If there is no smallest quantity, how do we derive an individuating standard from quantities at all?
    Up to this point, Cartwright has been arguing that mass reference is closely analogous to talk of sets: a set of cats is similar to a quantity of gold. Yet how do we derive one "set" from something whose components are not precisely identifiable? Cartwright attempts to resolve this problem in "Amounts and Measures of Amount."
    Cartwright furthers her discussion of the logical significance of the syntax of mass nouns in "Amounts and Measures of Amount". She describes units of water or gold as singletons of water or gold, and asks us to assume "...that there is a set Q whose members are the contents of each of the buckets [of water]..."16 A singleton of Q is one quantity of water. Each quantity has the value of m, allowing that each subset of Q can be measured in a standard way. Importantly, m is a measure function on a calculus of individuals;17 that is, of each individual quantity of water. Again the question is raised: how can we have an individual quantity of something not standardly measurable? Where are the borders for a quantity drawn?
    An obvious candidate for the value function of a quantity is atomic units. One molecule of H2O, perhaps, could be one quantity of water. There are problems, however, with resorting to atomism in this way, which Cartwright makes clear. Since our measurement for quantities is additive (m), molecules (or atoms) must be the smallest amounts of quantities of water. Yet is unclear whether one H2O molecule is minimal in amount. Further, to describe a single H2O molecule as a measurement of water seems wrong. How could we measure impure water, for instance? More puzzling is how an "atomic" view would measure coffee, or other mixtures.
    Cartwright recognizes these problems with atomism, and notes that "[q]uantity inclusion cannot, I think, be defined by recourse to atoms..."18  If this is so, then what would comprise a quantity of water? Cartwright considers an alternative to atomism:
...we can suppose the elements of the domain of m [units/singletons of water] are the occupants of spatio-temporal regions about points of space time.19
    Unfortunately, these space-time units would be subject to the same discrepancies as other methods of measurement. If the temperature is lowered, for example, the value of the quantity may be lowered, since it occupies less space. Yet the actual quantity has not really changed. Space-time units, then, display the same deficiencies as other units of measurement, and cannot be considered absolute for measuring quantities.
    Although we don't appear to have an unarbitrary, absolute way of measuring water, flour and the like, we nonetheless can understand statements like Cartwright's "[e]very bucket contains as much water as every other."20 Although we cannot express the full domain of quantities precisely, Cartwright argues, there are nonetheless unit quantities of stuff. Importantly, these unit quantities are arbitrarily selected, based on nothing more than the kind of stuff being referred to.
    Anything referred to through the use of a mass noun is a quantity of stuff. Since there are no natural least unit quantities of, say, coffee, we specify individual units of coffee through our reference to a measured amount of it. In this way we can order quantities by kind. When we compare different kinds of stuff and try to linearly order them, however, more needs to be said to qualify our ordering. Are we discussing weight, for example, or volume? Regardless, units of stuff are arbitrary; they are "right on the surface," they are what is referred to.
    Considering this thesis of Cartwright's then, in the realm of her set analogy, we see again the obvious difference between sets and quantities. Namely, the components of quantities are arbitrary, while the components of, say, a set of cats are the cats. And this, according to Cartwright, is how mass terms individuate. Recall:
Identical cats are one -- one cat or one set of cats. "One cats" like "one gold" is ungrammatical; but the adjunct "set" -- unlike "breed" or "litter" -- furnishes a device tailor-made for saying what there is one of...21
    Similarly with quantities:
...there is one thing which that gold is or constitutes; all that is needed to say what that one thing is a tailor-made device like "set of"...[i]t is a certain quantity...22
    Despite the qualifications that have been made to Cartwright's notion of quantity, however, problems still remain. This can be seen most clearly in the quotes mentioned directly above, where quantities and sets are said to indicate individual entities.
    Recall that Cartwright's aim in introducing her notion of quantity is to explain the ontological status of what is referred to by mass nouns. Quantities are individual objects, "out there" in the world. To see this, she asks us to compare quantities with sets. The identity of a set, we have seen, is much clearer than that of a quantity: a set's identity is determined by its members, the five cats. The identity-criteria of quantities, conversely, is arbitrary. With sets, however, the leap to an individual entity (ontologically speaking) is dubious; similarly it is not clear how quantities could achieve ontological individuation.
    Simply because I have logically defined a set does not mean I have ontologically defined one object. For example, our set of cats, logically defined, is one logical object. When we consider our set of cats in the world, however, we don't have one entity; instead, we have just five cats, contingently grouped together. In turn, it is unclear how quantities, as analogous with sets, could individuate ontological objects either. Yet recall that this is the purpose of Cartwright's exercise:
...I have, in effect, assumed the legitimacy of something like [Russell's theory of quantity] in defending the ontological status of things which are, for example, quantities of water...23
    At best, instead, we seem to have one grammatical subject, which falls short of Cartwright's higher ontological aims.24 
    Cartwright may indeed recognize the deficiencies in the set/quantity analogy; in her 1975 article, "Some Remarks About Mass Nouns and Plurality," she moves away from discussing sets as analogous with quantities, and moves to pluralities.
    Cartwright asks us to consider the following sentences containing mass nouns (A) with sentences containing plural count nouns (B):
 
  (A) Water is a fluid. 
Water is fluid (colorless). 
Water flows. 
Lamb is scarce (plentiful, disappearing). 
Petroleum is various in origin. 
Fuel is a necessity.
(B) Lions are a carnivore. 
Lions are carnivores. 
Lions like red meat. 
Lions are scarce (numerous, disappearing, widespread). 
Apples are various in origin. 
Shoes are a necessity.25
Cartwright hopes to show that the important difference between mass and count nouns is in their grammatical structures, not in the semantics of the terms.
    It is clear in the examples above, that mass nouns appear to have much in common with some plural count nouns. Cartwright goes on to note that (A) and (B) differ from
 
  (C) This water is frozen. 
The wine in the cupboard is fast disappearing.
and
 
  (D) The lions in the cage like red meat. 
These apples are various in origin.26
    In (C) and (D), Cartwright feels, we are finally "getting somewhere" in our discussion of mass nouns. Briefly, Cartwright notes that the mass nouns in (A) are "weasel words," "there is something primitive or archaic" about them.27
    In the sentences in (A), Cartwright notes, we cannot speak of the same water or the same eggs. Prefacing the phrases with "all" won't work either; we don't necessarily mean that all snow is white when we say, "Snow is white." Similarly with plural count nouns: it is possible, she hypothesises, that there are herbivore lions wandering about; nonetheless, we still say "Lions are carnivores." Ultimately both unmodified mass and plural count nouns do not bear fruit in a discussion concerning the ontology of those things being considered, Cartwright notes. Instead we must begin with complex cases like (C) and (D) in order to understand the role of count and mass nouns in our language.
    In "Some Remarks About Mass Nouns and Pluralities," Cartwright attempts to show the semantic similarities between mass nouns and plural count nouns, all the while relying on her notion of quantities. She concludes, as mentioned, with the thesis that we must investigate cases like (C); if we rely only on unmodified mass nouns like those in (A) we will find "...no obvious connection between such constructions and the sophisticated apparatus of quantification theory,"28 and we will be left investigating phrases without certain identifiable objects of reference. The same holds true, Cartwright notes, regarding plural count nouns. Cartwright bases her argument in "Parts and Partitives: Notes on What Things are Made Of," on these beliefs; most notably we see Cartwright's belief that we must consider modified cases of mass nouns and plural count nouns like those in (C) in order to make sense of logical questions concerning such terms.
    Cartwright defines a partitive construction as one which distinguishes a part from a whole. For example, the phrase "some of the coffee" is a partitive construction. Further, where the unstressed 'some' and 'some of' appears and can be replaced with a partitive noun with 'of' (for example, 'cup of coffee'), the result is a nominal partitive.29 Constructions of mass and count terms which preface the mass or count term with modifiers like 'this', 'some (sm)', 'one', 'many', 'all' and the like are nominal partitives. Concerning mass nouns in particular, those prefaced with 'ounce', 'cup', or 'piece' of the gold are part-whole partitives, while those simply referring to an ounce of gold are non-part-whole partitives. Further,
...both sorts of nominal partitives occur with an article or a quantifier, and with 'the' or 'this' and perhaps a restrictive clause, they form referential phrases which are non-singular.30
This is in line with Cartwright's earlier insistence on using modified forms of mass nouns in order to discover fundamental aspects about them. Yet we have not lost sight of quantities here: subquantities are like parts, and fall in the realm of part-whole partitive relations. As the brother of the brother of the brother of John is John's brother, so too a part of a part of a part of this water is a part of (or subquantity of) this (quantity of) water. In either case we have a unique referent, according to Cartwright, and seen in light of her previous remarks concerning quantities, a unique particular being referred to.
    To bring Cartwright's remarks concerning the syntactical nature of mass nouns in line with her general aim of affirming the individuating nature of mass nouns, then: Cartwright began by affirming the individuating nature of mass nouns through her notion of quantity. Again, it is the ontological nature of those things being referred to by mass nouns that Cartwright is concerned with. Quantities may be divided into subquantities. For both, there is no standard unit of measurement. Quantities and subquantities are measured arbitrarily; they are determined by what is being referred to. I attempted to show that Cartwright's quantity/set analogy as a means of showing how quantities individuate will not work: neither quantities nor sets show that what is being referred to is an ontological individual.
    Cartwright's next move to plural reference seems more fruitful. When I consider my cup of water, although I may grammatically refer to it, I seem instead to be referring to a bunch of stuff. I can pour half of the contents of my cup on the floor, and still have some stuff left. Yet I don't have half of one thing left, I just have half as much stuff as I started out with. Cartwright, however, goes beyond this simple analogy with plural reference, in her insistence that what is referred to by a mass noun is an ontological particular.
    As was the case with sets, so too with plural reference: when I refer to 'those birds' I am not, ontologically speaking, referring to one thing. There is no natural unity to the group of birds which allows that one object, "out there" in the world, is being referred to. I am grammatically referring to one collection of individual objects; "That is a big group of birds," for example. Yet there is nothing binding the collection of individual birds together as a single object: they can disperse and in an important way nothing is destroyed. I grammatically grouped the birds together as one, yet my grouping the birds together is wholly a contingent matter. Another example is families: we can refer to the Smiths and talk about them as a single unit, but moving outside of grammar we just have Susan, Beth and John. Susan, Beth and John are being referred to, not one single entity.
    So too with quantities. What single thing is being referred to when we discuss water? Cartwright argues that it is a collection (quantity) of water (subquantities). But if a quantity is a collection of subquantities, it seems that, at most, we are referring to the individual subquantities of stuff. As I refer to Susan, Beth and John when I talk about the Smiths, so we refer to subquantities a, b, and c when we talk about the glass of water. However, subquantities and quantities generally are whatever is being referred to; they are arbitrarily determined. How, then, do they individuate?
    What is left, then, is that quantities individuate through reference. By referring to some water I am individuating an ontological particular through my reference to the water. I certainly am using a grammatical particular: I am talking about this glass, ounce, puddle, even quantity, of water. That I am referring to an ontological particular, however, is not evident. Moreover, the fact that, through my reference I am individuating something, seems dubious.
    I may make reference to nothing at all when I speak. Perhaps I am telling a story about my day, and in an effort to get a few more laughs I refer to a strange bus driver who never actually existed. We may talk then, of objects, without referring to anything at all. Although this is not quite the case with Cartwright's quantities (since she is talking about the water in the glass) it does begin to cast doubt on what reference does, more generally.
    A more immediate problem for Cartwright is the case where we refer to some thing grammatically, without referring to one thing ontologically. Again recall the Smiths. The idea that plural reference has some ontological significance, we saw, is dubious at best. Even when we take quantities out of the realm of plural reference, however, the more general problem concerning the role of reference remains.
    When I talk about the Smiths it is not evident that I am referring to one ontological subject, despite my grammatical reference to one thing. Similarly with quantities of stuff: when I refer to this water, it is not clear that I am referring to one thing. This will become clearer, perhaps, by looking at the case where a grammatical subject is referring to an ontological subject.
    When I speak of this mouse, it can be argued that I am referring to one particular thing. Mice have natural "boundaries" which make them singular entities. They exist as individual things. This does not appear to be the case with stuff. My glass of water can be spilled, part of it can evaporate, some of it may be drunk. Yet the water still exists; it is just scattered, or reduced. The same cannot be said of the mouse; it cannot be scattered in any way and still remain the mouse. When viewed in this way, it is unclear how stuff can be considered in the realm of individuals at all. Individuals must be unified in order to be considered as individuals. Stuff, on the other hand, need not be. Cartwright's claim concerning the individuating nature of mass nouns seems wrong-headed from the start: viewing the objects of mass nouns as individual objects would require such a complete revamping of our notion of individuals that the concept would make little sense at all.31
    Perhaps, as Laycock has argued, it is Cartwright's dependence on the "ontology of objects," whereby all things exist as individuals, that her theory runs into problems.32 It would seem that Cartwright's reference to pluralities looked promising for reasons already mentioned. Unfortunately Cartwright falls back on her insistence that matter exists as individuals. Matter exists, yet it seems instead to exist as stuff: as water, gold, flour or coffee. Perhaps as Laycock has argued we need to move away from our belief that everything exists as individuals, in order to understand what is referred to by mass nouns. Something like this surely seems likely; Cartwright's insistence to the contrary appears untenable.
 

Endnotes

 1 See F.J. Pelletier, "Non-Singular Reference: Some Preliminaries," Mass Terms: Some Philosophical Problems, ed. F.J. Pelletier (Dordrecht, Holland: D. Reidel, 1979), pp. 1-14 for a more detailed analysis of mass/count noun distinctions, and how these distinctions compare with sortal/non-sortal distinctions.  [Back to text]

 2 Helen Morris Cartwright, "Amounts and Measures of Amount," Mass Terms: Some Philosophical Problems, ed. F.J. Pelletier (Dordrecht, Holland: D. Reidel, 1979), p. 179.  [Back to text]

 3 Helen Morris Cartwright, "Heraclitus and the Bath Water," Philosophical Review 74 (1965), 466.  [Back to text]
 
 4 Ibid., p. 468.  [Back to text]

 5 Ibid., p. 469.  [Back to text]

 6 Ibid., p. 472.  [Back to text]
 
 7 Ibid., p. 475.  [Back to text]

 8 Ibid., p. 480.  [Back to text]

 9 Ibid., p. 484.  [Back to text]
 
 10 P.F. Strawson, "Particular and General," Proceedings of the Aristotelian Society LIV (1953-54), 242 as quoted in Helen Morris Cartwright, "Quantities," Philosophical Review 79 (1970), 26.  [Back to text]

 11 "Quantities," p. 27.  [Back to text]

 12 Ibid., p. 28.  [Back to text]

 13 Ibid., p. 29 and p. 38.  [Back to text]

 14 Ibid., p. 28.  [Back to text]

 15 Ibid., p. 31.  [Back to text]

 16 "Amounts and Measures of Amount," p. 183.  [Back to text]

 17 Ibid., p. 185.  [Back to text]

 18 Ibid., p. 187.  [Back to text]

 19 Ibid., p. 187.  [Back to text]

 20 Ibid., p. 182.  [Back to text]

 21 "Quantities," p. 27.  [Back to text]

 22 Ibid., p. 28.  [Back to text]

 23 "Amounts and Measures of Amounts," p. 180.  [Back to text]

 24 See Henry Laycock, "Theories of Matter," Mass Terms: Some Philosophical Problems, ed. F.J. Pelletier (Dordrecht, Holland: D. Reidel, 1979) for more on Cartwright's use of sets as analogous with quantities.  [Back to text]

 25 Helen Morris Cartwright, "Some Remarks About Mass Nouns and Plurality," Mass Terms: Some Philosophical Problems, ed. F.J. Pelletier (Dordrecht, Holland: D. Reidel, 1979) , p. 37.  [Back to text]

 26 Ibid., p. 41.  [Back to text]

 27 "Some Remarks About Mass Nouns and Pluralities," p. 42.  [Back to text]

 28 "Some Remarks," p. 42.  [Back to text]

 29 "Parts and Partitives: Notes on What Things are Made Of," Synthese 58 (1984), 258.  [Back to text]

 30 Ibid., p. 267.  [Back to text]

 31 See Henry Laycock's "The Concept of an Ideal Language" (unpublished) and his "The Foundational Science of Goo" (unpublished) for more on not considering matter as individual objects.  [Back to text]

 32 Laycock, "Theories of Matter."  [Back to text]

Bibliography

Cartwright, Helen Morris.  "Amounts and Measures of Amount." Mass Terms: Some Philosophical Problems.  Ed. F.J. Pelletier.  Dordrecht, Holland: D. Reidel, 1979.

---.  "Heraclitus and the Bath Water." Philosophical Review 74 (1965).

---.  "Parts and Partitives: Notes on What Things Are Made Of." Synthese 58 (1984).

---.  "Quantities." Philosophical Review 79 (1970).

---.  "Some Remarks About Mass Nouns and Plurality." Mass Terms: Some Philosophical Problems.  Ed. F.J. Pelletier.  Dordrecht, Holland: D. Reidel, 1979.

---.  "Theories of Matter." Mass Terms: Some Philosophical Problems.  Ed. F.J. Pelletier.  Dordrecht, Holland: D. Reidel, 1979.

Laycock, Henry.  "The Concept of an Ideal Language."  Unpublished.

---.  "The Foundational Science of Goo: How to Speak of This and That Without Speaking of Anything in Particular."  Unpublished.
 
Pelletier, F.J.  "Non-Singular Reference: Some Preliminaries." Mass Terms: Some Philosophical Problems.  Ed. F.J. Pelletier.  Dordrecht, Holland: D. Reidel, 1979.
 

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