in defence of kripkenstein: on lewis’ proposed solution to the sceptical argument

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In Defence of Kripkenstein: OnLewis’ Proposed Solution to theSceptical ArgumentJohn Newson Wright aa University of Newcastle, Australia

To cite this article: John Newson Wright (2012) In Defence of Kripkenstein: On Lewis’Proposed Solution to the Sceptical Argument, International Journal of PhilosophicalStudies, 20:5, 603-621, DOI: 10.1080/09672559.2012.713377

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In Defence of Kripkenstein: OnLewis’ Proposed Solution to the

Sceptical Argument

John Newson Wright

Abstract

In Wittgenstein: On Rules and Private Language, Saul Kripke argues for anextreme form of meaning scepticism. One influential reply to Kripke’sarguments was developed by David Lewis. The reply developed by Lewismakes use of the notion of mind-independent relations of similarity anddifference. The aim of the paper is to argue that Lewis’ reply is not satis-factory: the challenge to find a refutation of Kripke’s sceptical argumentsremains unmet.

Keywords: Kripkenstein; Kripke; Lewis; meaning; scepticism; realism

In Wittgenstein: On Rules and Private Language, Saul Kripke presents aseries of arguments for an extreme form of meaning scepticism.1 Accord-ing to this extreme scepticism, there is no such thing as meaning any-thing by any word.2 One important reply to this extreme scepticism hasbeen developed by David Lewis.3 In this paper we examine Lewis’response to Kripke. It will be argued that Lewis’ response is not satisfac-tory. The ‘bizarre sceptic’ of Kripke’s invention can effectively challengeLewis’ claim to have produced a fact (or class of facts) in virtue of whichour words have the meanings we believe them to have.

1. Background to Lewis’ Proposed Solution to Kripke’s Problems:Armstrong’s Theory of Universals

Lewis’ solution to the sceptical problems raised by Kripke relies on atheory of universals advocated by David Armstrong.4 Armstrong’stheory of universals is ‘Realist’ in two senses of the word. In the firstand most straightforward sense, Armstrong’s theory is Realist in thesense that he holds that universals exist. In the second, less straight-forward but (for our purposes) more important sense, Armstrong holdsthat the universals that exist do so independently of our language, our

International Journal of Philosophical Studies Vol. 20(5), 603–621

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concepts and our systems of categorization or classification.5 So, on thisview, it is not the case our use of general terms determines what univer-sals there are. Consequently, for Armstrong, it does not necessarily fol-low from the fact that we have some general term that there must alsoexist a universal corresponding to that term. For example, although theterm ‘grue’ exists it does not, on Armstrong’s view necessarily followthat there is some property of grueness.

Armstrong’s theory of universals is sparse, in the sense that number ofuniversals that actually exist on his view is small compared, for example,to the number of general terms we can formulate. What universals actu-ally exist is, for Armstrong, determined by the way the world in whichwe live happens to be. Just as it is an empirical fact that our solar systemcontains eight planets, in something the same way, it is, on Armstrong’sview, just an empirical fact that our world happens to contain the univer-sals it does. What universals exist cannot be determined a priori. Findingout what those universals are is, for Armstrong, ultimately a matter forempirical science to discover.

In summary, Armstrong’s theory of universals is Realist in two senses:

(1) Universals exist.(2) What universals there are is something that is independent of our

general terms, or concepts, or systems of classification.

We might call (1) the existence dimension of Armstrong’s realism aboutuniversals, while (2) is the independence dimension.

2. Lewis’ Modification of Armstrong’s Theory

Lewis suggests a modified version of Armstrong’s theory of universals.Very roughly, Lewis’ modification is to reject (1) – the existence dimen-sion – while retaining the independence dimension.6 More specifically,Lewis suggests we ought to refrain from asserting statements of the form:

There is a universal that A and B share.__________________(1)And instead assert:

A and B are similar.__________________________________ (2)

where the similarity referred to in (2) is objective and holds indepen-dently of our general terms, concepts, etc. Note that (1), but not (2),commits us to the existence of universals.

Lewis introduces the concept of a natural class of objects. A class C isa natural class if and only if each member of A resembles every othermember, in Armstrong’s objective, language independent sense ofresemblance7.

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Lewis further argues that some classes are more natural than otherclasses. One class A is more natural than another class B if the extent towhich the members of A resemble each other is greater than the extentto which the members of B resemble each other, again in Armstrong’sobjective sense of resemblance8. So, for example, the class of red thingsis, presumably, a more natural class than the class of things that are redor orange, which in turn is more natural than the class of things that arered or orange or green. Lewis argues the notions of a natural class ofobjects, and of classes that are more natural than others, can solve awide range of problems. In particular, he argues that they can solve themeaning-sceptical problems Kripke raises in Wittgenstein: On Rules andPrivate Language.9

3. Lewis’ Solutions to Kripke’s Problems

There are two problems that Lewis suggests can be solved by the notionof natural classes. The first is the problem of ‘going on in the right way’when using a word; the second is the problem of specifying the fact(s) invirtue of which a speaker means one thing rather than another by aword. Although it will be argued later in this paper that the first problemis in fact a special case of the second, it is useful to initially discuss themseparately.

One natural solution to the problem: ‘In virtue of what does a speakerS mean ‘plus’ rather than ‘quus’ by ‘+’?’ appeals to the notion of ‘goingon in the same way’. The bizarre sceptic, who asserts that the rightanswer to ‘What is 57 + 68?’ is ‘5’, appears to be claiming that the rightway for S to use ‘+’ is to change the way S has used ‘+’ in the past, orstarting to use it in a new way. But the common sense response – thatthe right answer is ‘125’ – appears to assume that the right way for S touse ‘+’ in this is simply for him to use it in the same way he has used itin the past. Kripke’s response is to assert that these appearances aredeceptive: for Kripke, any way of going on from some limited set ofinstances can be taken to be ‘going on in the same way’.10 Lewis’response to Kripke is to simply deny this last assertion: not all ways ofcontinuing on from some limited set of examples have an equal claim tobe ways of going on in the same way.11 There can be a way of going onthat is objectively the same (or, at least the most similar) way. And it isthe notions of objective similarity and of a natural class of events thatenable us to say why some ways of going on can to be classified asobjectively the same.

Lewis’ suggestion can be illustrated with the following example. Con-sider the following sequence of numbers:

IN DEFENCE OF KRIPKENSTEIN

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1, 1, 1, 1, 1,..................(1)

There are at least two ways of going on from this sequence that couldboth, with some plausibility, be seen as ways of going on in the sameway. One is as follows:

1, 1, 1, 1, 1, 1, 1, 1, 1, 1,........................(2)

And another is:

1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 8, 8, 8, 8, 8,.................(3)

Although both these sequences have a claim to be ways of going on inthe same way, Lewis would say that the first is objectively the betterbecause the subsequent members of (2) resemble the members of (1)more closely than do the members of (3). Since the degree of resem-blance is higher, the claim to be going on in the same way is stronger.

It is important to note the role that objective similarity plays in Lewis’account. The bizarre sceptic might claim that the members of (3) aresimilar. More specifically, the bizarre sceptic might invent a predicate Mwhich applies to ‘1’, ‘2’, ‘4’, ‘8’ and so on, and assert that the membersof (3) are as similar to each other as are the members of (2) since themembers of (3) are all M. The members of (2) are all ‘1’, the membersof (3) all M. However, this reply by the sceptic is not satisfactory if thetype of similarity involved is objective. Objective similarity is not a prod-uct of our choice of predicates: it holds independently of our predicates.Given this notion of objective similarity, the members of (2) are(presumably) objectively more similar to each other than are themembers of (3).

The second of Kripke’s problems that Lewis says can be solved by thenotion of objective similarity is that of determining the reference of ourgeneral terms. Lewis suggests that our general terms take as their exten-sions the most objectively similar classes of objects compatible with theother reference-constraining facts.12 Suppose, for example, that aspeaker S has used a general term ‘R’. Up until now, let us say, S hasonly applied R to red things. And let us also suppose that these applica-tions by S of R to red things are, in this case, the only reference-con-straining facts for ‘R’. Then, one possible interpretation of ‘R’,compatible with these facts, is that ‘R’ refers to red things generally –not just to those that S has seen so far, but to all red things everywhere.But this is only one of the interpretations compatible with all of the ref-erence-constraining facts. Another is that R refers to red things up tothe present, and to green things thereafter. And another is that it refersto red things up to the present, and dogs thereafter. There are, clearly,an infinite number of possible extensions of ‘R’ compatible with the


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reference-constraining facts. Lewis suggests that we say that, under theseconditions, ‘R’ has as its extension the class of red things.13 This isbecause the members of the class of red things objectively resemble eachother to a greater degree than do the members of the other classes thatare eligible candidates. That is, the class of red things is the most naturalclass compatible with the other reference-constraining facts. More gener-ally, Lewis says that if there are a number of possible candidates for theextension of a general term, and all those candidates are compatible withall the (other) reference-constraining facts, then the extension of thegeneral term is the candidate that is the most natural class.

It is again worth noting that the notion of objective similarity has acrucial role in Lewis’ system. The class of red things (we may assume) isobjectively more similar than, for example the class of things that are,say, red before time t and green thereafter. A sceptic might invent apredicate ‘reen’ (by analogy with ‘grue’) and assert that the members ofthe class of things that are red before t and green thereafter are all simi-lar because they are all reen. But this would not establish the objectivesimilarity of the members of this class since relations of objective simi-larity hold independently of our use of predicates.

Lewis holds that the notions of objective similarity and of natural clas-ses enables us to state a fact in virtue of which a speaker S means ‘plus’rather than ‘quus’ by ‘+’. Briefly, Lewis’ suggestion is that ‘+’ takes as itsextension the set of numbers that is the most natural class compatiblewith the other reference-constraining facts. Lewis does not elaborate onwhat he means by the ‘extension’ of ‘+’, but presumably what he hasin mind in something like the following. The ordered triple of numbers<2, 2, 4> can be regarded as an element of the extension of ‘+’ becausethe third member of this triple is the result of applying ‘+’ to the firsttwo members. So, <1,2, 3> will be a member of the extension of ‘+’ but<2, 4, 7> will not. The extension of ‘+’ is just the set of all triples suchthat the third member of the triple is the result of applying ‘+’ to thefirst two members.

Now, there are (at least) two candidates for the extension of ‘+’. Com-mon sense says the extension of ‘+’ is something like the following set:

{<1,1,2>, <1,2,3>, <2,2,4>,........,<56,56, 112>, <56, 57, 113>,...., <57,68,125>,.......}

But the bizarre sceptic says the extension of ‘+’ is the following set:

{<1,1, 2>, <1,2,3>, <2,2,4>,.........<56,56, 112>, <56, 57, 5>,.....,<57, 68,5>,.........}

Lewis says that of the above two sets the better candidate for theextension of ‘+’ is the first because it is more natural, that is, its members


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objectively resemble each other to a greater degree than do the membersof the second set. The first set is, in fact, the most natural class compati-ble with the other facts constraining the reference of ‘+’, and so, Lewissuggests, the first set is in fact the extension of ‘+’. Lewis therefore con-cludes that the notion of objective similarity gives us a way of stating thefact in virtue of which S means ‘plus’ rather than ‘quus’ by ‘+’.

4. Evaluation of Lewis’ Solutions

Let us begin by discussing Lewis’ proposed solution to the problem ofcontinuing on a sequence in the right way. It is worth distinguishing twodistinct theses in Lewis’ proposed solution:

Thesis (1): The correct answer to the question: ‘What is the same way ofcontinuing a sequence?’ is given by the notion of objective similarity.The same way of continuing a sequence is that way in which the newmembers of the sequence have the highest degree of objective similarityto the initial members.

Thesis (2): The correct answer to the question: ‘What is the right way ofcontinuing a sequence?’ is ‘The same (or, at least, the most similar)way.’

There are a number of ways in which the bizarre sceptic might ques-tion Thesis (1). Perhaps most obviously, the sceptic could questionwhether there are any such things as objective relations of similarity anddifference. This is, of course, a distinct philosophical question in itselfand we will not enter in to it here. For the purposes of subsequent dis-cussion, we will assume such objective relations do in fact exist.

The bizarre sceptic might accept that objective relations of similarityexist, but hold that we are wrong about what they are. We might think weare going on in the same, or most similar, way when we continue to add –but we are simply wrong about this. The sceptic might claim that theobjectively most similar way of going on in using ‘+’ is to quadd, not add.

It is worth discussing in some detail the way in which this scepticalsuggestion bears on the overall discussion. Perhaps the first thing to noteabout it is that it does raise an important epistemological question.According to the Armstrong/Lewis theory of objective similarity, suchrelations are sparse, exist independently of our use of predicates, andultimately are to be discovered by empirical science. Therefore, a claimof the form ‘A is objectively similar to B’ is to a degree epistemologi-cally risky. And so the question arises: ‘What evidence do we have thatit is our claims about what objective similarity relations there are that isright while those of the sceptic are wrong?’


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This epistemological question is (at least prima facie) quite indepen-dent of the type of scepticism Kripke discusses. Kripke (or, ratherKripkenstein) says that there is no fact in virtue of which S means ‘plus’rather than ‘quus’. We (with common-sense) wish to say there are suchfacts. It is possible to assert that our knowledge of what objectiverelations of similarity there are is risky, while at the same time agreewith the common-sense position that there are facts in virtue of whichwe mean ‘plus’: It is just that our knowledge of those facts is less thancertain. On such a view, it may be that ‘S means ‘plus’ by ‘+’’ is indeedtrue, but our knowledge of that fact is fallible. This kind of epistemologi-cal scepticism is different from the ontological scepticism advocated byKripkenstein.

Nonetheless, there is perhaps a difficulty that this epistemologicalquestion creates for Lewis’ proposed solution. Kripke says that any satis-factory solution to the problem must be able to account for the confi-dence a speaker has that they are using a word correctly. But on Lewis’view, we are using a word correctly in going on the way we do if ournew use is objectively similar to previous uses, where the claim that it isobjectively similar is a risky claim concerning relations that are ulti-mately to be discovered by empirical science. On such a view, it seems,we ought not to be confident that we are using a word correctly, butactually rather tentative and diffident. And so a question arises forLewis’ proposal: what, if anything, justifies our confidence we are usingwords correctly?

Let us now consider Thesis (2): The same way of going on is the rightway. This is not necessarily a trivial or straightforwardly correct thesis: itis something that needs to be established by argument.

There are at least four considerations which show it would be an errorto unquestioningly or uncritically assume that the right way of going onis the most similar way. First, and most obviously, rightness and similar-ity are distinct notions. Similarity is a relation that can be determinedpurely empirically. We can determine purely empirically that a speaker’spresent uses are similar to their past uses, to the same extent that wecan determine empirically that the way a sample of sodium is behavingtoday is similar to the way it has behaved in the past. But, as noted byKripke, there seems to be something like a ‘normative’ component tothe notion of rightness: to say that a particular way of using a word isthe right way seems to imply that, given what we have meant by thisword in the past, this is, in some sense, the way we ought to use it onthis occasion. To say that a way of going on is the right way seems tomean something more than that is the same way of going on. So: itwould seem we need some kind of argument to show that the twonotions coincide.


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A second reason for doubting that the same way of going on is trivi-ally or straightforwardly the right way stems from the fact that some-times there can be a way of continuing to use a word that is clearly thesame as the way we have used it in the past, but where we would hesi-tate to say that there the concept of rightness had any application. Sup-pose a man says ‘Yip’ every time he sees a dog, where this is merely akind of spasm or reflex. In such a case, it is clear that the same way ofgoing on in using ‘Yip’ is to continue to utter it in the presence of dogs.But in this case I do not think we would say there was any such thing asthe right way of using ‘Yip’. Neither would we say there was a way itought in the future to be used. So, here we have a case of sameness ofuse without there being any such thing as the right way of using a word.To be the same way of going on is not necessarily what it is to be theright way of going on.

It might be objected that the thesis that sameness and rightness arethe same is only meant to apply to words, and that ‘Yip’, as a merespasm or reflex, is not a word at all. But if we make this move, then itseems we are vulnerable to the type of doubt raised by Kripke’s sceptic.Plausibly, at least a part of the difference between a word uttered by aspeaker and a mere vocal spasm has to do with the intentions of thespeaker.14 These intentions might be, for example, to use the word inthe same way in the future, to use it in accordance with a rule, or, per-haps to elicit a particular response. But Kripke’s sceptic might offer analternative interpretation of those intentions. And according to that alter-native interpretation, the term the speaker is using might not be a‘straight’ term, but a ‘bent’ term, like ‘grue’ or ‘quus’. And if the scep-tic’s deviant interpretation of the speaker’s intentions were the correct,then the right way for the speaker to go on using the term in new casesmight be quite different from the same way. So: if we allow that a speak-er’s intentions are at least part of what makes one of their utterances aword rather than a mere noise, then there is at least the possibility thesame way of going on and the right way of going on might diverge. Togo on in the same way need not be to go on in the right way.

Of course, it is natural to protest that the sceptic’s bizarre interpreta-tions of the speaker’s intentions are not correct. But then, of course, weare confronted with a new question: in virtue of what fact is our inter-pretation of the speaker’s intentions right and the sceptic’s interpretationwrong.

A third line of argument for the thesis that sameness and rightness aredistinct notions appeals to the fact that that, in some situations, therecan be several equally good candidates for the same way of going on,only one of which is clearly the correct way, while the others are clearlywrong. But if rightness were sameness, the equally good candidates forthe same way of going on ought also to be equally good candidates for


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the right way. Suppose, for example, that a child is learning the meaningof ‘red’ by ostension. An adult might, for example, show the child anumber of red objects and tell the child that they are all red. However,we can imagine possible circumstances in which the ostended redobjects, by accident, also happen to have some property in commonother than redness. For example, it may be through a fluke that all theobjects happen to be owned by Mr Smith. Or perhaps all the objectshappen to weigh exactly half a kilogram. Under such circumstances, oneway in which the child could go on to use the word ‘red’ in the sameway would be to apply it to red objects. But another way would be toapply it to things owned by Mr Smith. Another would be to apply it tothings that weighed exactly one half a kilogram. All these ways of goingon have the child applying the term ‘red’ to things that are objectivelysimilar to the objects that were ostended when the child was learningthe term. But, intuitively at least, only one of these – going on to applyit to red objects – is the correct way. And so: being the same way ofgoing on (or a way of doing so) need not be the right way.

Of course, it may be protested that in a case of this sort there areother factors we can point to which make it the case that the other pos-sible ways of going on (applying it to objects that weigh half a kilogram,etc.) are wrong. For example, if the adult intends to teach the child acolour-word, and the child also understands they are being taught a col-our-word, then – it is surely natural to protest – the other candidates areclearly ruled out. But, again, it is obvious how Kripke’s sceptic willrespond. The sceptic may claim we have misinterpreted the child’s beliefsconcerning the general category of word they are being taught. Perhapsthe child does not think they are being taught a colour-word, but, forexample, a ‘colass’ word, where a ‘colass’ word refers to the colour of anobject up to a particular time, and to its mass thereafter. Consequently,we are now confronted with the question: in virtue of what is the scep-tic’s interpretation of the child’s beliefs wrong and ours correct? And sowe may say, if in this case we do not appeal to the intentions of theadult or child learning ‘red’, then the same way (or ways) of going on isnot necessarily the right way of going on: there can be a number of waysof going on that can all be claimed to be the same way, but intuitively itis clear that only one of these is the right way. But if we do appeal tothe intentions of the speakers, we are confronted with a new problem: invirtue of what is our interpretation of the speakers’ intentions correctand the sceptic’s wrong?15

A fourth reason for doubting that the right way of going on must coin-cide with the same way springs from a fact noted by Kripke: it is possi-ble for a person to be disposed to make mistakes. Suppose Smithintends to use ‘+’ in the same way as the rest of us; he intends to use ‘+’to mean addition, not some other function. But suppose that he is


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disposed to use ‘+’ incorrectly; he may, for example, be inclined to for-get to ‘carry’. I think would be inclined to say that he means addition by‘+’, but he has, in the past at least, used it incorrectly. But, if he meansaddition by ‘plus’ then the right way for him to go on is to start to‘carry’. And obviously, this is different from the way he has used it inthe past: if he were to use ‘+’ in the same way he has used it in the pasthe would continue to not ‘carry’. So, the right way for Smith to go on is,it seems, not the same way he has used ‘+’ in the past.

In summary, there are four reasons for at least doubting Thesis (2) –the claim that the right way of going on is the same way – given above.First: intuitively, the notions are distinct; to say that a way of going on isright implies that, in some sense, it is the way we ought to go on but thiswould not seem to be contained within the idea that something is merelythe same way of going on. Second: we can imagine cases in which someway of going on is clearly the same way, but in which the notion of the‘right’ way does not seem to be applicable. Third: we can imagine casesin which there are several candidates for the same way of going on, butonly one of which is, intuitively at least, the right way. A defender ofLewis might claim at least some of these cases can be dealt with if wetake in to consideration the beliefs or intentions of the speakers; but thisonly shifts the problem to: what is the correct interpretation of thosebeliefs and intentions? Finally, the right way of going on and the sameway would clearly seem to part company in those cases in which aspeaker has, in the past, been disposed to use a symbol incorrectly.These four arguments are not intended to show that thesis that samenessis rightness is false; merely that is a thesis that is subject to possibledoubt. It is a thesis that can be reasonably questioned, and so it is athesis that needs to be defended by some kind of argument.

It is at this point that the sceptic can raise an objection to Lewis’ pro-posed solution. The sceptic can simply deny that the right way of goingon is the same way. Note that this sceptical response is different fromthe one Kripke considers. Kripke says there is no such thing as one,unique way of going on in the same way; a number of ways of going onfrom some initial set can all be seen as the same way of going on. Thepresent objection from the sceptic agrees that there can be such a thingas the same way of going on from some initial set, but questions whetherthis must be the correct way.

It is worth considering in a little more detail the alternative suggestionthe sceptic might make at this point. Lewis suggests the right way ofgoing on is the way that ensures that the class consisting of the initialmembers together with the new member is the most natural class possi-ble. The sceptic might suggest that the right way of going on is the waythat produces the second most natural class. Or: the sceptic might claimthe right way of going on is the way that produces the seventh, or


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fifteenth, or twenty-ninth most natural class. And so the question arises:in virtue of what is Lewis’ suggestion right and the sceptic’s wrong?

Note the sceptic is not questioning the existence of objective relationsof similarity, neither is he disputing that they can have a role in deter-mining what counts as the right way of going on. All the sceptic is doingis offering an alternative account of how those objective relations ofsimilarity determine what is to count as the right way of going on. Point-ing out, or suggesting (as Lewis does), that there is one way of going onthat is objectively the most similar fails to rule out this scepticalobjection. The sceptic can happily agree there is such an objectivelymost similar way, but deny this is sufficient to make it the right way. Iconclude that the sceptic can raise a problem for Lewis’ proposed solu-tion to the problem of going on in the same way.

If merely going on in the same way is not enough to ensure a speakeris going on in the right way, the question arises: ‘What does make it thecase that a speaker is going on in the right way?’ Perhaps the mostobvious answer to this question is, as we have already noted, to appealto the intentions of the speaker. A way of going on is right, it is naturalto suggest, if it is in accordance with the way a speaker had intended touse the word. And it is at this point that Lewis’ proposed solution tothe second of Kripke’s problems can come in to play. Kripke, of course,would point out a difficulty with the proposal that appealing to a speak-er’s intentions can determine the right way of going on: he wouldremind us we need to determine the meaning of the words used in theexpression of the speaker’s intention. But, as noted, this simply raisesthe sceptical problem with which Kripke is concerned: in virtue of whatdo our words have the meaning we believe them to have? It is here thatLewis’ second suggestion may be of help. Lewis suggests that we take asthe referents of our terms the most natural class compatible with theother reference-constraining facts. If this can indeed fix the referents ofour terms, then perhaps the speaker’s intentions can determine the rightway of going on.

However, it is clear from the foregoing discussion that the sceptic canraise a problem for Lewis’ suggestion. Instead of our terms taking astheir referents the most natural class, the sceptic can suggest that per-haps they take as their extension the second, or seventh or fifteenth mostnatural class compatible with the other reference-constraining facts. Notethat (as in the previous case) the sceptic is not denying the existence ofthe objective relations of similarity, and neither is he questioning thatthey can have a role in fixing reference: it is merely that the sceptic isoffering alternative account of what that role is. And so the questionagain arises: In virtue of what is the common sense account of the refer-ence of our terms right while that offered by the sceptic wrong?


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It is worthwhile noting how this problem arises for Lewis’ account.Both Kripkenstein and Lewis accept that the various types of fact towhich we might initially appeal in determining meaning and reference(facts such as those about behaviour, dispositions to behaviour and soon) fail to pick out one meaning or referent uniquely. So, there will bemany (presumably, infinitely many) candidates for the extension of ‘+’,for example, all compatible with these reference constraining factors.Lewis suggests one way of further narrowing the range of candidates:the notion of objective similarity. More specifically, Lewis suggests termstake as their extensions those sets the members of which exhibit thehighest possible degree of objective resemblance to each other, compati-ble with the other reference constraining factors. But the sheer fact thatthose other reference constraining factors so underdetermine the refer-ence of our terms also ensures there will be ways of further narrowingreference other than the one Lewis recommends. Moreover, these otherways of further narrowing reference will, like Lewis’ proposal, all becompatible with all of the other reference constraining factors. So, wecannot rule any of the other ways out by appeal to those other con-straints. The sceptic can therefore ask: in virtue of what are these otherpossible ways wrong and Lewis’ right?

Of course, Lewis’ proposal seems to be much more natural and inaccord with common-sense than any other proposal. If a speaker has sofar used a word R in the same way we use ‘red’ it is obviously muchmore natural and ‘commonsensical’ to say R refers to red things than tothe class of things that are red before t and green thereafter. But thisdoes not make Lewis’ suggestion right. Firstly, if accordance with com-mon sense were a fact sufficient to make a system of reference right, itwould be trivially easy to solve Kripke’s problem. After all, it is clearlymuch more in accord with common sense to say that ‘+’ refers to addi-tion than to quaddition. But there is another, perhaps more fundamental,problem with the suggestion. Suppose it is said that the system of refer-ence Lewis favours is right because it is in accord with common sense.Then, if we are to know that it is an accord with common sense beliefs,we must at least know what it is that common sense asserts. But in orderto know this, we must know what our common sense beliefs mean, or towhat they refer. The sceptic can, of course, offer some deviant accountof what our common sense beliefs actually mean. And according to thisdeviant account, it is, perhaps, not Lewis’ system of reference that agreeswith our common sense beliefs, but the system of reference advocatedby the sceptic. Note that what is in question here is not the correctnessof our common sense beliefs, but their interpretation. So, the questionwould arise: in virtue of what is the sceptic’s interpretation of ourcommon sense beliefs wrong while ours is right? Therefore, if weattempt to show it is the position of Lewis, rather than that of the


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sceptic, that is in accord with common sense we find ourselves con-fronted with our original problem: in virtue of what is our interpretationof the items in our language the correct interpretation. We are back atsquare one.

There is another point that further casts doubt on the apparent intui-tive appeal of Lewis’ suggestion. Recall that on Lewis’ suggestion therelations of similarity that determine the reference of our terms areobjective, language and theory independent relations, to be discoveredby empirical science. But if these relations of similarity are to be discov-ered by empirical science, it is at least a possibility that objects are infact objectively similar in this sense might not appear to pre-theoreticaljudgement to be similar. Ordinary, scientifically untrained, speakersmight even be inclined to deny that some class of objects, objectivelysimilar in Lewis’ sense, were similar at all. And so, such speakers wouldnot be naturally inclined to apply the same term to all the members ofthat class. This consideration, by itself, need not show Lewis is wrong,but it does perhaps undermine any claim that position might have tonatural intuitive appeal.

5. Lewis’ Defence of his Position

Lewis presents a number of arguments for his position. In this section itwill be argued that none of them provide a satisfactory response to thesceptic.

The first of Lewis’ arguments we will consider concerns the generalnature of the facts that are eligible candidates for the facts in virtue ofwhich a speaker refers to one object rather than another. Kripke seemsto assume that the facts in virtue of which S means one thing rather thananother must be facts about S himself, or at least facts about the linguis-tic community of which S is a member. But Lewis points out that refer-ence is a binary relation, holding between a speaker (or community) andan object (or objects) in the world. There is, therefore, no reason whythe facts in virtue of which the relation holds should not come from bothrelata, that is, from both the speaker and the objects to which thespeaker refers.16 However, even if this point is granted, it is of no forceagainst the sceptical objection currently under consideration. The currentsceptical objection grants that properties holding between the objectsthemselves (specifically, objective relations of similarity) can have a rolein fixing reference. It merely offers an alternative account of the preciseway in which they do so.

Lewis says that ‘only if we have an independent, objective distinctionbetween natural and unnatural [classes] and we impose the presumptionin favour of eligible content a priori as a constitutive constraint, does the


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problem of interpretation have any solution at all’.17 However, whatLewis says here can be given two possible construals. On the first, per-haps less plausible construal, Lewis is suggesting we postulate or conjec-ture that reference has the feature of holding between our terms and themost natural (i.e., objectively similar) eligible classes of objects. In thissense, we might, for example, postulate that there are microbes on Mars,or a distant, unobserved planet. But postulating (in this sense of ‘postu-late’) would seem to be of little help in our present situation. We can, ofcourse, conjecture that it is true that reference has the features Lewissuggests. But postulating that something is true obviously does not makeit true: postulating microbes on Mars does not make it true that thereare microbes on Mars. Neither does postulating that reference holdsbetween words and natural classes make it true that reference has thisfeature.

Perhaps we can conjecture that reference holds between words andthe most natural of eligible classes. But so it seems, can the bizarre scep-tic conjecture that it holds between words and the second most naturalof the eligible classes. Then, of course, the question arises: in virtue ofwhat is our conjecture true while that of the bizarre sceptic is false?Clearly neither our past behaviour nor dispositions to behaviour will dothe job, at least for some deviant interpretations of the meaning of theword ‘reference’. And neither will appealing to definitions of ‘reference’that have been given in the past be able to do the job either: the scepticwill be able to offer an alternative interpretation of the terms in any pastdefinitions. The sceptical arguments that apply to ‘+’ and to other termsequally apply to the term ‘reference’ itself. It is not enough for Lewis, orthe sceptic, to merely postulate, in the sense of conjecture that it is true,that reference has this feature. What needs to be provided is some factin virtue of which it has this feature rather than one of many otherpossible candidates the sceptic might advance.

A related interpretation of Lewis is that he is asserting that referenceis identical with the (or with ‘a’) relation holding between our terms andthe most natural classes compatible with the other reference - determin-ing constraints. On this interpretation, Lewis is asserting that referencejust is a particular relation between our words and the world. But, again,it is obvious how the sceptic might reply. The sceptic may assert that ref-erence is identical with a relation holding between our words and thesecond (or fifth, or twelfth) most natural classes compatible with theother constraints. If Lewis can assert reference just is one relation, thenit seems the sceptic can assert it ‘just is’ another. And if both claimsabout the identity of reference are compatible with the other constraints,the question arises: whose claim – Lewis’ or the sceptic’s – is correct?Note that the doubt here is not an epistemic one. We can assume wehave a complete knowledge of the other constraints; for example, that


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we have a complete knowledge of our own past behaviour, dispositionsto behaviour, psychological states and so on. But still, given Kripken-stein’s arguments, such complete knowledge would fail to determinewhether it is Lewis’ claim about the identity of reference that is correct,rather than that offered by the sceptic.

There is also, however, another construal that can be given to thepassage from Lewis. On this interpretation, Lewis is suggesting that westipulatively re-define reference.18 We are, as it were, suggesting or pro-posing that from now on we attach a new meaning (presumably closelyrelated to its old meaning) to the term ‘reference’. Perhaps, given theearlier, pre-existing meaning of ‘reference’, there is no determinate factof the matter as to whether words refer to the most natural eligible clas-ses of objects or to classes of some other sort. But if we accept Lewis’proposed re-definition of reference, they will determinately refer to themost natural eligible class. This determinacy of reference will, on thissuggestion, be a consequence of our acceptance of Lewis’ proposedre-definition of reference.

There is, however, a difficulty the sceptic can raise for this suggestion.On this view, reference only becomes determinate in consequence of usaccepting Lewis’ re-definition of reference. The sceptic can therefore callin to question what it is that we are doing when we initially propose there-definition of reference. The sceptic can offer an alternative interpreta-tion of what the proposed redefinition of reference means.

We can, perhaps, make this point more clearly by consideringexplicitly what it is, on this view, that Lewis is proposing. Lewis isputting forward the following:Proposal L: Reference be re-defined as a relation holding between ourwords and the most natural eligible classes of objects.

Lewis is suggesting we ought to accept Proposal L. The difficulty isthat the sceptic might be quite ready to accept L, but give an alternativeinterpretation of what the words in it mean. More specifically, the scep-tic might offer an alternative interpretation of the words in L accordingto which reference becomes the relation the sceptic himself favours –perhaps a relation between the words and the second (or seventh, or fif-teenth) most eligible class of objects. If we accept L – as the scepticinterprets it – then ‘reference’ would come to mean what the scepticclaims it to mean. So the question would arise: is the sceptic’s interpreta-tion of the words in L correct, or is ours? Obviously, appealing to Litself is not relevant, since what is in dispute is the meaning that L hasprior to our accepting it. And the various reference-constraining factorsin force prior to our acceptance of L fail to determine what L means.Prior to our accepting L, common sense says L means one thing, thesceptic says it means another. Accepting L would only confer upon ‘ref-erence’ the meaning Lewis wishes it to have if, prior to accepting L, the


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words in L already have the meaning common sense believes them tohave. But this is the very point the sceptic denies.

It is worth emphasizing that the point being made here is not merelythat it is possible, in some sense of the word ‘possible’, to give an inter-pretation of L different from the one that Lewis apparently wishes it tobe given. Rather, the point is that, prior to the acceptance of L, thereare (at least) two interpretations of L compatible with all of the other ref-erence-determining constraints. To assume that prior to the acceptance ofL, L itself has the meaning Lewis (apparently) assumes it has, ratherthan the meaning the sceptic says it has, is therefore to beg the questionagainst the sceptic.

In summary, the sceptic might agree to accept L, but dispute what it iswe are doing when we accept it. To assert that in accepting L we areconferring upon ‘reference’ the meaning Lewis wishes that term to have,is to beg the question at issue. I conclude that Lewis’ proposed solutiondoes not work if ‘postulate’ is given its ‘stipulative’ interpretation.

It might be objected to the above argument against Lewis that it com-mits a ‘foul’: after all, surely if philosophical discussion is to take placeat all, then it must be granted, for the sake of argument, that words havetheir typical meanings, and that the items of our language are to begiven their usual interpretations. And so, it might be objected, it mustbe granted to Lewis that when he offers for our acceptance Proposal L,we ought to grant to him the assumption that the words in it have theirusual meanings and referents. But it should be noted the particular rolethat L is being asked to play here. L is not merely contributing to a dis-cussion concerning the nature of meaning or reference. L is also beingasked, by Lewis, to play a role in modifying what reference actually is.Perhaps, if philosophical discussion is to be possible at all, we mustaccept that words have their usual referents, but if Lewis asserts thataccepting L will modify the nature of reference in one particular wayrather than another, then he is advancing a philosophical thesis. And it isa philosophical thesis that Kripke’s sceptic might dispute.

Lewis might claim that if we accept L (as he wishes it to be inter-preted) then many things we pre-theoretically believe to be true (that ‘+’refers to addition, ‘table’ to tables, etc.) will follow. This might beclaimed to constitute something like abductive evidence for the truth ofL. Whether or not this is an appropriate use of the notion of abductiveevidence, the fundamental question remains: ‘What is it we are doing inthe act of accepting L?’ To say we are conferring upon ‘reference’ themeaning Lewis wishes it to have is to beg the question against the scep-tic. Even if desirable consequences would come from conferring upon‘reference’ the meaning Lewis recommends, the question remains: arewe capable of conferring this desired meaning on ‘reference’?


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It might be suggested that Lewis is not offering a re-definition but analternative account of that which constitutes reference. But again,whether it is a re-definition, an alternative account of its constitution, orsomething else, the question arises: ‘In virtue of what are we modifyingthe meaning, or constitution, of reference in the way common sense sup-poses we are, rather than the way claimed by the sceptic.

A related possibility is that Lewis is making a suggestion about whatwe ought to take to be the identity of reference. On this interpretation,Lewis is suggesting that we ought to accept that reference just is thatrelation which holds between our terms and the most natural of the eli-gible candidates for their referents. But this suggestion is confrontedwith at least two difficulties. First, the difficulty noted in the previousparagraph also applies here. Suppose a Lewisian recommends we accept:

Reference just is the relation that holds between our terms and themost natural of their eligible referents._________________(RI)

The sceptic might go along with the suggestion we ought to accept (RI),dispute what we are doing when we accept it. The sceptic might say thatwhen we accept (RI), we are not accepting Lewis’ theory of reference,but rather: the one favoured by the sceptic. Then the question arises: invirtue of what does (RI) convey the meaning that Lewis wishes it to con-vey rather than the meaning that the bizarre sceptic might attribute toit? We find ourselves back at square one.

There is another difficulty with the suggestion that we might be ableto reply to Kripke’s sceptic by making a recommendation about what weare to take as the identity of reference. The obvious difficulty is that thesceptic can offer an indefinitely large number of alternative recommen-dations. Here are some:

Reference is to be taken to be the relation that holds between ourterms and the second most natural of the eligible classes of refer-ents.__________________(RI⁄)

Reference is to be taken to be the relation that holds between ourterms and the fifth most natural of the eligible class of referents.__________________________(RI⁄⁄)

And so we are confronted with the question: why ought we to acceptLewis’ recommendation rather than the one offered by the sceptic? Tosay that (RI) is to be preferred to the others because it delivers ‘theright’ extensions for our terms is clearly to beg the question against thesceptic. It seems that, no matter how we interpret Lewis’ suggestions,there are sceptical doubts that remain unanswered.


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The same difficulty arises for the suggestion that Lewis is offering aclaim about the identity of reference; that is, asserting that reference justis the relation holding between our terms and the most eligible classes ofreferents. The sceptic can, of course, make the incompatible claim thatreference just is the relation described by (R1⁄), or by (R1⁄⁄). And sowe are confronted with the question: ‘Is there some fact of the matter invirtue of which what Lewis, rather than the sceptic, says is right?’

6. Concluding Remarks

In this paper we have been concerned to evaluate David Lewis’ responseto the meaning sceptical argument Saul Kripke develops in hisWittgenstein: On Rules and Private Language. It has been argued thateven if the ontology of objective relations and their eligibility as facts invirtue of which a speaker means one thing rather than another areaccepted, Lewis’ proposed solution is not satisfactory. The sceptic canoffer alternative accounts of the way in which those objective relationsof similarity help to determine meaning. Kripke’s challenge, to providesome fact in virtue of which there is such a thing as meaning somethingby any word, remains unmet.

University of Newcastle, Australia

Notes

1 See S. Kripke, Wittgenstein: On Rules and Private Language (Oxford, BasilBlackwell, 1982).

2 See Kripke, Wittgenstein, p. 55.3 See, for example, Lewis’ paper, ‘New Work for a Theory of Universals’, Aus-

tralasian Journal of Philosophy, 61 (1983), pp. 343–77.4 See D. Armstrong Universals and Scientific Realism, vol. 1, A Theory of Uni-

versals (Cambridge: Cambridge University Press, 1978).5 See, for example, Armstrong’s discussion of ‘Predicate Nominalism’. There,

Armstrong is concerned to argue against the thesis that, for example, a classof white objects are similar because they are all called ‘white’, or because thepredicate ‘white’ applies to them all.

6 See Lewis, ‘New Work’, pp. 48–51. Lewis, adopting a possibly misleading ter-minology, identifies properties with classes. He accepts the existence of ‘prop-erties’, but he understands them to be classes. What I take to be essential toLewis’ position is that he denies the existence of Universals in Armstrong’ssense, but retains a distinction between natural and non-natural classes.

7 See Lewis, ‘New Work’, p. 350.8 See Ibid.9 Ibid., pp. 375–7.10 See Kripke, Wittgenstein, p. 18.11 Lewis, ‘New Work’, p. 376.


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12 Lewis, ‘New Work’, p. 371.13 Lewis does not assert it is impossible to refer to, example, grue things. But in

order to refer to grue things it is not enough for a speaker to merely use aterm that they have in the past only applied to green things. In the absenceof any additional reference constraining features a word will refer the mostnatural class, in this case the class of green things. (Lewis, ‘New Work’,p. 372.)

14 Of course, by this this I do not wish to imply that factors such as communityusage and linguistic conventions also may have a role in determining whethera given utterance is the utterance of a word.

15 It might be suggested that the thesis that the same way of going on is theright way could do the job of fixing the speaker’s beliefs or intentions. Morespecifically, it might be suggested that it could be used to show that the term‘colour’ in the child’s belief ‘I am being taught a colour word’ means ‘colour’not ‘collass’. But we can imagine situations in which the difficulties notedabove recur. Perhaps the objects used when the child was learning how touse the word ‘colour’ also happened to have some incidental property, suchas a certain mass, in common.

16 See Lewis, ‘New Work’, p. 371.17 Ibid., p. 377.18 That this is the correct interpretation of Lewis is I think suggested by his use

of the word ‘impose’, with its suggestion that we modify or ‘add to’ the mean-ing of reference. That Lewis is offering something like a stipulative re-defini-tion of reference is further supported by his comment on this view ofreference that accepting it does not involve postulating ‘any contingent factof psychology, either daringly or on evidence’ (Lewis, op cit., p. 377).

References

Armstrong, D. M. (1978) Universals and Scientific Realism, Volume 1, A Theoryof Universals, Cambridge: Cambridge University Press.

Kripke, S. A. (1982) Wittgenstein: On Rules and Private Language, Oxford: BasilBlackwell.

Lewis, D. K. (1983) ‘New Work for a Theory of Universals’, The AustralasianJournal of Philosophy 61: 343–77.


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in defence of kripkenstein: on lewis’ proposed solution to the sceptical argument

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