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					                     DRAFT: Matthias Haase The Representation of Language, Chicago 25.01.08


                                   The Representation of Language
                                               Matthias Haase




1. Introduction
This essay inquires how the notion of a social practice is to enter into the philosophy of
language. That it should at all is, of course, one of the famous teachings of the later
Wittgenstein. In Bemerkungen über die Grundlagen der Mathematik he writes: “In order to
describe the phenomenon of language, one has to describe a practice, not a singular event, no
matter of what kind.” And he adds: “This is a very difficult insight.”1 In the following I argue
that if we come to appreciate what is supposed to be so “difficult” about this insight we will
realize that the notion of practice must play a quite different role than is usually assumed.
        The passage stands in the context of what has come to be called the „rule-following
considerations‟. The rough upshot of the dialectic presented in those notoriously dark sections
in the Philosophische Untersuchungen can be put like this. There is a puzzle about how a
word can guide its use on a particular occasion – or, quite generally, about how a concept can
guide its application in an act of judgment, as it must if the act is to have conceptual content.
In order to dissolve this puzzle Wittgenstein appeals to “customs (uses, institutions)”.2 To put
it schematically: we are told that there will be no riddle as to how an act of applying a concept
can be faithful to its content, if we look to the wider context and recognize the acts as an
instantiation of a social practice.
        That much, at least, is by now fairly well established.3 Much more controversial is
how this bare structure is to be filled in. The passage from the Bemerkungen über die


1
         Ludwig Wittgenstein, Bemerkungen über die Grundlagen der Mathematik, Part VI, §34. In the
following cited as BGM.
2
         See, for instance, Ludwig Wittgenstein, Philosophische Untersuchungen, §199. In the following cited as
PU.
3
         There is, of course, some controversy about the nature of the rule-following problem. Many
philosophers would deny the general nature I just ascribed to it. Some argue that it should be restricted to
mathematics, other claim that it is peculiar to linguistic meaning, yet other hold that it is the epistemological
problem how we can know which rule or concept someone else follows. I won‟t discuss these readings here. I
hope however that my introduction of the rule-following problem in §3 will raise some doubts about these
readings. Since for my purposes in this paper nothing hangs on the differences between them, I will often move
freely between the case of using a word in accord with its meaning and the case of applying a concept in an act
of judgment.


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Grundlagen der Mathematik is instructive in this connection, because it points to a question
that has received surprisingly little attention in the standard literature on the later
Wittgenstein. Read against the background of the rule-following discussion the passage
suggests that understanding the possibility of using a word in accord with its meaning requires
realizing what a language is. Wittgenstein calls it a “practice”. But he doesn‟t seem to think
that it is easy to apprehend what it means to characterize a language as a practice; on the
contrary, he says that it is “very difficult”. This suggests that the decisive question is how the
those notorious terms like “language-game”, “custom”, “practice” or “form of life” are to be
understood so that the appeal to them will make the riddle about rule-following “completely
disappear” as Wittgenstein demands of a proper treatment of a philosophical problem.4
         In the literature following Wittgenstein the notion of a social practice is often treated
as something we can take for granted while doing philosophy of language. It tends to be either
used as the explanans in a noncircular explanation of the possibility of conceptual content or
employed in order to show that questions like „How is conceptual content possible?‟ are bad
questions, since they rest on the illusion that we can adopt a standpoint “outside” our life with
concepts. Obviously these two approaches work with very different ideas of what a practice
is.5 On both sides of the divide, however, one might wonder from where are we supposed to
get the relevant concept in the first place. Is it something that the philosopher receives from
the empirical sciences, perhaps sociology, or is it simply a “bit of common sense”, as John
McDowell suggests? 6 Whatever ones preferred answer might be, one thing should be clear:

4
         See PU, §133.
5
           In the first approach the notion of a social practice is regarded as logically independent from our
semantic and intentional vocabulary. The official task is then to define the particular structure a social practice
must exhibit, if it is to count as a linguistic practice. (See, for instance, Robert Brandom, Making It Explicit;
Michael Dummett, “What is a Theory of Meaning (II)”) The opposed camp insists, by contrast, that one must not
conceive of a practice as something that is intelligible independently from being represented as the practice of
using words in accord with their meaning. (See, for instance, Cora Diamond, “Rules : Looking in the Right
Place”, Warren Goldfarb, “Rule-Following Revisited”, John McDowell, “Wittgenstein on Following a Rule” ) If
this is right, then it seems that one cannot account for the constitution of meaning by appealing to the notion of a
practice. For, if it is there is a puzzle about how it is possible to use a word in accord with its meaning, it would
seem that it must be equally puzzling how there can be a practice of doing precisely that. According to the
second approach, then, the talk about practices is not supposed to explain the possibility of meaning; its point is,
rather, to cure us from our explanatory ambitions by making us see that they are ill-motivated.
6
           See John McDowell, “Meaning and Intentionality in Wittgenstein‟s Later Philosophy”, 276-277. Even
though I can‟t argue for it here, it seems to me that these two answers basically exhaust the options available in
the standard debate. For it is hard to avoid thinking that on both sides of the divide the answer to the question
„From where has the philosopher is received the relevant concept?‟ must in the end be: „Not from philosophy‟. In
the case of the first approach it is difficult to see how the notion of social practice could play its assigned


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the notion of a social practice will not be apt to play its assigned role in the rule-following
dialectic, if the pointing to the wider context of a practice is simply a pointing to more of the
same. For if it is puzzling how an act of using a word in accord with its meaning is possible,
the same puzzle will inevitably arise for every other linguistic act we find in its surroundings.
If the appeal to it is to make a difference at all, a practice cannot be the mere sum of the acts
of its participants. As Michael Thompson would puts it, the look to the wider context cannot
be “the look to the left or to the right”.7 But if that is so, where exactly are we supposed to
look when we are told to look to the wider context of a practice?
         Our passage from Bemerkungen über die Grundlagen der Mathematik gives a first hint
for how to approach the question „What is a practice?‟. For the familiar point is made there in
terms of a distinction between two kinds of description: the description of an event and the
description of a practice. On the face it, there are, of course, many ways in which one might
distinguish between different kinds of descriptions. But when we turn the Philosophische
Untersuchungen, we find a specific determination of the kind of distinction we are supposedly
dealing with: In PU §199 Wittgenstein accompanies his remark that to follow a rule is a
custom with the commentary that it should be read as “a note on the grammar of the
expression „to follow a rule‟”.8 And he famously writes: “Grammar tells what kind of object
anything is.” (PU, §373) This seems to suggest that the relevant distinction between two kinds
of description not supposed to be one of content, but rather one of form. According to
Wittgenstein philosophical problems “arise through the misinterpretation of our forms of
language” (PU, §111), and they can be solved by “giving prominence to distinctions which
our ordinary forms of language easily make us overlook” (PU, §132). A “grammatical
remark”, then, is a remark about the proper interpretation of the grammar of our language.
The difficulty to which Wittgenstein alludes in the passage from Bemerkungen über die
Grundlagen der Mathematik I quoted at the outset must accordingly pertain to the
interpretation of the grammatical form that the statements exhibit with which we describe a

explanatory role, unless it something that the philosopher ultimately receives from elsewhere. And in the second
case it seems that the aim of putting our very longing for philosophical explanations to rest would hardly be
served, if the appeal to practices functioned as a conveyor belt that simply lead us to the question what a practice
is. In consequence, it looks like the only way in which the notion of practice can appear in the second approach
is as something about which no serious philosophical question can arise.
7
          See Michael Thompson, “The Representation of Life”. – As every reader of his work will notice, I‟m
deeply indebted to his considerations.
8
          My italics, M.H..


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language. So if we want to know what the alleged “insight” is – that is, what it means to
characterize a language as a „practice‟ – we need to investigate their grammar. Appreciating
the specificities of this kind of description is what is supposed to put us in the position to
realize that what appears to be a problem about the very possibility of conceptual content is in
the end nothing but “grammatical confusion”, as Wittgenstein would put it.
         In the following I want to suggest that this diagnosis is just a negative way of saying
that the source of riddle about rule-following is the failure to notice that those descriptions
exhibit a way of uniting subject and predicate that is sui generis – a „form of predication‟, as
one might say. If that is right, then the notion of practice is a pure or „formal‟ concept, just as
“logically basic” as concept, object and relation are according to Frege.9
         That is to say, on the reading I want to propose the rule-following considerations result
neither in the scandalous claim that we have to reject the idea that a concept determines its
future applications,10 nor in the provocative insistence that what we need to learn is, as Cora
Diamond would put it, “open-eyedly giving up” the “demand for a philosophical account” of
how a concept can determine its future applications.11 Rather, the scandal about
Wittgenstein‟s later philosophy is the insight that the distinctions recognizable in the logical

9
           Wittgenstein notion of grammar is, of course, notoriously hard to understand. And I will not touch on
the difficult question what exactly happens to the idea of a formal concept in the move from “logic” to
“grammar” that marks the transition from early to late Wittgenstein. I would insist however that the idea that
there are formal concepts should go – with whatever reservation required – on what Jim Conant calls the “list
devoted … to detailing moments of continuity in Wittgenstein‟s thought.” (See James Conant, “Mild Mono-
Wittgensteinianism”, 107) To be sure, one can‟t simply introduce further “logically basic” terms into the
Fregean Begriffsschrift; rather, it seems that distinguishing a multiplicity of different forms of predication
ultimately requires a correction of Frege‟s very conception of logic that already the early Wittgenstein took issue
with. That said, I think it is legitimate to leave this issue for later and focus for the time being on the later
Wittgenstein‟s insistence that we need much more distinctions of the kind Frege draws between concept and
object. In other words, to begin with I think it is helpful to approach this dimension of the complex relation
between Frege and the later Wittgenstein in the way Anscombe suggest we should approach the relation between
the later Wittgenstein and Plato. Anscombe writes: “[A] man who complains of the forcing of diverse things into
one generic mould may be doing so because he wants many more specific patters described: not because he
wants to change the direction of interest of the enquiry. Plato saw the grammatical difference between
„Theaetetus‟ and „walks‟, Wittgenstein, the grammatical difference between „Theaetetus‟ and „two‟. If „proper
name‟ is a grammatical category, then so in his conception is „numeral‟ and so is „colour-name‟ and so is
„psychological verb‟. But by Wittgensteinian considerations even all of these turn out to be somewhat generic:
that is, there are „categorial‟ differences within each kind.” (G.E.M. Anscombe, “A Theory of Language?”, 155-
156)
10
           See, for instance, Crispin Wright, “Rule-Following, Meaning and Constructivism”, 72.
11
           According to Diamond‟s Wittgenstein the “hardest thing” in philosophy is “open-eyedly giving up …
the demand that a philosophical account of what I mean make clear how it is fixed, out of all the possible
continuations, out of some real semantic space, which I mean.” (Cora Diamond, Realism and the Realistic Spirit,
69)


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framework we inherited from Frege are insufficient in order to apprehend what it is to employ
a concept in an act of judgment. Frege‟s famously taught us that general judgments are to be
understood as quantified judgments. The point of Wittgenstein‟s insistence that to describe a
language is to describe a practice is precisely that descriptions of a natural language cannot be
represented in quantificational terms – at least so I like to argue.
          In order to make some steps towards supporting this view I will first point out that it
seems, at least on the face of it, indeed “difficult” to fit Wittgenstein‟s remarks on the
metaphysics of language into the established framework committed to what I will call “the
Quantificational Model” of the existence of a natural language (§2). In a second step I will
introduce the rule-following problem and suggest that its solution requires precisely such an
ill-fitting notion of language (§3). Finally I will argue that in order render this notion
intelligible we need to recognize a kind of generality that cannot be assimilated to the
Quantificational Model (§§4-7).


2. The Quantificational Model
To make a beginning, let us consider the notion of language underlying formal semantics for a
moment. As far as formal semantics is concerned, a language is a complex abstract object that
can be individuated by giving a set of types of sounds or graphic marks, rules for the
concatenation of those types of expressions into sequences and a function that assigns, given
states of affairs, semantic value to every „well-formed‟ string of types of sounds or of graphic
marks. Languages are thus conceived of as changeless, unobservable entities that have no
causal powers and don‟t exist in space and time. All that matters from this point of view are
the logical possibilities concerning the combinations of types of expressions into
concatenations and the function that assigns semantic values to those concatenations.12
         Delimited in this way, the class of languages includes many more elements than what
are usually called „natural languages‟ such as English, French or Urdu. Since the

12
          It should be obvious that these descriptions operate on a level of abstraction on which it is not essential
that the concatenated types are types of sounds or graphic marks. We have to do with a quite general model for
the representation of the semantic or intentional „systems‟ by means of a formal calculus. In order to get the
equivalent theory for a mental instead of linguistic content, one just has to replace „types of sounds or graphic
marks‟ with the suitable description of the types of the relevant mental whatnots. The aim is to represent a
language – or a system of concepts – as a function; what are taken as the material bearers or „tokens‟ of the types
in the domain of the function is quite irrelevant for this purpose. For the sake of simplicity I focus on the
linguistic case here.


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individuation is determined by logical possibility alone, all kinds of entities besides spoken
languages are picked out by the above definition. Apart from the artificial languages we know
countless formal patterns no one even thought about belong to the class of languages in the
realm of abstract objects. This gives rise to the question what distinguishes spoken languages
from the other elements in the class. However the answer to this question might look, it will
not be not part of formal semantics whose task is, as David Lewis points out, restricted to
providing a “description of possible languages or grammars as abstract semantic systems
whereby symbols are associated with aspects of the world”.13 The inquiry into the spoken –
or, as one might be tempted to say, „actual‟ – languages is another matter. To approach it is to
move from formal semantics to the “sphere of human action”.14
         According to Donald Davidson what I said so far basically exhaust what can
intelligibly said about the metaphysics of language. Davidson writes:


[W]e talk so freely about language, or languages, that we tend to forget that there are no such things in the world;
there are only people and their various written and acoustical products. This point, obvious in itself, is
nevertheless easy to forget, and it has consequences that are not universally recognized. A feature of a language
as I have described it is, then, that there must be an infinity of „languages‟ no one ever has spoken or ever will
speak. To say someone speaks a particular language, say French, is just to say that his or her datable utterances
and writings are tokens of French expressions. … The existence of the French language does not depend on
anyone‟s speaking it, any more than the existence of shapes depends on there being objects with those shapes. It
follows that there is nothing about the existence of a particular language that imbues it with anything more than
the sort of interest any abstract object may have; as logicians we can study it as one example among countless
others of a formal pattern.15


On Davidson‟s view all languages are abstract objects. What exists in the world and is
causally efficacious are particular utterances or inscriptions of sentences; the types, of which
these are tokens, are abstract and intangible. After all one cannot run into a language. The
distinction between spoken languages and those other countless abstract semantic systems
boils down to this: in the former case there are instances of the formal pattern, whereas in the
latter case there are none. Whether a particular language is instantiated by a given utterance is,
of course, a crucial question, when we are trying to figure out which semantic value we are to
assign to the utterance. This gives rise to all kinds of interesting problems. But they do not
concern the metaphysics of language. For, they only arise in the context of trying to figure out

13
         David Lewis, “General Semantics”, 190. My italics, M.H..
14
         David Lewis, “Language and Languages”, 164.
15
         Donald Davidson, “The Second Person”, 108-109.


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to which one of those countless abstract semantic systems that include the relevant type we
should relate the utterances at hand. To the language it makes no difference whether it is
spoken or not: it is, in any case, nothing but a “formal pattern”. This is pretty much all that
can sensibly be said in response to our question what kind of object a language is.
        Other philosophers hold that the distinction between „actual‟ and „possible‟ languages
bears more philosophical significance than Davidson wants to allow. Widely shared however
is his approach of starting with the notion of language underlying formal semantics and then
defining natural languages as abstract semantic systems that are realized in the world.16 Or as
Lewis puts it: a given language L is actual, if it is “used by, or is a (or the) language of, a
given population P”.17 In order to render such a formula intelligible one has to say what
makes a language the language of an individual or a population. This task is thought to be a
tricky matter, and accounts of how it is to be carried out vary over a wide range.18 For our
present purposes we can focus on the common shape exhibited by the different accounts on
offer. Central for understanding the notion of an „actual‟ language, then, is the relation
between an abstract entity and something that actualizes, exemplifies or manifests it. The
standard way to describe the actualization or „realization‟ of an abstract semantic system is to
say that it is „known‟, „possessed‟, ‟spoken‟ or „understood‟ by an individual speaker or a
community of speakers. However they are interpreted in detail, such phrases as „known by‟,
‟spoken by‟, „understood by‟ or „used by‟ determine that what „realizes‟ an abstract semantic
system in the world can only be a particular speaker or a group of speakers. Leaving the rather
exotic position of treating groups or „populations‟ as ontologically irreducible plural subjects



16
         Michael Dummett, for instance, insists that there are no languages that are never spoken. He shares,
however, with Davidson the view that languages must be regarded as abstract and thus causally inert. The
disagreement about the existence of languages that are never spoken results from a different view of the
metaphysics of abstract objects. Contrary to Davidson, Dummett holds that “in general, the existence of abstract
objects depends upon what concrete objects there are: for instance, sets or sequences of concrete objects”. (See
Michael Dummett, Frege: Philosophy of Language, 504) On his view, the idea of “pure abstract objects”, which
would have to be recognizable independently of any concrete objects, is ultimately unintelligible.
17
         David Lewis, “Language and Languages”, 166.
18
         Among the controversial issues is, of course, whether the task can be accomplished in terms that are
logically independent from our semantic and intentional vocabulary, as Dummett thinks it needs to be, or
whether we have to retreat to “modesty” as Davidson urges. Another point of dispute is the question whether the
primary notion of an actual language is that of an idiolect, as Davidson claims, or that of a language shared by a
whole population, as Dummett holds. The decisive point in the present context is that, despite their vast
differences, the parties to these familiar debates tend to share the same overall picture of what a language is –
namely: an abstract object


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aside for now,19 the elements that are available for the realization of an abstract semantic
system are limited to individual speakers, their acts and states and social constellations
thereof. 20
         Depending on the nominalistic proclivities of the philosopher at hand, abstract entities
might be thought to require further analysis. In this case the assumption will be, to use Wilfrid
Sellers‟ formula, that the “talk about any abstract entity can be unfolded into talk about
linguistic … tokens”.21 Common to all parties of the debate is the idea that all we need to
introduce into our ontology in order to account for metaphysics of spoken languages are
individual speakers, their acts and states, and the relations between them. We can call this
„the Quantificational Model‟ of language, insofar as it takes the existence of a spoken
language to come to the truth of some sort of quantified statement about the acts and states of
actual speakers.
         If the Quantificational Model exhausted what can intelligibly be said about the
ontology of language, then Davidson would be quite right when he claims that the notion of a

19
           In certain texts Michael Dummett seems to hold this view: “The knowledge possessed by the
community is neither the intersection nor the union of the knowledge possessed by each member. Within the
community, some individuals are communally acknowledged as speaking with authority on certain matters; an
item of knowledge possessed by the community as a whole even though only very view are aware of it, provided
that it is accessible to all who acquire the necessary expertise.” (Michael Dummett, “The Social Character of
Meaning”, 428)
20
         The whole point of Lewis‟ account of conventions is precisely to show that one can afford the notion of
a common language with these limited conceptual resources. For if conventions can be described in terms of
constellations of causally interdependent psychological states of individuals, they can be fit into the conceptual
framework I just described. (See David Lewis, Convention). Lewis‟ treatment of conventions depends, of course,
on the assumption that thought is prior to language. The commitment to the idea that spoken languages or,
generally, “social practices” can be accounted for in terms of the relations between speakers is quite independent
from this assumption. Robert Brandom‟s “social-pragmatist” approach, for instance, rests on the claim that the
notion of a social practice can be analyzed in terms of social constellation of normative attitudes. (See Robert
Brandom, Making It Explicit)
21
          Wilfred Sellars, Naturalism and Ontology, 96. Once again, how the executions of this program look like
in detail varies over a wide range. But I think we can get a hold of the basic idea when we take a look at the
account of the individuation of words that David Kaplan offers for the syntactic level. Rejecting the classic type-
token model as hopelessly platonist, Kaplan proposes to replace it with what he calls the “stage-continuant
model”. (David Kaplan, “Words”, 98) On this view several utterances or inscriptions are reappearances of the
same word not in virtue of being tokens of a type, but rather in virtue of being causally related to each other. This
causal relation between them is what makes them phases or “stages” of the continuing existence of the word.
Among the proponents of this view there is a dispute about whether a full account of language that reaches the
level of semantics can be given in causal terms alone or whether it has to include some irreducible notion of
normative attitudes, as Sellars himself would insist. The basic idea, however, is the same: we can eliminate the
talk about abstract semantic systems in favor of an account of the complex history of the interactions and actual
attitudes of the speakers of the language. Even though such a view is radically different from what the picture
that Davidson draws in the passage I quoted above, it should be clear that it belongs to the ontological
framework for the representation of spoken languages I sketched in the last paragraph.


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spoken language is metaphysically quite uninteresting. For there would be basically only two
options: either it picks out a subclass of the class of all languages in the realm of abstract
objects, or it can be defined it in terms of “people and their various written and acoustical
products”. In both cases nothing needs to be added to Davidson‟s inventory of the
linguistically relevant “things” to be found “in the world”. The ontological assumption that
defines the terms of this debate and determines the available options can be put like this: what
is general can only be an abstraction; if something is to be actual and causally efficacious, it
must be a particular – something that is „here‟ and „now‟.
        Against the background of this admittedly rough overview of the standard debate we
can begin to see why Wittgenstein‟s alleged “insight” that to describe a language is “to
describe a practice and not a singular event, no matter of what kind” must indeed be a “very
difficult” one, if it is one at all. Following Davidson one would think the relevant alternative
to the description of a “singular event” could only be the description of an ordered set of types
of events. Wittgenstein, however, denies explicitly that the notion of language he is interested
in is the notion of an abstract entity:


We are talking about the spatial and temporal phenomenon of language, not about some non-spatial, non-
temporal phantasm. [...] But we are talking about it as we do about the pieces in chess when we are stating the
rules of the game, not describing their physical properties. (PU, § 108)

From the perspective of the framework I described above this must seem like a rather peculiar
remark. For when we are “stating the rules of the game”, we are surely not talking about a
particular event of playing a game of chess. And so it will seem that we can only be talking
about chess as an abstract system of types of moves and precisely not as a “spatial and
temporal phenomenon”.22 In turn one might think that Wittgenstein intends to be talking
about what usually or „normally‟ happens at events of playing a game or, alternatively, about
how talk about the abstract entity called „chess‟ can be, as Wilfred Sellars would put it,
“unfolded into” talk about the complex history of the causally related events of playing. On
the face of it, however, it seems hard to square such a reading with Wittgenstein‟s insistence


22
         On the standard view the game of chess is, of course, just as much an abstract entity as an abstract
semantic system. Michael Dummett, for instance, writes: “Games themselves have proper names, but are hardly
concrete objects: an evening‟s play at Poker might be classified as an event, and thus a concrete object, but the
game of Poker itself is as much an abstract object as the letter A.” (Michael Dummett, Frege: Philosophy of
Language, 487)


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that to describe a language is not to describe “a singular event, no matter of what kind”. For
the emphasis would be quite misleading, if the point could be expressed by saying that in
order to describe the phenomenon of language, we need to describe several events. Moreover,
it seems that in the loose sense in which Wittgenstein uses the word „event‟ here,23 any history
of the causal interactions between events is itself an event. One might seek refuge in the claim
that “stating the rules of the game” is normative or „prescriptive‟ and thus not an act
describing of anything at all. But then one will have trouble accounting for Wittgenstein‟s
claim that a natural language is something existing in the world. After all, the remark that got
us going is about what it is to “describe the phenomenon of language”.
        On the face of it, it looks like the whole project of mapping Wittgenstein‟s note on
what a language is onto one of the positions available in the established framework is rather
hopeless. According to what he seems to be saying a language is neither an abstract entity nor
a singular event or sum of events of any kind. Leaving the word „practice‟ aside his original
remark can be put like this: „In order to describe a language one must describe something
general that is actual and not abstract.‟ From the point of view of the standard debate such a
statement must seem simply incomprehensible. The same must hold in consequence for
Wittgenstein‟s use of the word „practice‟. In order to decide whether it is worth pursuing the
question what he might have meant, let‟s take a look at the problem that is supposed to be
solved by appeal to this notion.


3. The rule-following problem
Many interpreters of the later Wittgenstein present the rule-following problem as the
epistemological difficulty about how we can find out whether a given utterance is an instance
of this or that language in the set of the countless abstract semantic systems that equally fit the
linguistic behavior the speaker exhibited so far. Davidson is one of these readers. And he
holds that this problem has a “relatively simple answer”:




23
         In the original has “Vorgang” which is neutral between the specificities that the English words „process‟
or „event‟ bring in and might best be translated with „happening‟.


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The longer we interpret a speaker with the apparent success as speaking a particular language, the greater our
legitimate confidence that the speaker is speaking that language. Our strengthening expectations are as well
                                                             24
founded as our evidence and ordinary induction make them.


Whether this response is satisfying or not, it should be clear that there is a question that has to
be answered before we can even turn to the epistemological issue – namely the metaphysical
question, what it is for given utterance to be an instance of those countless formal patterns?
This is the rule-following problem, as I understand it. Let‟s take a look how it is presented in
Wittgenstein‟s text.
         In the Philosophische Untersuchungen, Wittgenstein asks us to imagine the scenario
of a student learning how to extend a number series according to the formula „(n, n + 2)‟. To
teach the pupil the meaning of the formula we show him what to do in several cases and ask
him to continue. If he gets the hang of it, the plus-function will figure in his proceedings as
the rule that determines at each stage whether the number he writes down is correct or
incorrect. Now, whether his behavior can be seen in this light depends on whether he actually
got the hang of it. And that will not be clear from the first steps he takes. It depends on how
he goes on. If it‟s haywire after a couple of steps, we will suspect that, all along, he was just
randomly writing figures on the paper, or anyway hasn‟t yet grasped the principle we have in
mind. What our initial hesitation brings out nicely is this. When we describe his writing „8‟ on
the paper as the result of his adding 2 to 6, we implicitly reach ahead to his adding 2 to 1000,
even though he might never actually get that far. Despite our firm knowledge that he will not
go on forever and, quite reasonably, has no intention to, as soon as we describe him as
following the rule, our description of each step he takes implicitly points ahead to an in
principle unlimited series of potential acts of adding. For in order to interpret his writing „6,8‟
as an act of adding we need to refer his present behavior to the rule of addition which already
sorts all his potential steps into those that would and those that would not be in accord with it.
Since the plus-function only determines at any particular stage which number comes next if it
determines its whole extension of the series, the pupil is only conceived as adding if the
numbers he actually writes are regarded as “a visible section of rails laid out to infinity”.25


24
        Donald Davidson, “The Second Person”, 111.
25
        See PU, § 218. In the literature it is often suggested that Wittgenstein rejects this picture. This is a
misunderstanding. Calling it in PU §221 a “mythological description” does not function to take back his
statement from PU §220 that it can be used “to bring into prominence a difference between being causally


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         Now, the decisive question is what underwrites our implicitly reaching ahead in this
somewhat peculiar way when we describe the student as adding 2 to 6. By excluding
candidates for this rule we, step by step, gather more and more constraints on what can count
as following a rule until it begins to seem puzzling how there can be such a thing. To make a
beginning, the behavior the pupil exhibited so far can surely not figure in this role. For there
are multiple directions in which he might go from there. Without a point of reference that
determines the relevant respect of sameness, anything the pupil might do could count as
„going on in the same way‟. He might, for instance, write „2, 4, 6, 8…‟, but after having
reached 1000 go on to write „1004, 1008, 1012‟. His procedure before 1000 is not only
compatible with the rule „Add 2‟ but also, for instance, with the bent rule „Add 2 up to 1000,
4 up to 2000, 6 up to 3000 and so on‟. However many figures he writes down, there will
always be an infinite number of patterns or „rules‟ with which his behavior accords. If his acts
are to be connected in a determinate fashion with any one of them, then the pattern cannot
figure only as that with which his acts accord, it must somehow enter into the explanation of
his acts.26 Unless there is a sense in which the pupil‟s behavior happens because of the rule, it
might as well be a mere coincidence that it exhibits the pattern specified by the rule.
         Having accepted this constraint, one might think that rule-follwing can be defined by
this formula: “Subject S is following the rule R, if S does A,B, C…, because R says „Do A, B,
C…‟.” On reflection, however, it should be clear that we cannot leave the sense of the
„because‟ unspecified. For our student must conceive of himself as following the rule if we
are to truly describe him as following the rule. We would certainly take back our statement
that in writing those numbers on the paper he is extending a number series by adding 2, if he
informed us: „I was not trying to do whatever it is you asked me to. I just put down those
figures that looked pretty on the paper. Let me go on and you we will see that they are part of
a smiling face drawn in numbers.‟ In this case it would obviously be a mere accident that the
first couple of numbers he wrote down accorded with the rule. But now it seems that our
original statement would be equally falsified, if it turned out that he is simply writing down a

determined and being logically determined”. As usual he goes on to point out that there is something misleading
about this picture. But the crucial point is that what is misleading is not that it suggests that the rule determines
its extension up to infinity.
26
         As Sellars would put it, there is a world of difference between behavior that merely conforms to a
pattern and behavior that is governed by the pattern. See Wilfred Sellars, “Some Reflections on Language
Games”, 322ff.


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sequence of numbers he happens to know by heart. Imagine that his father discovered that the
most efficient way to put his son to sleep is to say out „2, 4, 6, 8…‟ and so on.27 Being
submitted to this procedure every night our student just can‟t help but recreating the order
inscribed in his subconscious whenever he thinks of numbers. Under the assumption that the
father extended the number series by adding 2, the plus-function enters into the explanation of
the pupil‟s behavior. But it does so in the wrong way. For as far as the student‟s grasp of the
meaning of „+‟ is concerned his conforming to the rule of addition is still a mere accident. In
order to count as adding, he must know that he is continuing in the same way, where the
relevant respect of sameness is defined by the concept of addition. It is thus not enough that
his behavior is just in some way or other explained by the rule; he must be “guided” by it, as
Wittgenstein sometimes puts it.28 That is to say, the plus-function must enter, in such a way
into the explanation of the student‟s act that his behavior becomes intelligible as an acting on
an understanding of the plus-function.
         It follows that our description of his act can only implicitly reach ahead to an
unlimited series of acts, only if his own conception of his act somehow does. That is to say,
our peculiar reaching ahead in describing his as adding 2 to 6 must be underwritten by his
doing so in his mind. In consequence, it is tempting to be drawn to the picture that in
understanding the concept his “soul” must, as Wittgenstein puts it, “as it were fly ahead and
take all the steps before he physically arrived at this or that one”. (PU § 188) And then it
looks as if his “soul” has already done what he could never hope to do with the pen in his
hand – namely extend the series up to infinity. Obviously, the pupil‟s understanding of the
plus-function cannot consist in the whole extension of the number series being present in his
mind. For, then there would simply be no space anymore for the idea of executing the
operation of addition.
         This is, in a nutshell, the rule-following paradox. It presents itself as a dilemma. One
of its horns is the attempt to give up on the idea that the plus-function determines the acts of
our student up to infinity and retreat to the claim that what determines, at each stage, his next
step is something that happens on a datable occasion – for instance, his particular acts of

27
          Since philosophers can be as cruel as they like in their thought experiments, we can arrange that the
pupil has insomnia, that the father is a sadist and that, in turn, the sequence of numbers the pupil knows by heart
is as long as the one he would write down were we to force him to continue the exercise for hours.
28
          See Ludwig Wittgenstein, “The Brown Book”, §43.


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interpreting the rule. This leads to into an infinite regress, since we would always have to
introduce a further act of interpretation, in order to explain what gives the original one the
peculiar determinacy it needs to have if it is to sort the numbers written on the paper into
those that are correct and those that are incorrect.29 Recoiling from these consequences we
might want to insist that the plus-function is a strictly atemporal phenomenon, an abstract
entity detached from any worldly acts of adding. But this leads us simply to the other horn of
the dilemma, since we have now made it impossible to render intelligible how our student‟s
doings are supposed to be „guided‟ by such a thing.
       Now, it is easy to become absorbed in Wittgenstein‟s mathematical case and to lose
sight of the larger context of issues to which the rule-following problem is relevant. I want to
suggest that the problem is one that concerns any concept whatsoever and that has its source
in what an older tradition would have called the “finitude” of our faculty of understanding.
And I think that once we see the problem in its full generality, it becomes clear why
something of the nature of a practice must be a condition of the possibility of deploying
concepts in acts of judgment.
       On this reading, then, nothing hangs on the mathematical nature of the scenario. The
example of extending a number series is just a vivid way to bring out something that holds for
every act of applying a concept. Take, for instance, the simple singular judgment „a is F‟
framed by a particular subject. If „F‟ is to figure as a predicate in this judgment, it must be
such that it can also appear in indefinitely many other judgments.30 The predicative element
reaches, in this sense, beyond any given act of mind in which it is deployed. It is not that it
must be possible for other objects to fall under the concept – that might not always be the
case. Rather, the decisive point is that it must be possible to deploy the concept in other
judgments of affirmation and denial. A concept is thus something inherently general insofar
as it sets no limit to how often and by how many subjects it can be deployed. Each act of
judgment therefore points to an in principle unlimited series of possible judgments by the
same or other subjects. The elements of the series are united under a principle or “rule” –
namely, the concept that is applied in the judgment and determines whether the object brought
under it actually falls under it. Only by being conceived as springing from such a common

29
       See PU §§ 139-142, 198, 201.
30
       Gareth Evans termed this the “Generality Constraint”. See his Varieties of Reference, 104 ff.


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source and thereby seen in the light of a principle that determines their correctness or
incorrectness are the acts of an individual intelligible as acts of judgment. In order to conceive
of oneself as framing a judgment one must therefore conceive of ones act as an instance such
an infinite series of acts. And since one only judges that Fa if one knows that one does, the
principle uniting the elements of the series must be known to the subject. In framing the
judgment the subject must thus act on an understanding of, or „be guided by‟, the concept she
deploys in the judgment. In short, the idea of deploying a concept presents itself as a certain
determination of the relation between the general and the particular – namely: one in which
the general stands in an interpretative, explanatory and normative relation to its instances and
is somehow „understood‟ or „represented‟ in them.
       As soon as we ask what this „understanding‟ of a concept amounts to the structure just
described can easily seem impossible. For it cannot consist in having framed all judgments in
which it can appear. Such a picture might fit the idea of the divine intellect who has always
already judged everything. Finite rational beings, by contrast, have what Aquinas and Kant
call a “discursive” intellect insofar as they cannot „intuit‟ the forms directly, but have to
acquire knowledge by bringing particulars under concepts. Such an intellect can, as Kant puts
it, “make no other use of these concepts than that of judging by means of them”.31 Now the
whole idea of a finite rational being begins to seem puzzling. For, how can such a creature be
„guided‟ in his judgments by his understanding of a concept, if the only access it has to the
concept is by deploying it judgments? Once again we seem to be confronted with a dilemma:
either we conceive of the grasp of a concept as something akin to an act of judgment and run
into a regress, since an act of judgment must be guided by the understanding of a concepts; or
we claim that concepts are „intuited‟ and can, consequently, not account anymore for how
such a thing is possible for finite creatures like us.
       In the second half of PU §201 Wittgenstein gives a formal characterization of the
element that would allow us to avoid the dilemma just sketched. After stating the rule-
following paradox he writes: “What this shews is that there is a way of grasping a rule which
is not an interpretation, but which is exhibited in what we call „following the rule‟ and „going
against it‟ in actual cases.” (PU, §201) Wittgenstein regards the rule-following paradox as a
reductio of the conception of understanding according to which the subject‟s apprehension of

31
       See Immanuel Kant, Kritik der reinen Vernunft, B 93.


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a concept is an act that happens on a particular occasion.32 Instead we are told to look for
something general that is instantiated, manifested or “exhibited” in “actual cases” of
“following the rule”.
         On the face of it, it is quite clear which words fit this formal description. In a way it
was obvious all along that in setting up the problem we were working with an impoverished
conceptual framework that left out two notions that play a prominent role in the literature. I
mean, of course, the terms „capacity‟ and „practice‟, which name the items in reality that
correspond to the two dimensions in which a concept is, as we said, „unlimited‟ – namely, as
to how often and by how many subjects it can be deployed. Intuitively, a capacity, ability or
disposition of an individual is something that doesn‟t exhaust itself in any particular act, but
can be in exercised in a potentially unlimited series of acts by this individual. At the same
time, it natural to think that a capacity is not something abstract, but rather something real
insofar as it exists in an individual and is, to use Anthony Kenny wording, “a positive
explanatory factor in accounting for his performance”.33 A social practice is, similarly, also
something general that is not abstract, but real. By contrast to capacity, however, it exists in a
principally unlimited multiplicity of subjects and figures as the common source of their acts.
         In the vast literature there is, at least to my knowledge, not one attempt to solve the
rule-following problem that doesn‟t appeal to at least one of these terms. The decisive
question is, however, how we get a hold of these notions while doing philosophy. If we
presuppose them as understood, then we have ultimately no other way of picking out an item
of the relevant kind except the one we receive from psychology and sociology respectively
and, thus, from considerations that would seem to be irrelevant for the metaphysical problem
we are dealing with. As I specified them so far, the words „capacity‟ and „practice‟ are just
labels for the sort of thing we need to understand. From our description of the problem we can
conclude, of course, what they would have to be like, if their invocation is to get us out of
trouble: they must be general and at same time explanatory of their instances, etc. But to
know what would be needed to solve our problem is not yet to have seen how there can be

32
          As many authors have pointed out, the fact that the skeptical paradox figures in PU §201 as a reductio
is, of course, a strong argument for the view that the “skeptical solution” that Saul Kripke tentatively ascribes to
Wittgenstein cannot have anything to do with how Wittgenstein conceived of what he was doing. Kripke‟s
reading rests on the assumption that Wittgenstein accepts the skeptical paradox and then tries to show us how we
can live with the consequences. (See Saul Kripke, Wittgenstein on Rules and Private Languages, 55ff.)
33
         See Anthony Kenny, Will, Freedom and Power, 135.


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such a thing. From the perspective of the Quantificational Model we have simply painted
ourselves into the metaphysical corner of idle wishing. In such a situation it doesn‟t seem very
helpful to simply insist that such a thing is an irreducible conceptual primitive. Wittgenstein,
in any case, doesn‟t seem to think so:


The criteria which we accept for …, „being able to‟, „understanding‟, are much more complicated than might
appear at first sight. The role of these words in our language … is what we need to understand in order to
resolve philosophical paradoxes. And hence definitions usually fail to resolve them; and so, a fortiori does the
assertion that a word is „undefinable‟. (PU, §182)


Wittgenstein‟s advice was that if we want to understand the relevant notion of ability we need
to investigate the grammar of the statements describing such a language. I hope that by now it
seems worthwhile to give at try.


4. The grammar of capacities and practices
Our considerations up to this point have the following implication. If our investigation of the
description a language is to be relevant for our purpose, we cannot focus on the statements
that would be framed by a field linguist or “radical interpreter”. Reflection on the inquiries
carried out by such a character can contribute nothing to the clarification of our problem. For,
the notes that the linguist takes in the field only amount to descriptions of the linguistic
behavior of the observed native – and thereby to “evidence” for his theory about her language
– if his notes represent her behavior as springing from her own understanding of her
language. The field linguist‟s representation of the language is thus secondary, since it must in
a certain sense already contain a different kind of representation of the language – namely the
one that could be articulated by the native speaker herself.
        In “Must We Mean What We Say?”, Stanley Cavell gives a useful account of the
difference between these two kinds of representation of language: while the field linguist
confronts the English as an object of empirical investigation, the native speaker speaks “from
within the language.”34 The difference to which this metaphor alludes becomes clearer as
soon as we ask what justifies the field linguist and the native in their respective statements
about English. The linguist is only justified in his assertion, if he has gathered sufficient


34
        Stanley Cavell, “Must We Mean What We Say?”, 16.


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“evidence of a certain kind”, whereas in the case of the native speaker “there is”, so Cavell,
“no evidence (which it makes sense, in general, to say) he has: the question of evidence is
irrelevant.”35 For, were the native speaker‟s assertion evidence-based, we would have to
assume that she had undertaken an unsystematic version of linguistic fieldwork, and that her
assertion rests on correspondingly shaky grounds, which would be absurd. This reductio is
supposed to show that the relation between a speaker and his language cannot be
characterized by appeal to a certain notion of knowledge: namely, the sort of knowledge that
rests on evidence uncovered in an empirical investigation. Knowledge that rests on such
evidence is observational knowledge. Thus, in asserting that “the question of evidence is
irrelevant”, Cavell is claiming that the knowledge that a speaker has of her language must be
non-observational knowledge.
         It follows from our considerations about rule-following that this must be true for our
understanding of the words we possess.36 For, if the word is to be something that „guides‟ the
speaker in deployment of it on particular occasion, the speaker cannot need to observe her
own linguistic behavior – and maybe that of others – in order to arrive at a statement about
how the word is used in general. On the contrary: the representation of how the word is used
in general must somehow be contained in each and every of her particular speech acts and
must, thus, be available to be articulated on reflection. This follows from the nature of
judgment: we said that each act of judgment points to an in principle unlimited series of
possible judgments and that the principle uniting the elements of the series must be known to
the judging subject since she must conceive of her act as an element of the series in order to
conceive of herself as making a judgment at all. We can also put this by saying that in framing
the judgment „a is F‟ my mind must operate simultaneously on two levels: on the particular
level on which I conceive of myself as bringing the object a under the concept F and on a
general level on which I conceive of F as something that can also appear in other judgments.


35
         Ibid., “Must We Mean What We Say?”, 13.
36
          Read as a comment about the origin of our possession of concepts this would, of course, be quite a mad
claim. For if there is to be such a think as empirical concept, it must be possible to acquire them, in some way or
other, through the encounter with the world. But the acquisition of concepts doesn‟t concern us here. If
Wittgenstein‟s critique of the empiricist idea of arriving at concepts by abstraction from sense data is accute, it
should be equally clear that not all concepts – probably not even all empirical ones can be – can be acquired in
this way. Cavell intended his remark as pertaining primarily to the statements of ordinary language philosophers
– something equivalent to what Wittgenstein calls “grammatical remarks”.


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        If we apply this structure to the linguistic case and imagine how two levels on which
my mind operates to be articulated, then we get the two statements “I think that a is F” and
something like “In English the word „F‟ is used in such-and-such a way”. These two
statements are not independent from each other; they are intrinsically connected. The
statement “I think that Fa” must, in certain way, already contain a statement like “‟F‟ is used
in such-and-such a way” or “One uses „F‟ in such-and-such a way”. It thus transpires that the
latter statement cannot be something that one could arrive at by generalizing over statements
of the former kind, since it is, in a certain sense, prior to them.
        It is often claimed that the upshot of Wittgenstein‟s considerations is that, on pain of a
vicious regress, rule-following cannot require any conscious or „articulate‟ knowledge of the
rules. Prior to our “explicit” grasp of the norms governing our language, so the idea goes,
there must be a way in which these norms are “implicit” in our doings; our knowledge of
them must be “tacit”. On the fundamental level, we thus “follow the rule blindly”, as
Wittgenstein seems to be saying. 37 If that were true, the project of investigating language as it
must be represented „from the inside‟ would be a non-starter. But I think these readings rest
on a misunderstanding. As we have seen, Wittgenstein thinks that the solution to the rule-
following problem requires recognizing the difference between the understanding of a
concept, on the one hand, and acts of thinking and judging, on the other hand. But he
decisively denies that this difference should be modeled on the contrast between “explicit”
and “implicit”:

Nothing would be more confusing here than to use the words “conscious” and “unconscious” for the contrast
between states of consciousness and dispositions. For this pair of terms covers up a grammatical difference. (PU,
§149)


What needs to be rendered intelligible in order to solve the rule-following problem is the
logical relation between a power or “disposition” and its actualizations; the contrast between
“explicit” and “implicit” only creates confusion in this connection. It is certainly true that
being able to dance tango doesn‟t necessarily include the ability to give a text-book
description of this dance. In same way, And it is certainly true that being a competent speaker

37
         For arguments along this lines see, for instance, Robert Brandom, Making It Explicit; Gareth Evans,
“Semantic Theory and Tacit Knowledge”; Wilfrid Sellars, “Some Reflections on Language-Games”. It is often
overlooked that in PU §219 the contrast to following the rules “blindly” is not following the rules “consciously”,
but rather following the rule by making a “choice”.


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of English doesn‟t require that one is able to state the rules of the grammar of English. But
that is not our topic. Our topic is the peculiar sense in which a judgment points ahead to an
unlimited series of judgments. And we have seen that for an act be an element of such series it
is not enough that in performing it the subject exercises a power that she can also exercise
elsewhere. Rather, in predicating F of a, the judging subject must conceive of F as a
predicative element, and to do so, she must apprehend it as something general that can also
be instantiated elsewhere, again and again. The relevant power or disposition must in this
sense be a self-conscious capacity – a dynamis meta logou, as Aristotle calls it. And if the
subject must comprehend its own act as an instance of something general, then we should
expect that she is also able to give voice to what she comprehends, perhaps not in the
sophisticated terms of the semantic theorist, but in some rough and ready way.
       In order to count as understanding a concept or a word, one must, at the very least, be
able to give an example of its use. This I take it, will be granted. But in giving an example one
already presents a particular as an instance of something general. To mark that the movement
that I am now performing is supposed to be an example of a tango step, I might say „Look:
this is how to dance the tango‟. To understand what I am aiming at with my awkward twirling
motions means to understand that my movement is supposed to exemplify how one dances the
tango. Correspondingly, to offer the sentence „Fa‟ as an example for the use of the word „F‟
means to perform an act of mind that if articulated is expressed in a sentence of the form “„F‟
is used thusly: one says „Fa‟ …” or simply “One uses „F‟ in such-and-such a way”, where the
„such-and-such a way‟ stands for the example. This is the kind of statement we need to
investigate. Considering the space left in the remainder of this paper, this will be rather
dogmatic and sketchy.


5. Counterfactuals and habituals
To begin with, let‟s focus on the grammatical form of the predicate that appears in these
statements and leave the investigation of the subject term for later. When I articulate my use
of „F‟ by giving an example I do not talk about something I‟m doing here and now or what I
did yesterday; I describe my general use of the word – my capacity or disposition. I already
mentioned above the two features of capacities or dispositions that make them relevant for our
purposes: (i) a disposition is something general insofar as it doesn‟t exhaust itself in a



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particular act, but can be actualized in an in principle unlimited series of act; (ii) a disposition
is not something abstract, but rather something real insofar as it explains its instances.
Because dispositions have these features, they seem like good candidates for what underwrites
our peculiar reaching ahead when we describe our student as adding 2 to 6.
         That dispositions have these two features is widely recognized. But in order to fit them
in the Quantificational Model the sentences describing a disposition are usually interpreted in
the following way. The standard view is that dispositional statements are to be rendered as
counterfactuals or “hypotheticals” as Gilbert Ryle puts it. According to this analysis, an object
S is disposed to M when C iff S would M if it were the case that C. In consequence, it looks
like dispositional statements don‟t describe anything actual at all; we seem to be talking only
about potential acts. If that were the case, dispositions would be useless for our purposes,
since they would turn out to be explanatory inert.38 The standard reaction to this problem is to
claim that the disposition has a “causal basis”, which is understood as an underlying state – in
our case probably some neurological state of brain of the person.39 But whether or not the
relevant causal basis is rendered in neurological terms, in the established Quantificational
framework the resources for treating dispositional statements is limited to counterfactuals or
generalizations about what normally happens, on the one hand, and to state ascription
referring to the “causal basis” on the other hand.
          Wittgenstein is famously skeptical about rendering understanding as a state.40 And, on
reflection, it seems rightly so: a state ascription seems to be quite unsuited to underwrite our
implicitly reaching ahead to an unlimited series of acts. If understanding is a state our pupil is
in, then it would have to be one and the same state that explains his present act of moving
from 2 to 6 and that would explain his act of adding 2 to 5000 that he might be performing
next week etc. In consequence, it seems that we need some further element besides his
understanding that explains what keeps him in that peculiar unchanging state all this time.

38
         This is the consequence Elisabeth Prior, Robert Pargetter and Frank Jackson draw in their paper “Three
Theses about Dispositions”.
39
         See, for instance, Donald Davidson, “Representation and Interpretation”, 96 and W.V.O. Quine, Roots
of Reference, 10 ff.
40
         See, for instance, Ludwig Wittgenstein, The Brown Book, §43: “[…] B is guided by the particular
combination of words in one of our three sentences if he could also have carried out orders consisting in other
combinations of dots and dashes. And if we say this, it seems to us that the „ability‟ to carry out other orders is a
particular state of the person carrying out the orders […] And at the same time we cannot in this case find
anything which we should call such a state.” See also PU, §146 und §149.


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Ordinary state ascriptions are tied to particular periods in time, which can be seen from the
fact that they come in two tenses: „This a is F‟ and „This a was F‟. As Wittgenstein points
out, it is characteristic of statements like “a is sad” or “b is red” that they do not reach ahead
in an unlimited way.41 And because this is so, asserting „This a is F‟ at t1 and asserting „This a
is F‟ at t2 is to express two different thoughts – even if a was F all through the period from t1
until t2. The content of the assertion made at t1 is properly expressed at t2 by saying „This a
was F‟. In consequence, ordinary state ascriptions cannot underwrite the peculiar reaching
ahead of the pupil‟s adding 2 to 4. For, if the appeal to the pupil‟s understanding of addition is
to explain how his adding 2 to 4 at t1 can point ahead to his adding 2 to 1000 at t2, then
asserting „He understands the plus-function‟ at t1 and asserting „He understands the plus-
function‟ at t2 must mean to express the same thought twice. If one takes a capacity to be an
underlying state, then one ties the pupil‟s understanding to a specific period in time. In
consequence, it will seem impossible how his act of adding 2 to 6 can reach ahead to an
unlimited series of acts.
         Wittgenstein‟s diagnosis of the source of the trouble is that we have been misled by
the tense of the verb phrases with which we ascribe a capacity:

There are […] various reasons which incline us to look at the fact of something being possible, someone being
able to do something, etc. as the fact that he or it is on a particular state. …] And his way of representation, …
is embodied in the expressions “He is capable of…”, “He is able to multiply large numbers in his head.”, “He
can play chess”: in these sentences the verb is used in the present tense, suggesting that the phrases are
descriptions of states which exist at the moment when we speak.42

The first step towards a solution to the rule-following problem is to realize that there are
judgments about finite beings that are properly expressed with sentences in present tense that
are neither about a process unfolding in time nor about states existing in certain period of
time. Dispositional statements have the form of habituals: they neither describe what an
individual is doing now nor which state it is in at a particular period in time; they say what
the individual does in general. They are non-temporal or “timeless” sentences; or we can also
say they are “time-general.”43 Even though one acquires a disposition at some point in time,


41
         See PU, §150.
42
         Ludwig Wittgenstein, The Brown Book, 117.
43
         See Michael Thompson, “Two Forms of Practical Generality” and Sebastian Rödl, Kategorien des
Zeitlichen, 173ff.


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once one has the disposition it is (ceteris paribus) there to stay. And because this is so the
sentence „He understands the plus-function‟ uttered at t1 and the sentence „He understands the
plus-function‟ uttered at t2 express the same thought.
       Recognizing the peculiar features of habituals can only be a first step towards a
solution to the rule-following problem. As far as we specified the grammar of our exemplary
sentences „He understands the plus-function‟ they do not differ from a description of habits.
Intuitively, however, the way in which one implicitly points beyond a present act by
describing it as the deployment of a concept is very different from the way in which one
reaches beyond a present act by describing it as an instance of a habit.
       Suppose I had the strange habit of eating chocolate soaked in melted lemon sorbet.
This habit can be instantiated in an in-principal-unlimited series of acts. But the way all those
acts of eating chocolate soaked in melted lemon sorbet are united with each other is quite
different from the way in which a series of judgments is united under the concept that is
deployed in them. For, the fact that chocolate and melted lemon sorbet is somehow connected
in me in a general fashion has nothing do with those items themselves. It is my habit that
makes it possible to give a unified account of all those cases of my eating chocolate soaked in
melted lemon sorbet. The habit explains why it is no accident that I eat them in this peculiar
combination every time. Since the relevant connection between my acts is thus constituted by
something specific to me as an individual, the reaching ahead to an unlimited series of acts is
framed or “restricted” by my finitude. As long as I‟m there with my strange habit, each of my
acts reaches ahead to a series of acts that is „unlimited‟ in the sense that it is not determined
how many there will be. But it does not point beyond me; it is, in that sense, limited insofar as
it depends on the existence of that habit in me. If you focus on that combination of foods,
what you can see in my present act of eating chocolate soaked in melted lemon sorbet is thus
not a “visible section of rails laid out to infinity”, but rather a visible section of a sad man‟s
life governed by a peculiar habit.
        When we describe our student as adding we are reaching not only beyond his present
act, we are reaching beyond him. This dimension of our reaching ahead is precisely what is
required in order to bring the difference between „correct‟ and „incorrect‟ onto the scene. For
in judging that he is executing the operation of addition correctly when he writes „4+2=6‟, we
affirm the thought expressed by this sentence ourselves. And making that judgment we



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exercise the very same concepts that he exercises in his act. Our act must be explained thus by
the same thing that explains his act. So the general item we are after must be something that
can be actual in both of us. A habit like my habit to eat chocolate soaked in melted lemon
sorbet cannot figure in this way: in describing me as eating those things in such peculiar
combinaton you do not bring yourself under my habit. Undoubtedly someone else might have
the same weird habit than I do; but what explains her and my acts are two different habits: her
and mine.
       Habitual sentences provide us with a first clue to the solution of our problem, since
they describe something general that is not abstract but actual and that explains its own
instantiations. But this first step is not yet sufficient. What we need is an account of a
particular kind of capacity – namely one in which the relation between the capacity and its
actualizations exhibits the peculiar logical features that characterizes the relation between a
concept and the judgment in which it is deployed. Wittgenstein suggested that this
accomplished, if we see the individual‟s dispositions against the background of a social
practice. According to him, the idea of a conceptual capacity is internally related to the
concept of a practice, in that a social practice is the very thing one has “mastered” when one
has such a capacity. In order for this clue to lead us to a solution to the rule-following
problem, we must understand what a practice is.


6. Three forms of the first person plural
Let‟s turn, then, to the subject-term of statements like “One uses „F‟ thus-and-so” or “English
speakers use „F‟ thus-and-so.” The latter sentence could be used by a field linguist describing
the English language. A speaker of English can also say: “We use „F‟ thus-and-so”. Let us call
the latter proposition S, and the proposition of the linguist T. Although S and T describe the
same state of affairs and have the same truth-value, they are not arbitrarily interchangeable.
The linguist cannot assert S, since he is not an English speaker. The expressions „we‟ and
„English speakers‟ have – to use Frege‟s terminology – the same referent but different
senses.44
       Cavell thinks that apprehending the logical features of „we‟ as it appears in statements
of type S is central to understanding the non-observational character of the knowledge that a

44
       See Gottlob Frege, “Über Sinn und Bedeutung”.


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speaker has of her language. Cavell writes:


The clue to understanding the sort of statement S is lies in appreciating the fact that „we‟, while plural, is first
personal. First person singular forms have recently come in for a great deal of attention, and they have been
shown to have very significant logical-epistemological properties. The plural form has similar, and equally
                                                                       45
significant, properties; but it has been, so far as I know, neglected.


According to this remark, propositions of type S articulate a special form of self-
consciousness – a self-consciousness that, in some yet-to-be-determined sense, extends
beyond the individual „self‟ to embrace a unity that, also in some yet-to-be-determined sense,
comprehends a plurality of subjects. This special form of self-consciousness will become
intelligible, the remark promises, if we investigate the “logical-epistemological properties” of
the first person plural. Although Cavell does not immediately pursue these programmatic
remarks further, it is already clear from this passage that, on his view, the philosophy of
language could hardly be guilty of a greater omission than this neglect of the first person
plural. For if the situation is as Cavell describes it, then only the investigation of the first
person plural can clarify what it is to speak a language.
         In abstraction we know already what “logical-epistemological properties” the first
person plural must have, if it‟s invocation is to be of help in the context of the rule-following
problem. For, we said that in framing the judgment Fa the subject must conceive of her act as
an instantiation of the concept F, and that, her comprehension of the general use of F must
therefore be contained in her original judgment. Applied to the linguistic this means that the
comprehension of the general use of a word must be contained in every employment of this
word on a particular occasion. If that is right, then it follows that a thought of the form “We
use „F‟ thus-and-so” must somehow be contained the statement „I think that Fa‟. What is
needed is, thus, an account of the first person plural that explains how the „we‟ can be
contained in the „I‟ in this peculiar way. Our question is, in other words, this: What kind of
proposition must statements of type S be so that they can be contained in each of our
judgments while describing, at the same time, something that stands in a normative and
explanatory relation to our judgments?
         If Cavell is to be believed investigating the “logical-epistemological properties” will


45
         Stanley Cavell, “Must We Mean What We Say”, 14.


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provide us with an answer. Without further elucidation, however, this suggestion can at best
provoke astonishment. The fact that first person pronouns cannot be replaced salva sensu by
descriptive expressions such as „speakers of English‟ is widely accepted. But how, beyond
this, an investigation of the first person plural might make progress toward its designated goal
is, to begin with, anything but clear. Imagine the following scenario. Suppose a prison guard
remarks while on his rounds: „The prisoners in Cell 20 have red dots on their noses.‟
Thereupon one of the cell-occupants looks in the mirror and then at his sleeping cellmates and
says: „We have red dots of our noses.‟ The two propositions are evidently not interchangeable
salva sensu. Nevertheless, the guard and the prisoner know about the red dots in the same
way: by observation.
        There is certainly is something the prisoner can say without observation. His
statement implies the proposition „I have red dots on my nose‟. To establish whether he
indeed does have red dots on his nose, he relies on a glance in the mirror; but that he is the
person of whom he asserts that he has red dots on his nose – this he need not and cannot
discover by observation. Precisely this distinguishes the first person singular formally from
demonstrative pronouns and definite descriptions.46 In both of the latter cases the judging
subject always needs to make a further judgment to determine that he is identical to the object
to which his judgment refers. In the first case, by contrast, the knowledge that he himself is
the object of which the concept ___has red dots on the nose is predicated is not mediated by
such an identity-judgment; rather, it is already contained in his original judgment. If further
investigation were required in this case, our cell-occupant could never discover that he is
speaking of himself. For each mediating judgment „I am this one‟ would require a further
identity judgment, and no matter where he looked, nothing could show him that he was
identical to the object to which he was referring. The knowledge that he is predicating the
concept ___has red dots on the nose of himself must therefore enter into the constitution of
his judgment „I have red dots on the nose‟. To judge in the first person singular involves
knowing, in virtue of the form of one‟s judgment, that one is oneself the object characterized
in that judgment. Let us call judgments of this form self-predications.
       Perhaps this much will be granted. But doubts about the feasibility of our program
cannot be waved away simply by appealing to this point. For how could the prisoner, in

46
        See G.E.M. Anscombe, “The First Person”.


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judging „We have red dots on our noses,‟ have non-observational knowledge of the existence
of his cellmates? After all, he is not identical with them! Whatever “significant logical-
epistemological properties” the first person singular may have, they do not seem to be
reproduced in the first person plural.
       We can gather from this consideration what must be the case if our program is to be
feasible. Our red nose scenario must be unsuited to bring out the “logical-epistemological
properties” of the „we‟ that stands in the subject-position of S-type propositions. That is to
say, there must be another form of the first person plural. The judgment „We have red dots on
our noses‟ can be analyzed into several judgments that are independent of one another. It can
be represented as a conjunction of the following singular judgments: first our prisoner notices
that he himself has red dots on his nose; then he brings prisoner a under the concept ___has
red dots on the nose; and finally he brings prisoner b under this concept. He then unites this
series of independent singular judgments into a plural judgment, in which he refers with „we‟
to the set of individuals of which he is an element. The plural judgment is in this sense
distributive. Its truth-value is wholly determined by the truth-values of prior singular
judgments. Any distributive proposition will be inappropriate for our purposes, no matter
what concept we put in place of ___have red dots on our noses. For if „we‟ is distributive,
then it cannot be contained in „I‟.


6.1. The distributive we
It is a widely assumed that all uses of „we‟ are structurally analogous to the one just
discussed. I will call this view the „Distributive Conception of the first person plural‟. That
propositions of type S differ from propositions like „We have red dots on our noses‟ is plain
enough. While the latter is a proposition about the state of individuals a, b, c at a certain time
t, our proposition S is not an assertion about what particular speakers said at a certain time.
Rather, it describes how speakers of English use the relevant expression in general. No one
will deny this. The decisive question is how to understand this generality. According to the
standard view in contemporary philosophy of language all generality is quantificational
generality. On this assumption, there is no other alternative but to analyze propositions of type
S as some sort of quantification over individual speakers and their relations. However the
details of such an analysis run, it will be structurally analogous to the distributive analysis,



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inasmuch as the truth-values of the quantified judgments are determined by the truth-values of
the corresponding particular judgments. The particular judgment must thus be regarded as
prior and cannot already contain the general judgment. It should be obvious that if our
propositions of the type S fit into the quantificational model of generality, then they cannot
express knowledge without observation.
         Robert Brandom, for example, begins his book Making It Explicit with the thesis that
rational beings are the beings who say „we‟. He adds, however, that this is only an empty
formula waiting to be filled with content. The goal must be to “specify in other terms what
one must be able to do in order to count as saying „we‟”.47 That is, Brandom holds that the
first person plural is not logically simple; he thinks we need an analysis which decomposes it
into its elements. His thesis is that a linguistic practice can be characterized in terms of a
complex social structure of interdependent ascriptions of commitment and entitlement taking
place between individuals. On this view, the „we‟ that sentences of type S bring to expression
is secondary to the attitudes that particular individuals adopt toward each other. In other
words, the „we‟ is “instituted” by their interdependent normative attitudes. The „I-thou‟
relation, as Brandom puts it, is prior to the „I-we‟ relation. He writes:


[What we treat as fundamental is] I-thou sociality rather than I-we sociality. Its basic building block is the
relation between an audience that is attributing commitments and thereby keeping score and a speaker who is
undertaking commitments, on whom score is being kept. The notion of discursive community – a „we‟ – is to be
                                                   48
built up out of these communicating components.


On this view, the “we” that propositions of type S bring to expression is secondary to the
assessment-behavior of particular individuals; it is instituted by their interdependent
normative attitudes.49 I cannot go into the details of Brandom‟s view here, but it should be
clear that this approach commits him to a Distributive Conception. If Cavell is right, then such
a project is doomed to failure, since one cannot describe those individual attitudes without
already referring to the very “we” that these attitudes are supposed to institute.



47
         See Robert Brandom, Making It Explicit, 4.
48
        Robert Brandom, Making It Explicit, 508. See also ibid., 39: “Assessing endorsing, and so on are all
things we individuals do and attribute to each other, thereby constituting a community, a „we‟.”
49
          Ibid., 39: “Assessing, approving, and so on are all things that we do individually and grant others the
right to do, and thereby a community, a „We‟, is constituted.”


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        Cavell‟s insight is that a judgment of type S cannot be a “generalization,”50 since the
corresponding particular judgments must already contain it. It must, therefore, involve some
other form of the first person plural. On closer inspection, there is a whole range of judgment-
types that resist the distributive analysis.51 The proposition “Prisoners a, b, and c are
cellmates,” for instance, cannot be analyzed into conjunction of singular judgments. What is
true if it is true is not something that holds of all three because it holds of each one
individually. Rather, it can only hold of them all together. “We are cellmates” is thus an
example of a non-distributive use of “we.” But since our prisoner is evidently not identical to
his cellmates, this example does nothing to alter the impression that his reference to the other
two can only be demonstrative.


6.2. The collective we
Let‟s look at the alternative that Cavell proposes. Cavell emphasizes that a sentence of type S
is “not […] an assertion about how a word is used by me (or „some given person‟),” but rather
“a statement about how the word is used in English.”52 According to Cavell to put forward a
proposition of this kind means “presenting [oneself] as an example, as the representative of
the community.”53 Thus, for Cavell, the central question to be answered in an investigation of
judgments of type S is the question how I, on the basis of my “experiences,” can speak for
others. He asks: “How can I, what gives me the right to, speak for the group of which I am a
member?”54
        Cavell‟s answer has two parts, one negative and the other positive. The negative part
can be summarized as follows: Since each speech act must in a certain sense contain
judgments of type S, the latter cannot rest on comparative judgments in which I state that
others speak as I do. The positive part of his answer then consists in the account of those
propositions as expressing “claims to community”:


When [a speaker] „says what we say‟, what he produces is not a generalization […], but a (supposed) instance of


50
        Stanley Cavell, The Claim of Reason, 19.
51
        Compare T. J. Kay, Plural Predication.
52
        Stanley Cavell, “Must We Mean What We Say?”, 37.
53
        Stanley Cavell, “The Argument of the Ordinary. Scenes of Instruction in Wittgenstein and Kripke”,72.
54
        Stanley Cavell, The Claim of Reason, 18.


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what we say. We may think of it as a sample. The introduction of the sample by the words „We say…‟ is an
invitation for you to see whether you have such a sample, or can accept mine as a sound one. 55


The claim that I make with a proposition of type S can never be secured by me alone, because
my judgment requires the agreement of the others: the thought that I express depends in its
constitution on the fact that my interlocutors also think it. If my interlocutor withholds his
agreement, even after lengthy argument, then “we have to conclude that”, as Cavell writes a
few lines later, “on this point we are simply different; that is, we cannot speak for one
another.” In this case my judgment has turned to be not false, but rather empty. For it has
become clear that “there is no us […] to say anything about.”56 As Cavell recognizes himself
understanding judgments of type S in this way has rather unsettling consequences. For it
means that there is no explanation for the fact that we agree with each other in this
fundamental way; it is a groundless factum that we must simply accept, and that holds only
insofar as we accept it.
        The difference between Cavell‟s picture and the Distributive Conception turns on the
idea that the elements united under the „we‟ are not intelligible prior and independently of the
we. The picture Cavell aims at is the picture of a kind of an agreement among elements
which, like our cellmates, are what they are only as elements of this relation – only in their
“attunement to one another.” But this distinction alone cannot make the possibility of
judgments of type S intelligible: the bees in a beehive be said to be mutually attuned, yet they
have no concept of the beehive. In order to arrive at a difference, we must introduce the
further condition that the “attunement to one another” be self-conscious. If we do this, then
the relation of agreement that constitutes the elements must be a relation that only obtains if
the elements think that it obtains. That is to say: In judging, the subjects must understand
themselves as “mutually attuned.” Cavell‟s thesis is consequently this: In thinking „I assert
that p‟ I implicitly think „We use A thus-and-so‟; and in thinking this latter thought, I think a
thought that depends in its very constitution on the fact that my fellow speakers think it as
well.
        Now it may seem doubtful whether there are any thoughts at all which depend in their
very constitution on the fact that others also think them. But this doubt would be misplaced.

55
        Stanley Cavell, The Claim of Reason, 19.
56
        Ibid., 20.


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Collective actions provide an example. The proposition “We are dancing a tango with each
other” cannot be analyzed distributively. The concept of dancing a tango cannot be
predicated in singular judgments; only a plural subject can fall under this concept. For, I can
only dance a tango with you if you dance a tango with me. It follows that our activity is a
case of dancing a tango only if we both think that we are dancing a tango with each other. If
this is right, then we cannot discover by observation that we are doing so. For that would
require that each of us grasp the thought “We are dancing a tango with each other”
independently of the other. But dancing a tango is not something one does in relation to
another person; it is something one does together with another person. My judgment “I‟m
dancing a tango with you” must already contain your corresponding judgment that you are
dancing with me. Otherwise our turn on the dance floor would be something that we each do
in relation to the other, not that harmonious movement which two can only perform together.
We can put this as follows: My relation to you, on the basis of which you can appear in my
thinking as my partner in action, consists in the fact that you think of me as your partner in
action. If you do not think this, then my judgment remains incomplete and is finally empty.57
Since, for this reason, perception cannot be the source of my knoweldge of the other, the
relevant “we” cannot be constituted from a first person singular and a demonstrative reference
to another person. That you are the one my judgment is about is not something I can first
discover through further investigation; this knowledge must enter into the constitution of my
judgment. Consequently we cannot think the thought “We are dancing a tango with each
other” independently of each other; we can only think it together. If we do this, then we do
not make two judgments with the same content; we make the very same judgment. Our
judgment is a collective self-predication – that is, a judgment in which you and I have, in
virtue of the form of our judgment, a knowledge of the unity that we together constitute.
        If this admittedly somewhat sketchy line of thought is right, then we have identified a
form of the first person plural that is distinct from the distributive form. Let us call it the
collective We. Cavell certainly does not claim that a natural language is a collective action.
He endorses the following thesis: A natural language is the collective disposition of its
speakers. One must defend such a thesis if one thinks that the first person plural in


57
       On this logical structure see also to Sebastian Rödl, “Is the Second Person Concept a Logical
Concept?”.


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propositions of type S stands for the community of speakers of the relevant language. For if
the use of “we” in propositions of type S is the same as the one in propositions about
collective actions, then the difference between the two forms of proposition can only consist
in their tempus. Propositions of type S must consequently be a special sort of habitual
propositions. They express judgments in which a collective subject is brought under a concept
in a time-general manner, and furthermore in such a way that a thought is grasped only if this
judgment is made together by the members of the community – that is, only if the judgment is
an act of a collective subject. Judgments of type S would accordingly be habitual collective
self-predications.
       I do not wish to deny that there are judgments that exhibit these logical properties. If
the category of habitual collective self-predications turned out to be a grammatical fiction,
much that we commonly take to be real would turn out to be mere appearance. For the
proposition “We play in an orchestra” seems to be an example. “We have a love affair” is
another. “We live in a democracy” is perhaps a third one. In the present context, however,
the only relevant question is whether referring to this form of judgment supplies us with the
right interpretation of the grammar of propositions of type S.
       One of the considerations that leads Cavell to this thesis is the observation that
communicating is a “cooperative activity.”58 This thesis is quite plausible. For I can tell you
something only if you think that I am telling you something, and not making a joke or talking
with somebody else. But it is another question altogether whether the language that we speak
when we communicate is the disposition of a collective subject. Our brief reflection on
collective actions suffices to make clear why this cannot be so. The unity of multiple subjects
in a collective agent or a “community” must have a ground. If two people are dancing a tango
with each other, then, we said, it can be no accident that they both think that they are dancing
a tango with each other; they must make one judgment together. To say this is in the first
instance merely to describe what collective actions are; it does not yet explain how they are
possible. To make their possibility intelligible, we must explain what unites individuals into a
collective subject. In our example, the following answer suggests itself: What makes the
harmony of our movements on the dance floor possible is the fact that we both have learned to
dance the tango. Our “attunement with each other” is constituted by the fact that our thinking

58
       Compare “Must We Mean What We Say?”, 33.


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has the same source: the practice of tango-dancing. Our unity in action is thus secondary to
the practice under which our action falls.
       No doubt, not every collective action is underwritten by an established practice. But
however a general theory of collectivity might look like, the ground of the unity of a
community cannot consist, in the basic case, of relations between its members. Rather, it
must consist of something more than their attitudes and dispositions. For their unity in
thought must have a source. And this can only be the concept they employ in their common
judgment. It transpires that the idea of the collective We thus presupposes the possibility of
following a rule, and therefore cannot contribute to the clarification of the latter. As soon as
we advert to the collective We to elucidate the relation of accord between a concept and its
employment, we rob ourselves of all hope of explaining how it can be anything but a mere
accident that our movements on the dance floor harmonize so beautifully. The resulting
picture cannot, in the final analysis, be distinguished from the picture of a merely accidental
congruence of the dispositions of individuals.


6.3. The generic we
Cavell sees that judgments of type S cannot be “generalizations,” since we are warranted in
making them without receiving evidence of any kind, and since they consequently must
already be contained in each of our judgments. To turn this insight into a solution to the rule-
following problem, we must investigate exactly what form propositions of type S have, such
that they can be contained in each of our judgments. In so doing, we encountered the
analogue of the assumption that the alternative to describing a special process is describing an
ordered set of processes – namely the idea that the alternative to describing an isolated
speaker is to describe a group of speakers. Both versions of this idea have turned out to be
problematic. If the appeal to the concept of practice is to lead to a solution to the rule-
following problem, there must be a third form of the first person plural that is more
fundamental than the distributive and the collective We.
       Developing this form properly would require a separate investigation, but I think our
reflections justify us in drawing the following conclusion. Alluding to Wittgenstein, we can
express it by saying: To describe the phenomenon of language we must describe a practice
and not a group of individuals, no matter of what kind. This negative characterisation already



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contains a positive one. For judgments that neither refer a particular individual nor a group of
individuals, and nevertheless describe them, are judgments that are not only time-general but
also substance-general. They are generic judgments.59 Judgments of type S are judgments of
this sort. With them I describe, not a set of utterances of which my utterance is an element,
but rather the practice that I exemplify with this statement. If I do this, then I speak, not about
or for a group, but rather articulate the general from whose exemplar or bearer I am.
        Cavell presupposes that the existence of a natural language is bound to the existence of
several speakers of this language, since one can only acquire conceptual capacities by being
initiated into a practice. I don‟t want to deny this. To say that something general is not
abstract but actual is to say that it exists only as the “form” of its instantiations. A practice is
a “form” of a specific kind; it exists only as the form of a multiplicity of bearers. But from
the fact that the practice I actualize in my statements must also be exemplified by others, it
does not follow that I relate myself to these others in articulating the practice.
        Both, the Quantifiactional Model and Cavell‟s collective conception of practice rest on
a confusion between generic predication and plural predication. The difference between
generic and plural predication is orthogonal to the difference between singular and plural
predication. A generic proposition can occur in the singular or the plural. In a description of
chess, generic propositions must appear in the plural, since this is a game that people can only
play together. By contrast, if we explain how Patience is played, our description will consist
of generic propositions in the singular. After all, patience is a game that one plays alone
        This line of thought does not yet explain in what way judgments of type S express
knowledge. We have only seen that it must be so. And we have identified an assumption that
makes it impossible to comprehend how it can be so – namely, the assumption that the
relevant “we” relates me to a group of which I am a member. If the employment of “we” in
propositions of type S can be neither distributive nor collective, then it must involve a generic
We. Judgments of type S are generic self-predications. To make a judgment of this kind
means to understand oneself, in virtue of the form of one‟s judgment, as an exemplar of
something general, of which there are also other exemplars. And even if one is the last human
being left on earth: As long as one thinks, one thinks thoughts of the form “We use A thus-


59
         Compare Michael Thompson, “The Representation of Life”; as well as Sebastian Rödl, Kategorien des
Zeitlichen, 188ff.


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                    DRAFT: Matthias Haase The Representation of Language, Chicago 25.01.08


and-so” and thereby understands oneself as an exemplar of a practice of which other
exemplars once existed.


7. Practice and metaphysics of language
The following thought experiment might help to situate what Wittgenstein calls a practice.60
Imagine that on some remote island a game was invented that happened to have the same
rules as chess. Let us assume that for some strange reason it is called „twin-chess‟, even
though the islanders have no idea that in other parts of the world people play a game called
„chess‟ that has the same rules as the game they call „twin-chess‟. One fine day a cruising ship
strands on the island. One of the tourists, who is, of course, completely ignorant of the local
customs and thereby of the fact that the islanders have a game called „twin-chess‟, sees one of
the locals sitting in front of a checked board with wooden figures. He joins him and without
further ado they start moving figures on the board. It seems intuitive to say that whatever they
are doing they are not playing a game of chess with each other. For, I‟m only playing a game
of chess with you, if I know that you are playing chess with me and not just randomly moving
figures on the board. And since, by hypothesis, it is a mere accident that the moves of the
islander exhibits the same patterns as the moves of the tourist, they have no way of knowing
why the other is moving the figures in this way. They are thus not playing with each other;
each of them is merely reacting to the other‟s behavior that by coincidence fits with his
completely unjustified assumption about what they are doing.
        If this rendering of the thought experiment is sound, it follows that „chess‟ and „twin-
chess‟ are the names for two different games that happen to have rules with the same content.
Now it is, of course, true that the rules of both games specify the same pattern of possible
types of moves on a checked board. So if we want to we can call them both „chess‟ as long as
we keep in mind that we are then using this term as the name for an abstract system of two
possible types of moves that is exhibited by two actual games existing in the world. To avoid
misunderstandings it will be best to mark talk about the abstract system by using the name
„chess*‟ and then say that chess and twin chess are two instantiations of chess*. The
important thing to notice is that the event of playing a game of chess is in the first instance an

60
         The thought experiment is from Michael Thompson. See his “What is it to Wrong Someone? A Puzzle
abut Justice”, 362ff..


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                       DRAFT: Matthias Haase The Representation of Language, Chicago 25.01.08


actualization not of chess* but of chess. That is to say, what enters into the explanation of the
acts the tourist and the islander might be performing on a given occasion, is not the abstract
system of possible moves, but rather the real games called „chess‟ and „twin-chess‟
respectively.
         When we apply these distinctions to the case of language, we get the following result.
If we talk about our languages as something that can be individuated giving rules for the
concatenation of types of expressions and a function that assigns semantic value to every
well-formed concatenation, then we talk about an abstract entity in the realm of possible
abstract semantic systems. Let‟s call this thing, following our symbolism, „English*‟. This
abstract semantic system is exhibited by English as we know it. But it could also be exhibited
by Twin-English, a language that came – in complete independence from English – into
existence on some isolated island and happened to have the exactly the same rules for the
concatenation of types of expressions etc. as English. These two entities in the world called
„English‟ and „Twin-English‟ are actualized by the acts and states of English speakers and
Twin-English speakers respectively. We thus get the following chart:


Level 1: Abstract semantic systems                                             English*
Level 2: Natural Languages/“Practices“          English                             Twinenglish
Level 3: Acts and states of speakers            English speech acts                 Twinenglish speech acts


When Davidson talks about languages he talks about such things as English* and never about
such things as English proper. Many contemporary philosophers of language have argued that
this is a mistake. They tend, however, to assimilate the talk about English to the talk about the
complex collections of the acts and states of the speakers of English.61 This is no coincidence.
The Quantificational Model that governs the contemporary philosophy of language leaves
only two option for interpreting the grammar of statements describing a language: either we
situate them on Level 1 or we locate them on Level 3 and regard them as some kind of
statement generalizing over the acts and states of actual speakers.

61
         Ruth Millikan, for instance, writes: “The phenomenon of public language emerges, I believe, not as
set of abstract objects, but as a real sort of stuff in the real world, neither abstract nor arbitrarily constructed by
the theorist. It consists of actual utterances and scripts, forming crisscrossing lineages.” (Ruth Garrett Millikan,
“In Defense of Public Language”, 10) The whole point of the notion of lineage is, of course, that it can be
defined in evolutionary terms – that is, by talk about the complex history of the causal interactions between
events.


                                                                                                                      36
                   DRAFT: Matthias Haase The Representation of Language, Chicago 25.01.08


       I have suggested that Wittgenstein‟s remark “In order to describe the phenomenon of
language, one has to describe a practice, not a singular event, no matter of what kind” should
be read as the insight that the primary notion of language is situated on Level 2 and that one
must, under all circumstance, resist the temptation to assimilated the descriptions of a natural
language to statements that belong to Level 3. This is “a very difficult insight” insofar as it
requires recognizing a kind generality that is not quantified generality. But if my presentation
of the rule-following paradox is acute, then it transpires that its solution requires nothing less
than this scandalous step. For looks like apprehending the possibility that a judgment points to
an unlimited series of possible judgments such that the principle uniting the elements of the
series known to the judging subject, requires the availability of such peculiar general items as
English which, by contrast to such things as English*, exist by way of being known to its
speakers.
       To be clear, our problem is not the one that the nominalist worried about – namely,
that posing the existence of countless languages in the realm of abstract objects would be
somehow metaphysically suspicious. (After all, these objects are not supposed to be real
anyways.) Rather, our difficulty is that in order to apprehend how a given utterance can be
connected in a determinate fashion to any one of those entities, we also need a notion of
language in sense of which there only a few hundred of them in the world. What I tried to
show is that the Quantificational Model prevents us from even making a comprehending the
possibility of these things.




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