WETZEL ON TYPES AND TOKENS

=20 The subject of types and tokens, one way of construing the = subject of=20 universals and particulars, has been debated since philosophy began, and = the=20 debate is in no danger of ending in our time. The controversy is too = vigorous: the contending parties seem = united in=20 regarding their views as obvious and their opponent's views as = absurd. I fear that my disagreement = with=20 Professor Wetzel has something of this character. For the most part, what one of = us=20 confidently asserts the other confidently denies. One significant exception may = be the=20 scope of our dispute. = Wetzel is=20 concerned to oppose nominalism and to defend (or at least make = occasional=20 remarks in support of) a kind of thorough-going realism. The scope of my contentions = will be much=20 narrower. I will oppose = what she=20 says about types and also reject some familiar claims about universals, = but I=20 will not support any general nominalist thesis. That goes further than I am = prepared to=20 go.

In her first chapter = on "data,"=20 Wetzel calls attention to many sentences by which many people have = ostensibly=20 referred to and quantified over entities she considers types. What should we conclude from = this=20 data? Wetzel thinks that = if we=20 cannot provide a "systematic semantics" for these sentences that avoids = such=20 reference and quantification, we should conclude that types exist. I think another conclusion is=20 warranted. The conclusion = I draw is=20 that many people believe = types exist,=20 or would believe it if they were appropriately informed about = philosophical=20 terminology and sufficiently reflective about their habits of = speech. I draw this weaker conclusion = because,=20 if types are supposed to be what Wetzel says they are, I myself don't = believe=20 they exist and wouldn't refer to (or quantify over) them if I were = speaking=20 carefully. The basic = reason for my=20 attitude is that types, as she describes them, have the attributes of=20 particulars, and these attributes do not belong to anything reasonably=20 considered "abstract."

Consider Wetzel's = assertion,=20 "The grizzly bear is ferocious." = What does she mean by the predicate "ferocious"? Presumably the usual = thing. My desk dictionary defines = "ferocious"=20 as "savagely fierce, violently cruel." =20 But could an abstract object actually be cruel? Could it scratch and bite = me? To scratch and bite (in the = manner of an=20 animal) a thing would need teeth and claws. Could an abstract object have = teeth and=20 claws? The idea seems = absurd to=20 me. I am not afraid of the big bad bear; I am afraid = only of=20 nonabstract bears, real creatures with real teeth. Abstract bears, if it made = sense to=20 speak of such things, would be harmless.

=20 I am attracted by the view that singular terms such as "the = grizzly" in=20 Wetzel's specimen sentence are distributive singular terms. The definition schema commonly = given by=20 those who "reduce" types to tokens is this:

Wetzel objects to this schema. It fails, she says, because = all the=20 relevant tokens don't normally possess the attributes ostensibly = attributed to=20 the type. To take my = favorite=20 example from Hilaire Belloc, although it is perhaps true that

it is certainly not true that every actual llama = satisfies=20 this description. Shaved = or burned=20 llamas are not wooly and fleecy; beaten llamas do not have indolent = expressions;=20 and starved ones probably lack undulating throats. I agree with this criticism of = the=20 standard definition schema. = Even in=20 cases where the ingredient general term seems to apply to all members of = a=20 class, the relevant class appears to be restricted (as I have argued=20 elsewhere)[1]=20 to typical or ideal examples. = If=20 such favored llamas have wooly, fleecy coats, we can say that "the" = llama has=20 such a coat; and if we are justified in making this last assertion, we = can=20 justifiably conclude that all favored llamas have such a coat. Our "the" statement has the = assertive=20 content of a universal statement restricted to a domain of favored = cases.[2]

=20 Wetzel has objections to this qualified view, however. Her first objection is that = the notion=20 of what is normal or properly constituted--and therefore what is ideal-- = should=20 be viewed with suspicion; it is not, she suggests, scientifically = credible (p.=20 98). She might be right = that these=20 notions are scientifically dubious, but the corresponding distributive=20 statements (the ones about the llama=20 and the grizzly) would = evidently be=20 scientifically dubious as well. = If=20 I say the llama has an indolent expression and an undulating throat, a = hectoring=20 critic might say, "Okay, Aune, how do you identify a typical llama, or a "good example" of the = species?" Since I am not an expert on = domestic=20 animals, I would have to appeal to someone who is. But I don't think even an = expert can=20 provide a definition than can single out typical, or "good," llamas with = precision. I say this = because I=20 think the notion of a typical or good instance of something is vague, = and I=20 expect that even llama breeders might disagree about the qualities = llamas should=20 ideally have--just as Airedale breeders do disagree about the qualities=20 Airedales should ideally have, some thinking that, because they are = terriers,=20 Airedales ought not to be the eighty to ninety pound animals that others = admire. Belloc's = statement about=20 "the" llama, like ordinary statements about the cat or the Airedale, is = not=20 strict or precise. It = calls=20 attention, in an amusing way, to striking features of the healthy,=20 well-cared-for llamas that one might see in a field or a zoo--but it = does not=20 pretend to be scientifically exact. =20

=20 The imprecision of ostensible type statements sometimes leads to = problems=20 about verification. = Wetzel=20 acknowledged that not that all grizzlies are big, not all are brown, and = not all=20 have humps. Yet it is = still true,=20 she insisted, that "the" grizzly is a big, humped brown bear native to = North=20 America (p. 96). But how = do we know that this is true? Aren't we generalizing from = some=20 grizzlies or other? In = this case I=20 should say yes, though in the case of the llama and the Airedale, which = have=20 been bred to suit human purposes, our conception of "the" animal is = partly based=20 on our wants rather than our observations. =20 But there are often striking differences between the = instances--the good=20 examples --from which we generalize. =20 Some relevant differences are associated with sex. When we think of a Black Widow = spider,=20 for instances, we are probably thinking of the female, for the males are = small,=20 insignificant, and eaten by the female at the completion of the = inseminating=20 act. Yet the Black Widow = species=20 contains males as well as females. =20 I suspect that we simply ignore sex (we abstract from it) when we = make=20 statements about the Black = Widow=20 spider. When sexual = differences are=20 brought up, we are apt to make more restrictive statements. We would probably do the same = if we=20 discovered that most female grizzlies do not have humps. Instead of = speaking=20 about "the" grizzly generally, we might then speak about the male = grizzly, the=20 female grizzly, and possibly even the adolescent grizzly, the cub = grizzly, and=20 the aged grizzly (male or female)--if there are distinctive traits that = such=20 grizzlies possess.

=20 This brings me to another of Wetzel's objections to the = distributive=20 analysis. She says, in = effect, that=20 such analyses fail because some properties of the type are derived from = the distribution rather than the = common features of its = tokens. To support her claim she says = that Ursus horribilis, the grizzly = bear, "had=20 at one time a U.S. range of most of the West, and numbered 10,000 in = California=20 alone. Today its range is = Montana,=20 Wyoming, and Idaho, and numbers less than 1000. [But no] =85particular flesh = and blood=20 bear numbers 1,000 or had a range comprising most of the West" (p. = 102). Her example here is convincing = if her=20 opponents are expected to apply a distributional analysis in a = mechanical way,=20 but if they are allowed to use their ingenuity in interpreting = predicates, a=20 broadly distributional reading is easily achieved. Take the assertion "The = grizzly bear=20 once ranged over most of the western U.S." =20 Put in vernacular terms, this tells us that grizzly bears once = ranged=20 over most of the western U.S. =20 Saying that they had = this=20 range is not saying that each one had this range; the predicate is = applicable to=20 the grizzlies collectively: = they were distributed over = this=20 area. The predicate of = the second=20 statement is also collective, a plural predicate taking a plural = subject: they (certain grizzlies) = numbered 10,000=20 in California alone. The = same=20 principles apply to the two statements about the grizzly today: grizzlies now have three = states as their=20 range, and they now number 1,000. =20 These collective predications are, of course, reducible to = singular=20 ones: Saying that = grizzlies are distributed over a certain = area=20 amounts to saying that individual grizzlies exist here and there = throughout that=20 range.

=20 Reflection convinces me that not all statements about "the" = grizzly are=20 distributional in the ways I have so far described. If one says that the grizzly = was seen in=20 Washington State in 1975, one is not saying that typical instances were = seen=20 there then; one is saying that some=20 instance was so seen. And = if one=20 says (as another philosopher recently has) "Many rich people now = transfer=20 nothing to the poor," one is evidently speaking of the poor collectively = rather=20 than individually, although one is certainly implying that no poor = person is=20 receiving any goods or money from certain rich people. As I see it now, there is = considerable=20 ambiguity to terms like "the poor" and "the grizzly," and no single = distributive=20 analysis is applicable to all of them.

Wetzel agrees that = many=20 assertions ostensibly about types can be paraphrased by assertions about = tokens,=20 but she insists that we can have no assurance that this can always be = done=20 unless we have a systematic way of doing so. As I have implied in my last = paragraph,=20 I do not believe that a systematic way of providing such paraphrases can = be=20 found; but I have no doubt that the predicates included in Wetzel's = favored=20 examples of ostensible type terms apply only to particulars, to = "tokens." Only individual grizzlies can = be found=20 in the United States (only they can have such a range) and only they can = scratch, bite, and become more or less numerous. If the relevant "the" = statements cannot=20 be interpreted as saying something about tokens, they will not make = sense and=20 they cannot be true. The = lack of a=20 systematic means of paraphrasing all examples will not, therefore, at = least as I=20 see it, support a commitment to types. =20 The requirement of a systematic paraphrase for everyday = assertions=20 ostensibly about types is, in any case, excessively demanding.

=20 Wetzel says that Wollheim and Wolterstorff have "shown" that = types are=20 crucial for aesthetics (she thinks that Beethoven's Eroica Symphony is a type), = but I think=20 they have shown nothing of the sort. =20 For my part, the broadly distributional treatment that seems = appropriate=20 for statements about "the" grizzly also seems appropriate for statements = about=20 works of art. Most = predicates that=20 we attach to a grammatical subject such as " Beethoven's Eroica Symphony " properly = apply to=20 tokens (performances), for they, not something abstract, can actually be = in a=20 certain key, have rhythm and dynamics (be loud or soft), and can = actually be=20 heard. We say that a = musical work=20 exists if an appropriate score exists or someone knows how to produce a=20 performance, so some predicates we attach to the relevant grammatical = subjects=20 are not implicitly distributional. =20 Still, the features recorded by these latter predicates are not = (so far=20 as I can tell) "intrinsic"; they are relational, relating the supposed = object to=20 other things. And even = they=20 ultimately involve tokens or potential tokens: a token is produced, or = directions are=20 given for producing a token, and we say the composition exists. But the essence of the = composition (as=20 Berkeley would say) is percipi: its qualities are audible, the qualities of a=20 performance.[3]

=20 Wetzel often writes as if the types she associates with "the = grizzly" are=20 kinds or (roughly speaking) species. =20 But I think that species are quite different from what Wetzel = considers=20 types. On p. 134 she says = that=20 there are four major ways in which biologists characterize species. According to the first, = Darwin's, a=20 species is a set of individuals closely resembling each other; the = individuals=20 evidently "comprise" the species. =20 According to the second, a species "corresponds to a cluster of = genes"=20 (p. 36). According to the = third,=20 species are "groups of interbreeding natural populations that are = reproducibly=20 isolated from other such groups" (p. 137); and according to the fourth, = G.G.=20 Simpson's, "an evolutionary species is a lineage (an = ancestoral-dependent=20 sequence of populations) evolving separately from others and with its = own=20 unitary evolutionary role and tendencies" (p. 138). On all four approaches, = species are=20 sets, clusters, or sequences. =20 Contemporary philosophers influenced by the practice of = mathematicians=20 are apt to think of sets, clusters, and sequences as the sort of = abstract entity=20 postulated by set theory, but it is doubtful that biologists think of = them this=20 way: mathematical sets = are not=20 "comprised" by their members. = Most=20 biologists have a much vaguer notion in mind when they speak of a set, = cluster,=20 or sequence: for them, a cluster is probably more like a bunch of = attached=20 parts, and a sequence of populations is probably something like a = temporally=20 extended aggregate of causally related organisms. Such bunches or aggregates are = certainly=20 not described as having the features of the organisms comprising = them. In this respect they are very different from "the" = grizzly or=20 Mozart's twenty-fourth piano concerto, as Wetzel describes them.

=20 Wetzel also writes as if she thinks that when we (or people = generally)=20 speak of the grizzly, the species Ursus=20 horribilis, Bach's Chaconne, the=20 property of being red, the number five, or the ordered pair <Cassio,=20 Desdemona>, we are referring to discrete, determinate objects whose = nature=20 and identity can be ascertained by philosophical reflection. She discloses such an attitude = when she=20 endorses Benacerraf's criticism of set-theoretical treatments of natural = numbers=20 and applies it to alternative definitions of an ordered pair. I think this attitude is = misguided. People often speak as if they = are=20 referring to specific things when they have only very vague notions of = what they=20 are ostensibly referring to; and sometimes, as in apparent references to = the=20 supposed entities I have just mentioned, there is no generally accepted = and=20 acceptable conception of the intrinsic nature of those (supposed) = entities. I have supported this = contention for the=20 case of species; and I think it is clearly applicable to the case of = "the"=20 grizzly and Bach's Chaconne, since=20 Wetzel and I disagree about it in a way that many other philosophers = do. As for numbers and ordered = pairs, the=20 Russell analyses of numbers and the Kuratowski and Weiner analyses of = ordered=20 pairs were given precisely because those offering them had no idea = (prior to=20 arriving at their analyses) of precisely what these entities were = supposed to=20 be--other than having certain relational properties. The analyses can be viewed as = ways of=20 making the relevant concepts precise, so that determinate objects could = be=20 singled out. The fact = that=20 alternative analyses are possible only shows that numbers and sets can = be=20 adequately conceived of in different ways; it doesn't show (I believe) = that=20 certain abstract objects are "really" not what one or the other = "arbitrary"=20 analysis ("construction" would be a better word) takes them to be.

=20 The notion of a property (or "universal") requires an extra = comment. At the beginning of her essay = Wetzel=20 says that she is not defending the view that types are universals, but = she=20 appears to accept this idea in her last chapter, when she replies to = David=20 Lewis's criticism of structured universals. She writes as if it is = generally known=20 what universals are supposed to be and what sort of relation = exemplification is;=20 the latter, she says, is "too fundamental to be analyzed further" than = saying=20 "things exemplifying types are instances of them" (see p. 153). I am very doubtful about these = beliefs. It seems obvious = to me=20 that theories of universals fall into two sharply distinguishable groups = and=20 that the notion of exemplification is elaborated very differently by = those who=20 accept these rival theories. = The=20 elaborations show that the relevant notions of exemplification are not too fundamental for = helpful=20 clarification.

The first sort of = theory may be=20 called an A-theory, for both Aristotle and David Armstrong held theories = of this=20 kind. The distinctive = feature of=20 these theories is that they take universals to be present in the things=20 exemplifying them. If a = thing a is red, the universal = redness is=20 present in a; it is, as = Armstrong=20 says, a component of a's = nature. The second sort of theory can = be called=20 a P-theory, for Plato held a theory of this kind, at least in the Republic. According to P-theories, = universals are=20 not present in the things "exemplifying" them; they exist in a realm = apart: in=20 the Phaedo Plato referred = to this=20 realm as "the invisible world." =20 Frege is a modern philosopher holding a P-theory; he called his = abstract=20 objects "concepts" and said that particular things "fall under" them. = Judging=20 from an observation by Elizabeth Anscombe, the terminology of objects = falling=20 under concepts is evidently not unusual in everyday German. She reported that Michael = Dummett once=20 saw in a M=FCnster railway station a notice beginning =93All objects = that fall under=20 the concept hand-luggage....=94 (Alle Gegenst=E4nde, die unter den = Bergriff=20 Handgep=E4ck fallen...).[4]=20 Obviously, the relation of "falling under" a concept is very = different from=20 that of having an abstract component. =20 Since both relations have been denoted by the term "exemplifies," = philosophers expounding a theory of universals need to say enough about = the=20 relation of universals they favor to identify the alternative they have = in=20 mind.

In different places = Wetzel says=20 things that suggest she adopts both kinds of theory. In one place she says "I = disagree with=20 Armstrong's characterization of structural universals in terms of what = structure=20 their tokens must have, rather than in terms of what structure they themselves have" (p. = 175). If, as she says in criticizing = Nelson=20 Goodman's nominalism, a token of the word-type "Paris" need not contain = five=20 letters, a five-lettered type can hardly be present in a less than five = lettered=20 token, or a two-legged bear-type can hardly be present in a one-legged = bear=20 token. (When I was a boy = attending=20 a summer camp, I was terrified by tales of a one-legged bear that was = said to=20 inhabit the woods in which we were camping.) On the other hand, in her = first chapter=20 she expressed approval for Richard Wollheim"s characterization of the = difference=20 between types and universals such as being white or being between when he said = that "not=20 only is the type present in all its tokens like the [property] in all = its=20 instances, but for much of the time we think and talk of the type as = though it=20 were itself a kind of token, though a peculiarly important or preeminent = one"=20 (p. 2). And then in = speaking of=20 "the" bear and kindred things, she describes them as having the = attributes of=20 particulars--teeth, claws, and humps on their backs. A Fregian concept would not = have=20 features like this.

In a recent paper I = have argued=20 that A-theories are far less plausible than P-theories, because they = raise=20 intractable problems about the nature of both particulars and = universals. (Are particulars "bare," = intrinsically=20 characterless subjects in which attributes inhere, as Locke thought, or = are they=20 bundles of qualities? And = are=20 universals, which certainly differ from one another, intrinsically = characterless=20 subjects of higher-order attributes, or are they bundles of such = things?) Such theories also face = intractable=20 problems about vagueness. = A vague=20 predicate may neither apply nor fail to apply to a borderline case: for = example,=20 a chair may be altered to the point where one cannot confidently = classify the=20 result either as a chair or a nonchair; red paint may be added to white = paint=20 until the resulting mixture is indeterminate between being reddish white = (and so=20 white) and being whitish red (and so red and nonwhite). Yet if the attribute = supposedly=20 associated with the predicate were a definite immanent object, that = object would=20 either be or not be present in any given particular. There could be no borderline = cases.

A related difficulty = holds for=20 types generally. Bach's = famous Chaconne was written for the = violin; it=20 is the last movement of his D = Minor=20 Partita For Unaccompanied = Violin. But I first heard it = played on the=20 guitar, and Bussoni created a version for the piano with, as I recall, a = lot of=20 extra notes. Are these = versions or=20 "arrangements" tokens of the type Bach created? Are the creative arrangements = of the=20 Star Spangled Banner sung at important football games really instances = of the=20 type created by Francis Scott Key? =20 How much distortion of the original score is compatible with a=20 performance's being an instance of the original type? No definite answer is = possible, I would=20 say. Our ordinary = conception of a=20 type is not sufficiently precise to yield an answer to such a = question. We have a conception of the = Star=20 Spangled Banner, but no discrete object corresponds to it--just as no = discrete=20 object corresponds to our conception of Shakespeare's Hamlet. (The descriptions of Hamlet = that can be=20 extracted from Shakespeare's play are satisfied by an infinity of = possible men;=20 there is no way to single out a favored candidate.)

Wetzel says = "Word-types are=20 pigeonholes by means of which we classify tokens" (p. 140); she also = says=20 "Linguistic tokens are artifacts, our own inventions, and so are types = and the=20 theory we have of them" (p. 152). I=20 am sure that she would extend these claims to types of other kinds. I can accept the metaphor that = we fit=20 tokens into classificatory pigeon holes, and I certainly agree that=20 classifications (or classificatory schemes) are our own inventions. But I don't think we classify = tokens by=20 means of types; we classify them by means of predicates that represent = or=20 express concepts. What are concepts? According to tradition, = concepts are=20 general ideas, ideas applicable to many. =20 The model for a general idea is a general term, such as = "sentence" or=20 "grizzly bear." When we = speak of=20 ostensible types, we do so by means of general terms: "the grizzly bear" contains = the general=20 term "grizzly." Although = "the=20 grizzly bear" is a singular term, it is not, as I have argued, a = denoting term=20 in most occurrences but a distributive one. Wetzel will, of course, = dispute this,=20 but she cannot deny that it contains a general term by means of which we = classify certain animals as grizzlies. =20 The general term is the basic classifier; saying that grizzlies = are=20 instances of "the" grizzly is almost vacuous. But it is not vacuous to say = that=20 certain bears are grizzlies.

As I said, I think = the best=20 theories of universals are P-theories, well known instances of which = were=20 defended by Plato and Frege. = Since=20 the concepts by which we classify objects, however "natural" they may = seem, are=20 clearly invented by us, I think the best P-theory takes concepts as its = objects,=20 not the "eternal entities" postulated by Plato. Ostensible truths about = concepts reduce=20 to truths about predicates or predicative thoughts--just as ostensible = truths=20 about "the" grizzly reduce (in various ways) to truths about individual=20 grizzlies. (This has got = to be true=20 because the semantic predicates applicable to concepts fundamentally = apply to=20 tokens.) To adequately = support my=20 view, I must of course offer more detail than I have given here and also = resolve=20 other problems that Wetzel raised in her book, particularly the problem = of=20 nonexistent relevant tokens. = But=20 these problems can, I believe, be met.[5] For instance, one can find any = linguistic token of an ostensible English type in any instance of the = English=20 alphabet: one simply has = to go=20 through the alphabet in the right way. =20 But I have said enough for my purposes here. The big questions we are = concerned with=20 can't be resolved in a single meeting, if they can be resolved at = all. We might have to agree to = disagree.

[1]=20 See my paper, "Universals and Predication," in The Blackwell Guide to = Metaphysics,=20 Richard M. Gale, ed. (Oxford: Blackwell, 2002), pp. 131-150.

[2]=20 Wetzel shows that 'The K is F' does not = imply 'all=20 Ks are F'; the implication evidently does not go the other way either, = since=20 some things truly predicable of every grizzly are apparently not = predicable of=20 "the" grizzly. = Contingent,=20 accidental features seem to be exceptions. =20 If every actual grizzly lost a claw in a trap or a fight, I doubt = we=20 would say that the grizzly lacks a claw.

[3]=20 A conclusion to draw from my claims in these last two sentences is that = a=20 composition exists just = when an=20 appropriate performance is available--just when a satisfactory basis = exists for=20 producing such performances.

[4]=20 Se G.E.M. Anscombe, An = Introduction to=20 Wittgenstein's Tractatus (London: Hutchinson, 1959), p. = 122.

[5]=20 Again see "Universals and = Predication."