Ludwig Wittgenstein’s reflections onrule-following—principally, sections 138–242 ofPhilosophical Investigations and section VI ofRemarks onthe Foundations of Mathematics—raise a series of provokingquestions and puzzles about the nature of language and thought. Theliterature on this topic is vast. We’ll structure our discussionaround Saul Kripke’sWittgenstein on Rules and PrivateLanguage (1982), the most widely discussed commentary onWittgenstein on rule-following.^[1] In this book, Kripke’s Wittgenstein famously develops a“sceptical challenge” to the idea that that there arefacts about the meanings of linguistic expressions and contents ofthoughts, and goes on to propose a “sceptical solution” tothe challenge, which attempts to preserve the propriety of talk ofmeaning and content while conceding to the sceptic the non-existenceof the kind of semantic or intentional facts on which she casts doubt.After some preliminary comments about rules, meaning, and content(§1), we’ll outline the sceptical argument (§2), andwe’ll offer an overview of some of the main responses to it.First, we’ll discuss sceptical responses of the sort proposed byKripke’s Wittgenstein himself (§3). Then, we’llconsider straight responses, which advance candidatemeaning-constituting facts. We’ll examine in detail the twoforms of straight solution that are most widely discussed in thesecondary literature, reductive dispositionalism (§4) andnon-reductionism (§5).

For the purposes of this entry, we’ll understand‘intentionality’ in a broad sense, so that it covers themeanings of linguistic expressions (and utterances) and also thecontents of propositional attitudes. Clearly, these notions areclosely related: just as we can say of the sentence‘\(68+ 57 = 125\)’ that it meansthat 68 plus 57 is 125, we can say of Octavia’s beliefthat it has the contentthat 68 plus 57 is 125 (or thatOctavia believesthat 68 plus 57 is 125).

• 1. Rules, Meaning, and Content
• 2. The Sceptical Argument
  • 2.1 The Extensionality Condition
  • 2.2 The Normativity Condition
• 3. The Sceptical Solution
  • 3.1 Error Theories
  • 3.2 Non-Factualist Theories
  • 3.3 An Alternate Form of Factualism
• 4. Reductive Dispositionalism
  • Postscript to section 4: Lewis on Natural Properties
• 5. Non-Reductionism
• Bibliography
• Academic Tools
• Other Internet Resources
• Related Entries

1. Rules, Meaning, and Content

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

If the rule I’m following isadd 2, thecontinuation

iscorrect, in that it accords with the rule I’mfollowing, while the continuation

isincorrect, in that it fails to accord with the ruleI’m following.

We have here an analogy with my meaning something by a linguisticexpression. Say that I meanblue by ‘blue’. Then,‘blue’ is correctly applicable to, for example, a USpostbox but not to a ripe (Roma) tomato. We can express this point by sayingthat the former application accords with the predicate’s meaningwhile the latter application fails to do so. Given this analogy,arguments about rule-following have consequences for our conception oflinguistic meaning: if an argument shows that there are no facts aboutwhich rule an agent is following, it may also show that there are nofacts about what a speaker means by a linguistic expression.

Note that the notion of accord in play in the case of following a ruleis also in play in our conception of mental states with intentionalcontent generally. Say that one intends to attend the performance ofSartre’s playNo Exit at the Hopewell Theatre onWednesday. Then, one’s attending the performance at the Hopewellon Wednesday accords with one’s intention (in the sense that itfulfils it), while one’s staying at home to grade logic examsfails to accord with it. Say that one believes that the cat is on themat. Then, the state of affairs in which the cat is on the mat accordswith one’s belief (in the sense that it renders it true), whilethe state of affairs in which the cat is on the roof does not. Saythat one desires to smoke aBolivar Number 3. Then,one’s smoking aBolivar Number 3 accords withone’s desire (in the sense that it satisfies it), whileone’s smoking aCafé Crème does notaccord with it. Given this, arguments about rule-following haveconsequences for our conception of mental content: if an argumentshows 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 athinker’s mental states.

Before considering the arguments themselves, we’ll pause toreflect on views about the relative priority of linguistic meaning andmental content, and on what presuppositions are required in order forthe arguments to be run.

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

• The Sellarsian View: the notion of linguistic meaning isexplanatorily prior to the notion of mental content (Sellars1956).
• The Gricean View: the notion of mental content isexplanatorily prior to the notion of linguistic meaning (Grice1989).

Boghossian suggests that, irrespective of which of these views isadopted, it will not be possible to develop a sceptical argument thatexclusively targets linguistic meaning. On the Sellarsian View, theconclusion that there are no facts about linguistic meaning willensure that there are no facts about mental content, since on thatview it is from the former sort of fact that the latter sort of factwould have to be derived. On the Gricean view, raising a scepticaldoubt about linguistic meaning cannot be done without raising asceptical doubt about mental content.

We would add a third possible view:

• The Davidsonian View: the notions of mental content andlinguistic meaning are explanatorily interdependent; neither takesexplanatory priority over the other (Davidson 1984, 2001).

Clearly, on the Davidsonian view, one cannot pose a sceptical threatto the existence of facts about the meanings of linguistic expressionswithout also threatening the existence of facts about mental content,and vice versa. And we can add Boghossian’s furtherobservation:

If [the sceptical arguments are] effective at all, they should be aseffective against linguistic content as they are against mentalcontent. This is evident from the fact that the arguments constructtheir skeptical case by exploiting features of content properties, butwithout exploiting any facts about the putativebearers ofthose properties. Thus, they would apply to anything said to possesscontent, whether it was mental or not. (1990 [2008: 62])

In what follows, then, we’ll move freely between consideringarguments about rule-following, linguistic meaning, and mental content.^[2]

2. The Sceptical Argument

We’ll begin with a brief outline of the argument ofKripke’s sceptic. Suppose that I’ve never dealt withnumbers larger than 57.^[3] (Given our finite nature and the infinitude of the natural numberseries, there will always in fact be such a number.) I’m askedto perform the computation‘\(68+57\)’,and I arrive at theanswer ‘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 asaddition if the numbers are lower than 57, and 5 otherwise, so thecorrect result of the aforementioned computation is ‘5’,not ‘125’. I should answer ‘5’ if I intend touse ‘plus’ in the same way in which I have been using itin the past, or so the sceptic suggests.

Kripke allows that the sceptic’s proposal is “absolutelywild”, 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 somefact about my past usage that can be cited to refute” thathypothesis (1982: 9). That is, there must be some fact about my pastusage that determines that I meantaddition by‘plus’ in the past, and thus that (again, assuming that Iintend to use the expression in the same way I have been using it sofar) I should answer ‘125’ rather than ‘5’.Importantly, the sceptic does not question my memory concerning pastuse; indeed, she goes as far as to allow that the exercise of mycognitive powers is faultless, and that I have access to all the factsabout my mind and behaviour that are potentially constitutive of mymeaning one thing rather than another (1982: 14). Her thought is thatif I am not able, even in such cognitively ideal conditions, toprovide the fact in virtue of which I meanaddition, a factthat properly singles out the function of addition rather than thefunction of quaddition, it is because there is no such fact.Furthermore, the focus is on past use because “if I use languageat all, I cannot doubt coherently that ‘plus’, as I nowuse it, denotes plus” (1982: 13). But, if the sceptic’schallenge succeeds, it can be generalized, for “if there was nosuch thing as my meaning plus rather than quus in the past, neithercan there be any such thing in the present” (1982: 21). (Thefact that the sceptic grants the idealisation of our cognitive powersin the way that she does shows that her argument is not of a piecewith the argument of the epistemological sceptic, who is concernedwith whether our actual cognitive capacities can lead to knowledge.See Boghossian 1989 [2002: 150]. For dissent over this point, seeGinsborg 2018. Martin Kusch takes the argument to be metaphysical[2006: xiv], but, in contrast with Boghossian, he takes the dialogicsetting to play an essential role in it.)

As we’ll see, the search for a fact fails, and the scepticconcludes that “the entire idea of meaning vanishes into thinair” (Kripke 1982: 22). Kripke rejects this paradoxicalconclusion as “insane and intolerable” (1982: 60) and“incredible and self-defeating” (1982: 71), and goes on todevelop, on behalf of Wittgenstein, a sceptical solution, which hetakes to be similar in some respects to David Hume’s solution tothe sceptical problem about causation (1982: 4; 62–69), andwhich purports to conceive of meaning in a way that does not lead toparadox. We discuss the sceptical solution insection 3. (George Wilson was the first to insist on the significance of thedistinction between the parts of the sceptic’s positionKripke’s Wittgenstein accepts and the parts herejects—between thebasic sceptical conclusion,according to which there are no facts about a speaker of the sort thatthe sceptic is seeking that constitute her meaning something by anexpression, and theradical sceptical conclusion, accordingto which no one means anything by an expression [Wilson 1994, 1998].We will return to Wilson’s view insection 3.3.)

Why does Kripke take the search for candidate meaning facts to fail?Recall that all my previous uses of ‘+’ are compatiblewith my meaningquaddition, which is what enables the scepticto say that I meant that all along. One might complain that thechallenge operates from a “ridiculous model ofinstruction” (1982: 15), which fails to take into account thatto be a competent adder is to have internalized a general instructionor 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 beraised again with respect to the general instruction or rule, which isjust as susceptible to being interpreted in a deviant way as theinitial expression. Kripke then considers a variety of othercandidates, 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 operationsembody the function of addition (1982: 32–35), the simplicity ofthe addition hypothesis (1982: 37–39), my having a distinctiveexperience “with its own special quale, known directly”through introspection (1982: 41), my having an image in mind thatsupposedly singles out addition (1982: 42), my being in a primitive,irreducible state of meaning addition (1982: 51–53), and mygrasping an abstract entity, such as a Fregean sense, which singlesout addition (1982: 53–54). None of them, Kripke argues, issuccessful in ruling out the skeptic’s hypothesis that I meantquaddition rather thanaddition.

As mentioned above, dispositionalism and non-reductionism are the mostprominently discussed proposals, and we’ll consider them morecarefully insection 4 andsection 5, respectively. At this stage, we should ask the following question:what are the conditions that a candidate meaning fact must meet? Thereis controversy in the literature about their nature andplausibility.

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 mustgive an account of what fact it is (about my mental state) thatconstitutes my meaning plus, not quus. But further, there is acondition that any putative candidate for such a fact must satisfy. Itmust, in some sense, show how I am justified in giving the answer‘125’ to‘\(68+57\)’.The‘directions’ … that determine what I should do ineach instance, must somehow be ‘contained’ in anycandidate for the fact as to what I meant. Otherwise, the skeptic hasnot 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 thata speaker means addition by ‘+’ must single out theaddition function, as opposed to the quaddition function, as what ismeant. It follows from this that the putative meaning-constitutingfact must account for the conditions of correct application of‘+’. In other words, the fact in which my meaning additionby ‘+’ consists must single out ‘4’ as thecorrect response to‘\(2 + 2\)’,‘110’ as the correct response to‘\(55+ 55\)’, ‘125’ asthe correct response to the query‘\(68 +57\)’, and so on. Meaning facts render the applicationsof expressions correct or incorrect, and so a fact cannot count as ameaning-constituting fact unless it does this. This is anuncontroversial claim, which most philosophers accept. As SimonBlackburn notes, this

distinguishes the production of terms from mere noise, and turnsutterance into assertion—into the making of judgement,

and so

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

Moreover, this is something on which those who seek to offer areductive account of meaning (e.g., Fodor 1990; Millikan 1984) andthose 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 theextensionalitycondition. In the case of a predicate like ‘green’,for example, it requires that the fact which constitutes its meaningdetermines the appropriate class of things to which‘green’ is correctly applicable. This will be the class ofgreen things as opposed, say, to the class ofgrue things(where an object is grue if and only if it is green before somespecified timet and blue thereafter), and in the arithmeticalcase 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 theextensionality condition, consider a simple form of dispositionaltheory of meaning which proposes as constitutive of my meaningaddition the fact that I’m disposed to answer with thesum (as opposed, say, to thequum) when faced witharithmetical queries of the form‘\(x +y\)’. The sceptic argues that this fact doesn’tsingle out the addition function:

Let ‘quaddition’ be redefined so as to be a function whichagrees with addition for all pairs of numbers small enough for me tohave any disposition to add them, and let it diverge from additionthereafter (say, it is 5). Then, just as the skeptic previouslyproposed the hypothesis that I meant quaddition in the old sense, nowhe proposes quaddition in the new sense. A dispositional account willbe impotent to refute him. As before, there are infinitely manycandidates the skeptic can propose for the role of quaddition. (Kripke1982: 27)

We’ll consider whether dispositionalism can muster resources todeal plausibly with this problem concerning the satisfaction of theextensionality condition below (insection 4).

2.2 The Normativity Condition

According to a prominent line of thought, the notion of correctnessinvolved in the seemingly platitudinous claim that meaningfulexpressions have conditions of correct application isintrinsically normative. On this reading, meaning facts arenormative facts—they not only sort the applications ofexpressions into correct or incorrect, but also prescribe howexpressions ought to be applied. They issue semantic categoricalobligations that bind speakers in determinate ways; the justifiedapplications are precisely those that fulfil these semanticobligations. (The kind of normativity at stake is meaning engendered,rather than meaning determining; it is grounded in meaning, ratherthan grounding meaning. See Glüer and Wikforss 2009 for thishelpful distinction.)

To illustrate how the second condition, thus construed, constrainsaccounts of meaning, let us again consider Kripke’s discussionof dispositionalism. He thinks that the dispositionalist offers“a descriptive account” of the relation between what onemeans by an expression and one’s uses of that expression, butthat “this is not the proper account of the relation, which isnormative, not descriptive” (1982: 37). More generally,Kripke says, “the relation of meaning and intention to futureaction isnormative, notdescriptive” (1982:37). Among the commentators who read the second condition in this wayare Wikforss 2001, Glüer and Wikforss 2009, Hattiangadi 2006 and2007, and Miller 2011, 2012. Thus construed, the sceptical argumentcan be compared to arguments in metaethics that purport to establish,by drawing on J. L. Mackie’s (1977) argument from queernessconcerning the seemingly problematic metaphysical and epistemologicalstatus of moral properties, an error-theory of moral judgment (Miller2010a, 2020). (See the entry onmoral anti-realism.)^[4]

Kripke’s discussion has resulted in a vigorous debate aboutwhether meaning really is normative, as well as about how thenormativity of meaning is best understood. For a defence of the claimthat meaning is normative, see Whiting 2007, 2009, 2016 (note thatWhiting focuses on the idea that meaning facts engender permissions toapply words correctly and obligations not to apply them incorrectly,though both the permissions and the obligations are defeasible). Forcriticism of the view that meaning is normative, see Fodor 1990,Glüer and Pagin 1998, Glüer 1999, Wikforss 2001, Boghossian2005, Miller 2006, Hattiangadi 2006, 2007, and Glüer and Wikforss2009. (See also the entry on thenormativity of meaning.) Some philosophers seek to carve a middle ground between thenormativist and the anti-normativist positions—for instance, byclaiming that meaning facts are essentially justificatory (Gampel 1997), orthat they have hypothetical implications that are essential to them,thus being fundamentally unlike natural facts, which may behypothetically normative only accidentally (Verheggen 2011; Chapter 2of Myers and Verheggen 2016). Hannah Ginsborg proposes a novelconception of normativity as more basic than rules (Ginsborg 2011b,2012, forthcoming), which we shall briefly discuss in the lastsection.

Some commentators take the normativity condition to amount to anagential requirement, one that primarily concerns theapplications oruses of expressions. The thought isthat meaningful uses of expressions are not arbitrary—they arenot unjustified leaps in the dark. An adequate conception of meaningmust be able to account for this. This view of the normativitycondition claims to shed light on Kripke’s numerous appeals tothe metaphor of blindness (1982: 10, 15, 17, 23, 87). Kusch thinksthat the requirement of non-blindness is best understood as fallingunder the purview of semantic normativity (which, contra thenormativist interpreters, he does not take to involve categoricalobligations), and that it is best understood as indicating that thespeaker’s “meaning-constituting mental state guides andinstructs” her on how to apply the expression, that the speaker“can refer to this mental state in order to justify heruse” of the expression, and that this state

not only justifies certain applications—in the sense thatmeaning addition justifies ‘125’ in answer to‘\(68+57=\ques\)’—italsojustifies the way in whichthe answer is usually produced.(Kusch 2006: 8–9, italics added)

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

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

Some interpreters take the sceptical argument to involve theimposition of an epistemological constraint—a constraint relatedto the epistemic justification of semanticjudgments, ratherthan to the rationality of the applications of expressions. WarrenGoldfarb notes that Kripke “does seem to mean that thejustifications must in some sense be transparent” (1985 [2002:98]). José Zalabardo takes Kripke to be demanding that themeaning-constituting facts provide speakers with justification fortheir judgments about the correctness of the applications of theirpredicates. Justification is construed in an internalist sense:speakers possess the relevant justification if the procedure throughwhich they decide whether predicates apply to objects involved“conscious engagement with the facts that determine howthese questions should be answered” (1997 [2002: 286]). (Seealso Jackman 2003, Guardo 2012, and Merino-Rajme 2015). Crispin Wrightproposes a more specific epistemic constraint, namely, that ofaccounting for the seemingly puzzling fact that the epistemology ofmeaning is first-person authoritative even though meaning something byan expression is in crucial respects akin to having a dispositionaltrait. In Wright’s words, the constraint is to explain

how it is possible to be effortlessly, non-inferentially and generallyreliably authoritative about psychological states which have nodistinctive occurrent phenomenology and which have to answer, afterthe fashion of dispositions, to what one says and does in situationsso far unconsidered. (2001: 150)

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

3. The Sceptical Solution

If the sceptical argument is cogent, it seems to follow that there areno meaning-constituting facts, no facts in virtue of which linguisticexpressions mean one thing rather than another. As noted above, thisappears to imply the paradoxical conclusion that “the entireidea of meaning vanishes into thin air” (1982: 22). Kripkedistinguishes between two broad ways in which one might attempt toavoid this conclusion (1982: 66–7). On the one hand, one mightprovide astraight response, by identifying somemeaning-constituting fact of the sort called into question by thesceptic. The various proposals discussed briefly insection 2 above are instances of straight responses. The two most prominenttypes of straight response in the literature—reductivedispositionalism and non-reductionism—are discussed in moredetail insection 4 andsection 5 below. On the other hand, one might provide ascepticalresponse. That is, one might concede that there are nomeaning-constituting facts of the sort demanded by the sceptic butdeny that this leads to a paradoxical conclusion. In this section, weshall focus on this strategy.

The proponent of the sceptical solution can be understood as rejectingeliminativism about our practices of ascribing meaning. Mirroringparallel discussions in metaethics, the two most obvious pathsavailable to her involve providing either an error-theoretic accountor a non-factualist account of ascriptions of meaning. We shall followBoghossian in viewing these paths as forms ofirrealism aboutmeaning, content and rules (Boghossian 1989, 1990). A prominentgeneral line of argument in the recent literature suggests thatirrealist views of any area make presuppositions that irrealist viewsof meaning and content are bound to deny, so that irrealism aboutmeaning and content is ultimately incoherent (Boghossian 1989, 1990;Hattiangadi 2007, 2017, 2018; Miller 2011, 2015a, 2020). We’llillustrate this general line of attack by sketching an argument to theeffect that, regardless of whether one pursues an error-theoretic or anon-factualist approach, adopting irrealism leads inexorably to an“insane and intolerable” and “incredible andself-defeating” form ofeliminativism on which thenotions of meaning and content do turn out to “vanish into thinair”. We’ll then briefly consider an alternative way ofproviding a sceptical response, which aims to revise the conception ofmeaning 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, positivestatements ascribing meaning, content, or the following of a rule, arefalse. While some error theories are eliminativist (e.g., Churchland1981 on propositional attitudes), the error theorist need notsubscribe to eliminativism. For instance, J.L. Mackie (1977) arguesthat although moral judgements are uniformly false, eliminativism canbe avoided given that some moral judgements are such that theiracceptance facilitates securing the benefits of social cooperation incircumstances where “the limitation of men’ssympathies” (1977: 108) threaten their attainment.^[5] On this view, even though our practice of making moral judgmentsresults in falsehoods, it meets a subsidiary norm (or norms) in termsof whose satisfaction its pragmatic utility can be secured.^[6] Might an error theorist about meaning, content and rule-followingattempt to avoid eliminativism by following a similar strategy?

It might seem that there is room for this approach. In the case ofmeaning, 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 thecommunity in enough cases, especially the simple ones (and if his“wrong” answers are not oftenbizarrely wrong, asis ‘5’ for‘\(68 +57\)’, but seem to agree with ours inprocedure,even when he makes a “computational mistake”). (Kripke1982: 92)

This norm would thus be cashed out in terms ofagreement withrespect to inclinations “to go on” in certain ways, andthe utility of our complying with it would be that it enables us tomake helpful discriminations—for example, when seeking to buyfive apples—between grocers whose inclinations match ours andgrocers with “bizarre” quus-like inclinations.^[7]

While this strategy might seem to some to be promising in the moralcase, it faces special problems in the case of meaning, content andrules (Boghossian 1989, 1990; Miller 2015a). In order for the strategyto be able so much as to be pursued, there has tobe such athing as complying or failing to comply with a subsidiarynorm—and so,a fortiori, such a thing as complying orfailing to comply with a norm as such. An error theorist aboutrule-following, however, deniesprecisely that there arefacts about norm-compliance and non-compliance. Having argued that allstatements about rule-compliance are false, the error theoristapparently lacks the resources for telling a story about the pragmaticutility of our continuing to engage in the practice of makingjudgements about rule-following. The upshot seems to be that, if weaccept that there are no facts about speakers in virtue of whichexpressions have meaning, embracing an error theory will not preventthe notion of meaning from “vanishing into thin air”.

3.2 Non-Factualist Theories

One might attempt to avoid eliminativism about meaning by embracing adifferent type of irrealism, namely, non-factualism. Anon-factualist about a domain maintains that judgments and claims madewithin that domain are not in the business of stating facts. Indeed,the standard view in the secondary literature is that Kripke’sWittgenstein himself is proposing a form of semantic non-factualism inthe 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 theconclusion 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; Miller2011, 2020). The non-factualist about meaning proposes that weconstrue ascriptions of meaning as having a purpose or functiondifferent from that of stating facts. But, insofar as a sentence isregarded as having a function, there is an intelligible distinctionbetween correct and incorrect uses of that sentence; in other words,the sentence is rule-governed. That the notion of correctness in thesecases cannot be identified with truth or warranted assertibility makesno difference to the applicability of a generalised version of theextensionality condition, which we outlined insection 2. Thus, suppose that‘\(S\)’ is asentence that has a non-descriptive semantic function. Consider thesetwo 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 correctiff the conditions in which it is uttered accord with \(R_1\);

(b)

Uttering‘\(S\)’ is correctiff the conditions in which it is uttered accord with \(R_2\).

Whatever makes it the case that (a) provides the correctnessconditions for utterances of‘\(S\)’must rule out (b) as providingthose conditions.

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

(a*)

‘Let’s write a fugue!’, as uttered by Glenn, iscorrect iff Glenn plans to write a fugue

and

(b*)

‘Let’s write a fugue!’, as uttered by Glenn, iscorrect iff either (a) it is timet earlier thant* andGlenn plans to write a fugue or (b) it is timet later than orequal tot* and Glenn plans to write a novel.

Glenn’s finite nature together with the infinitude of thetemporal sequence ensures that the sceptic will always be able toargue that no fact about Glenn is capable of ruling in something like(a*) and ruling out something like (b*) as the relevant correctnesscondition. The non-factualist is entitled to regard “Let’swrite a fugue!” as having a determinate meaning only if she canprovide some fact about Glenn or his speech community that determinesthat that sentence is governed by (a*) rather than (b*). The sameargument can be pressed against the suggestion that “Jones meansaddition by ‘+’” should be regarded as having somenon-descriptive semantic function. The non-factualist will be able toregard “Jones means addition by ‘+’” as havinga determinate meaning only if she can provide some fact about Jones orhis speech community that determines that that sentence is governed byone rule or correctness condition rather than another.

So, a non-factualist account of any region of thought and talk, whichis committed to the claim that there are no facts of the relevantsort, would seem to presupposes a realist account of meaning, contentand rules according to which there are semantic facts, intentionalfacts, and facts about normative accord. So, a non-factualist accountof meaning, content and rules, which is committed to the claim thatthere are no semantic facts, intentional facts, or facts aboutnormative accord that our semantic, intentional, or normativediscourse purports to capture, presupposes a realist account ofmeaning, content and rules according to which there are semanticfacts, intentional facts, and facts about normative accord. It thusfaces a charge of incoherence.

As noted above, we chose “plans” as our stalking horsehere in order to make explicit the problem this poses for AllanGibbard’s (2012) account of meaning (it makes no difference tothe argument whether “plans” are taken to be linguisticitems possessing meaning or mental states possessing intentionalcontent). A Gibbard-style expressivist approach to an area such asmorality denies that there are moral facts, but presupposes that thereare facts about meaning, content and normative accord (facts thatdetermine what accords and fails to accord with a plan). AGibbard-style approach to meaning, content and rules thus, on the onehand, denies that there are semantic facts, intentional facts andfacts about normative accord (facts that determine what accords andfails to accord with a plan), and, on the other, presupposes thatthere 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 accountof 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 anoblique explanation in the moral case presupposes a straightexplanation of intentionality. In parallel, an oblique explanation ofmeaning and intentionality would presuppose a straight explanation ofmeaning and intentionality, again threatening the view withincoherence. In a reply to Hattiangadi, Gibbard reflects on thestrategy of the metaethical expressivist and attempts to use it tocounter Hattiangadi’s worry. He writes:

A parallel can be found in ethics: Suppose we claim that being goodconsists in being pleasurable. The concept of being pleasurable can becompletely non-ethical and naturalistic, but the claim “Beinggood consists in being pleasurable” is ethical—and so, ifMoore and others are right, nonnaturalistic. Is there, then, “astraight or substantive explanation of intentionality”? Thecorrect answer will parallel that for the question, “Is there astraight substantive explanation of being good?” If ethicalhedonists are right and being good consists in being pleasurable, thenthere’s a straight, substantive explanation of being good in thesense of a naturalistic explanation of the property that being goodconsists in. But the claim “Being good is beingpleasurable” 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 thereare no meaning facts, but rather that a certain conception of suchfacts, which he callsclassical realism, is hopeless, andconceives of the sceptical solution as accommodating meaning factswhen conceived in a different way (Wilson 1994; see also Wright 1992:chapter 6). Classical realism is sometimes referred to as semanticplatonism, the view that “the meanings of our words areguaranteed by the pre-existing structure of reality” (Pears1988: 363; cf. Child 2001, Verheggen 2003, Zalabardo 2003, Hanks2017). What is essential to classical realism or semantic platonism isthat the properties that guarantee meaningfulness must be antecedentlysingled out by individuals (or communities) in order to endow theirwords with semantic standards (Wilson 1994 [2002: 251]). As Zalabardoputs it, what is required is

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

Wilson takes the sceptical challenge to reveal that no sense can bemade of this idea, for it is not possible for an individual (orcommunity) non-linguistically to single out properties as “thede re subject of her meaning-constituting intentions”(1998: 105). But, to repeat, what this allegedly shows is not thatthere are no meaning facts, but rather that we must reform ourconception of them.

The alternative picture of meaning that Wilson fleshes out conceivesof expressions as not connected to properties that serve as“pre-established” standards of correctness” (2003:181–182), and suggests that “what we mean by [anexpression] is something that gets settled only over the course oftime” (2003: 186). In response to Wilson’s proposal, ithas been argued that it is susceptible to collapsing into a form ofsubjectivism (Kremer 2000), and that it is untenable, for it fallsprey to the sceptical challenge that it purports to bypass (Miller2010b). It has also been argued, contra Wilson, that classical realismis merely an instance of a more general conception of meaning thattakes standards of correctness to be determined byentities—whether abstract properties or real features of theworld around us—that are considered independently of how wemight describe them linguistically; it is this conception that must berejected, 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 thesceptical challenge is reductive dispositionalism. According to asimple version of reductive dispositionalism, the fact that Jones hasthe concept ofaddition rather than ofquaddition isto be identified with (or is constituted by) his disposition toproduce the result of adding (and not quadding) the numbersxandy in response to arithmetical queries of the form‘\(x+ y = \ques\)’, and the fact thathe meanscat by ‘cat’ is to be identified with(or is constituted by) his disposition to apply ‘cat’ tocats. (See Horwich 1998, 2010, 2012 for a systematic development ofdispositionalism; an answer to Kripke’s challenge is articulatedin Horwich 2015.)

As Boghossian notes (1989 [2002: 164–165]), the general form ofdispositionalism targeted by the sceptic covers bothconceptualrole theories andcausal/informational theories. In bothcases, the account is intended to be reductive, insofar as thecontent-determining dispositions are to be characterized in whollynon-semantic and non-intentional terms. The sceptic’s attack onreductive dispositionalist theories is thus an attack on two of themost popular accounts of the determination of content in contemporaryphilosophy of mind and language.

The sceptic argues that dispositionalist theories face three problems.The first problem—the finitude problem—is that there is asense in which, much like the totality of our previous linguisticbehaviour, our dispositions arefinite. Given that theextension of the addition function is infinite, containing adenumerably infinite number of triples \(\langle x, y, z\rangle\) suchthatx plusy is identical toz, Jones’smeaning addition by ‘+’ cannot be identified with herdispositions to respond to arithmetical queries since it is simplyfalse that she is disposed to answer with the sum when faced with thequery‘\(x + y = \ques\)’. Insome (indeed, most) cases, the numbers involved will be so large thatJones’s brain’s capacity for computation is far exceeded,and Jones may even die long before she is able to grasp the relevantnumbers. We might follow Boghossian in dubbing such numbers“inaccessible” (2015: 335), and we might define quadditionto be a function that diverges from addition over only inaccessiblenumbers. In this case, the problem is that, given Jones’sdispositions, it is indeterminate whether he meansplus orquus.

The second problem—the error problem—is that someone mightbe systematically disposed to makemistakes. Take Smith, whois systematically disposed to miscarry when responding to‘\(x+ y = \ques\)’ queries. WhenSmith produces ‘28’ in response to‘\(19+ 19 = \ques\)’, we want to beable to say that her answer is incorrect in the light of what shemeans by ‘+’. However, if what she means is determined byher dispositions, we are forced to say that she actually means somenon-standard function (one that corresponds to addition with thecarrying operation removed), so that her answer ‘28’ iscorrect.

The third problem—the normativity problem—is that thedispositionalist view seems unable to capture thenormativityof meaning. Given what she means by ‘+’, Jonesought to respond to arithmetical queries of the form‘\(x+ y = \ques\)’ by producing thesum ofx andy, but the meaning-constituting factproposed by the dispositionalist is at most a fact about how she wouldrespond to queries of the relevant form:

Suppose I do mean addition by ‘+’. What is the relation ofthis supposition to the question how I will respond to the problem‘\(68+57\)’? Thedispositionalist gives adescriptive account of thisrelation: if ‘+’ meant addition, then I will answer‘125’. But this is not the proper account of the relation,which isnormative, not descriptive. The point isnot that, if I meant addition by ‘+’, Iwill answer ‘125’, but that, if I intend toaccord with my past meaning of ‘+’, Ishouldanswer ‘125’. Computational error, finiteness of mycapacity, and other disturbing factors may lead me not to bedisposed to respond as Ishould, but if so, I havenot acted in accordance with my intentions. The relation of meaningand intention to future action isnormative, notdescriptive. (Kripke 1982: 37)

Insection 2, we outlined a number of ways in which a normativity condition mightbe thought to impose a constraint on accounts of meaning. We suggestedthat in all of these ways this condition puts at least prima faciepressure on dispositionalist theories of meaning. We will limitourselves in the remainder of this section to some remarks on thefinitude problem and the error problem. These two problems indicatetwo obstacles that the dispositionalist must overcome in order to meetthe extensionality condition.

Blackburn responds to the finitude problem by pointing out thatfamiliar dispositional properties (such as fragility) are in a senseinfinitary: “there is an infinite number of places andtimes and strikings and surfaces on which it could be displayed”(1984 [2002: 35]). If a glass has infinitary dispositions, perhaps ahuman does too, and perhaps this will yield an extended dispositionthat covers the case of queries involving inaccessible numbers. Eventhough 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 aspossessing an extended disposition to break there: breaking is whatthe glass would be disposed to do were its dispositions on earthallowed to manifest themselves on Alpha Centauri. Likewise, eventhough Jones has no disposition to answer queries involvinginaccessible numbers, responding with the sum is what Jones would bedisposed to do were her dispositions in accessible cases allowed tomanifest themselves in inaccessible cases. This would in turn allow usto say that the answer that she would accept in those cases is“the one thatwould be given by reiterating procedures[Jonesis] disposed to use, a number of times” (1984[2002: 35]).

Blackburn’s response to the finitude problem is open tocriticism. First, Blackburn’s talk of procedures Jones isdisposed to use is illegitimate in this context: to “use”a “procedure” is to follow a rule, and we cannot helpourselves to the idea that Jones is following the rule for additionhere (or any rule, for that matter), as it is Jones’s status asa rule-follower that we are hoping to recover from facts about herdispositions. What we can say is that as far as the accessible casesgo, the answers Jones is disposed to giveconform to the rulefor addition. But, of course, they alsoconform to the rulefor quaddition. What makes Jones an adder, and not a quadder,according to Blackburn’s suggestion, is that were Jones’sdispositions in the accessible cases allowed to manifest themselves inthe inaccessible cases, she would respond with the sum, and not thequum.

However, Boghossian (2015: 341) points out that there is a crucialdisanalogy between this case and the extended disposition to break onAlpha Centauri plausibly ascribed to the glass. To think of thedispositions the glass has on earth as manifesting themselves on AlphaCentauri, we don’t need to think of the glass in any way that isinconsistent with its nature as a physical object. It can be regardedas having the same intrinsic physical characteristics on AlphaCentauri as it has on earth, and if it is true that, given thosecharacteristics, it would break if struck on Alpha Centauri, thatsuffices for the attribution of the extended disposition to break onAlpha Centauri. Matters stand differently with Jones. In order tothink of Jones’s dispositions to respond in accessible cases asmanifesting themselves in inaccessible cases, we would have to thinkof her in a way that is inconsistent with her nature as a finitebiological being. This is because responding to queries involvinginaccessible numbers would require, let’s suppose, a brain thesize of the universe. But the fact that with a brain the size of theuniverse the sum would be produced no more warrants the attribution ofthe relevant extended disposition to Jones than does the fact thatwith a brain the size of the universe she would outplay Magnus Carlsenwarrant the attribution to her of the potential to win the world chesschampionship. Jones has no extended disposition of the sort adumbratedby Blackburn.^[10] The upshot, then, is that Jones’s dispositions do not determinewhether 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 finitudeproblem as fundamentally a problem about determinacy. In a recentpaper, Jared Warren admits that solving the finitude problem, thusconstrued, turns on solving the error problem (2020: 268), andproceeds to offer an attempted solution to that problem. Consider thefollowing proposal: the fact which constitutes Jones’s meaningaddition by ‘+’ is the fact that, when faced witharithmetical queries involving the ‘+’ sign, Jones isstably disposed to reply with the sum in the overwhelming majority ofnormal situations.^[12] What are normal situations, and what is it for a disposition to bestable? Normal situations are those in which neither external norinternal factors are interfering with Jones’s general cognitivefunctioning. More specifically, the normal situations are those inwhich Jones is clearheaded—situations in which the air is notpermeated with mind-bending chemicals, in which Jones is not drunk,exhausted, or badly hungover, so that neither external causes norinternal causes are interfering with her cognitive performance.Furthermore, to say that Jones’s disposition to respond with thesum is stable is to say that, as the number of arithmetical queriesshe has faced increases, the ratio of answers that give somethingother than the sum to answers that give the sum tends towards zero.And to keep the bar relatively low, we don’t require that innormal conditions it ismetaphysically impossible for Jonesto answer with something other than the sum. We only require that,when such conditions obtain, it is rational to benearlycertain that she will answer with the sum. Call the dispositionwhich we have described heredisp.dispcorresponds to the meaning-constitutingdispositions that Warren proposes as offering a solution to the errorproblem. The proposal is intended to be reductive. Warren notes that“normalcy”, defined as he defines it, “isn’tsemantic or intentional or otherwise problematicallyquestion-begging” (2020: 271).

However, Warren’s attempt to solve the error problem can bequestioned. The error problem arises as a result of the fact that thefollowing two possibilities are consistent with Jones’spossession ofdisp. First, Jones meansaddition by ‘+’ and is respondingcorrectly tothe relevant queries. Second, Jones means some quus-like function andis respondingincorrectly. What Warren thus needs is acharacterisation of normal situations such that the latter possibilityis ruled out. Thus, what is required is a characterisation of normalsituations such that, when those situations obtain, we are entitled tobe nearly certain that Jones will answer with the sum,and that inanswering with the sum Jones is responding correctly. The troubleis that there is an infinite range of functions \(F_1\),…,\(F_n\) that have different extensions from the addition function. IfJones means some function \(F_i\) among them, and if she answers withthe sum,she would be answering incorrectly. Thus, the normalsituations have to be such that their obtaining ensures that Jonesmeans by ‘+’ none of the functions in this open-ended andinfinite set. The question that drives Kripke’sWittgenstein’s objection is: how could this be achieved otherthan through the inclusion of a clause in the characterisation ofnormal situations to the effect that Jonesmeans addition by‘+’ (or at least, that Jonesmeans a functionwith the same extension as addition)? How could the obtaining of anon-semantically characterised set of situations have the effect ofexcluding every member of an open-ended and infinite set ofsemantically or intentionally characterised states of affairs (Jonesmeans \(F_1\) by ‘+’, Jones means \(F_2\) by‘+’, and so onad infinitum)?^[13]

Thus, it can be argued that the dispositionalist account offered byWarren either fails to resolve the indeterminacy problem or does soonly 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 therule-following literature is suggested by David Lewis in his“New Work for a Theory of Universals” (1983). Lewiswrites:

The naive solution is that adding means going on in the same way asbefore when the numbers get big, whereas quadding means doingsomething different; there is nothing present in the subject thatconstitutes an intention to do different things in different cases;therefore he intends addition, not quaddition. We should not scoff atthis naive response. It is the correct solution to the puzzle. But wemust pay to regain our naiveté. Our theory of properties musthave adequate resources to somehow ratify the judgement that instancesof 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 apar with unit charge or sphericality. And the property of quadding isnot perfectly unnatural. But quadding is worse by a disjunction. Soquaddition 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 intendto do. (1983: 376)

Take a predicate like ‘green’. The totality of facts aboutour previous use and dispositions to use ‘green’ areconsistent with it referring to the propertygreenbut also with it referring to the propertygrue. So, whatmight ground the claim that the propertygreen is somehowprivileged as the referent of ‘green’? Lewis can be takento advocate a form of “interpretationism” according towhich semantic facts are constitutively determined by the best theoryof the data (J. R. G. Williams 2007). Among the a priori constitutiveconstraints governing what counts as the best theory is a principlerequiring that the referents assigned to expressions be the mostnatural of those consistent with the data. Sincegreen ismore natural thangrue, it is more “eligible”than grue to be assigned to ‘green’ as its referent.Likewise for adding and quadding. In this way, the indeterminacy leftopen by facts about use is fended off, Lewis thinks.

Lewis’s proposal is notad hoc, as the notion of anatural property that it utilises is required, for example, by hisaccount of laws of nature (see the entry onDavid Lewis, section 4.6). However, its application to the rule-following problemfaces a number of challenges. First, it is not obvious how it extendsto the mathematical examples that are the focus of Kripke’sWittgenstein. Boghossian writes,

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

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

Lewis’s proposal is also likely to be challenged onepistemological grounds similar to those used by Kripke and Wright indismissing the suggestion that quaddition can be ruled out in light ofthe fact the hypothesis that Jones meant quaddition islesssimple than the hypothesis that he meant addition. A speaker canknow that in response to the query‘\(68+57\)’,‘125’ is theanswer that accords with what she meant by ‘+’, withouthaving toinfer this from facts about her previous linguisticbehaviour. That is to say, in recognising that the answer‘125’ fits what we mean by ‘+’, we do notproceed “by inference to the best semantic explanation of [our]previous uses of that expression” (Wright 2001: 109; see alsoKripke 1982: 40). But this is apparently what we would have to do ifthe “simplicity” suggestion were correct: the bestexplanation would be yielded by the simplest of the hypothesesconsistent with our previous linguistic behavior. The“simplicity” suggestion thus apparently makes a mystery ofour (generally) non-inferential semantic knowledge. Lewis’ssuggestion will be challenged on similar grounds. We do not infer whatwe mean by ‘+’ from facts about naturalness together withconstitutive principles governing interpretation. Again, the accountappears to make a mystery of the non-inferential nature of much of oursemantic knowledge. Moreover, it faces difficulties in accommodatingtheauthority normally credited to self-ascriptions ofmeaning. For Lewis, in virtue of the role they play in his account ofscientific 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 hypothesesabout it, are generally authoritative, unless there are specialreasons to doubt them. What might the basis for this default authoritybe, if what she means is determined by facts about simplicity andnaturalness?

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 meaningwhat we do by our words is somehow guaranteed by the structure ofreality. But it might be taken to be a radical form of semanticplatonism, in so far as it seems to leave no room for thespeaker’s contribution to the singling out of properties (seesection 3.3). Unlike other versions of semantic platonism, it is vulnerable to acomplaint to the effect that the subjective perspective of the thinkeror speaker is entirely annihilated.

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

5. Non-Reductionism

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

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

More generally, we might say that the facts constitutive of thesemantic domain cannot be characterised or explained in non-semanticterms, that is, without employing the notions of meaning orunderstanding; the facts constitutive of rule-following cannot becharacterised or explained without employing the notion ofrule-following. Some philosophers who embrace non-reductionism alsodefend the view according to which semantic facts do not supervene onanything; they are metaphysically fundamental. Boghossian relies onthe 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 tonon-reductionism (cf. Child 2019b): at the core of the position is theidea that any attempt to account for meaning in more basic terms ishopeless or philosophically confused.

Kripke briefly considers the possibility that the states of meaning orunderstanding, or the facts about meaning and understanding, areprimitive orsui generis, which he cashes out as the ideathat

meaning addition by “plus” … is simply a primitivestate, not to be assimilated to sensations or headaches or any“qualitative” states, nor to be assimilated todispositions, but a state of a unique kind of its own. (1982: 51)

He raises two complaints against this approach. First, hecharacterizes it as desperate, insofar as “it leaves the natureof this postulated primitive state … completelymysterious” (1982: 51), for such an approach does not provide anaccount 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 scepticalargument” (1982: 51), which is that it would seem that we couldnot “conceive of a finite state whichcould not beinterpreted in a quus-like way” (1982: 52).

Some philosophers claim that Kripke’s treatment of thenon-reductionist position is unsatisfactory. McGinn, who appears toignore Kripke’s brief discussion of non-reductionism, thinksthat there is an

undefended and undisclosed premise [in the sceptic’s argument],namely that semantic discourse cannot be regarded asirreducible. (1984: 82)^[15]

McGinn also notes that Kripke has no qualms with adopting anon-reductionist view of meaning in other works—see, forinstance, Kripke 1972: 94–97. Goldfarb thinks that “theconception Kripke exploits is basically physicalistic” (1985[2002: 95]), and thus that pursuing a non-physicalist approachhasn’t been ruled out. Boghossian thinks that what Kripke needsfor his treatment of non-reductionism to succeed is an argument fromqueerness aiming to show that there is something inherently queerabout meaning properties, which he fails to provide (1989 [2002: 180];cf. Hattiangadi 2007: 47–50). Ultimately, Boghossian issympathetic to the non-reductionist approach, though he thinks that“it really is not plausible” that such a conception mightbe true of linguistic meaning (1989 [2002: 179]); on his view, it isfacts about mental content that are irreducible.

Before exploring several of the non-reductionist positions proposed inrecent years, we should note that some of the proponents ofnon-reductionism think that Kripke’s sceptical challenge isbased on confusion, and that our task is to unearth that confusion.Thus, on their view, the proper response is not tosolve thesceptical problem by showing that the sceptic failed properly toacknowledge some set of facts (or some features of some such facts),but todissolve it by showing that there is, in fact, noproblem. McDowell, for instance, argues that Kripke misunderstands thedialectic pursued by Wittgenstein inPhilosophicalInvestigations. On his view,

the right response to the paradox, Wittgenstein in effect tells us, isnot to accept it but to correct the misunderstanding on which itdepends, (1984 [1998: 229])

which puts us in a position to dissolve the paradox and, with it, theproblem of how meaning is possible. This involves renouncing theproblematic assumption that understanding an expression requiresinterpreting that expression. McDowell’s diagnosis isn’tconfined to linguistic expressions. What we ought to resist is thethought that,

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

Similarly, Stroud thinks that the paradox is “an expression ofan unsatisfiable demand” (1990 [2000: 88]), namely, the demandfor

some facts, the recognition of which would not require that we alreadyspeak and understand a language, and some rules, which would tell uswhat, given those facts, it was correct to say.

Such facts and such rules would have to be such as to “serve toget us into language in the first place” (Stroud 1990b [2000:94]). The demand is most strongly manifested in Kripke’sassumption that there must be an item that instructs or tells thespeaker what to do with her expressions. Stroud claims that properengagement with Wittgenstein’s remarks reveals this assumptionto be misguided, for it embarks us on a regress (Stroud 1996 [2000:180–185]). Once we recognize the misguidedness of the picturethat Kripke assumes, we will no longer feel the force of the scepticalchallenge, Stroud thinks. However, contra Stroud, it seems that theextensionality condition is all we need in order to pose astripped-down version of the question that the sceptic is raising,namely, the question of what makes the standards of correctness thatgovern our uses of expressions and our deployments of conceptspossible.

It might be argued that the urgency of this question, or even its veryintelligibility, is merely a symptom of a frame of mind from withinwhich meaning seems impossible, and that our proper task is to leavethis confused frame of mind behind (e.g., McDowell 1992 [1998: 272,274]; 1998a: 57–58). However, this line of reasoning might betaken to presume that a question is urgent or intelligible only if itis in principle possible to offer a reductive answer to it, thatconstructive philosophy is necessarily reductive philosophy. Verheggenargues that the rejection of reductionism does not commit one toquietism. As she sees it, non-reductionism can be constructive; it canrevolve around advancing and defending positive claims (Verheggen2000, 2003). Even though the project of providing necessary andsufficient conditions for meaning is hopeless, the non-reductionistcan still aspire to articulate necessary conditions that aren’t“even remotely trivial” (Myers and Verheggen 2016: 3), andto draw illuminating connections between meaning and other irreduciblephenomena. Through a creative reconstruction of Davidson’striangulation argument, Verheggen argues that interaction with asecond individual and aspects of the shared world is a necessarycondition for one’s having a language and thoughts (see chapter1 of Myers and Verheggen 2016). The constitution of the standards ofcorrectness that govern language and thought necessitates that theindividual be aware of the possibility of being mistaken, an awarenessthat can only be grounded in linguistic interactions with anotherindividual and features of the world. Thus, the triangulation argumentis taken by Verheggen to reveal the hopelessness of the reductiveambition, insofar as it shows that we cannot offer an account of theconstitution of the standards of correctness that govern language andthought without presupposing that a commitment to those standards isalready in place. (See also Sultanescu and Verheggen 2019 for anaccount of the Davidsonian answer to Kripke’s scepticalchallenge and Verheggen 2017a for an account of the Davidsonian answerto Wittgenstein’s paradox.) William Child also defends a varietyof non-reductionism, one that “does not give merely pleonasticanswers but aims to say something genuinely informative” (Child2019a: 97). He does so by relying on Wittgenstein’s remarks onmeaning and rule-following.

According to Wright, “it is an important methodological preceptthat we do not despair of giving answers to constitutive questions toosoon” (2001: 191). He goes on to propose a non-reductionist viewthat is sensitive to the difficulty of accounting for our knowledge ofwhat we mean. (As we noted insection 2, Wright takes Kripke’s sceptic to impose a legitimateepistemological constraint on answers to the skeptical challenge.) Heoffers a “judgment-dependent” account of intention,according to which what one intends is determined by one’s bestjudgment about what one intends. Insofar as the concepts of intentionand meaning are “relevantly similar” (2001: 206), thisaccount can also claim to shed light on the nature of meaning. Thus,we might say, on Wright’s behalf, that what one means by anexpression is determined by one’s best judgment about what onemeans. The notion of judgment is taken by Wright as primitive. Still,the authoritative nature of first-personal avowals is allegedlyvindicated. See especially essays 5–7 in Wright 2001.^[16]

Wright and Boghossian recently offered independent arguments to theeffect that the adoption of a non-reductionist view of meaning doesnot secure the intelligibility of the idea of guidance by a rule.According to Wright, the only way in which rule-following can beunderstood is if it conforms to what he calls “the modus ponensmodel” (2007: 491). The model states that an act is a genuineinstance of rule-following if it can be rationalized by, on the onehand, citing the rule and, on the other, indicating that thecircumstances, which must be specifiable without appealing to therule, call for its application. Wright investigates basic cases oflanguage use, and argues that if we assume that the modus ponens modelapplies to these cases, we are saddled with an Augustinian picture,according to which conceptual capacities are necessarily prior tocapacities to use language. At the same time, he accepts thatWittgenstein has revealed the bankruptcy of the Augustinian picture inPhilosophical Investigations; so, the idea of antecedentconceptual capacities is unintelligible. This is taken to show thatthe modus ponens model cannot apply to basic cases. Wright calls this“the minor premise problem”, and argues that it compels usto accept that “in the basic case we do not reallyfollow—are not really guided by—anything”(2007: 497).

Boghossian also relies on the modus ponens model to argue that anon-reductionist position does not allow us to make sense of theintelligibility of rule-following. He offers “an intuitivecharacterization” of the phenomenon of rule-following, accordingto which it has the following structure:

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

What allows us to say that the rule explains and rationalizes thebehaviour is an act of inference from the rule to what it requires inparticular contexts. But inference is, according to Boghossian,“an example of rule-followingpar excellence”(2012: 40), which indicates that the act of inference must fit theintuitive characterization above, thus requiring a further act. Aregress 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 ofreasoning, especially in his remark, mentioned earlier in thissection, to the effect that the non-reductionist view faces a logicaldifficulty (1982: 51–52). The difficulty seems to arise fromthree claims that seem uncontroversial but are inconsistent:

1. the state of meaning plus by ‘+’ must guide thespeaker 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 cannotguide.

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

Miller offers an account of guidance by drawing on McDowell’swritings on Wittgenstein. He argues that the inference problem and theminor premise problem are not genuine difficulties for thenon-reductionist. On his view, the upshot of Wittgenstein’sreflections on rule-following is that

in applying a rule R in a particular case there need be nofurther inferential step—over and above that involvingRitself—mediating between acceptance of R and thatparticular application. (2015b: 405)

This is just what it is for rule-followingnot to be a matterof interpretation: the rule is applied immediately, as itwere—without the mediation of a further rule, such as aninference rule, in the manner suggested by Boghossian, or a rule forthe 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 beentrained into a practice or custom of following rules of that sort(2015b: 407), where the notions of training, practice, and custom aresemantically characterized and cannot receive further philosophicalillumination.

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

having a (first) language essentially depends on meaning byone’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 leastsome of) one’s words to communicate with others, (Myers andVerheggen 2016: 84; see also Verheggen 2006 for the initialarticulation of the distinction)

and goes on to defend the interpersonalist view. Relatedly, there isthe question of how we should understand the notions of practice andcustom and the role that they play in a correct conception ofintentionality, broadly construed. It might be thought, asWittgenstein seems to suggest inPhilosophical Investigations(e.g., #198; #201–202), that it is essential to thinking andspeaking that one be trained into practices or customs, and thus thatour 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 thecommunitarian view. (See also Section 4 of Haase 2018 for a differentkind of attempt to flesh out the Wittgensteinian notion of practice,and Pettit 1990 for a form of non-reductionism on which communalinteraction is required in at least some cases of rule-following). Buton the Davidsonian conception, at the centre of which is disagreementand the need to settle it rationally against the constraints of theshared world, the idea of practice might not serve any explanatorypurpose; even though shared beliefs may be essential for thought,shared standards of correctness are not essential for language. TheDavidsonian conception is a variety of interpersonalism. Thisintramural debate is very much ongoing.

Some philosophers have explored the possibility of a middle pathbetween reductive dispositionalism and non-reductionism. Thus, in apaper in which she discusses Stroud’s view, Ginsborgdistinguishes between austere forms of non-reductionism, which shetakes to be incompatible with constructive philosophising aboutmeaning, and “less austere and partly reductionist”approaches, which allow that “we could account for meaning interms of a more basic idea of goal-directed human activity”(2011a: 153), but without allowing that such activity can be capturedin purely dispositionalist or physicalist terms. She goes on toarticulate a less austere view, which explains meaning in terms of anotion of normativity that she takes to be primitive. On this view,for someone to mean something by an expression is for her to have adisposition to apply it in particular contexts and, crucially, to takethe manifestations of that disposition to be appropriate. Takingone’s responses to be appropriate

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

this establishes the primitive status of the notion ofappropriateness. Thus, Ginsborg provides a dispositionalist account ofmeaning, albeit with a crucial proviso to the effect that the relevantdispositions are to be characterized in normative terms. She thinksthat the account can serve as a straight solution to the scepticalchallenge. On the one hand, it purports to vindicate the normativityof meaning, and thus to meet the normativity condition; on the otherhand, it purports to account for the distinction between correct andincorrect applications of expressions, and thus to meet theextensionality condition. For Ginsborg, the set of correctapplications of an expression are the applications that one isdisposed to regard as appropriate—the applications that ought,in the primitive sense, to be made (see Ginsborg 2011b for a moredetailed account of her solution to Kripke’s problem).

Ginsborg’s view is in some respects similar to RobertBrandom’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 andpartly reductionist. We do not have room to explain the details ofBrandom’s intricate view; suffice it to say that, on that view,the proper specification of the use that determines meaningessentially involves normative vocabulary. The facts that determinemeaning are facts about theentitlements andcommitments that are implicit in the performances of speechacts. Thus, what a speaker means by an utterance is to be understoodas consisting, roughly, in the performances that she is committed toin virtue of the utterance as well as in the performances that entitleher to make it. Ultimately, these facts are “products of humanactivity” (xiv), being a matter of our adopting normativeattitudes toward one another--oftaking one another to becommitted or entitled, in light of our performances, to various otherperformances. However, although there are similarities, there are alsoimportant differences between Brandom’s approach andGinsborg’s. While for Brandom the norms that are constitutive ofmeaning are socially instituted, for Ginsborg they are natural.Moreover, the notion of appropriateness that Ginsborg fleshes out ismore basic than the notion of reason, and thus more basic than thenotions of entitlement and commitment that Brandom takes to beconstitutive of meaning (Ginsborg 2011a: 172fn21). Still, Ginsborgdoes think that “expressions have meanings only in virtue ofthere being ways in which they ought to be applied” (2012: 132).So, to put it crudely, on both accounts, meaning facts are reduced tofacts or considerations about what ought to be the case. The questionthat the austere non-reductionist will raise is whether the latterkinds of fact are apt to solve the indeterminacy problem, and thus tomeet the extensionality condition.

The challenge of the sceptic makes perspicuous the fact that anon-semantically described pattern is compatible with indefinitelymany interpretations. Does the appeal to the normative domain help usrule out the sceptic’s alternative hypotheses? Given that,arguably, on a partly reductionist picture of the sort that Brandomproposes, utterances are, ultimately, nothing more than“normatively constrained noise- or mark-makings” (Whiting2006: 11), that is, non-semantically described performances that standin normative relations to other non-semantically describedperformances, it does not seem that we have the resources to singleout as privileged a particular interpretation or standard ofcorrectness. Similarly, a normative pattern that instantiates how oneought, in the primitive sense proposed by Ginsborg, to go on withrespect to an expression seems to be consistent with more than onesemantic interpretation of that expression. It might be thought thatGinsborg could appeal to the non-semantically characterizeddisposition in order to fix the meanings of the relevant expression.However, we have already shown insection 4 that dispositionalist accounts face very serious obstacles (seeVerheggen 2015; Chapter II of Myers and Verheggen 2016, and Miller2019 for more discussion of the failure of dispositionalism inrelation to Ginsborg’s view). So, the proponent of the lessaustere approach to meaning owes the austere non-reductionist anaccount of how the extensionality condition might be met. (See Haddock2012 and Sultanescu 2021 for more discussion of Ginsborg’s view,and Rosen 1997, McDowell 2002, Hattiangadi 2003, and Whiting 2006 formore discussion of Brandom’s view.)

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We’re grateful to Claudine Verheggen for helpfulcomments. Thanks, too, to the SEP editors and reviewers for usefulfeedback and assistance.