## 1. Rules, Meaning, and Content



What does the notion of rule-following have to do with the notions of
linguistic meaning and mental content? For our purposes, the important
point is that meaning something by a linguistic expression is
analogous to following a rule. Suppose I write out the beginning of an
arithmetical series

 

\[
2, 4, 6, 8, 10, \ldots
\]


If the rule I'm following is *add 2*, the
continuation

 

\[
12, 14, 16, \ldots
\]


is *correct*, in that it accords with the rule I'm
following, while the continuation

 

\[
13, 19, 20, \ldots
\]


is *incorrect*, in that it fails to accord with the rule
I'm following.



We have here an analogy with my meaning something by a linguistic
expression. Say that I mean *blue* by 'blue'. Then,
'blue' is correctly applicable to, for example, a US
postbox but not to a ripe (Roma) tomato. We can express this point by saying
that the former application accords with the predicate's meaning
while the latter application fails to do so. Given this analogy,
arguments about rule-following have consequences for our conception of
linguistic meaning: if an argument shows that there are no facts about
which rule an agent is following, it may also show that there are no
facts about what a speaker means by a linguistic expression.



Note that the notion of accord in play in the case of following a rule
is also in play in our conception of mental states with intentional
content generally. Say that one intends to attend the performance of
Sartre's play *No Exit* at the Hopewell Theatre on
Wednesday. Then, one's attending the performance at the Hopewell
on Wednesday accords with one's intention (in the sense that it
fulfils it), while one's staying at home to grade logic exams
fails to accord with it. Say that one believes that the cat is on the
mat. Then, the state of affairs in which the cat is on the mat accords
with one's belief (in the sense that it renders it true), while
the state of affairs in which the cat is on the roof does not. Say
that one desires to smoke a *Bolivar Number 3*. Then,
one's smoking a *Bolivar Number 3* accords with
one's desire (in the sense that it satisfies it), while
one's smoking a *Cafe Creme* does not
accord with it. Given this, arguments about rule-following have
consequences for our conception of mental content: if an argument
shows that there are no facts about what rule an agent is following,
it may also show that there are no facts about the contents of a
thinker's mental states.



Before considering the arguments themselves, we'll pause to
reflect on views about the relative priority of linguistic meaning and
mental content, and on what presuppositions are required in order for
the arguments to be run.



In his influential 1989 survey, Paul Boghossian distinguishes between
two broad types of view:


* *The Sellarsian View:* the notion of linguistic meaning is
explanatorily prior to the notion of mental content (Sellars
1956).
* *The Gricean View:* the notion of mental content is
explanatorily prior to the notion of linguistic meaning (Grice
1989).



Boghossian suggests that, irrespective of which of these views is
adopted, it will not be possible to develop a sceptical argument that
exclusively targets linguistic meaning. On the Sellarsian View, the
conclusion that there are no facts about linguistic meaning will
ensure that there are no facts about mental content, since on that
view it is from the former sort of fact that the latter sort of fact
would have to be derived. On the Gricean view, raising a sceptical
doubt about linguistic meaning cannot be done without raising a
sceptical doubt about mental content.



We would add a third possible view:


* *The Davidsonian View:* the notions of mental content and
linguistic meaning are explanatorily interdependent; neither takes
explanatory priority over the other (Davidson 1984, 2001).



Clearly, on the Davidsonian view, one cannot pose a sceptical threat
to the existence of facts about the meanings of linguistic expressions
without also threatening the existence of facts about mental content,
and vice versa. And we can add Boghossian's further
observation:



> 
> 
> If [the sceptical arguments are] effective at all, they should be as
> effective against linguistic content as they are against mental
> content. This is evident from the fact that the arguments construct
> their skeptical case by exploiting features of content properties, but
> without exploiting any facts about the putative *bearers* of
> those properties. Thus, they would apply to anything said to possess
> content, whether it was mental or not. (1990 [2008: 62])
> 
> 
> 



In what follows, then, we'll move freely between considering
arguments about rule-following, linguistic meaning, and mental
 content.[2]


## 2. The Sceptical Argument



We'll begin with a brief outline of the argument of
Kripke's sceptic. Suppose that I've never dealt with
numbers larger than
 57.[3]
 (Given our finite nature and the infinitude of the natural number
series, there will always in fact be such a number.) I'm asked
to perform the computation '\(68+57\)',
and I arrive at the
answer '125', which I take to be right. However, a
"bizarre skeptic" (Kripke 1982: 8) questions my certainty.
She suggests that in the past I used 'plus' and
'+' to mean a different function, which she calls
"quaddition". Quaddition yields the same result as
addition if the numbers are lower than 57, and 5 otherwise, so the
correct result of the aforementioned computation is '5',
not '125'. I should answer '5' if I intend to
use 'plus' in the same way in which I have been using it
in the past, or so the sceptic suggests.



Kripke allows that the sceptic's proposal is "absolutely
wild", and that she is "crazy" if she
"proposes [her] hypothesis sincerely". He grants, however,
that it is not logically impossible, and so "there must be some
fact about my past usage that can be cited to refute" that
hypothesis (1982: 9). That is, there must be some fact about my past
usage that determines that I meant *addition* by
'plus' in the past, and thus that (again, assuming that I
intend to use the expression in the same way I have been using it so
far) I should answer '125' rather than '5'.
Importantly, the sceptic does not question my memory concerning past
use; indeed, she goes as far as to allow that the exercise of my
cognitive powers is faultless, and that I have access to all the facts
about my mind and behaviour that are potentially constitutive of my
meaning one thing rather than another (1982: 14). Her thought is that
if I am not able, even in such cognitively ideal conditions, to
provide the fact in virtue of which I mean *addition*, a fact
that properly singles out the function of addition rather than the
function of quaddition, it is because there is no such fact.
Furthermore, the focus is on past use because "if I use language
at all, I cannot doubt coherently that 'plus', as I now
use it, denotes plus" (1982: 13). But, if the sceptic's
challenge succeeds, it can be generalized, for "if there was no
such thing as my meaning plus rather than quus in the past, neither
can there be any such thing in the present" (1982: 21). (The
fact that the sceptic grants the idealisation of our cognitive powers
in the way that she does shows that her argument is not of a piece
with the argument of the epistemological sceptic, who is concerned
with whether our actual cognitive capacities can lead to knowledge.
See Boghossian 1989 [2002: 150]. For dissent over this point, see
Ginsborg 2018. Martin Kusch takes the argument to be metaphysical
[2006: xiv], but, in contrast with Boghossian, he takes the dialogic
setting to play an essential role in it.)



As we'll see, the search for a fact fails, and the sceptic
concludes that "the entire idea of meaning vanishes into thin
air" (Kripke 1982: 22). Kripke rejects this paradoxical
conclusion as "insane and intolerable" (1982: 60) and
"incredible and self-defeating" (1982: 71), and goes on to
develop, on behalf of Wittgenstein, a sceptical solution, which he
takes to be similar in some respects to David Hume's solution to
the sceptical problem about causation (1982: 4; 62-69), and
which purports to conceive of meaning in a way that does not lead to
paradox. We discuss the sceptical solution in
 section 3.
 (George Wilson was the first to insist on the significance of the
distinction between the parts of the sceptic's position
Kripke's Wittgenstein accepts and the parts he
rejects--between the *basic* sceptical conclusion,
according to which there are no facts about a speaker of the sort that
the sceptic is seeking that constitute her meaning something by an
expression, and the *radical* sceptical conclusion, according
to which no one means anything by an expression [Wilson 1994, 1998].
We will return to Wilson's view in
 section 3.3.)



Why does Kripke take the search for candidate meaning facts to fail?
Recall that all my previous uses of '+' are compatible
with my meaning *quaddition*, which is what enables the sceptic
to say that I meant that all along. One might complain that the
challenge operates from a "ridiculous model of
instruction" (1982: 15), which fails to take into account that
to be a competent adder is to have internalized a general instruction
or rule that is now "engraved on my mind as on a slate"
and which "justifies and determines my present response"
(1982: 15-16). But the sceptic will reply that the worry can be
raised again with respect to the general instruction or rule, which is
just as susceptible to being interpreted in a deviant way as the
initial expression. Kripke then considers a variety of other
candidates, which are the kernel of various philosophical theories,
and argues, on behalf of the sceptic, that none of them fit the bill.
Among the facts considered are my being disposed to produce the sum
(1982: 22-32), my instantiating a machine whose operations
embody the function of addition (1982: 32-35), the simplicity of
the addition hypothesis (1982: 37-39), my having a distinctive
experience "with its own special quale, known directly"
through introspection (1982: 41), my having an image in mind that
supposedly singles out addition (1982: 42), my being in a primitive,
irreducible state of meaning addition (1982: 51-53), and my
grasping an abstract entity, such as a Fregean sense, which singles
out addition (1982: 53-54). None of them, Kripke argues, is
successful in ruling out the skeptic's hypothesis that I meant
*quaddition* rather than *addition*.



As mentioned above, dispositionalism and non-reductionism are the most
prominently discussed proposals, and we'll consider them more
carefully in
 section 4
 and
 section 5,
 respectively. At this stage, we should ask the following question:
what are the conditions that a candidate meaning fact must meet? There
is controversy in the literature about their nature and
plausibility.


### 2.1 The Extensionality Condition



Here is how Kripke first lays out the two conditions:



> 
> 
> An answer to the skeptic must satisfy two conditions. First, it must
> give an account of what fact it is (about my mental state) that
> constitutes my meaning plus, not quus. But further, there is a
> condition that any putative candidate for such a fact must satisfy. It
> must, in some sense, show how I am justified in giving the answer
> '125' to '\(68+57\)'.
> The
> 'directions' ... that determine what I should do in
> each instance, must somehow be 'contained' in any
> candidate for the fact as to what I meant. Otherwise, the skeptic has
> not been answered when he holds that my present response is arbitrary.
> (1982: 11)
> 
> 
> 



To begin with, Kripke claims that whatever fact makes it the case that
a speaker means addition by '+' must single out the
addition function, as opposed to the quaddition function, as what is
meant. It follows from this that the putative meaning-constituting
fact must account for the conditions of correct application of
'+'. In other words, the fact in which my meaning addition
by '+' consists must single out '4' as the
correct response to '\(2 + 2\)',
'110' as the correct response to '\(55
+ 55\)', '125' as
the correct response to the query '\(68 +
57\)', and so on. Meaning facts render the applications
of expressions correct or incorrect, and so a fact cannot count as a
meaning-constituting fact unless it does this. This is an
uncontroversial claim, which most philosophers accept. As Simon
Blackburn notes, this 



> 
> 
> distinguishes the production of terms from mere noise, and turns
> utterance into assertion--into the making of judgement, 
> 
> 
> 



and so 



> 
> 
> it is not seriously open to a philosopher to deny that, in this
> minimal sense, there is such a thing as correctness and incorrectness.
> (1984 [2002: 29]; see also Wikforss 2001: 206; Hattiangadi 2006, 222;
> Gluer & Wikforss 2009: 35; see Travis 2006 for a dissenting
> view) 
> 
> 
> 



Moreover, this is something on which those who seek to offer a
reductive account of meaning (e.g., Fodor 1990; Millikan 1984) and
those who are sceptical about the prospects of reduction (e.g.,
Boghossian 1989; Verheggen 2011; Bridges 2014) seem to agree.



We'll call this first condition the *extensionality
condition*. In the case of a predicate like 'green',
for example, it requires that the fact which constitutes its meaning
determines the appropriate class of things to which
'green' is correctly applicable. This will be the class of
green things as opposed, say, to the class of *grue* things
(where an object is grue if and only if it is green before some
specified time *t* and blue thereafter), and in the arithmetical
case on which we have focussed so far, the extension of
'+' will contain the triple \(\langle 57, 68, 125\rangle\)
(and not the triple \(\langle 57, 68, 5\rangle\)).



To see how a candidate meaning-constituting fact might fail the
extensionality condition, consider a simple form of dispositional
theory of meaning which proposes as constitutive of my meaning
addition the fact that I'm disposed to answer with the
*sum* (as opposed, say, to the *quum*) when faced with
arithmetical queries of the form '\(x +
y\)'. The sceptic argues that this fact doesn't
single out the addition function:



> 
> 
> Let 'quaddition' be redefined so as to be a function which
> agrees with addition for all pairs of numbers small enough for me to
> have any disposition to add them, and let it diverge from addition
> thereafter (say, it is 5). Then, just as the skeptic previously
> proposed the hypothesis that I meant quaddition in the old sense, now
> he proposes quaddition in the new sense. A dispositional account will
> be impotent to refute him. As before, there are infinitely many
> candidates the skeptic can propose for the role of quaddition. (Kripke
> 1982: 27)
> 
> 
> 



We'll consider whether dispositionalism can muster resources to
deal plausibly with this problem concerning the satisfaction of the
extensionality condition below (in
 section 4).


### 2.2 The Normativity Condition



According to a prominent line of thought, the notion of correctness
involved in the seemingly platitudinous claim that meaningful
expressions have conditions of correct application is
*intrinsically normative*. On this reading, meaning facts are
normative facts--they not only sort the applications of
expressions into correct or incorrect, but also prescribe how
expressions ought to be applied. They issue semantic categorical
obligations that bind speakers in determinate ways; the justified
applications are precisely those that fulfil these semantic
obligations. (The kind of normativity at stake is meaning engendered,
rather than meaning determining; it is grounded in meaning, rather
than grounding meaning. See Gluer and Wikforss 2009 for this
helpful distinction.)



To illustrate how the second condition, thus construed, constrains
accounts of meaning, let us again consider Kripke's discussion
of dispositionalism. He thinks that the dispositionalist offers
"a descriptive account" of the relation between what one
means by an expression and one's uses of that expression, but
that "this is not the proper account of the relation, which is
*normative*, not descriptive" (1982: 37). More generally,
Kripke says, "the relation of meaning and intention to future
action is *normative*, not *descriptive*" (1982:
37). Among the commentators who read the second condition in this way
are Wikforss 2001, Gluer and Wikforss 2009, Hattiangadi 2006 and
2007, and Miller 2011, 2012. Thus construed, the sceptical argument
can be compared to arguments in metaethics that purport to establish,
by drawing on J. L. Mackie's (1977) argument from queerness
concerning the seemingly problematic metaphysical and epistemological
status of moral properties, an error-theory of moral judgment (Miller
2010a, 2020). (See the entry on
 moral anti-realism.)[4]



Kripke's discussion has resulted in a vigorous debate about
whether meaning really is normative, as well as about how the
normativity of meaning is best understood. For a defence of the claim
that meaning is normative, see Whiting 2007, 2009, 2016 (note that
Whiting focuses on the idea that meaning facts engender permissions to
apply words correctly and obligations not to apply them incorrectly,
though both the permissions and the obligations are defeasible). For
criticism of the view that meaning is normative, see Fodor 1990,
Gluer and Pagin 1998, Gluer 1999, Wikforss 2001, Boghossian
2005, Miller 2006, Hattiangadi 2006, 2007, and Gluer and Wikforss
2009. (See also the entry on the
 normativity of meaning.)
 Some philosophers seek to carve a middle ground between the
normativist and the anti-normativist positions--for instance, by
claiming that meaning facts are essentially justificatory (Gampel 1997), or
that they have hypothetical implications that are essential to them,
thus being fundamentally unlike natural facts, which may be
hypothetically normative only accidentally (Verheggen 2011; Chapter 2
of Myers and Verheggen 2016). Hannah Ginsborg proposes a novel
conception of normativity as more basic than rules (Ginsborg 2011b,
2012, forthcoming), which we shall briefly discuss in the last
section.



Some commentators take the normativity condition to amount to an
agential requirement, one that primarily concerns the
*applications* or *uses* of expressions. The thought is
that meaningful uses of expressions are not arbitrary--they are
not unjustified leaps in the dark. An adequate conception of meaning
must be able to account for this. This view of the normativity
condition claims to shed light on Kripke's numerous appeals to
the metaphor of blindness (1982: 10, 15, 17, 23, 87). Kusch thinks
that the requirement of non-blindness is best understood as falling
under the purview of semantic normativity (which, contra the
normativist interpreters, he does not take to involve categorical
obligations), and that it is best understood as indicating that the
speaker's "meaning-constituting mental state guides and
instructs" her on how to apply the expression, that the speaker
"can refer to this mental state in order to justify her
use" of the expression, and that this state 



> 
> 
> not only justifies certain applications--in the sense that
> meaning addition justifies '125' in answer to '\(68+57=\ques\)'--it
> also
> justifies the way in which *the answer is usually produced*.
> (Kusch 2006: 8-9, italics added) 
> 
> 
> 



Along similar lines, it has been suggested that the
meaning-constituting facts be able to accommodate the idea that
"the meaningful use of words must be revealed as
intentional" (Sultanescu and Verheggen 2019, 13; Sultanescu
forthcoming). The paradox has also been interpreted as belonging 



> 
> 
> to the philosophy of rational explanation, of explanations that
> account for what people do or think by citing their reasons for doing
> or thinking so. (Bridges 2014: 249; see also Bridges 2016)
> 
> 
> 



Some interpreters take the sceptical argument to involve the
imposition of an epistemological constraint--a constraint related
to the epistemic justification of semantic *judgments*, rather
than to the rationality of the applications of expressions. Warren
Goldfarb notes that Kripke "does seem to mean that the
justifications must in some sense be transparent" (1985 [2002:
98]). Jose Zalabardo takes Kripke to be demanding that the
meaning-constituting facts provide speakers with justification for
their judgments about the correctness of the applications of their
predicates. Justification is construed in an internalist sense:
speakers possess the relevant justification if the procedure through
which they decide whether predicates apply to objects involved
"*conscious engagement* with the facts that determine how
these questions should be answered" (1997 [2002: 286]). (See
also Jackman 2003, Guardo 2012, and Merino-Rajme 2015). Crispin Wright
proposes a more specific epistemic constraint, namely, that of
accounting for the seemingly puzzling fact that the epistemology of
meaning is first-person authoritative even though meaning something by
an expression is in crucial respects akin to having a dispositional
trait. In Wright's words, the constraint is to explain 



> 
> 
> how it is possible to be effortlessly, non-inferentially and generally
> reliably authoritative about psychological states which have no
> distinctive occurrent phenomenology and which have to answer, after
> the fashion of dispositions, to what one says and does in situations
> so far unconsidered. (2001: 150)
> 
> 
> 



Note that all the construals of the second condition appear to put
pressure on dispositionalism over and above that exerted by the
extensionality condition. Prima facie, dispositional facts are facts
about what we will or would do, not about what we ought to do;
dispositional facts appear not to be essentially justificatory or
hypothetically prescriptive; dispositions do not justify or
rationalise their manifestations, and in making semantic judgements we
do not typically engage with facts about our linguistic dispositions;
lastly, it is unclear how a dispositional account of meaning could be
rendered consistent with its intuitive first-person epistemology. See
 section 4
 for further discussion of dispositionalism.


## 3. The Sceptical Solution



If the sceptical argument is cogent, it seems to follow that there are
no meaning-constituting facts, no facts in virtue of which linguistic
expressions mean one thing rather than another. As noted above, this
appears to imply the paradoxical conclusion that "the entire
idea of meaning vanishes into thin air" (1982: 22). Kripke
distinguishes between two broad ways in which one might attempt to
avoid this conclusion (1982: 66-7). On the one hand, one might
provide a *straight* response, by identifying some
meaning-constituting fact of the sort called into question by the
sceptic. The various proposals discussed briefly in
 section 2
 above are instances of straight responses. The two most prominent
types of straight response in the literature--reductive
dispositionalism and non-reductionism--are discussed in more
detail in
 section 4
 and
 section 5
 below. On the other hand, one might provide a *sceptical*
response. That is, one might concede that there are no
meaning-constituting facts of the sort demanded by the sceptic but
deny that this leads to a paradoxical conclusion. In this section, we
shall focus on this strategy.



The proponent of the sceptical solution can be understood as rejecting
eliminativism about our practices of ascribing meaning. Mirroring
parallel discussions in metaethics, the two most obvious paths
available to her involve providing either an error-theoretic account
or a non-factualist account of ascriptions of meaning. We shall follow
Boghossian in viewing these paths as forms of *irrealism* about
meaning, content and rules (Boghossian 1989, 1990). A prominent
general line of argument in the recent literature suggests that
irrealist views of any area make presuppositions that irrealist views
of meaning and content are bound to deny, so that irrealism about
meaning and content is ultimately incoherent (Boghossian 1989, 1990;
Hattiangadi 2007, 2017, 2018; Miller 2011, 2015a, 2020). We'll
illustrate this general line of attack by sketching an argument to the
effect that, regardless of whether one pursues an error-theoretic or a
non-factualist approach, adopting irrealism leads inexorably to an
"insane and intolerable" and "incredible and
self-defeating" form of *eliminativism* on which the
notions of meaning and content do turn out to "vanish into thin
air". We'll then briefly consider an alternative way of
providing a sceptical response, which aims to revise the conception of
meaning fact that is at work in the sceptic's mindset.


### 3.1 Error Theories



Suppose we adopt an error theory: the view that all atomic, positive
statements ascribing meaning, content, or the following of a rule, are
false. While some error theories are eliminativist (e.g., Churchland
1981 on propositional attitudes), the error theorist need not
subscribe to eliminativism. For instance, J.L. Mackie (1977) argues
that although moral judgements are uniformly false, eliminativism can
be avoided given that some moral judgements are such that their
acceptance facilitates securing the benefits of social cooperation in
circumstances where "the limitation of men's
sympathies" (1977: 108) threaten their
 attainment.[5]
 On this view, even though our practice of making moral judgments
results in falsehoods, it meets a subsidiary norm (or norms) in terms
of whose satisfaction its pragmatic utility can be
 secured.[6]
 Might an error theorist about meaning, content and rule-following
attempt to avoid eliminativism by following a similar strategy?



It might seem that there is room for this approach. In the case of
meaning, the subsidiary norm might be something like the following:
one ought to assert "Jones means addition by
'+'" only when Jones's 



> 
> 
> particular responses to arithmetical queries agree with those of the
> community in enough cases, especially the simple ones (and if his
> "wrong" answers are not often *bizarrely* wrong, as
> is '5' for '\(68 +
> 57\)', but seem to agree with ours in *procedure*,
> even when he makes a "computational mistake"). (Kripke
> 1982: 92) 
> 
> 
> 



This norm would thus be cashed out in terms of *agreement* with
respect to inclinations "to go on" in certain ways, and
the utility of our complying with it would be that it enables us to
make helpful discriminations--for example, when seeking to buy
five apples--between grocers whose inclinations match ours and
grocers with "bizarre" quus-like
 inclinations.[7]



While this strategy might seem to some to be promising in the moral
case, it faces special problems in the case of meaning, content and
rules (Boghossian 1989, 1990; Miller 2015a). In order for the strategy
to be able so much as to be pursued, there has to *be* such a
thing as complying or failing to comply with a subsidiary
norm--and so, *a fortiori*, such a thing as complying or
failing to comply with a norm as such. An error theorist about
rule-following, however, denies *precisely* that there are
facts about norm-compliance and non-compliance. Having argued that all
statements about rule-compliance are false, the error theorist
apparently lacks the resources for telling a story about the pragmatic
utility of our continuing to engage in the practice of making
judgements about rule-following. The upshot seems to be that, if we
accept that there are no facts about speakers in virtue of which
expressions have meaning, embracing an error theory will not prevent
the notion of meaning from "vanishing into thin air".


### 3.2 Non-Factualist Theories



One might attempt to avoid eliminativism about meaning by embracing a
different type of irrealism, namely, non-factualism*.* A
non-factualist about a domain maintains that judgments and claims made
within that domain are not in the business of stating facts. Indeed,
the standard view in the secondary literature is that Kripke's
Wittgenstein himself is proposing a form of semantic non-factualism in
the sceptical solution outlined in chapter 3 of Kripke (1982). See,
e.g., McGinn (1984), Wright (1984), Boghossian (1989), and Hale
(2017). Might semantic non-factualism afford us a way to embrace the
conclusion of the sceptical argument while avoiding eliminativism?



This move faces difficulties parallel to those faced by error theories
(Boghossian 1989, 1990; Hattiangadi 2007: chapter 4, 2018; Miller
2011, 2020). The non-factualist about meaning proposes that we
construe ascriptions of meaning as having a purpose or function
different from that of stating facts. But, insofar as a sentence is
regarded as having a function, there is an intelligible distinction
between correct and incorrect uses of that sentence; in other words,
the sentence is rule-governed. That the notion of correctness in these
cases cannot be identified with truth or warranted assertibility makes
no difference to the applicability of a generalised version of the
extensionality condition, which we outlined in
 section 2.
 Thus, suppose that '\(S\)' is a
sentence that has a non-descriptive semantic function. Consider these
two specifications of the conditions in which uttering '\(S\)'
is correct, where \(R\_1\) and
\(R\_2\) would confer different correctness-values on utterances of
'\(S\)':



(a)
 Uttering '\(S\)' is correct
iff the conditions in which it is uttered accord with \(R\_1\);
(b)
 Uttering '\(S\)' is correct
iff the conditions in which it is uttered accord with \(R\_2\).


Whatever makes it the case that (a) provides the correctness
conditions for utterances of '\(S\)'
must rule out (b) as providing
those conditions. 



Now, let's consider the case of plans, which are expressed in
sentences that wear their non-descriptive semantic function on their
sleeves. (We choose the case of plans deliberately here, as a view of
this kind is mooted in Gibbard 2012.) Take the sentence
'Let's write a fugue!'. Consider two possible
correctness conditions for it:



(a\*)
 'Let's write a fugue!', as uttered by Glenn, is
correct iff Glenn plans to write a fugue


and



(b\*)
 'Let's write a fugue!', as uttered by Glenn, is
correct iff either (a) it is time *t* earlier than *t*\* and
Glenn plans to write a fugue or (b) it is time *t* later than or
equal to *t*\* and Glenn plans to write a novel.


Glenn's finite nature together with the infinitude of the
temporal sequence ensures that the sceptic will always be able to
argue that no fact about Glenn is capable of ruling in something like
(a\*) and ruling out something like (b\*) as the relevant correctness
condition. The non-factualist is entitled to regard "Let's
write a fugue!" as having a determinate meaning only if she can
provide some fact about Glenn or his speech community that determines
that that sentence is governed by (a\*) rather than (b\*). The same
argument can be pressed against the suggestion that "Jones means
addition by '+'" should be regarded as having some
non-descriptive semantic function. The non-factualist will be able to
regard "Jones means addition by '+'" as having
a determinate meaning only if she can provide some fact about Jones or
his speech community that determines that that sentence is governed by
one rule or correctness condition rather than another.



So, a non-factualist account of any region of thought and talk, which
is committed to the claim that there are no facts of the relevant
sort, would seem to presupposes a realist account of meaning, content
and rules according to which there are semantic facts, intentional
facts, and facts about normative accord. So, a non-factualist account
of meaning, content and rules, which is committed to the claim that
there are no semantic facts, intentional facts, or facts about
normative accord that our semantic, intentional, or normative
discourse purports to capture, presupposes a realist account of
meaning, content and rules according to which there are semantic
facts, intentional facts, and facts about normative accord. It thus
faces a charge of incoherence.



As noted above, we chose "plans" as our stalking horse
here in order to make explicit the problem this poses for Allan
Gibbard's (2012) account of meaning (it makes no difference to
the argument whether "plans" are taken to be linguistic
items possessing meaning or mental states possessing intentional
content). A Gibbard-style expressivist approach to an area such as
morality denies that there are moral facts, but presupposes that there
are facts about meaning, content and normative accord (facts that
determine what accords and fails to accord with a plan). A
Gibbard-style approach to meaning, content and rules thus, on the one
hand, denies that there are semantic facts, intentional facts and
facts about normative accord (facts that determine what accords and
fails to accord with a plan), and, on the other, presupposes that
there are such facts. It thus faces a charge of incoherence.



A similar objection to Gibbard's view is outlined in Hattiangadi
(2018). According to Hattiangadi, a Gibbard-style expressivist account
of moral claims, for example, aims to give an "oblique"
explanation of them in terms of the states of mind they express
(rather than a "straight" explanation in terms of (moral)
states of affairs which potentially render them true). But such an
oblique explanation in the moral case presupposes a straight
explanation of intentionality. In parallel, an oblique explanation of
meaning and intentionality would presuppose a straight explanation of
meaning and intentionality, again threatening the view with
incoherence. In a reply to Hattiangadi, Gibbard reflects on the
strategy of the metaethical expressivist and attempts to use it to
counter Hattiangadi's worry. He writes:



> 
> 
> A parallel can be found in ethics: Suppose we claim that being good
> consists in being pleasurable. The concept of being pleasurable can be
> completely non-ethical and naturalistic, but the claim "Being
> good consists in being pleasurable" is ethical--and so, if
> Moore and others are right, nonnaturalistic. Is there, then, "a
> straight or substantive explanation of intentionality"? The
> correct answer will parallel that for the question, "Is there a
> straight substantive explanation of being good?" If ethical
> hedonists are right and being good consists in being pleasurable, then
> there's a straight, substantive explanation of being good in the
> sense of a naturalistic explanation of the property that being good
> consists in. But the claim "Being good is being
> pleasurable" isn't itself naturalistic. If Ayer was right,
> it amounts to "Hurrah for all and only what"s pleasurable.
> (Gibbard 2018: 770)
> 
> 
> 



We leave assessment of Gibbard's reply as an exercise for
 readers.[8]



### 3.3 An Alternate Form of Factualism



Wilson takes the lesson of the sceptical argument to be not that there
are no meaning facts, but rather that a certain conception of such
facts, which he calls *classical realism*, is hopeless, and
conceives of the sceptical solution as accommodating meaning facts
when conceived in a different way (Wilson 1994; see also Wright 1992:
chapter 6). Classical realism is sometimes referred to as semantic
platonism, the view that "the meanings of our words are
guaranteed by the pre-existing structure of reality" (Pears
1988: 363; cf. Child 2001, Verheggen 2003, Zalabardo 2003, Hanks
2017). What is essential to classical realism or semantic platonism is
that the properties that guarantee meaningfulness must be antecedently
singled out by individuals (or communities) in order to endow their
words with semantic standards (Wilson 1994 [2002: 251]). As Zalabardo
puts it, what is required is 



> 
> 
> a conscious act in which I decide to pair the predicate with the
> property in such a way that the satisfaction conditions of the
> predicate, as I mean it, are determined by the instantiation
> conditions of the property. (2003: 314) 
> 
> 
> 



Wilson takes the sceptical challenge to reveal that no sense can be
made of this idea, for it is not possible for an individual (or
community) non-linguistically to single out properties as "the
*de re* subject of her meaning-constituting intentions"
(1998: 105). But, to repeat, what this allegedly shows is not that
there are no meaning facts, but rather that we must reform our
conception of them.



The alternative picture of meaning that Wilson fleshes out conceives
of expressions as not connected to properties that serve as
"pre-established" standards of correctness" (2003:
181-182), and suggests that "what we mean by [an
expression] is something that gets settled only over the course of
time" (2003: 186). In response to Wilson's proposal, it
has been argued that it is susceptible to collapsing into a form of
subjectivism (Kremer 2000), and that it is untenable, for it falls
prey to the sceptical challenge that it purports to bypass (Miller
2010b). It has also been argued, contra Wilson, that classical realism
is merely an instance of a more general conception of meaning that
takes standards of correctness to be determined by
entities--whether abstract properties or real features of the
world around us--that are considered independently of how we
might describe them linguistically; it is this conception that must be
rejected, as it is ultimately responsible for generating the paradox
(Verheggen
 2003).[9]


## 4. Reductive Dispositionalism



The most widely discussed attempt at a straight solution to the
sceptical challenge is reductive dispositionalism. According to a
simple version of reductive dispositionalism, the fact that Jones has
the concept of *addition* rather than of *quaddition* is
to be identified with (or is constituted by) his disposition to
produce the result of adding (and not quadding) the numbers *x*
and *y* in response to arithmetical queries of the form '\(x
+ y = \ques\)', and the fact that
he means *cat* by 'cat' is to be identified with
(or is constituted by) his disposition to apply 'cat' to
cats. (See Horwich 1998, 2010, 2012 for a systematic development of
dispositionalism; an answer to Kripke's challenge is articulated
in Horwich 2015.) 



As Boghossian notes (1989 [2002: 164-165]), the general form of
dispositionalism targeted by the sceptic covers both *conceptual
role* theories and *causal/informational* theories. In both
cases, the account is intended to be reductive, insofar as the
content-determining dispositions are to be characterized in wholly
non-semantic and non-intentional terms. The sceptic's attack on
reductive dispositionalist theories is thus an attack on two of the
most popular accounts of the determination of content in contemporary
philosophy of mind and language.



The sceptic argues that dispositionalist theories face three problems.
The first problem--the finitude problem--is that there is a
sense in which, much like the totality of our previous linguistic
behaviour, our dispositions are *finite*. Given that the
extension of the addition function is infinite, containing a
denumerably infinite number of triples \(\langle x, y, z\rangle\) such
that *x* plus *y* is identical to *z*, Jones's
meaning addition by '+' cannot be identified with her
dispositions to respond to arithmetical queries since it is simply
false that she is disposed to answer with the sum when faced with the
query '\(x + y = \ques\)'. In
some (indeed, most) cases, the numbers involved will be so large that
Jones's brain's capacity for computation is far exceeded,
and Jones may even die long before she is able to grasp the relevant
numbers. We might follow Boghossian in dubbing such numbers
"inaccessible" (2015: 335), and we might define quaddition
to be a function that diverges from addition over only inaccessible
numbers. In this case, the problem is that, given Jones's
dispositions, it is indeterminate whether he means *plus* or
*quus*.



The second problem--the error problem--is that someone might
be systematically disposed to make *mistakes*. Take Smith, who
is systematically disposed to miscarry when responding to '\(x
+ y = \ques\)' queries. When
Smith produces '28' in response to '\(19
+ 19 = \ques\)', we want to be
able to say that her answer is incorrect in the light of what she
means by '+'. However, if what she means is determined by
her dispositions, we are forced to say that she actually means some
non-standard function (one that corresponds to addition with the
carrying operation removed), so that her answer '28' is
correct*.*



The third problem--the normativity problem--is that the
dispositionalist view seems unable to capture the *normativity*
of meaning. Given what she means by '+', Jones
*ought* to respond to arithmetical queries of the form '\(x
+ y = \ques\)' by producing the
sum of *x* and *y*, but the meaning-constituting fact
proposed by the dispositionalist is at most a fact about how she would
respond to queries of the relevant form:



> 
> 
> Suppose I do mean addition by '+'. What is the relation of
> this supposition to the question how I will respond to the problem
> '\(68+57\)'? The
> dispositionalist gives a *descriptive* account of this
> relation: if '+' meant addition, then I will answer
> '125'. But this is not the proper account of the relation,
> which is *normative*, not descriptive. The point is
> *not* that, if I meant addition by '+', I
> *will* answer '125', but that, if I intend to
> accord with my past meaning of '+', I *should*
> answer '125'. Computational error, finiteness of my
> capacity, and other disturbing factors may lead me not to be
> *disposed* to respond as I *should*, but if so, I have
> not acted in accordance with my intentions. The relation of meaning
> and intention to future action is *normative*, not
> *descriptive*. (Kripke 1982: 37)
> 
> 
> 



In
 section 2,
 we outlined a number of ways in which a normativity condition might
be thought to impose a constraint on accounts of meaning. We suggested
that in all of these ways this condition puts at least prima facie
pressure on dispositionalist theories of meaning. We will limit
ourselves in the remainder of this section to some remarks on the
finitude problem and the error problem. These two problems indicate
two obstacles that the dispositionalist must overcome in order to meet
the extensionality condition.



Blackburn responds to the finitude problem by pointing out that
familiar dispositional properties (such as fragility) are in a sense
*infinitary*: "there is an infinite number of places and
times and strikings and surfaces on which it could be displayed"
(1984 [2002: 35]). If a glass has infinitary dispositions, perhaps a
human does too, and perhaps this will yield an extended disposition
that covers the case of queries involving inaccessible numbers. Even
though we have no way of getting an ordinary glass to Alpha Centauri
(it would decay long before it got there), we can think of it as
possessing an extended disposition to break there: breaking is what
the glass would be disposed to do were its dispositions on earth
allowed to manifest themselves on Alpha Centauri. Likewise, even
though Jones has no disposition to answer queries involving
inaccessible numbers, responding with the sum is what Jones would be
disposed to do were her dispositions in accessible cases allowed to
manifest themselves in inaccessible cases. This would in turn allow us
to say that the answer that she would accept in those cases is
"the one that *would* be given by reiterating procedures
[Jones *is*] disposed to use, a number of times" (1984
[2002: 35]).



Blackburn's response to the finitude problem is open to
criticism. First, Blackburn's talk of procedures Jones is
disposed to use is illegitimate in this context: to "use"
a "procedure" is to follow a rule, and we cannot help
ourselves to the idea that Jones is following the rule for addition
here (or any rule, for that matter), as it is Jones's status as
a rule-follower that we are hoping to recover from facts about her
dispositions. What we can say is that as far as the accessible cases
go, the answers Jones is disposed to give *conform* to the rule
for addition. But, of course, they also *conform* to the rule
for quaddition. What makes Jones an adder, and not a quadder,
according to Blackburn's suggestion, is that were Jones's
dispositions in the accessible cases allowed to manifest themselves in
the inaccessible cases, she would respond with the sum, and not the
quum.



However, Boghossian (2015: 341) points out that there is a crucial
disanalogy between this case and the extended disposition to break on
Alpha Centauri plausibly ascribed to the glass. To think of the
dispositions the glass has on earth as manifesting themselves on Alpha
Centauri, we don't need to think of the glass in any way that is
inconsistent with its nature as a physical object. It can be regarded
as having the same intrinsic physical characteristics on Alpha
Centauri as it has on earth, and if it is true that, given those
characteristics, it would break if struck on Alpha Centauri, that
suffices for the attribution of the extended disposition to break on
Alpha Centauri. Matters stand differently with Jones. In order to
think of Jones's dispositions to respond in accessible cases as
manifesting themselves in inaccessible cases, we would have to think
of her in a way that is inconsistent with her nature as a finite
biological being. This is because responding to queries involving
inaccessible numbers would require, let's suppose, a brain the
size of the universe. But the fact that with a brain the size of the
universe the sum would be produced no more warrants the attribution of
the relevant extended disposition to Jones than does the fact that
with a brain the size of the universe she would outplay Magnus Carlsen
warrant the attribution to her of the potential to win the world chess
championship. Jones has no extended disposition of the sort adumbrated
by
 Blackburn.[10]
 The upshot, then, is that Jones's dispositions do not determine
whether she means plus rather than some quus-like function by
'+', where quus diverges from plus for inaccessible
 numbers.[11]



We've followed Boghossian (2015) in setting up the finitude
problem as fundamentally a problem about determinacy. In a recent
paper, Jared Warren admits that solving the finitude problem, thus
construed, turns on solving the error problem (2020: 268), and
proceeds to offer an attempted solution to that problem. Consider the
following proposal: the fact which constitutes Jones's meaning
addition by '+' is the fact that, when faced with
arithmetical queries involving the '+' sign, Jones is
stably disposed to reply with the sum in the overwhelming majority of
normal
 situations.[12]
 What are normal situations, and what is it for a disposition to be
stable? Normal situations are those in which neither external nor
internal factors are interfering with Jones's general cognitive
functioning. More specifically, the normal situations are those in
which Jones is clearheaded--situations in which the air is not
permeated with mind-bending chemicals, in which Jones is not drunk,
exhausted, or badly hungover, so that neither external causes nor
internal causes are interfering with her cognitive performance.
Furthermore, to say that Jones's disposition to respond with the
sum is stable is to say that, as the number of arithmetical queries
she has faced increases, the ratio of answers that give something
other than the sum to answers that give the sum tends towards zero.
And to keep the bar relatively low, we don't require that in
normal conditions it is *metaphysically impossible* for Jones
to answer with something other than the sum. We only require that,
when such conditions obtain, it is rational to be *nearly
certain* that she will answer with the sum. Call the disposition
which we have described here disp. disp
corresponds to the meaning-constituting
dispositions that Warren proposes as offering a solution to the error
problem. The proposal is intended to be reductive. Warren notes that
"normalcy", defined as he defines it, "isn't
semantic or intentional or otherwise problematically
question-begging" (2020: 271).



However, Warren's attempt to solve the error problem can be
questioned. The error problem arises as a result of the fact that the
following two possibilities are consistent with Jones's
possession of disp. First, Jones means
addition by '+' and is responding *correctly* to
the relevant queries. Second, Jones means some quus-like function and
is responding *incorrectly*. What Warren thus needs is a
characterisation of normal situations such that the latter possibility
is ruled out. Thus, what is required is a characterisation of normal
situations such that, when those situations obtain, we are entitled to
be nearly certain that Jones will answer with the sum, *and that in
answering with the sum Jones is responding correctly*. The trouble
is that there is an infinite range of functions \(F\_1\),...,
\(F\_n\) that have different extensions from the addition function. If
Jones means some function \(F\_i\) among them, and if she answers with
the sum, *she would be answering incorrectly*. Thus, the normal
situations have to be such that their obtaining ensures that Jones
means by '+' none of the functions in this open-ended and
infinite set. The question that drives Kripke's
Wittgenstein's objection is: how could this be achieved other
than through the inclusion of a clause in the characterisation of
normal situations to the effect that Jones *means* addition by
'+' (or at least, that Jones *means* a function
with the same extension as addition)? How could the obtaining of a
non-semantically characterised set of situations have the effect of
excluding every member of an open-ended and infinite set of
semantically or intentionally characterised states of affairs (Jones
means \(F\_1\) by '+', Jones means \(F\_2\) by
'+', and so on *ad
 infinitum*)?[13]



Thus, it can be argued that the dispositionalist account offered by
Warren either fails to resolve the indeterminacy problem or does so
only at the expense of deploying semantic and intentional notions,
which is inconsistent with its reductive
 aspirations.[14]


### Postscript to section 4: Lewis on Natural Properties



A reductionist position that has been somewhat neglected in the
rule-following literature is suggested by David Lewis in his
"New Work for a Theory of Universals" (1983). Lewis
writes:



> 
> 
> The naive solution is that adding means going on in the same way as
> before when the numbers get big, whereas quadding means doing
> something different; there is nothing present in the subject that
> constitutes an intention to do different things in different cases;
> therefore he intends addition, not quaddition. We should not scoff at
> this naive response. It is the correct solution to the puzzle. But we
> must pay to regain our naivete. Our theory of properties must
> have adequate resources to somehow ratify the judgement that instances
> of adding are all alike in a way that instances of quadding are not.
> The property of adding is not perfectly natural, of course, not on a
> par with unit charge or sphericality. And the property of quadding is
> not perfectly unnatural. But quadding is worse by a disjunction. So
> quaddition is to that extent less of a way to go on doing the same,
> and therefore it is to that extent less of an eligible thing to intend
> to do. (1983: 376)
> 
> 
> 



Take a predicate like 'green'. The totality of facts about
our previous use and dispositions to use 'green' are
*consistent* with it referring to the property *green*
but also with it referring to the property *grue*. So, what
might ground the claim that the property *green* is somehow
privileged as the referent of 'green'? Lewis can be taken
to advocate a form of "interpretationism" according to
which semantic facts are constitutively determined by the best theory
of the data (J. R. G. Williams 2007). Among the a priori constitutive
constraints governing what counts as the best theory is a principle
requiring that the referents assigned to expressions be the most
natural of those consistent with the data. Since *green* is
more natural than *grue*, it is more "eligible"
than grue to be assigned to 'green' as its referent.
Likewise for adding and quadding. In this way, the indeterminacy left
open by facts about use is fended off, Lewis thinks.



Lewis's proposal is not *ad hoc*, as the notion of a
natural property that it utilises is required, for example, by his
account of laws of nature (see the entry on
 David Lewis,
 section 4.6). However, its application to the rule-following problem
faces a number of challenges. First, it is not obvious how it extends
to the mathematical examples that are the focus of Kripke's
Wittgenstein. Boghossian writes, 



> 
> 
> I see no obvious notion of naturalness that will cover both the notion
> of a natural property, as it might figure in an account of similarity
> or lawlikeness, and that of a natural function. (2015: 355) 
> 
> 
> 



It has also been argued that even if Lewis's proposal might meet
the extensionality condition, it cannot meet the normativity condition
(Merino-Rajme 2015). 



Lewis's proposal is also likely to be challenged on
epistemological grounds similar to those used by Kripke and Wright in
dismissing the suggestion that quaddition can be ruled out in light of
the fact the hypothesis that Jones meant quaddition is *less
simple* than the hypothesis that he meant addition. A speaker can
know that in response to the query '\(68+57\)',
'125' is the
answer that accords with what she meant by '+', without
having to *infer* this from facts about her previous linguistic
behaviour. That is to say, in recognising that the answer
'125' fits what we mean by '+', we do not
proceed "by inference to the best semantic explanation of [our]
previous uses of that expression" (Wright 2001: 109; see also
Kripke 1982: 40). But this is apparently what we would have to do if
the "simplicity" suggestion were correct: the best
explanation would be yielded by the simplest of the hypotheses
consistent with our previous linguistic behavior. The
"simplicity" suggestion thus apparently makes a mystery of
our (generally) non-inferential semantic knowledge. Lewis's
suggestion will be challenged on similar grounds. We do not infer what
we mean by '+' from facts about naturalness together with
constitutive principles governing interpretation. Again, the account
appears to make a mystery of the non-inferential nature of much of our
semantic knowledge. Moreover, it faces difficulties in accommodating
the *authority* normally credited to self-ascriptions of
meaning. For Lewis, in virtue of the role they play in his account of
scientific laws, simplicity and naturalness are objective notions.
However, a speaker's opinions about what she means, unlike, say,
her opinions about the structure of the world or of our hypotheses
about it, are generally authoritative, unless there are special
reasons to doubt them. What might the basis for this default authority
be, if what she means is determined by facts about simplicity and
naturalness?



Moreover, the Lewisian view seems to be a form of semantic platonism
(Child 2011: 126), in so far as it upholds the idea that our meaning
what we do by our words is somehow guaranteed by the structure of
reality. But it might be taken to be a radical form of semantic
platonism, in so far as it seems to leave no room for the
speaker's contribution to the singling out of properties (see
 section 3.3).
 Unlike other versions of semantic platonism, it is vulnerable to a
complaint to the effect that the subjective perspective of the thinker
or speaker is entirely annihilated.



For a lucid exposition and critique of Lewis's position, see
J.R.G. Williams (2007). For rare examples of treatments of
Lewis's views in the context of the rule-following literature,
see Merino-Rajme (2015), Gluer (2017), and Azzouni (2017).


## 5. Non-Reductionism



The apparently very serious problems we outlined for the
dispositionalist conception of meaning have been taken by a number of
philosophers to show that we ought to resist the temptation to explain
meaning and content in more basic terms. How might one formulate a
non-reductionist position? On Stroud's view, it amounts to
denying that we can explain 



> 
> 
> the phenomena of meaning and understanding "from outside"
> them, as it were, without attributing intentional attitudes or
> supposing that anything means anything or is understood in a certain
> way to those whose understanding is being accounted for. (Stroud 2000:
> viii) 
> 
> 
> 



More generally, we might say that the facts constitutive of the
semantic domain cannot be characterised or explained in non-semantic
terms, that is, without employing the notions of meaning or
understanding; the facts constitutive of rule-following cannot be
characterised or explained without employing the notion of
rule-following. Some philosophers who embrace non-reductionism also
defend the view according to which semantic facts do not supervene on
anything; they are metaphysically fundamental. Boghossian relies on
the finitude problem to argue that, if meaning facts are determinate,
then they cannot supervene on non-semantic facts (Boghossian 2015).
However, the denial of supervenience is not essential to
non-reductionism (cf. Child 2019b): at the core of the position is the
idea that any attempt to account for meaning in more basic terms is
hopeless or philosophically confused.



Kripke briefly considers the possibility that the states of meaning or
understanding, or the facts about meaning and understanding, are
primitive or *sui generis*, which he cashes out as the idea
that 



> 
> 
> meaning addition by "plus" ... is simply a primitive
> state, not to be assimilated to sensations or headaches or any
> "qualitative" states, nor to be assimilated to
> dispositions, but a state of a unique kind of its own. (1982: 51) 
> 
> 
> 



He raises two complaints against this approach. First, he
characterizes it as desperate, insofar as "it leaves the nature
of this postulated primitive state ... completely
mysterious" (1982: 51), for such an approach does not provide an
account of what makes it possible for one to "be confident that
[one] *does*, at present" mean what one does (1982: 51).
Second, he thinks that a non-reductionist account does not address the
"logical difficulty implicit in Wittgenstein's sceptical
argument" (1982: 51), which is that it would seem that we could
not "conceive of a finite state which *could* not be
interpreted in a quus-like way" (1982: 52).



Some philosophers claim that Kripke's treatment of the
non-reductionist position is unsatisfactory. McGinn, who appears to
ignore Kripke's brief discussion of non-reductionism, thinks
that there is an 



> 
> 
> undefended and undisclosed premise [in the sceptic's argument],
> namely that semantic discourse cannot be regarded as
> *irreducible*. (1984:
>  82)[15]
> 
> 
> 
> 



McGinn also notes that Kripke has no qualms with adopting a
non-reductionist view of meaning in other works--see, for
instance, Kripke 1972: 94-97. Goldfarb thinks that "the
conception Kripke exploits is basically physicalistic" (1985
[2002: 95]), and thus that pursuing a non-physicalist approach
hasn't been ruled out. Boghossian thinks that what Kripke needs
for his treatment of non-reductionism to succeed is an argument from
queerness aiming to show that there is something inherently queer
about meaning properties, which he fails to provide (1989 [2002: 180];
cf. Hattiangadi 2007: 47-50). Ultimately, Boghossian is
sympathetic to the non-reductionist approach, though he thinks that
"it really is not plausible" that such a conception might
be true of linguistic meaning (1989 [2002: 179]); on his view, it is
facts about mental content that are irreducible.



Before exploring several of the non-reductionist positions proposed in
recent years, we should note that some of the proponents of
non-reductionism think that Kripke's sceptical challenge is
based on confusion, and that our task is to unearth that confusion.
Thus, on their view, the proper response is not to *solve* the
sceptical problem by showing that the sceptic failed properly to
acknowledge some set of facts (or some features of some such facts),
but to *dissolve* it by showing that there is, in fact, no
problem. McDowell, for instance, argues that Kripke misunderstands the
dialectic pursued by Wittgenstein in *Philosophical
Investigations*. On his view, 



> 
> 
> the right response to the paradox, Wittgenstein in effect tells us, is
> not to accept it but to correct the misunderstanding on which it
> depends, (1984 [1998: 229]) 
> 
> 
> 



which puts us in a position to dissolve the paradox and, with it, the
problem of how meaning is possible. This involves renouncing the
problematic assumption that understanding an expression requires
interpreting that expression. McDowell's diagnosis isn't
confined to linguistic expressions. What we ought to resist is the
thought that, 



> 
> 
> whatever is in a person's mind at any time, it needs
> interpretation if it is to sort items outside the mind into those that
> are in accord with it and those that are not. (1992 [1998: 268]) 
> 
> 
> 



Similarly, Stroud thinks that the paradox is "an expression of
an unsatisfiable demand" (1990 [2000: 88]), namely, the demand
for 



> 
> 
> some facts, the recognition of which would not require that we already
> speak and understand a language, and some rules, which would tell us
> what, given those facts, it was correct to say. 
> 
> 
> 



Such facts and such rules would have to be such as to "serve to
get us into language in the first place" (Stroud 1990b [2000:
94]). The demand is most strongly manifested in Kripke's
assumption that there must be an item that instructs or tells the
speaker what to do with her expressions. Stroud claims that proper
engagement with Wittgenstein's remarks reveals this assumption
to be misguided, for it embarks us on a regress (Stroud 1996 [2000:
180-185]). Once we recognize the misguidedness of the picture
that Kripke assumes, we will no longer feel the force of the sceptical
challenge, Stroud thinks. However, contra Stroud, it seems that the
extensionality condition is all we need in order to pose a
stripped-down version of the question that the sceptic is raising,
namely, the question of what makes the standards of correctness that
govern our uses of expressions and our deployments of concepts
possible.



It might be argued that the urgency of this question, or even its very
intelligibility, is merely a symptom of a frame of mind from within
which meaning seems impossible, and that our proper task is to leave
this confused frame of mind behind (e.g., McDowell 1992 [1998: 272,
274]; 1998a: 57-58). However, this line of reasoning might be
taken to presume that a question is urgent or intelligible only if it
is in principle possible to offer a reductive answer to it, that
constructive philosophy is necessarily reductive philosophy. Verheggen
argues that the rejection of reductionism does not commit one to
quietism. As she sees it, non-reductionism can be constructive; it can
revolve around advancing and defending positive claims (Verheggen
2000, 2003). Even though the project of providing necessary and
sufficient conditions for meaning is hopeless, the non-reductionist
can still aspire to articulate necessary conditions that aren't
"even remotely trivial" (Myers and Verheggen 2016: 3), and
to draw illuminating connections between meaning and other irreducible
phenomena. Through a creative reconstruction of Davidson's
triangulation argument, Verheggen argues that interaction with a
second individual and aspects of the shared world is a necessary
condition for one's having a language and thoughts (see chapter
1 of Myers and Verheggen 2016). The constitution of the standards of
correctness that govern language and thought necessitates that the
individual be aware of the possibility of being mistaken, an awareness
that can only be grounded in linguistic interactions with another
individual and features of the world. Thus, the triangulation argument
is taken by Verheggen to reveal the hopelessness of the reductive
ambition, insofar as it shows that we cannot offer an account of the
constitution of the standards of correctness that govern language and
thought without presupposing that a commitment to those standards is
already in place. (See also Sultanescu and Verheggen 2019 for an
account of the Davidsonian answer to Kripke's sceptical
challenge and Verheggen 2017a for an account of the Davidsonian answer
to Wittgenstein's paradox.) William Child also defends a variety
of non-reductionism, one that "does not give merely pleonastic
answers but aims to say something genuinely informative" (Child
2019a: 97). He does so by relying on Wittgenstein's remarks on
meaning and rule-following.



According to Wright, "it is an important methodological precept
that we do not despair of giving answers to constitutive questions too
soon" (2001: 191). He goes on to propose a non-reductionist view
that is sensitive to the difficulty of accounting for our knowledge of
what we mean. (As we noted in
 section 2,
 Wright takes Kripke's sceptic to impose a legitimate
epistemological constraint on answers to the skeptical challenge.) He
offers a "judgment-dependent" account of intention,
according to which what one intends is determined by one's best
judgment about what one intends. Insofar as the concepts of intention
and meaning are "relevantly similar" (2001: 206), this
account can also claim to shed light on the nature of meaning. Thus,
we might say, on Wright's behalf, that what one means by an
expression is determined by one's best judgment about what one
means. The notion of judgment is taken by Wright as primitive. Still,
the authoritative nature of first-personal avowals is allegedly
vindicated. See especially essays 5-7 in Wright
 2001.[16]



Wright and Boghossian recently offered independent arguments to the
effect that the adoption of a non-reductionist view of meaning does
not secure the intelligibility of the idea of guidance by a rule.
According to Wright, the only way in which rule-following can be
understood is if it conforms to what he calls "the modus ponens
model" (2007: 491). The model states that an act is a genuine
instance of rule-following if it can be rationalized by, on the one
hand, citing the rule and, on the other, indicating that the
circumstances, which must be specifiable without appealing to the
rule, call for its application. Wright investigates basic cases of
language use, and argues that if we assume that the modus ponens model
applies to these cases, we are saddled with an Augustinian picture,
according to which conceptual capacities are necessarily prior to
capacities to use language. At the same time, he accepts that
Wittgenstein has revealed the bankruptcy of the Augustinian picture in
*Philosophical Investigations*; so, the idea of antecedent
conceptual capacities is unintelligible. This is taken to show that
the modus ponens model cannot apply to basic cases. Wright calls this
"the minor premise problem", and argues that it compels us
to accept that "in the basic case we do not really
*follow*--are not really guided by--anything"
(2007: 497).



Boghossian also relies on the modus ponens model to argue that a
non-reductionist position does not allow us to make sense of the
intelligibility of rule-following. He offers "an intuitive
characterization" of the phenomenon of rule-following, according
to which it has the following structure: 



> 
> 
> a state that can play the role of rule-acceptance; and some
> non-deviant causal chain leading from that state to a piece of
> behavior that would allow us to say that the rule explains and (in the
> personal-level case) rationalizes the behavior in question. (2012: 31)
> 
> 
> 
> 



What allows us to say that the rule explains and rationalizes the
behaviour is an act of inference from the rule to what it requires in
particular contexts. But inference is, according to Boghossian,
"an example of rule-following *par excellence*"
(2012: 40), which indicates that the act of inference must fit the
intuitive characterization above, thus requiring a further act. A
regress is unavoidable for the proponent of non-reductionism,
according to Boghossian. This is the inference problem.



Arguably, the two problems are anticipated in Kripke's line of
reasoning, especially in his remark, mentioned earlier in this
section, to the effect that the non-reductionist view faces a logical
difficulty (1982: 51-52). The difficulty seems to arise from
three claims that seem uncontroversial but are inconsistent: 


1. the state of meaning plus by '+' must guide the
speaker in her applications of the expression '+';
2. a state of meaning can be interpreted in more than one way;
3. something that can be interpreted in more than one way cannot
guide.



We might think that one's state of meaning something by an
expression is not the sort of thing that one can interpret (thus
denying (ii)), or that whether something can be interpreted in more
than one way is irrelevant for the question of whether it can guide
(thus denying (iii)). But neither of these options entitles us to
reject (i); the non-reductionist still owes us an account of what it
is to be guided by a rule (or by one's understanding of an
expression).



Miller offers an account of guidance by drawing on McDowell's
writings on Wittgenstein. He argues that the inference problem and the
minor premise problem are not genuine difficulties for the
non-reductionist. On his view, the upshot of Wittgenstein's
reflections on rule-following is that 



> 
> 
> in applying a rule R in a particular case there need be no
> *further* inferential step--over and above that involving
> R *itself*--mediating between acceptance of R and that
> particular application. (2015b: 405) 
> 
> 
> 



This is just what it is for rule-following *not* to be a matter
of interpretation: the rule is applied immediately, as it
were--without the mediation of a further rule, such as an
inference rule, in the manner suggested by Boghossian, or a rule for
the deployment of a prior concept, in the manner suggested by Wright.
What puts an agent in a position to follow a rule is her having been
trained into a practice or custom of following rules of that sort
(2015b: 407), where the notions of training, practice, and custom are
semantically characterized and cannot receive further philosophical
illumination.



Thus, according to some defenders of non-reductionism, rule-following
has an essentially social character. One dispute that is intramural to
the non-reductionist approach concerns the precise way in which this
social character should be understood. When it comes to meaning,
Verheggen distinguishes between communitarian views, according to
which 



> 
> 
> having a (first) language essentially depends on meaning by
> one's words what members of some community mean by them, 
> 
> 
> 



and interpersonalist views, according to which 



> 
> 
> having a (first) language essentially depends on having used (at least
> some of) one's words to communicate with others, (Myers and
> Verheggen 2016: 84; see also Verheggen 2006 for the initial
> articulation of the distinction) 
> 
> 
> 



and goes on to defend the interpersonalist view. Relatedly, there is
the question of how we should understand the notions of practice and
custom and the role that they play in a correct conception of
intentionality, broadly construed. It might be thought, as
Wittgenstein seems to suggest in *Philosophical Investigations*
(e.g., #198; #201-202), that it is essential to thinking and
speaking that one be trained into practices or customs, and thus that
our conception should reflect the centrality of these notions
(McDowell 1984, M. Williams 1999, Stroud 2000, M. Williams 2010,
Miller 2015b); at least initially, this appears to favour the
communitarian view. (See also Section 4 of Haase 2018 for a different
kind of attempt to flesh out the Wittgensteinian notion of practice,
and Pettit 1990 for a form of non-reductionism on which communal
interaction is required in at least some cases of rule-following). But
on the Davidsonian conception, at the centre of which is disagreement
and the need to settle it rationally against the constraints of the
shared world, the idea of practice might not serve any explanatory
purpose; even though shared beliefs may be essential for thought,
shared standards of correctness are not essential for language. The
Davidsonian conception is a variety of interpersonalism. This
intramural debate is very much ongoing.



Some philosophers have explored the possibility of a middle path
between reductive dispositionalism and non-reductionism. Thus, in a
paper in which she discusses Stroud's view, Ginsborg
distinguishes between austere forms of non-reductionism, which she
takes to be incompatible with constructive philosophising about
meaning, and "less austere and partly reductionist"
approaches, which allow that "we could account for meaning in
terms of a more basic idea of goal-directed human activity"
(2011a: 153), but without allowing that such activity can be captured
in purely dispositionalist or physicalist terms. She goes on to
articulate a less austere view, which explains meaning in terms of a
notion of normativity that she takes to be primitive. On this view,
for someone to mean something by an expression is for her to have a
disposition to apply it in particular contexts and, crucially, to take
the manifestations of that disposition to be appropriate. Taking
one's responses to be appropriate 



> 
> 
> does not depend on the antecedent grasp of a rule or standard
> determining that response as correct rather than incorrect, or even on
> the awareness that there is such a rule or standard; (2011a: 169) 
> 
> 
> 



this establishes the primitive status of the notion of
appropriateness. Thus, Ginsborg provides a dispositionalist account of
meaning, albeit with a crucial proviso to the effect that the relevant
dispositions are to be characterized in normative terms. She thinks
that the account can serve as a straight solution to the sceptical
challenge. On the one hand, it purports to vindicate the normativity
of meaning, and thus to meet the normativity condition; on the other
hand, it purports to account for the distinction between correct and
incorrect applications of expressions, and thus to meet the
extensionality condition. For Ginsborg, the set of correct
applications of an expression are the applications that one is
disposed to regard as appropriate--the applications that ought,
in the primitive sense, to be made (see Ginsborg 2011b for a more
detailed account of her solution to Kripke's problem).



Ginsborg's view is in some respects similar to Robert
Brandom's. Brandom seeks to explain meaning in terms of use,
where use is specified in a way that is 



> 
> 
> neither so generous as to permit semantic or intentional vocabulary,
> nor so parsimonious as to insist on purely naturalistic vocabulary.
> (1994: xiii) 
> 
> 
> 



Thus, his approach to meaning might also be viewed as less austere and
partly reductionist. We do not have room to explain the details of
Brandom's intricate view; suffice it to say that, on that view,
the proper specification of the use that determines meaning
essentially involves normative vocabulary. The facts that determine
meaning are facts about the *entitlements* and
*commitments* that are implicit in the performances of speech
acts. Thus, what a speaker means by an utterance is to be understood
as consisting, roughly, in the performances that she is committed to
in virtue of the utterance as well as in the performances that entitle
her to make it. Ultimately, these facts are "products of human
activity" (xiv), being a matter of our adopting normative
attitudes toward one another--of *taking* one another to be
committed or entitled, in light of our performances, to various other
performances. However, although there are similarities, there are also
important differences between Brandom's approach and
Ginsborg's. While for Brandom the norms that are constitutive of
meaning are socially instituted, for Ginsborg they are natural.
Moreover, the notion of appropriateness that Ginsborg fleshes out is
more basic than the notion of reason, and thus more basic than the
notions of entitlement and commitment that Brandom takes to be
constitutive of meaning (Ginsborg 2011a: 172fn21). Still, Ginsborg
does think that "expressions have meanings only in virtue of
there being ways in which they ought to be applied" (2012: 132).
So, to put it crudely, on both accounts, meaning facts are reduced to
facts or considerations about what ought to be the case. The question
that the austere non-reductionist will raise is whether the latter
kinds of fact are apt to solve the indeterminacy problem, and thus to
meet the extensionality condition.



The challenge of the sceptic makes perspicuous the fact that a
non-semantically described pattern is compatible with indefinitely
many interpretations. Does the appeal to the normative domain help us
rule out the sceptic's alternative hypotheses? Given that,
arguably, on a partly reductionist picture of the sort that Brandom
proposes, utterances are, ultimately, nothing more than
"normatively constrained noise- or mark-makings" (Whiting
2006: 11), that is, non-semantically described performances that stand
in normative relations to other non-semantically described
performances, it does not seem that we have the resources to single
out as privileged a particular interpretation or standard of
correctness. Similarly, a normative pattern that instantiates how one
ought, in the primitive sense proposed by Ginsborg, to go on with
respect to an expression seems to be consistent with more than one
semantic interpretation of that expression. It might be thought that
Ginsborg could appeal to the non-semantically characterized
disposition in order to fix the meanings of the relevant expression.
However, we have already shown in
 section 4
 that dispositionalist accounts face very serious obstacles (see
Verheggen 2015; Chapter II of Myers and Verheggen 2016, and Miller
2019 for more discussion of the failure of dispositionalism in
relation to Ginsborg's view). So, the proponent of the less
austere approach to meaning owes the austere non-reductionist an
account of how the extensionality condition might be met. (See Haddock
2012 and Sultanescu 2021 for more discussion of Ginsborg's view,
and Rosen 1997, McDowell 2002, Hattiangadi 2003, and Whiting 2006 for
more discussion of Brandom's view.)