According to metaphysical realism, the world is as it is independentlyof how humans or other inquiring agents take it to be. The objects theworld contains, together with their properties and the relations theyenter into, fix the world’s nature and these objects existindependently of our ability to discover they do. Unless this is so,metaphysical realists argue, none of our beliefs about our world couldbe objectively true since true beliefs tell us how things are andbeliefs are objective when true or false independently of what anyonemight think.

Many philosophers believe metaphysical realism is just plain commonsense. Others believe it to be a direct implication of modern science,which paints humans as fallible creatures adrift in an inhospitableworld not of their making. Nonetheless, metaphysical realism iscontroversial. Besides the analytic question of what it means toassert that objects exist independently of the mind, metaphysicalrealism also raises epistemological problems: how can we obtainknowledge of a mind-independent world? There are also prior semanticproblems, such as how links are set up between our beliefs and themind-independent states of affairs they allegedly represent. This isthe Representation Problem.

Anti-realists deny the world is mind-independent. Believing theepistemological and semantic problems to be insoluble, they concluderealism must be false. In this entry I review a number of semantic andepistemological challenges to realism all based on the RepresentationProblem:

1. The Manifestation Argument: the cognitive and linguistic behaviourof an agent provides no evidence that realist mind/world linksexist;
2. The Language Acquisition Argument: if such links were to existlanguage learning would be impossible;
3. The Brain-in-a-Vat Argument: realism entails both that we could bemassively deluded (‘brains in a vat’) and that if we werewe could not even form the belief that we were;
4. The Conceptual Relativity Argument: it is senseless to ask whatthe world contains independently of how we conceive of it, since theobjects that exist depend on the conceptual scheme used to classifythem;
5. The Model-Theoretic Argument: realists must either hold that anideal theory passing every conceivable test could be false or thatperfectly determinate terms like ‘cat’ are massivelyindeterminate, and both alternatives are absurd.

I proceed by first defining metaphysical realism, illustrating itsdistinctive mind-independence claim with some examples anddistinguishing it from other doctrines with which it is oftenconfused, in particular factualism. I then outline the RepresentationProblem in the course of presenting the anti-realist challenges tometaphysical realism that are based on it. I discuss metaphysicalrealist responses to these challenges, indicating how the debates haveproceeded, suggesting various alternatives and countenancinganti-realist replies.

The aim throughout will be to see whether the realist can respond tothe anti-realist challenges and so much of the subsequent discussionwill be taken up with attempts to formulate realist replies to thesechallenges that have some initial credibility. However it needs to benoted that all these replies are provisional: anti-realism gains muchof its force by highlighting a gap between realist metaphysics andepistemology that no one really knows how to bridge.

• 1. What is Metaphysical Realism?
• 2. Carnap and Mind-Independent Existence
• 3. Anti-Realist Challenges to Realism
  • 3.1 Language Use and Understanding
  • 3.2 Language Acquisition
  • 3.3 Radical Skepticism
  • 3.4 Conceptual Schemes and Pluralism
  • 3.5 Models and Reality
• 4. Metaphysical Realist Responses
  • 4.1 Language Use and Understanding
  • 4.2 Language Acquisition
  • 4.3 Radical Scepticism
  • 4.4 Conceptual Schemes and Pluralism
  • 4.5 Models and Reality
• 5. Summary
• Bibliography
• Academic Tools
• Other Internet Resources
• Related Entries

1. What is Metaphysical Realism?

Metaphysical realism is the thesis that the objects, properties andrelations the world contains exist independently of our thoughts aboutthem or our perceptions of them. Anti-realists either doubt or denythe existence of the entities the metaphysical realist believes in orelse doubt or deny their independence from our conceptions ofthem.

Metaphysical realism is not the same as scientific realism. That theworld’s constituents exist mind-independently does not entailthat its constituents are as science portrays them. One could adopt aninstrumentalist attitude toward the theoretical entities posited byscience, continuing to believe that whatever entities the worldactually does contain exist independently of our conceptions andperceptions of them.

Henceforth, we shall often just use the term ‘realism’ tomean metaphysical realism. Opposition to realism can take many formsso there is no single theoretical view denoted by the term‘anti-realism’. One approach, popular in continentalphilosophy, is to reject realism in favour of the view that words canonly acquire their meaningintra-linguistically, throughtheir semantic relations with other words, rather than through any(fanciful) ‘referential’ relations to the world outside oflanguage.

Within the ranks of analytic philosophy, verificationists andpragmatists also reject realism, though for different reasons. Weshall focus in this entry on the types of criticism voiced by thesetwo groups of analytic philosophers with Michael Dummett advocatingverificationism and Hilary Putnam pragmatism. Both reject realism bydeploying semantic considerations in arguments designed to show thatrealism is untenable. The goal of this entry is to outline these‘semantic’ challenges to realism and to see whether theycan be answered.

This characterization of realism in terms of mind-independence is notuniversally accepted. Some object that mind-independence isobscure. Others maintain that realism is committed, in addition, to adistinctive (and tendentious) conception of truth [Putnam 1981, 1985,1992; Wright 1991] or, more radically, that realism just is a thesisabout the nature of truth—that truth can transcend thepossibility of verification, ruling statements for which we can gatherno evidence one way or the other to be determinately either true orfalse. An example would be “Julius Caesar’s heart skippeda beat as he crossed the Rubicon.” Thus the realist on this viewis one who believes the law of bivalence (every statement is eithertrue or false) holds for all meaningful (non-vague) statements[Dummett 1978, 1991, 1993].

These semantic formulations of metaphysical realism are unacceptableto realists who are deflationists about truth, denying that truth is asubstantive notion which can be used to characterise alternativemetaphysical views [see theentry on thedeflationary theoryof truth]. Such realists tend to ignore the anti-realist’ssemantic and epistemological challenges to their position.

It is a mistake to identify realism with factualism, the view thatsentences in some discourse or theory are to be construed literally asfact-stating ones. The anti-realist views discussed below arefactualist about discourse describing certain contentiousdomains. Adopting a non-factualist or error-theoretic interpretationof some domain of discourse commits one to anti-realism about itsentities. Factualism is thus a necessary condition for realism. But itis not sufficient. Verificationists like Dummett reject the idea thatsomething might exist without our being able to recognize itsexistence. They can be factualists about entities such as numbers andquarks while maintaining anti-realism about them since they deny thatany entities can exist mind-independently.

2. Carnap and Mind-Independent Existence

Why do some find the notion of mind-independent existence inadequatefor the task of formulating metaphysical realism? The most commoncomplaint is that the notion is either obscure, or, more strongly,incoherent or cognitively meaningless. An eloquent spokesman for thisstrong view was Rudolf Carnap: “My friends and I have maintainedthe following theses,” Carnap announces [Carnap 1963,p.868]:

(1) The statement asserting the reality of the external world(realism) as well as its negation in various forms, e.g. solipsism andseveral forms of idealism, in the traditional controversyarepseudo-statements, i.e., devoid of cognitive content. (2)The same holds for the statements about the reality or irrealityofother minds (3) and for the statements of the reality orirreality ofabstract entities (realism of universals orPlatonism, vs. nominalism).

In spite of his finding these disputes meaningless, Carnap indicateshow he thinks we could reconstruct them (sic.) so as to make somesense of them: if we were to “replace the ontological thesesabout the reality or irreality of certain entities, theses which weregard as pseudo-theses, by proposals or decisions concerning the useof certain languages. Thus realism is replaced by the practicaldecision to use the reistic language”.

Carnap does not have in mind a factualist reformulation ofmetaphysical realism here—his “reistic” language isstrictly limited to the description of “intersubjectivelyobservable, spatio-temporally localized things or events”.

What matters for our purposes is not Carnap’s sense of acommensurability between a metaphysical thesis about reality and apractical decision to speak only about observable things, but ratherthat he thinks he can explain how the illusion of meaningfulnessarises for the metaphysical theses he declares “devoid ofcognitive content”.

His explanation has to do with a distinction between two types ofquestions:internal andexternal questions. By wayof illustration Carnap shows how the distinction works in thecontroversy over the existence of abstract entities:

An existential statement which asserts that there are entities of aspecified kind can be formulated as a simple existential statement ina language containing variables for these entities. I have calledexistential statements of this kind, formulatedwithin agiven language,internal existential statements. [Carnap1963, p. 871]

Carnap contends that

Just because internal statements are usually analytic and trivial, wemay presume that the theses involved in the traditional philosophicalcontroversies are not meant as internal statements, but ratherasexternal existential statements; they purport to assertthe existence of entities of the kind in question not merely within agiven language, but, so to speak, before a language has beenconstructed. [1963, p. 871]

Declaring all such external existential questions devoid of cognitivecontent, Carnap now feels emboldened to dismiss both realism thatasserts the ontological reality of abstract entities and nominalismthat asserts their irreality as “pseudo-statements if they claimto be theoretical statements” (ibid).

More importantly, Carnap has hit upon an explanation for thepersistent allure of the notion of mind-independent reality: we oftenwish to know whether some existence claim is true. Provided we realizeexistence claims can only be properly formulated and evaluated withina language \(L\) our query is perfectly reasonable and can veryoften be answered by examining the specification of the domainof \(L\)’s quantifiers. Thus, to use Carnap’s ownexample, suppose a theorist wishes to know for alanguage \(L'\) whose domain contains material objects,classes of objects and classes of classes of objects, the answer tothe following existential question:

• (1)Does there exist an \(x\) and a \(y\) suchthat \(x\) is an element of an element of \(y\)?

Carnap maintains (ibid) that an affirmative answer to thisquestion is both true and provable in \(L'\) (though hedoes not specify any theory expressible in \(L'\) in which(1) is derivable).

But suppose that instead of \(L'\), our theorist had askedthe same question of another language \(L''\) the universeof discourse for which contained material objects and classes of thesebut no classes of classes of them. Then the following universalstatement would now be provable in \(L''\), Carnap claims(again without specifying any theory expressible in \(L''\)for which this might hold), as well as true in that language:

• (2)For every \(x\) and \(y\), \(x\) is not an elementof an element of \(y\)

Suppose our theorist, Al let’s call him, though initiallyattracted to \(L'\) for its superior expressive anddeductive power when compared to \(L''\), now starts to havemisgivings about the content and consistency of some of itsexistential assertions. After deliberating he decides:

• (3)There are classes of objects.

But he also accepts:

• (4)There are no classes of classes of objects.

This brings him into conflict with his good friend Bob. For Bobbelieves not only in classes of objects but also in classes of classesof objects and thus endorses \(L'\) as a language bestsuited to represent his ontological beliefs. That is, like Al, Bobbelieves (3), but Bob also accepts (5):

• (5)There are classes of classes of objects.

Is there a genuine dispute between Al and Bob? Is there a fact of thematter as to who is right, whose ontological views reflect the way theworld is really structured? Carnap says “No”: seeking toelevate the modal status of their linguistic decisions from merepreferences for one language over another to unconditional obligationsto reflect how realityis independently of any representaton,Al and Bob have temporarily lost sight of the particular linguisticcontexts that give meaning to the existential claims they respectivelyadvanced at (4) and (5). All that can be meaningfully said, accordingto Carnap, is that whilst (4) is true in \(L''\) it is falsein \(L'\) and, conversely, whilst (5) is truein \(L'\), it is false in \(L''\). The cognitivecontent of (5) for Bob is given by (1) and that of (4) for Al by(2). As Carnap puts it:

Thus we see the difference between (them) isnot a differenceintheoretical beliefs [DK: as Bob seems to think when hemakes the pseudo-assertion at (5)]; it is merelyapractical difference in preferences and decisionsconcerning the acceptance of languages. [loc. cit., p. 873]

This is a beguiling story but it does not do what Carnap wishes it todo: it does not spirit away all troubling metaphysical questions aboutmind-independent existence by parlaying them into (or replacing themwith) sanitized questions about the entities the quantifiers rangeover in this or that language. Here’s why. Consider thefollowing case. Suppose the year is 1928, the year Carnap publishedhisAufbau. A mathematician, Cass, working in classicalmathematics (sometimes shortened to “CM”), comes acrossthe following question:

• (Q)Are there irrational numbers \(a\) and \(b\) suchthat \(a^b\) is rational?

Cass realizes at once that she can answer this question, reasoningfrom premise (A):

• (A)Either \(\sqrt{2}^{\sqrt{2}}\) is rational or it isirrational.

The reasoning continues:

Suppose this number \(\sqrt{2}^{\sqrt{2}}\) is rational. Then since\(\sqrt{2}\) is irrational, our problem is solved by taking \(a =\sqrt{2}, b = \sqrt{2}\). Suppose alternatively that\(\sqrt{2}^{\sqrt{2}}\) is irrational. Then that very irrationalnumber raised to the power \(\sqrt{2}\) must be rational. For thisnumber is equivalent to \(\sqrt{2}^{\sqrt{2} \times \sqrt{2}}\)which is just the rational number 2. So in this latter case, byselecting \(a = \sqrt{2}^{\sqrt{2}}, b = \sqrt{2}\) we ensure thatwe have selected two irrational numbers \(a\), \(b\) such that \(a^b\) isrational.

Whence, we have a solution to our problem:

• (C)Either \(a = \sqrt{2}\), \(b = \sqrt{2}\) or else \(a = \sqrt{2}^{\sqrt{2}}\), \(b = \sqrt{2}\) are two irrationalnumbers \(a\), \(b\) such that \(a^b\) is rational.

Now as the background logic for CM is classical there is nothing wrongwith Cass’s reasoning proceeding, as it does, from an instanceof the classically valid Law of Excluded Middle at (A). It is anexample of a “non-constructive” existence proof:demonstrating that one or another alternative must hold withoutproviding a means for ascertaining which one does hold.

Suppose now we ask Cass which of the two statements below is true inclassical mathematics:

1. \(\sqrt{2}\) is an irrational number such that\(\sqrt{2}^{\sqrt{2}}\) is a rational number.
2. \(\sqrt{2}^{\sqrt{2}}\) and \(\sqrt{2}\) are irrational numberssuch that \((\sqrt{2}^{\sqrt{2}})^{\sqrt{2}}\)is a rational number.

Cass, working in 1928, believes one or the other of these statementsmust be true in classical mathematics but she has no means fordetermining which is true. So she cannot answer our question. Further,let us suppose that no one everdoes find a method fordetermining which alternative holds good.

Aside: As it turns out (and this is the reason for indexingthe example to a particular time) this last supposition is contrary tofact. In 1934 Gelfond and Schneider independently proved thatif \(a, b\) are algebraic numbers with \(a \ne 0\) or \(1\)and \(b\) not rational then any valueof \(a^b\) [\(= \exp(b \log a)\)]is a transcendental number. The Gelfond-Schneider Theorem answered inthe affirmative David Hilbert’s Seventh Problem: whether\(2^{\sqrt{2}}\) is transcendental. It also follows that\(\sqrt{2}^{\sqrt{2}}\) is irrational so that (II) istrue-in-CM.

Now even though she lacks any method for deciding which alternativeholds, according to Cass either (i) is true-in-CM or else (ii) istrue-in-CM. But if so, Cass in 1928 has an instance of amind-independent existence claim holding of aninternalexistence statement: one of these two pairs of numbers\((a, b)\) in question, either\((a=\sqrt{2}, b=\sqrt{2})\) or else\((a=\sqrt{2}^{\sqrt{2}}, b=\sqrt{2})\) is suchthat \(a\) and \(b\) are both irrationalbut \(a^b\) is rational even though we maynever be able to determine which pair of numbers it is (andwecould have been in Cass’s situation today had theGelfond-Schneider Theorem lain forever undiscovered).

But what should Carnap say about this case? He cannot protest thatCass’s assertion that one or other element of thesentence pair {i), (ii)} is true-in-CM is a pseudo-statement as he didfor Bob’s assertion (5) that there are classes of classes ofobjects. For the statement that either (i) is true-in-CM or else (ii)is true-in-CM is aninternal statement and thus, byCarnap’s lights, a statement that has cognitive content.

Hence, one cannot undermine the notion of mind-independent reality inthe simple way Carnap imagines, namely, by the internal/externaldistinction coupled with the claim that external statements arepseudo-statements. For, whatever its other virtues, theinternal/external distinction cannot explain why someone shouldbelieve that exactly one of (i) or (ii)has to be true in acertain language even though we might never be in a position todetermine which. And this is precisely what the belief inmind-independent reality amounts to.

3. The Anti-Realist Challenges to Metaphysical Realism

3.1 Language Use and Understanding

The first anti-realist challenge to consider focuses on the use wemake of our words and sentences. The challenge is simply this: whataspect of our linguistic use could provide the necessary evidence forthe realist’s correlation between sentences and mind-independentstates of affairs? Which aspects of our semantic behaviour manifestour grasp of these correlations, assuming they do hold?

For your representations of the world to be reliable, there must be acorrelation between these representations and the states of affairsthey portray. So the cosmologist who utters the statement “theentropy of the Big Bang was remarkably low” has uttered a truthif and only if the entropy of the Big Bang was remarkably low.

A natural question to ask is how the correlation between the statementand the mind-independent state of affairs which makes it true issupposed to be set up. One suggestive answer is that the link iseffected by the use speakers make of their words, the statements theyendorse and the statements they dissent from, the rationalizationsthey provide for their actions and so forth; cognitively, it will bethe functional role of mental symbols in thought, perception andlanguage learning etc. that effects these links.

When we look at how speakers actually do use their sentences,anti-realists claim, we see them responding not to states of affairsthat they cannot in general detect but rather to agreed uponconditions for asserting these sentences. Scientists assert “theentropy of the Big Bang was remarkably low” because they allconcur that the conditions justifying this assertion have beenmet.

What prompts us to use our sentences in the way that we do are thepublic justification conditions associated with those sentences,justification conditions forged in linguistic practices which imbuethese sentences with meaning.

The realist believes we are able to mentally representmind-independent states of affairs. But what of cases where everythingthat we know about the world leaves it unsettled whether the relevantstate of affairs obtains? Did Socrates sneeze in his sleep the nightbefore he took the hemlock or did he not? How could we possibly findout? Yet realists hold that the sentence “Socrates sneezed inhis sleep the night before he took the hemlock” will be true ifSocrates did sneeze then and false if he did not and that this is asignificant semantic fact.

The Manifestation challenge to realism is to isolate some feature ofthe use agents make of their words, or their mental symbols, whichforges the link between mind-independent states of affairs and thethoughts and sentences that represent them. Nothing in thethinker’s linguistic behaviour, according to the anti-realist,provides evidence that this link has been forged—linguistic useis keyed to public assertibility conditions, not undetectabletruth-conditions. In those cases, such as the Socrates one, where wecannot find out whether the truth-condition is satisfied or not, it issimply gratuitous to believe that there is anything we can think orsay or do which could provide evidence that the link has been set upin the first place. So the anti-realist claims [Dummett 1978, 1991,1993 Tennant 1997; Wright 1993].

Why should we expect the evidence to be behavioural rather than, say,neurophysiological? The reason anti-realists give is that the meaningsof our words and (derivatively for them) the contents of our thoughtsare essentially communicable and thus must be open for all speakersand thinkers to see [Dummett 1978, 1993].

3.2 Language Acquisition

The second challenge to be considered concerns our acquisition oflanguage. The challenge to realism is to explain how a child couldcome to know the meanings of certain sentences within his/herlanguage: the ones which the realist contends have undetectabletruth-makers associated with them. How could the child learn themeanings of such sentences if these meanings are determined by statesof affairs not even competent speakers can detect?

Consider the sentence (S) once more:

• (S)Socrates sneezed in his sleep the night before he took thehemlock.

Realists say (S) is either true or false even though we may (andalmost certainly will) never know which it is. The state of affairswhich satisfies (S)’s truth-condition when it is true, its‘truthmaker’, and the state of affairs which satisfies thetruth-condition of the negation of (S) when (S) is false are supposedto be able to hold even though competent speakers cannot detectwhether they do. How could the child ever learn about thisundetectable relation?

Suppose God (or nature) had linked our mental representations to justthe right states of affairs in the way required by the realist. If so,this is a semantically significant fact. Anyone learning their nativelanguage would have to grasp these correspondences between sentencesand states of affairs. How can they do this if even the competentspeakers whom they seek to emulate cannot detect when thesecorrespondences hold? In short, competence in one’s languagewould be impossible to acquire if realism were true [Dummett 1978,1993; Wright 1993]. This is the Language Acquisition challenge.

This challenge is exacerbated by the anti-realist’s assumptionthat since the linguistic meaning of an expression \(E\) isdetermined solely by competent speakers’ use of \(E\) thechild’s task in all cases is to infer the meaning of \(E\)from its use. Thus Dummett [1978 pp. 216–217], in discussing themeaning of mathematical statements, proposes a thesis he argues holdsfor the meanings of every kind of statement:

The meaning of a mathematical statement determines and is exhaustivelydetermined by its use. The meaning of a mathematical statement cannotbe, or contain as an ingredient, anything which is not manifest in theuse made of it, lying solely in the mind of the individual whoapprehends that meaning: if two individual agree completely about theuse to be made of the statement, then they agree about itsmeaning. The reason is that the meaning of a statement consists solelyin its role as an instrument of communication between individuals,just as the powers of a chess-piece consist solely in its role in thegame according to the rules.

W.V.O. Quine is even more insistent on the public nature of linguisticmeaning. Displaying his unshakable faith in Skinnerian models oflanguage-learning he writes [1992, pp. 37–38]:

In psychology one may or may not be a behaviourist, but in linguisticsone has no choice … There is nothing in linguistic meaningbeyond what is to be gleaned from overt behaviour in observablecircumstances.

3.3 Radical Skepticism

According to Hilary Putnam, the metaphysical realist subscribes notjust to the belief in a mind-independent world but also to the thesisthat truth consists in a correspondence relation between words (ormental symbols) and things in that mind-independent world. Call thisthesiscorrespondence truth (after Devitt 1991). Moreimportantly, metaphysical realists aver that an ideal theory of theworld could beradically false, Putnam contends:‘radical’ in the sense thatall (or almost all) ofthe theory’s theses could fail to hold. Such a global failurewould result if we were to be ‘brains-in-a-vat’ our brainsmanipulated by mad scientists (or machines, as in the movieTheMatrix) so as to dream of an external world that we mistake forreality. Call this thesisradical skepticism.

It is widely believed that states of affairs that are trulymind-independent do engender radical skepticism. The skeptic contendsthat for all we could tell we could be brains in a vat—brainskept alive in a bath of nutrients by mad alien scientists. All ourthoughts, all our experience, all that passed for science would besystematically mistaken if we were. We’d have no bodies althoughwe thought we did, the world would contain no physical objects, yet itwould seem to us that it did, there’d be no Earth, no Sun, novast universe, only the brain’s deluded representations ofsuch. At least this could be the case if our representations derivedeven part of their content from links with mind-independent objectsand states of affairs. Since realism implies that such an absurdpossibility could hold without our being able to detect it, it has tobe rejected, according to anti-realists.

A much stronger anti-realist argument due to Putnam uses thebrain-in-a-vat hypothesis to show that realism is internallyincoherent rather than, as before, simply false. A crucial assumptionof the argument is semantic externalism, the thesis that the referenceof our words and mental symbols is partially determined by contingentrelations between thinkers and the world. This is a semanticassumption many realists independently endorse.

Given semantic externalism, the argument proceeds by claiming that ifwe were brains in a vat we could not possibly have the thought that wewere. For, if we were so envatted, we could not possibly mean by‘brain’ and ‘vat’ what unenvatted folk mean bythese words since our words would be connected only to neural impulsesor images in our brains where the unenvatteds’ words areconnected to real-life brains and real-life vats. Similarly, thethought we pondered whenever we posed the question “am I a brainin a vat?” could not possibly be the thought unenvatted folkpose when they ask themselves the same-sounding question inEnglish. But realism entails that we could indeed be brains in avat. As we have just shown that were we to be so, we could not evenentertain this as a possibility, realism is incoherent [Putnam1981].

3.4 Conceptual Schemes and Pluralism

If the notion of mind-independent existence is incoherent, asanti-realists contend, what should we put in its stead? Berkeleyfamously answered “Mind-dependent existence!” where theMind in question, for the good Bishop, was, of course, the Mind ofGod. Modern anti-realists tend not to be theists and tend not torelativize existence to any single mind. Instead of God they positconceptual schemes as that on which the notion of existencedepends. To that extent they follow Kant rather than Berkeley, thoughunlike Kant they tend to be pluralists—it is conceptual schemeswhich they endorse rather than a single transcendental scheme whichKant held to be obligatory for all rational creatures.

According to this view, there can no more be an answer to the question“What objects and properties does the world contain?”outside of some scheme for classifying entities than there can be ananswer to the question of whether two events \(A\) and \(B\)are simultaneous outside of some inertial frame for dating thoseevents. The objects which exist are the objects some conceptual schemesays exists—‘mesons exist’ really means‘mesons exist relative to the conceptual scheme of currentphysics’.

Realists think there is a unitary sense of ‘object’,‘property’ etc., for which the question “whatobjects and properties does the world contain?” makes sense. Anyanswer which succeeded in listing all the objects, properties, eventsetc. which the world contains would comprise a privileged descriptionof that totality. Anti-realists reject this. For them‘object’, ‘property’ etc., shift their sensesas we move from one conceptual scheme to another. Some anti-realistsargue that there cannot be a totality of all the objects the worldcontains since the notion of ‘object’ is indefinitelyextensible and so, trivially, there cannot be a privileged descriptionof any such totality.

How does the anti-realist defend conceptual relativity? One way is byarguing that there can be two complete theories of the world which aredescriptively equivalent yet logically incompatible from therealist’s point of view. For example, theories of space-time canbe formulated in one of two mathematically equivalent ways: as anontology of points, with spatiotemporal regions being defined as setsof points; or as an ontology of regions, with points being defined asconvergent sets of regions. Such theories are descriptively equivalentsince mathematically equivalent and yet are logically incompatiblefrom the realist’s point of view, anti-realists contend [Putnam1985, 1990].

3.5 Models and Reality

Putnam’s Model-Theoretic Argument is the most technical of thearguments we have so far considered although we shall not reproduceall the technicalities here. The central ideas can be conveyedinformally, although some technical concepts will be mentioned wherenecessary. The argument purports to show that the RepresentationProblem—to explain how our mental symbols and words get hookedup to mind-independent objects and how our sentences and thoughtstarget mind-independent states of affairs—is insoluble.

According to the Model-Theoretic Argument, there are simply too manyways in which our mental symbols can be mapped onto items in theworld. The consequence of this is a dilemma for the realist. The firsthorn of the dilemma is that s/he must accept that what our symbolsrefer to is massively indeterminate. The second horn is that s/he mustinsist that even an ideal theory, whose terms and predicates candemonstrably be mapped veridically onto objects and properties in theworld might still be false, i.e., that such a mapping might not be theright one, the one ‘intended’.

Neither alternative can be defended, according toanti-realists. Concerning the first alternative, massive indeterminacyfor perfectly determinate terms is absurd. As for the second, forrealists to contend that even an ideal theory could be false is toresort to unmotivated dogmatism, since on their own admission wecannot tell which mapping the world has set up for us. Such dogmatismleaves the realist with no answer to a skepticism which undermines anycapacity to reliably represent the world, anti-realists maintain.

It might be useful to informally illustrate some basic ideasunderlying the Model-Theoretic Argument. The discussion to followtrades formal precision for intuitive accessibility. In logic, atheory is a set of sentences. We are going to consider what happens tothe interpretation of 3 simple sentences that comprise our theory whenwe vary the way we refer to the individuals those sentences talk aboutand also vary how we classify those individuals. So, imagine that youand your four year old niece Maddy are fortunate enough to be watchingthree elite sprinters at a training session—Usain Bolt, JustinGatlin and Assafa Powell. Suppose we let the letter b stand for Bolt,g stand for Gatlin and p stand for Powell. These letters are calledindividual constants. We will also need a single predicate letter Jrepresenting the English predicate ‘is Jamaican’ toformulate our 3 sentence theory. In logic we distinguish betweentheories (sets of sentences) and the things those theories talk about(usually not sentences). The collection of items the theory talksabout feature in abstract entities known as structures as the domainof the structure and what the theory says about those items receivesan interpretation in the structure. An interpretation function assignsobjects from the domain of a structure to individual constants such asour b, g and p and sets of objects (subsets of the domain) to monadicpredicates such as our J. If we wish to express relations betweenobjects such as one individual being faster than or taller thananother (binary relations) or one individual standing between twoothers (ternary relations) we will need sets of ordered pairs (for thebinary case) or ordered triples (for the ternary case) from thedomain. Generally, n-place relations will require our interpretationfunction to supply n-tuples of objects from the domain as extensionsfor n-place predicates. By ‘extension’ of a predicate wesimply mean the (sets of) things the predicate applies to.

We are going to focus on the simplest case. Our theory asserts that:(1) Bolt is Jamaican, (2) Powell is Jamaican, (3) Gatlin is notJamaican. We shall write these sentences as (1) \(Jb\), (2) \(Jp\),(3) \(\neg Jg\) respectively. This simple theory is true. When youinform Maddy of these facts you mean to refer to the man Usain Boltwhen you use the name ‘Bolt’, to Assafa Powell by the name‘Powell’ and to Justin Gatlin by ‘Gatlin’. Youalso mean to be describing the first two sprinters as Jamaican and thelast as non-Jamaican when you use the predicate ‘isJamaican’ in sentences (1), (2) and (3).

A structure in which \(b\) denotes Bolt, \(p\) denotes Powell and \(g\) denotesGatlin and in which the extension of \(J\) is {Bolt, Powell}will make the sentences (1), (2) and (3) all true. Such a structure issaid to be a model of the theory. Furthermore, as the model representsthe names ‘Bolt’, ‘Powell’,‘Gatlin’ as applying to exactly the right individuals andthe predicate ‘is Jamaican’ as applying to just the rightset of individuals we say the model is anintendedmodel.

However, it is perfectly possible for a structure for a theory to makeall its sentences true (and thus be a model of the theory) withoutthat structure being anintended model. Suppose Maddymistakes which particular individuals you are referring to when youuse the names ‘Bolt’, ‘Powell’ and‘Gatlin’. Perhaps these sprinters lined up in that orderfor one trial and now line up in a different order for the nexttrial. Suppose she is also misinformed about what ‘isJamaican’ describes. Maybe she thinks it applies to a sprinterin the outside or middle lane and although that was the order for Boltand Powell in the first trial, in the second one which is just aboutto start Gatlin and Bolt are in the outside and middle lanes.

Let us use \(M\) to denote the intended model of the 3 sentence theoryand use \(M^*\) to denote Maddy’s non-standard model. Suppose weuse the the following notation to mean the individual constant \(b\)refers to Bolt in the model \(M\): \(|b|_M =\) Bolt and so we alsorepresent the facts that in \(M\) the constant g refers to Gatlin and\(p\) refers to Powell respectively as \(|g|_M =\) Gatlin and \(|p|_M =\)Powell. Suppose finally that we symbolize the interpretation of thepredicate \(J\) in \(M\) by \(|J|_M =\) {Bolt, Powell}.

We can now compute the truth-values of sentences such as \(Jb\),\(Jg\) and \(Jp\) in the model \(M\). Simple sentences such as these willturn out true in the model if the individual denoted by the individualconstant in the model is included in the set of individuals comprisingthe extension of the predicate \(J\) in the model. Since the individualsassigned to b and p are indeed included in the set that comprises theextension of \(J\) in \(M\), viz. { Bolt, Powell }, we have \(Jb\) and\(Jp\) coming out true in \(M\). However since Gatlin is not included inthe set { Bolt, Powell } \(Jg\) comes out false in \(M\), whence \(\neg Jg\)comes out true in \(M\). This is exactly as it should be: Usain Bolt andAssafa Powell are both Jamaican sprinters but Justin Gatlin is anAmerican rather than Jamaican sprinter. We represent these truths as:(i) \(|Jb|_M =\) True, (ii) \(|Jg|_M =\) False, (iii) \(|Jp|_M =\)True.

Maddy’s model \(M*\) is a non-standard or unintended one. Shethinks the name ‘Bolt’ refers to Gatlin, the name‘Powell’ refers to Bolt and the name‘Gatlin’refers to Powell. Furthermore she thinks thepredicate ‘is Jamaican’ applies to Gatlin and Bolt but notto Powell. That is, we have that in \(M*\): \(|b|_{M*} =\) Gatlin,\(|g|_{M*} =\) Powell, \(|p|_{M*} =\) Bolt and for \(J\) our solepredicate \(|J|_{M*} =\) { Gatlin, Bolt }.

In spite of her misunderstanding the intended referents for thesprinters’ names and the intended extension of the predicate‘is Jamaican’, Maddy’s model \(M*\) assigns exactlythe right truth-values for the 3 sentences above as readers can checkfor themselves. That is: (i) \(|Jb|_{M*} =\) True, (ii) \(|Jg|_{M*}=\) False, (iii) \(|Jp|_{M*} =\) True. The model \(M*\) is said to beapermuted model of \(M\). It is as if the objects in thedomain were systematically shuffled around whilst the labels were keptfixed, as Tim Button puts it [Button (2013). The example in the texthere was inspired by Button’s Fig 2.1 p.15].

Now consider a very different structure \(N\) the domain of whichconsists only of the natural numbers 3, 4 and 5. We are going tointerpret our simple sprinter theory in \(N\). So suppose \(|b|_N =3\), \(|g|_N = 4\), \(|p|_N = 5\). Suppose also that our predicate \(J\)is interpreted in \(N\) so as to have the same extension in \(N\) asthe English predicate ‘is an odd number’, i.e. \(|J|_N =\){3,5}. Then, clearly \(N\) is a model of our three sentence theorysince we have (i) \(|Jb|_N =\) True, (ii) \(|Jg|_N =\) False, (iii)\(|Jp|_N =\) True. Let us call structures whose domains consist ofnumbers ‘numeric’ structures.

The nub of Putnam’s Model-Theoretic Argument against realism is that the realist cannot distinguish the intended model for his/her total theory of the world from non-standard interlopers such as permuted models or ones derived from numeric models, even when total theory is a rationally optimal one that consists, as it must do, of aninfinite set of sentences and the realist is permitted to impose the most exacting constraints to distinguish between models. This is a very surprising result if true! How does Putnam arrive at it?

Putnam actually uses a number of different arguments to establish the conclusion above. The one of most concern to realists, as Taylor (2006) emphasises, is the one based on Gödel‘s Completeness Theorem. For this argument purports to prove that an ideal theory of the world could not be false, a conclusion flatly inconsistent with realism. It will be useful to first state the logical theorems on which the argument is based.

Let us start with the Completeness Theorem. In 1930 Kurt Gödel proved that a certain type of predicate logic, first-order logic without identity (which we shall sometimes denote as FOL), is complete in the sense that all sentences of that logic that are true under every interpretation can be derived within that logic. This means that every set of FOL sentences S that is ‘syntactically’ consistent (i.e. consistent in the sense that no contradiction can be derived from S within this logic), also has a model [See the entry onKurt Gödel for further details and a proof of the theorem].

The other theorem we shall need for the Model-Theoretic Argument below goes by the name of the Löwenheim-Skolem Theorem. To understand this theorem, one needs to first know something of the work of the nineteenth century mathematician Georg Cantor in set theory—specifically, his discovery of the different sizes of infinity. Cantor showed that infinite sets could be subdivided into those whose elements could be counted in the sense that their elements could be put into one to one correspondence with the natural numbers and those whose elements could not in this sense be counted. The set of integers is countable, as, surprising as it may seem, is the set of rational numbers. The set of real numbers, however, along with the set of complex numbers and the set of all subsets of the natural numbers are all uncountably infinite. Cantor called the size of an infinite set its cardinality [See the entry onthe early development of set theory].

The Löwenheim-Skolem Theorem states that if a a set of FOL sentences has an infinite model, it has a model whose domain is countably infinite. The Upward Löwenheim-Skolem Theorem states that if a countable set of FOL sentences has an infinite model of some cardinality \(\kappa\) then it has a model of every infinite cardinality [See the entrySkolem’s paradox for the history of the theorems and the philosophical issues concerning them].

Now realists believe that even a rationally optimal or ‘ideal’ theory of the world could be mistaken. Putnam essays to prove that this belief is incoherent. But why can’t an ideal theory be false? To admit that this is possible is to admit that there is a gap between what is true and what is ideally warranted by our best theory, something no anti-realist can afford. But an argument is needed to show this is not possible. Anti-realists have one in the Model-Theoretic Argument. It proceeds thus:

Suppose we had an ideal theory which passed every observational andtheoretical test we could conceive of. Assume this theory could beformalized in first-order logic. Assume also that the world isinfinite in size and that our formalized ideal theory \(T\) saysit is. Assume, finally, \(T\) is consistent. Then given theseassumptions, Putnam argues, we can show that \(T\) is alsotrue:

Firstly, as \(T\) is syntactically consistent, by theCompleteness Theorem for first-order logic, \(T\) will have amodel. Then by the Upward Löwenheim-Skolem Theorem, there existsa model elementarily equivalent to the model generated by theCompleteness Theorem that is of the same size as the world (since by the UpwardLöwenheim-Skolem Theorem \(T\) will have modelsofevery infinite size). Call this model \(M\).

Nothing in the construction of \(M\) guarantees that the objectsin its domain are objects in the real world. To the contrary, thedomain of \(M\) may be comprised wholly of real numbers forexample. So to obtain, as required, a model whose domain consists ofobjects in the world, use Löwenheim-Skolem Theorem oncemore to project the model \(M\) onto the world by generatingfrom \(M\) a new model \(W\) whose domain consists of theobjects in the world and which assigns to all the predicatesof \(T\) subclasses of its domain and relations defined on thatdomain.

We now have a correspondence between the expressions of thelanguage \(L\) in which \(T\) is expressed and (sets of)objects in the world just as the realist requires. \(T\) willthen be true if ‘true’ just means‘true-in-\(W\)’.

If \(T\) is not guaranteed true by this procedure it can only bebecause \(W\) is not theintended model. Yet all ourobservation sentences come out true according to \(W\) and thetheoretical constraints must be satisfied because T’stheses all come out true in \(W\) also. So the realist owes us anexplanation of what constraints a model has to satisfy for it to be‘intended’ over and above its satisfying everyobservational and theoretical constraint we can conceive of.

Suppose on the other hand that the realist is able to somehow specifythe intended model. Call this intended model \(W''\). Then nothing therealist can do can possibly distinguish \(W''\) from a permutedvariant \(W^*\) which can be specified following Putnam 1994b,356–357:

We define properties of being a cat* and being amat* such that:

1. In the actual world cherries are cats* and trees aremats*.
2. In every possible world the two sentences “A cat is on amat” and “A cat* is on a mat*”have precisely the same truth value.

Instead of considering two sentences “A cat is on a mat”and “A cat* is on a mat*” nowconsider only the one “A cat is on a mat”, allowing itsinterpretation to change by first adopting the standard interpretationfor it and then adopting the non-standard interpretation in which theset of cats* are assigned to ’cat’ in everypossible world and the set of mats* are assigned to’mat’ in every possible world. The result will be thetruth-value of “A cat is on a mat” will not change andwill be exactly the same as before in every possible world. Similarnon-standard reference assignments could be constructed for all thepredicates of a language. [See Putnam 1985, 1994b.]

4. Realist Responses

4.1 Language Use and Understanding

We now turn to some realist responses to these challenges. TheManifestation and Language Acquisition arguments allege there isnothing in an agent’s cognitive or linguistic behaviour thatcould provide evidence that they had grasped what it is for a sentenceto be true in the realist’s sense of ‘true’. How canyou manifest a grasp of a notion which can apply or fail to applywithout you being able to tell which? How could you ever learn to usesuch a concept?

One possible realist response is that the concept of truth is actuallyvery simple, and it is spurious to demand that one always be able todetermine whether a concept applies. As to the first part, it is oftenargued that all there is to the notion of truth is what is given bythe formula “‘\(p\)’ is true if and onlyif \(p\)”. The function of the truth-predicate is todisquote sentences in the sense of undoing the effects ofquotation—thus all that one is saying in calling the sentence“Yeti are vicious”true is that Yeti arevicious.

It is not clear that this response really addresses theanti-realist’s worry, however. It may well be that there is asimple algorithm for learning the meaning of ‘true’ andthat, consequently, there is no special difficulty in learning toapply the concept. But that by itself does not tell us whether thepredicate ‘true’ applies to cases where we cannotascertain that it does. All the algorithm tells us, in effect, is thatif it is legitimate to assert \(p\) it is legitimate to assertthat ‘\(p\)’ is true. So are we entitled to assert‘either Socrates did or did not sneeze in his sleep the nightbefore he took the hemlock’ or are we not? Presumably that willdepend on what we mean by the sentence, whether we mean to beadverting to two states of affairs neither of which we have anyprospect of ever confirming.

Anti-realists follow verificationists in rejecting the intelligibilityof such states of affairs and tend to base their rules for assertionon intuitionistic logic, which rejects the universal applicability ofthe Law of Bivalence (the principle that every statement is eithertrue or false). This law is a foundational semantic principle forclassical logic.

A more direct realist response to the Manifestation challenge pointsto the prevalence in our linguistic practices of realist-inspiredbeliefs to which we give expression in what we say and do. We assertthings like “either there were an odd or an even number ofdinosaurs on this planet independently of what anyone believes”and all our actions and other assertions confirm that we really dobelieve this. Furthermore, the overwhelming acceptance of classicallogic by mathematicians and scientists and their rejection ofintuitionistic logic for the purposes of mainstream science providesvery good evidence for the coherence and usefulness of a realistunderstanding of truth.

Anti-realists reject this reply. They argue that all we make manifestby asserting things like “either there were an odd or an evennumber of dinosaurs on this planet independently of what anyonebelieves” is our pervasive misunderstanding of the notion oftruth. They apply the same diagnosis to the realist’s belief inthe mind-independence of entities in the world and to counterfactualswhich express this belief. We overgeneralize the notion of truth,believing that it applies in cases where it does not, theycontend.

An apparent consequence of their view is that reality is indeterminatein surprising ways—we have no grounds for asserting thatSocrates did sneeze in his sleep the night before he took the hemlockand no grounds for asserting that he did not and no prospect of everfinding out which. Does this mean that for anti-realists the worldcontains no such fact as the fact that Socrates did one or the otherof these two things? Not necessarily. For anti-realists who subscribeto intuitionistic principles of reasoning, the most that can be saidis that there is no present warrant to assert that Socrates either didor did not sneeze in his sleep the night before he took thehemlock.

Perhaps anti-realists are right about all this. But if so, they needto explain how a practice based on a pervasive illusion can be assuccessful as modern science. Anti-realists perturbed by themanifestability of realist truth are revisionists about parts of ourlinguistic practice, and the consequence of this revisionist stance isthat mathematics and science require extensive and non-trivialrevision.

Much could be and has been said by anti-realists in response to thispoint. Standing back from the debate between the two sides is notalways easy but at least this point should be made. Nothing said sofar solves the Representation Problem, the problem of how our mentalsymbols get to target mind-independent entities in the first place,let alone the right ones. Some natural mechanism for generating theright links must be at work for it cannot just be a primitiveinexplicable fact that ‘the Big Bang’ refers to the BigBang. If this problem could be solved, the Manifestation andAcquisition challenges would, presumably, be answered. It would thenbe the burden of the other pragmatist-inspired anti-realist challengesto show that the realist cannot solve the Representation Problem.

4.2 Language Acquisition

The challenge to realism posed by language acquisition is to explainhow a child could come to know the meanings of certain sentenceswithin his/her language: the ones which the realist contends haveundetectable truth-makers associated with them. How could the childlearn the meanings of such sentences if these meanings are determinedby states of affairs not even competent speakers can detect?

How should realists respond to this challenge? They should questionthe publicity of meaning principle as it applies to language learningand they should question this principle on empirical as well asconceptual grounds. That the meaning of a word is in some sensedetermined by its use in a given language is little more than aplatitude. That the meaning of a word is exhaustively manifest in itsuseas an instrument of communication is not.

The evidence from developmental psychology indicates some meaning ispre-linguistic and that some pre-linguistic meaning or conceptualcontent does indeed relate to situations that are not detectable bythe child. For example, psychologists have discovered systems of coreknowledge activated in infancy that govern the representationof,inter alia concrete objects and human agents [see Spelke2003; Spelke and Kinzler 2007]. An interesting finding frompreferential gaze experiments suggests 4 month old infants representoccluded objects as continuing behind their barriers.

Even more surprisingly, 2 day old chicks exposed to occluded objectsfor the first time do so as well [Spelke 2003]! Chicks who in theirfirst day of life had imprinted on a centre-occluded object wereplaced in an unfamiliar cage on their second day and presented with achoice between two versions of the object placed at opposite ends ofthe cage. In one version, the visible ends were connected; in theother these ends were separated by a visible gap matching the occluderthey’d seen the day before. “Chicks selectively approachedthe connected object, providing evidence that they, like humaninfants, had perceived the imprinted object to continue behind itsoccluder” [Spelke 2003, p.283].

So there is evidence that ‘verification-transcendent’conceptual content might be laid down in the earliest stages ofcognitive development.

Recent studies of conflict detection in reasoning suggest theanti-realist’s restriction of the basis for ascriptions ofmeaning to an overtly behavioural one is unwarranted. It iswell-attested that subjects unfamiliar with logic evince belief-biaswhen they reason, accepting conclusions as following from premisesonly when those conclusions accord with their background beliefs. Onthe basis of their inferential dispositions and their think-out-loudprotocols, most psychologists had concluded that these subjects aresimply unaware of the simple logical rules they appear to flout in theproblematic ‘conflict’ cases.

This is not necessarily so, however. In recent years psychologistsusing more subtle measures to detect recognition of logical rules havefound that even the poorest reasoners evince wide range of tacitbehavioural and neurological symptoms when they deny the conclusionsof valid conflict arguments: (i) lower confidence levels (ii) higherarousal (iii) more frequent saccades to the conflict conclusion andpremises (iv) impaired memory access to cued beliefs that conflictwith normative logical rules (v) heightened activity in an area of thebrain, the anterior cingulate cortex, known to be associated withconflict detection [See for instance De Neys & Glumicic 2008,Franssens & De Neys 2009].

4.3 Radical Skepticism

The Brains-in-a-Vat argument purports to show that, given semanticexternalism, realism is incoherent on the grounds that it is bothcommitted to the genuine possibility of our being brains in a vat andyet entails something inconsistent with this: namely, that were we tobe so envatted we could not possibly have the thought that wewere!

Realists have three obvious responses.

1. Deny realism entails that we could be brains in a vat.
2. Deny semantic externalism.
3. Deny there is any inconsistency between our being brains in a vatand our inability to think that we were brains in a vat were we to beso.

As for (i), naturalistic realists do question the coherence of theidea of our being brains in a vat. For them there is no externalvantage point from which one can assess our best overall theory andyet the skeptic’s hypothesis feigns to occupy just such avantage point. How so? By using terms which derive their meaning fromsuccessful theory to pose a problem which, if intelligible, would robthose very terms of meaning. In a similar vein some naturalisticrealists have claimed that the mad scientists face an insolubleproblem of combinatorial explosion the moment they give you anysignificant exploratory and volitional powers in the virtual world inwhich you are imprisoned.

As to the latter, it may be that the clever alien scientists havegenerated a convincing illusion of significant exploratory andvolitional powers in the mind of the poor envatted brain. Whether theskeptic’s prospect is intelligible only at the cost of robbingthe very terms in which it is framed of meaning is much more difficultto assess, however.

What of option (ii)—denying semantic externalism? Is this reallya live prospect for realists? The answer is“Yes”. Semantic externalism no longer commands theconsensus amongst realists that it did when Putnam formulated hisBrains-in-a-Vat argument—realists are today divided over thequestion of externalism. David Lewis, a prominent realist, rejectedexternalism in favour of a sophisticated semantic internalism based ona ‘Two-Dimensional’ analysis of modality. Frank Jackson[Jackson, F. 2000] contributed to the development of this internalist2D semantics and used it to formulate a version of materialismgrounded on conceptual analysis that provides a useful and persuasivemodel of a naturalistic realist’s metaphysics.

Other realists reject externalism because they think that theRepresentation Problem is just a pseudo-problem. When we say thingslike “‘cat’ refers to cats” or“‘quark’ refers to quarks” we are simplyregistering our dispositions to call everything we considersufficiently cat-like/quark-like,‘cat’/’quark’.

According to these semantic deflationists, it is just a confusion toask how the link was set up between our use of the term ‘the BigBang’ and the event of that name which occurred some fourteenbillion years ago. Some naturalistic story can, presumably, be toldabout how creatures like us developed the linguistic dispositions wedid, in the telling of which it will emerge how we come to assertthings like “the entropy of the Big Bang was verylow”.

But it is a moot question whether semantic deflationism reallydissolves the Representation Problem or merely fails to face up toit. However the story about the origins of our linguistic dispositionsis told, it had better be that our utterances of “the entropy ofthe Big Bang was very low” somehow end up evincing just theright sort of differential sensitivity to the Big Bang’s havinglow entropy. For if all there is to the story are our linguisticdispositions and the conditions to which they are presently attuned,the case has effectively been ceded to the anti-realist who denies itis possible to set up a correlation between our utterances or thoughtsand the mind-independent states of affairs which, according to themetaphysical realist, uniquely make them true.

The most effective realist rejoinder is (iii). We shall return to thisresponse after we have reviewed Putnam’s Brains-in-a-VatArgument, BIVA.

How does Putnam prove we can know we are not brains in a vat? Tounderstand Putnam’s argument, we need to first recall the‘Twin-Earth’ considerations used to support SemanticExternalism: on Twin-Earth things are exactly as they are here onEarth except for one difference—whereas for Earthly humanswater has the chemical composition H₂O, for ourdöppelgangers on Twin-Earth, twumans, water is instead composedof some substance unknown to us on Earth, XYZ. Now when you and yourtwuman counterpart say (or think) “’Water’ refers towater” both of you utter (or think) truths. But which truth youboth think or utter differs. For humans “’Water’refers to water” expresses the truth that the term‘water’ in English refers to that substance whose chemicalcomposition is H₂O. For our twuman Twin-Earth counterparts,however, their sentence “’Water’ refers towater” expresses the truth that their term ‘water’in Twenglish refers to that substance whose chemical composition isXYZ.

With these points about Externalism in mind, consider Putnam’sBIVA [we follow Anthony Brueckner’s formulation here: see theentryskepticism and contentexternalism]. Let us call whatever it is that an envattedbrain’s symbol ‘tree’ refers to, if it refers atall, \(v\)-trees. Then the BIVA is:

• (1)If I’m a BIV then it is not the case that if my word‘tree’ refers it refers to trees.
• (2)If my word ‘tree’ refers it refers to trees.
• (3)So, I amnot a BIV.

Now (1) is correct: if I am a brain-in-a-vat then my symbol‘tree’ cannot refer to trees since there aren’t anytrees in the vat-world—a BIV’s ‘tree’ symbolrefers to \(v\)-trees,not trees. But what reason do we haveto believe (2)?

Just as we can do, our twuman döppelgangers on Twin-Earth canjustifiably declare “If my word ‘water’ refers itrefers to water.” But despite the fact that the twumans’language Twenglish is a homophonic duplicate of English,‘water’ on Twin-Earth refers totwater, XYZ, notwater, H₂O.

Instead of (2) we really need two premises incorporating distincthypotheses about the language I am speaking:

• (2E)If the language I am speaking is English and my word‘tree’ refers, it refers to trees.
• (2V)If the language I am speaking is Venglish (Vattish English) andmy word ‘tree’ refers, it refers to trees.

To preserve the logical form of the original argument, (1) must alsobe modified to accept each hypothesis about the language I am speakingso that it now bifurcates into:

• (1E)(1E) If I’m a BIV then it is not the case that if the language Iam speaking is English and my word ‘tree’ refers it refersto trees.
• (1V)If I’m a BIV then it is not the case that if the language Iam speaking is Venglish and my word ‘tree’ refers itrefers to trees.

The problem with Putnam’s BIVA is that while (1V) is true, (2V)is false whereas although (2E) is true, (1E) is false. On eitherhypothesis about the language I am speaking, it appears that there isno sound argument to the conclusion that I am not abrain-in-a-vat.

Suppose the BIVA is unsound. What would this show? Even if the BIVAfails to achieve its goal, Putnam’s challenge to the realistremains unanswered. This was to show how realism could be coherent ifit is committed both to:

• (I)The real possibility that we are brains-in-a-vat

and to the consequence that:

• (II)Were we to be BIVs we could not have the thought that we were.

In fact, there is nological incoherence in accepting both (I)and (II)—as the figure below illustrates. There is thus nological incoherence in believing both that it is possible that one isa BIV and that if one is a BIV one could never come to know this.

Figure. If we arenot in factbrains-in-a-vat (so that the hypothesis \(v\) that we are brains in avat is false, \(\neg v\) is true at \(w^*\), the actual world) we cannonetheless entertain \((E)\), the hypothesis that we are (so that\(Ev\) is true at \(w^*\)), recognizing as we do so that were we toinhabit a world such as \(w'\) in which we are brains-in-a-vat (\(v\)holds at \(w'\), we would lack the semantic resources to articulatethoughts reflecting our own envatted state so that wecould notso much as entertain the thought that we were brains-in-a-vat (\(\negEv\) holds not only at \(w'\) but at all worlds accessible from \(w'\)such as \(w''\), \(w'''\), etc).

Nick Bostrom has recently argued it is quite likely that we humans areactuallyvirtual humans: computer simulations of flesh andblood creatures. Bostrom reasons that if our mental lives can besimulated it is in fact extremely likely that our distant descendants(more intelligent or at least more technologically advanced‘post-human’ successors) will eventually create such asimulation in which case it is more likely that we are the unwittingdenizens of a simulated world than the flesh and blood inhabitants ofthe real world we take ourselves to be. At least this will be sounless the chances that creatures of our intelligence are doomed tobecome extinct before reaching the technological sophistication tocreate simulations are overwhelmingly large or else almost no suchtechnologically capable civilizations have any interest in simulatingminds like ours in the first place [Bostrom, N., 2003].

Bostrom’s argument makes it look unlikely that we can knowapriori that we arenot brains-in-a-vat, when BIVs areunderstood to be virtual humans in a simulation. If this is correct,Putnam’s attempt to prove we are not BIVs must beflawed. Whether the Simulation Argument poses further problems forrealism is a moot point.

4.4 Conceptual Schemes and Pluralism

In this section I shall outline the anti-realist’s idea ofconceptual relativity and indicate some ways realists might wish tocontest that notion. I shall not try to distinguish between conceptualrelativism and conceptual pluralism. Conceptual relativism lookshighly counter-intuitive to realists since it seems to make theexistence of all things relative to the classificatory skills ofminds. Whilst it may be quite plausible to think that moral values orperhaps even colours might disappear with the extinction of sentientlife on Earth, it is not at all plausible to think that trees, rocksand microbes would follow in their train. If that is what it commitsus to, then the idea of conceptual relativity looks highlysuspect.

This is not how anti-realists understand conceptual relativity,however. As they see things, we accept a theory which licenses us toassert “ Electrons exist ” and also licenses us to assert“if humans were to disappear from this planet, electrons neednot follow in their train” since the theory assures us that theexistence of electrons in no way causally depends on the existence ofhumans. For the anti-realist our well-founded practices of assertionground at one and the same time our conception of the world and ourconception of humanity’s place within it.

Realists might still worry that whether there are to be any electronsin the anti-realist’s ontology apparently depends upon theconceptual schemes humans happen to chance upon. The relativity ofexistence to conceptual scheme is, in this respect, quite unlike therelativity of simultaneity to frame of reference.

Still, we have actual instances of conceptual schemes which explainthe same phenomena equally well yet which realists must adjudgelogically incompatible anti-realists maintain. The earlier example ofcompeting theories of space-time was a case in point. On one theory,space-time consists of unextended spatiotemporal points and regions ofspace-time are sets of these points. According to the second theory,space-time consists of extended spatiotemporal regions and points arelogical constructions—convergent sets of regions.

Anti-realists regard two theories as descriptively equivalent if eachtheory can be interpreted in the other and both theories explain thesame phenomena. Is there nothing more to the notion of descriptiveequivalence than this? Realists might not accept that thereisn’t.

At the stroke of midnight Cinderella’s carriage changes into apumpkin—it is a carriage up to midnight, a pumpkinthereafter. According to the region-based theory which takes temporalintervals as its primitives, that’s all there is to it. But ifthere are temporal points, instants, there is a further fact leftundecided by this story—viz, at the moment of midnight is thecarriage still a carriage or is it a pumpkin?

So does the region-based theory fail to recognize certain facts or arethese putative facts merely artefacts of the punctate theory’sdescriptive resources, reflecting nothing in reality? We cannotdeclare the two theories descriptively equivalent until we resolvethis question at least.

In general, then, realists either dismiss cases of apparent logicalincompatibility between two descriptively equivalent rival theories asmerely apparent or question the descriptive equivalence of the twotheories.

The conceptual relativity we have been discussing has its roots inCarnap’s views about linguistic frameworks. As we saw in section2, Carnap rejected the idea that we could answer existence questionsin any absolute sense. If we ask, as we did before, whether there areirrational numbers \(a, b\) suchthat \(a^b\) is rational, Carnap requires wefirst specify a framework before tendering any reply. If we chooseclassical mathematics the answer is “Yes” but if we chooseintuitionistic mathematics, the answer is “There is no warrantfor asserting such \(a\) and \(b\) exist.” Soaccording to Carnap whilst the claim that irrationalnumbers \(a, b\) suchthat \(a^b\) is rationalexist-in-CMis perfectly true, the claim that such \(a, b\)existsimpliciter is meaningless.

We saw in section 2, though, that the questions dividing realists fromanti-realists appear to survive indexation to frameworks. Revisionaryintuitionists who object to non-constructive existence proofs inmathematics are not just expressing apreference forconstructive methods: they find the notion of non-constructiveexistenceunintelligible not just unappealing:

So consider this case: Ernie looks into his bag and sees there are 3coins and nothing else, so he announces “There are exactly 3objects in my bag.” Max looks into Ernie’s bag and shakeshis head “No Ernie there are 7 objects in your bag!” hecorrects him. The Carnapian pluralist feels she can defuse theconflict and accommodate both points of view by maintaining thatwhilst 3 objects exist-in-\(E\) (where \(E\) isErnie’s everyday framework), 7 objects exist-in-\(M\)(with \(M\) Max’s mereological framework). But even if Maxcan endorse both of these claims (since the mereological objectsinclude Ernie’s 3 marbles), it is not at all certain Ernie cando so. If Ernie is unpersuaded that mereological fusions of objectsare themselves objects, then Max’s putative truthmaker for hisframework-relative existence claim “7 objectsexist-in-\(M\)” will be unconvincing to him.

For this case, there seems little reason to accept thepluralist’s description that whilst 3 objectsexist-in-\(E\), 7 objects exist-in-\(M\) and some goodreasons not to. By ‘object’ Ernie means ordinary object,by ‘object’ Max means mereological object. Nothing deeperthan that is required to explain their disagreement. What isrelativized in the first instance is not existence or truth butmeaning. To the non-relativist, it looks as if pluralists have simplymistaken a plurality of meanings for a plurality of modes ofbeing.

This is not to say thatall there ever is to such disputes is amisunderstanding about the meanings of words. There is still thesubstantive question of which of two theories conceived as rivals istrue. Thus in the dispute between classical and intuitionist logiciansthe attempt to import distinctive intuitionistic connectives intoclassical languages containing classical connectives results in the‘intuitionistic’ connectives obeying classical logicallaws.

The point is rather thatwhether there are mereological (orordinary) objects ought not to be prejudged by stipulating they existwithin some framework nor can it be resolved satisfactorily by thismeans. By way of comparison, consider the question of whetherspace-time is continuous or discrete. This looks like a substantiveempirical question. If String Theory which says space-time iscontinuous and Quantum Loop Gravity Theory which says it is discretewere to prove equally good ‘final’ theories of space-timeas judged by all the evidence, we would naturally take this todemonstrate that the matter of whether space-time was a continuum hadturned out to be empirically undecidable, not that space-time hadturned out in one sense to be continuous (continuous_ST) butin another to be discrete (discrete_QLGT)—if we canknow this type of thing at all, this is something we can knowapriori without heedingany evidence. Rightly or wrongly, wewould take the question “Is Space-Time continuous ordiscrete?” to remain unsolved in the envisaged circumstances,rather than equally well though divergently solved. We might then goon to cite this case as a good example of underdetermination of theoryby evidence.

Moreover, the space-time and mereological examples bring to lightanother problem for pluralism. If there is no framework-neutralmetalanguage neo-Carnapians can deploy to state their purportedframework-relative ontological truths, how can there be a fact to thematter as to what things exist in a framework? Realists might thenwonder whether the pluralist’s position doesn’t threatento become ineffable.

4.5 Models and Reality

If metaphysical realism is to be tenable, it must be possible for eventhe best theories to be mistaken. Or so metaphysical realists havethought. Whence, such realists reject the Model-Theoretic Argument MTAwhich purports to show that this is not possible. Here is an informalsketch of the MTA due to van Fraassen [1997]:

Let \(T\) be a theory that contains all the sentences we insistare true, and that has all other qualities we desire in an idealtheory. Suppose moreover that there are infinitely many things, andthat \(T\) says so. Then there exist functions (interpretations)which assign to each term in \(T\)’s vocabulary anextension, and which satisfy \(T\). So we conclude, to quotePutnam, “\(T\) comes out true, true of the world, providedwe just interpret ‘true’ as TRUE(SAT)”.

Here ‘TRUE(SAT)’ means “true relative to a mappingof the terms of the language of \(T\) onto (sets of) items in theworld”.

But why should we interpret ‘true’ as TRUE(SAT)? Becausetruth is truth in an intended model and, Putnam argues, amongst allthe models of \(T\) that make all its theses come out true thereis guaranteed to be at least one that passes all conceivableconstraints we can reasonably impose on a model in order for it to bean intended model of \(T\).

Realists have responded to the argument by rejecting the claim that amodel \(M\) of the hypothetical ideal theory \(T\) passesevery theoretical constraint simply because all of the theory’stheses come out true in it. For there is no guarantee, they claim,that terms stand in the right relation of reference to the objects towhich \(M\) links them. To be sure, if we impose anothertheoretical constraint, say:

Right Reference Constraint (RRC): Term \(t\) refers toobject \(x\) if and only if \(Rtx\) where \(R\) is the rightrelation of reference,

then \(M\) (or some model based on it) can interpret this RRCconstraint in such a way as to make it come out true.

But there is a difference between a model’s making somedescription of a constraint come out true and its actually conformingto that constraint, metaphysical realists insist [Devitt 1983, 1991;Lewis 1983, 1984].

For their part, anti-realists have taken the metaphysicalrealist’s insistence on a Right Reference Constraint to be‘just more theory’—what it is for a model toconform to a constraint is for us to be justified in asserting that itdoes. Unfortunately, this has led to something of astand-off. Metaphysical realists think that anti-realists are refusingto acknowledge a clear and important distinction. Anti-realists thinkrealists are simply falling back on dogmatism at a crucial point inthe argument.

On the face of it, the Permutation Argument presents a genuinechallenge to any realist who believes in determinate reference. But itdoes not refute metaphysical realism unless such realism is committedto determinate reference in the first place and it is not at allobvious that this is so.

Realist responses to this argument vary widely. At one extreme are the‘determinatists’, those who believe that Nature has set upsignificant, determinate referential connections between our mentalsymbols and items in the world. They contend that all the argumentshows is that the distribution of truth-values across possible worldsis not sufficient to determine reference.

At another extreme are ‘indeterminatists’, realists whoconcede the conclusion, agreeing that it demonstrates that word-worldreference is massively indeterminate or ‘inscrutable’.

Some infer from this that reference could not possibly consist incorrespondences between mental symbols and objects in the world. Forthem all that makes ‘elephant’ refer to elephants is thatour language contains the word ‘elephant’. This isDeflationism about reference.

In between these two extremes are those prepared to concede theargument establishes the real possibility of a significant andsurprising indeterminacy in the reference of our mental symbols butwho take it to be an open question whether other constraints can befound which pare down the range of reference assignments to just theintuitively acceptable ones. On this view ‘elephant’ maypartially refer to elephants according to one acceptable referenceassignment and may partially refer to elephant-stages or undetachedelephant parts according to other such assignments, but not refer,even partially, to quolls or quarks. In this spirit, Hartry Field[1998] has argued that an objective referential indeterminacy he calls‘correlative indeterminacy’ could exist quite undetectedin linguistic practices such as ours that assume determinacy ofreference for terms:

If ‘entropy’ partially refers to \(E_1\)and \(E_2\), then we can say that relative to anassignment of \(E_1\) to ‘entropy’,‘refers’ refers to a relation that holds between‘entropy’ and only one thing, viz. \(E_1\);and analogously for \(E_2\). In this way we can get theresult that even if ‘entropy’ partially refers to manythings (and hence does not determinately refer to anything), still thesentence “‘Entropy’ refers to entropy and nothingelse” comes out true. (Indeed, determinately true: true on everyacceptable combination of the partial referents of‘entropy’ and ‘refers’). The advocate ofindeterminacy can still ‘speak with thevulgar’. [loc. cit., p. 254]

The simplest and most direct response to the MTA questions itsvalidity—since all versions of the MTA challenge the realist tosay why terms arenot related to their right referents in thealternative models Putnam constructs, metaphysical realists have beenquick to respond. Thus Devitt and Lewis claim that Putnam’salternative model \(M\) has not been shown tosatisfyevery theoretical constraintmerely bymaking some description of each theoretical constraint true.

Skolem’s Paradox in set theory seems to present a strikingillustration of Lewis’s distinction. The Löwenheim-SkolemTheorem states that every consistent, countable set of first-orderformulae has a denumerable model, in fact a model in the set ofintegers \(\mathbb{Z}\). Now in ZF one can prove the existence of sets with anon-denumerable number of elements such as the set \(\mathbb{R}\) of realnumbers. Yet the ZF axioms comprise a consistent, countable set offirst-order formulae and thus by the Löwenheim-Skolem Theorem hasa model in \(\mathbb{Z}\). So ZF’s theorem \(\phi\) stating that\(\mathbb{R}\) is non-denumerable will come out true in a denumerable model\(\mu\) of ZF!

How can this be? One explanation is that \(\mu\) makes \(\phi\)true only at the cost of re-interpreting the term‘non-denumerable’ so that it no longermeansnon-denumerable. Thus \(\mu\) is not the intendedmodel \(M^*\) of ZF. It looks as if the metaphysicalrealist has a clear illustration of Lewis’s distinction at handin set theory.

Unfortunately for the realist, this is not the only explanation. Infact, Putnam used this very example in an early formulation of theMTA! Just because there are different models thatsatisfy \(\phi\) in some of which \(\mathbb{R}\) is non-denumerable butin others of which (such as \(\mu\)) \(\mathbb{R}\) is denumerable, Putnam argued, it is impossible to pin down the intended interpretation of‘set’ via first-order axioms. Moreover, well before Putnam, Skolem and his followers had taken the moral of Skolem’sParadox to be that set-theoretic notions are indeterminate [For further discussion, see the entry onSkolem’s paradox].

Now the thesis the metaphysical realist has to establish is that anideal theory could be false. If truth for our imagined ideal theory\(T\) is truth on its intended model(s) \(M^*\) this amounts to thepossibility that some thesis of \(T\) come out false in \(M^*\) evenif there are other models wherein that thesis along with every otherthesis of \(T\) comes out true. This brings us to the Right ReferenceConstraint (RRC) once more and the question of what it is for \(T\) tosatisfy (RRC). Discussing this issue in connection with set theoryTimothy Bays [2001] writes:

When a philosopher claims that the intended models of set theoryshould be transitive, she isdescribing the structures whichare to count as models for her axioms; she isn’t just adding newsentences to be interpreted at Putnam’s favoritemodels. Similarly, when she claims that intended models should satisfysecond-order ZFC, she is explainingwhich semantics (and,more specifically, which satisfaction relation) her axioms should beinterpreted under; she isn’t just adding new axioms to beinterpreted under a (first-order) semantics of Putnam’schoosing.

Putnam [1985] responded to this point by charging the realist withquestion-begging: simply assuming that terms such as‘satisfaction’ or ‘correspondence’ refer tothose relations to which the realist wishes them to refer. But, asBays points out, no questions are begged if realists assume for thepurposes of argument that semantic terms such as these refer to theintended relations. It is up to the anti-realist to show that thisassumption is flawed. Nonetheless, merely invoking an intuitivedistinction does not show the distinction marks a genuinedifference. So if realism is to be sustained, there had better be somemore convincing or, at any rate, less contentious examples thanSkolem’s Paradox to illustrate Lewis’s alleged differencebetween a model M’ssatisfying a constraint andM’s merely making a description of the constraint true. Arethere?

Michael Resnick thinks so [Resnick 1987]. Putnam maintainedthat \(M\), the model he constructs of the idealtheory \(T\), is an intended model because it passes everyoperational and theoretical constraint we could reasonably impose. Itpasses every theoretical constraint, he argues, simply because itmakes every thesis of \(T\) true. But unless the ReflectionPrinciple(RP) below holds, Resnick argues, this inference isjust anon-sequitur:

• (RP)To any condition \(f\) that a model of a theorysatisfies, there corresponds a condition \(C\) expressible in thetheory that that theory satisfies.

However, this principle is false. The simplest counterexample to it,Resnick points out, is Tarskian truth. Suppose we imposeon \(T\)’s model \(M\) acondition \(f^*\) that \(M\) makes allof \(T\)’s theses come out true. Then, unless \(T\) iseither inconsistent or too weak to express elementary arithmetic notruth predicate will be definable in \(T\). Whence there will beno condition \(C\) expressible in \(T\) corresponding tothis condition \(f^*\) on \(T\)’smodel(s) \(M\).

Resnick concludes (ibid):

Any true interpretation of \(T\) whatsoever—even one whichdoes not satisfy \(C\)—will make true every thesisof \(T\), including T’s assertion that \(C\)is satisfied. Which suffices to block the ‘just moretheory’ gambit.

If this is right, the metaphysical realist can indeed resist whatLewis calls “Putnam’s incredible thesis” that anideal theory \(T\)has to be true. More recently, therehave been some sophisticated anti-realist attempts to buttress theModel-Theoretic Argument against Lewis-styled criticisms [Taylor 2006;Button 2013]. Whether these newer formulations of the MTA succeed indoing so is an open question.

5. Summary

We have considered a number of semantic challenges to realism, thethesis that the objects and properties that the world contains existindependently of our conception or perception of them. Thesechallenges have come from two camps: (1) neo-verificationists led byDummett who assimilate belief in mind-independent world to a belief ina verification-transcendent conception of truth which they profess tofind unintelligible, and (2) pragmatists led by Putnam who alsoquestion the intelligibility of the realist’s mind-independentworld but for reasons independent of any commitment toverificationism.

On all fronts, debate between realists and their anti-realistopponents is still very much open. If realists could provide aplausible theory about how correspondences between mental symbols andthe items in the world to which they refer might be set up, many ofthese challenges could be met. Alternatively, if they could explainhow, consistently with our knowledge of a mind-independent world, nosuch correspondences are required to begin with, many of theanti-realist objections would fall away as irrelevant. In the absenceof such explanations it is still entirely reasonable for realists tobelieve that the correspondences are in place, however, and there can,indeed, be very good evidence for believing this. Ignorance ofNature’s reference-fixing mechanism is no reason for denying itexists.

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Acknowledgments

Thanks to Jesse Alama and a subject editor for theStanfordEncyclopedia of Philosophy for their helpful criticisms andcorrections. Special thanks to Marinus Ferreira for many usefulsuggestions and for help in writing and editing this entry.