WETZEL ON TYPES AND TOKENS

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

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

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

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

The K is F =df all Ks are F.

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

The llama is a wooly sort of fleecy hairy goat

With an indolent expression and an undulating throat,

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Bruce Aune

Umass, Amherst