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How Can We Ever Understand One Another?

Kripke and the Relation Between Meaning and Use

The forces of evolution and culture have shaped human language into our primary instrument for contact with other minds. The millennia of our cultural and intellectual development have seen language evolve from primitive vocalisations, simple modulations of animal sounds, into the most immensely complex, subtle and expressive mechanism yet devised by one mind for the influencing of another. Language is the most potent of the mind tools in the kitbag of our cultural technologies.

In this essay we shall briefly discuss the purpose of language and ask how it confers such a powerful selective advantage on those creatures able to use it? This raises the central question as to the nature of meaning – how does language allow more than just syntax to be transferred between two minds in a way that gives rise to our rich many-leveled interpretation of a conversation? On what basis do we understand each other’s utterances: through rule-following, dispositional tendencies, socio-cultural justifications? We shall examine the case for rule following as the basis of language use and briefly discuss some responses to Kripke’s sceptical assertion that there are in fact no underlying rules, that meaning is a chimera in the mist of evaporating truth-conditions. Are we in fact babbling inmates of the Tower of Babel or do we have some provably sound basis for understanding the emotional, literal and intentional meaning of the speaker? This is the key question that lies at the heart of the philosophy of language.

Let us begin by examining the original purpose of natural language as it has evolved in human society. Man is the only animal which exhibits this universal capacity to exchange complex and subtle concepts by means of modulated sound. Many animals use systems of instinctive signalling to convey simple propositions. For example, the dance of the honey bee expresses a number of simultaneous ideas important to the survival of the hive: distance and direction to a food source relative to the position (angle) of the sun. Other animals use conspicuous behaviour to convey important information of benefit to other members of their society: alarm calls in birds, screaming and pointing in chimpanzees, the ‘stotting’ of Thomson’s gazelles. All of these are essentially instinctive or conditioned responses to regular and frequently encountered stimuli – the behaviour is simple, invariant, unambiguous and hence easily recognised and understood by other members of the species. Most animals then have a small repertoire of signals from which to select an appropriate response given some triggering event, such as the perception of a cheetah in the long grass. Such signals are usually binary in character - either displayed (‘on’) or absent (‘off’) - and are incapable of conveying more than a single atomic assertion about the world: ‘there is a hawk’ for example, rather than ‘there is a small hawk flying at one hundred feet twenty degrees to the left of the sun.’

Man however is markedly different. Before fire, before the wheel and the iron blade, man possessed the gift of speaking in tongues. This single ability is a major differentiating factor between us and the higher primates – more fundamental than our use of tools, our hairlessness or our upright gait. But why did we evolve this remarkable ability in the first place? Language use after all requires both a large and highly developed brain and a uniquely developed vocal tract; both features requiring a significant investment in time and resources by the process of evolution. What is it about language that conveys such a winning selective advantage on its users?

It is difficult to find a convincing evolutionary argument why a complex verbal language per se should develop. The general consensus is the need for communication – to enable the exchange of mental concepts and images between two or more individuals It could be suggested that hunter gatherer societies would be more successful where the groups of hunting males were able to better co-ordinate their strategy and attacks through the use of language. Language however seems an unnecessarily expensive technology to develop for just this purpose – lions and hunting dogs manage to choreograph co-operative hunting strategies perfectly well without words. Forgetting the now discredited group selectionist viewpoint, how does the use of language give the utterer a personal advantage, a route towards the better fulfilment of his or her selfish ends rather than an advantage to the tribe as a whole?

A plausible answer it would seem lies in sex, i.e. the problem of attracting or winning the highest calibre mate available in the breeding community. Writers such as Matt Ridley point out that wit, intelligence and articulate conversation are high on the list of attractive features sought by both sexes. The art of seduction then it seems requires a sophisticated language facility incorporating recursion, relative clauses, subjunctives etc. A more Machiavellian justification for language is the need to bend others to our will – the purpose of language is not the sharing of truths but a means of deception aimed at causing others to behave in ways that will ultimately reap our reward.

But surely the important question is how we can and do understand the meaning of each other’s utterances. The meaning of a spoken sentence is a complex concept which has many levels of abstraction. The tokenising of a stream of modulated sound into phonemes and hence into words is a mechanical process performed by specialised areas of the brain. Given an identified stream of words our task is then to derive the syntactic structure of the sentence in terms of its parts and how they are combined in what relation. This is the process of natural language parsing which uncovers the deep structure of a sentence by means of a non-monotonic pattern matching process. Multiple trial parses are tried in parallel until the parse tree that best matches the ‘shape’ of the sentence is discovered; isolating the clauses and sub-clauses, noun and verb phrases, subject and object in the sentence. The task then is to abduce the surface meaning by identifying the sense and reference of each term. What does each term mean in virtue of itself and how is this mediated by its use within the sentence? This will involve analysis of the context of use within the body of surrounding text (speech) such that phonetically identical words such as ‘would’ and ‘wood’ can be disambiguated. At this point we arrive at our first cut of the meaning of the sentence – its public meaning as a piece of clear text where we take each term to mean what it says in accordance with the ‘public rules of usage’ (see below for discussion of what this means).

We are still some way however from the ‘meaning’ in the full sense i.e. the speaker’s meaning. What did the speaker (author) actually intend by this sentence. What did he intend us to believe by it and what do we believe about his intentions? Here we must draw on a variety of socially conditioned skills honed during our extended childhood where we have learned the rules of the language game in complex interaction with other minds that frequently use language to deceive us. We have evolved brains which maintain a detailed internal model of the world – a semantic model based upon networks of procedural knowledge which encapsulates the behaviour of the physical world. Our world model allows us to play out candidate strategies and actions mentally rather than physically – we are Popperian creatures who can let our hypotheses die in our steads. A large and complex part of this world model is devoted to modelling the likely inner mental states of others – our folk psychology module if you like. It is this demand on our mental capacity which has fuelled the evolutionary drive towards larger and larger brains over the past few million years. No other aspect of our lives as hunter-gathers can provide sufficient explanation for such a disproportionate increase in mental capacity – tool using, co-operative hunting, agriculture are all insignificant in comparison with the need to deduce what someone else is thinking or what they actually mean by what they say.

The question remains then as to how we impose meaning upon a string of tokens arranged in some ordered relation. The empiricist position says that words have acquired their public meanings through experience and association. The brain is a powerful associative mechanism and if the same set of phenomenal experiences are always accompanied by the same word(s) (linguistic experiences) then the two will become correlated. This simple view can be caricatured as the picture theory of meaning where each word conjures up its attendant mental image. The compositional nature of language allows us to understand references to new, impossible or imaginary objects by combining known components – the image of the ‘golden mountain’ or a fish riding a flying bicycle readily spring to mind.

Such a theory of meaning would suffice in a primitive society where conversation was restricted to discussion about the best place to find edible roots but fails to cope with the most basic elaborations. What images for example do the logical connectives AND, OR and NOT conjure up and what about descriptions of our inner mental states: pain, anger, anxiety? To find a more robust model of meaning we must discard the idea that words have some invariant meaning in isolation and move towards a more holistic approach. Surely words acquire meaning not from some inner property of themselves but from the ways that they are used within language. Words extract their meanings from the context within which they are embedded – the relationship with other words, the form of the sentence (subject-predicate, imperative, interrogative etc.) How then is it possible for us to understand one another if meaning is not derived from some innate property of the words themselves but from the way in which they are used? Do we unconsciously make use of some set of public rules which determine the appropriate use and form of words to use to convey our intention? In using the same public language both parties in a conversation attempt to conform to the same normative conventions in order to compose and deconstruct sentences. Can we explain understanding then in terms of conscious rule following?

To answer this we must be clear about what we mean by a rule. Rule following is a conscious intentional process which differs from the execution of an algorithm or to the mere conforming to a rule. An algorithm is a deterministic procedure comprising a sequence of simple steps which when performed in the correct order will reliably achieve some prescribed result. Algorithms are substrate neutral in that it does not matter what is performing the algorithm - mindless mechanism or conscious being. Executed correctly a well formed algorithm will provide guaranteed results – the standard algorithm for performing long division by hand for example. Rule following however is a qualitatively different process from the mindless performance of an algorithm – it requires the conscious intention of the performing agent to apply each step correctly so as to conform to the rule. This is of course different from the mere conformance to a rule – the motion of the planets for example conforms to Kepler’s and Newton’s laws and yet the individual planets are not consciously calculating each part of their orbit using the relevant equations. The laws of physics here provide a useful means of compressing an infinity of events into a single set of equations which can be used to predict the future behaviour of objects like the planets. The process of rule following however involves the making of a sequence of conscious judgements as to what is the correct choice from competing alternatives such that some rule is conformed to. This requires firstly that the rule be knowable to the rule follower, i.e. be finite, readable and understandable such that in any eventuality the rule unambiguously prescribes the correct action. This implies also that the rule follower is able to identify that s/he is in fact conforming to the rule i.e. the rule is verifiable. Furthermore the rule must be applicable in all conceivable circumstances and must therefore represent a compression of an infinite number of ordered pairs representing some stimulus-response mapping.

Any putative ‘rules of language use’ must provide a framework of normative constraint which guides us in our use and application of packets of language. What are these rules? How do we come to know them in a form which allows us to follow rather than conform to them? Are such rules entirely culturally conditioned or do we follow some deep grammar inherent within a genetically determined ‘language engine’ of the brain (a la Chomsky)? Before we can approach these questions we must be clear as to whether the concept of conscious rule following is a coherent concept at all – even for such simple cases as the laws of integer arithmetic.

Saul Kripke has famously adapted and extended the earlier work of Wittgenstein (Philosophical Investigations, 1953) in his Wittgenstein on Rules and Private Language (1982). Here he employs a sceptical argument to show that it is impossible for any individual to claim to be unambiguously following a known rule, whether in the past or in the present. This places the whole rule-following model of linguistic meaning in jeopardy since if we can never say which rule we are in fact using then how can we justifiably attach meaning to our utterances? Kripke uses this so-called sceptical paradox to claim that an individual in isolation cannot consistently or meaningfully employ a private language since he cannot know himself what he means. He then proceeds to show that language can only have acceptable meaning within a society of individuals whose collective behaviour provides the normative constraints previously supposed provided by rules of use. Since there are no facts which legitimise our use of language within the individual, says Kripke, meaning must be derived from the community by some form of culturally mediated consensus.

Before responding to this conclusion it is useful to briefly summarise the sceptical argument. Kripke’s sceptic questions the meaning I might attach to my use of the ‘+’ sign in approaching some arbitrary sum, such as 57+68. The challenge is for me to justify that by ‘+’ I mean normal arithmetic addition and not one of an infinite number of possible functions (rules) which have always in my past use of ‘+’ shared the same extension. Supposing that 57 and 68 are each larger than any two numbers I have yet applied ‘+’ to (and any two numbers can always be found, however large), then what is it that allows me to justify a result of 125 ( i.e. 57 + 68 in the arithmetic sense) rather than some other result 57 Å 68? {where Å (‘quus’) is defined as the function: x Å y = x + y if x, y < 57, otherwise 5} For any n-ary function (such as +) defined (taught) solely by a finite set of n-tuples of integers then there are an infinite number of other possible n-ary functions (such as Å ) which give indistinguishable results over the given interval. So, whether I know it or not, my past responses to computations have been in accord with Å just as much as they have been in accord with ‘+’. Thus, there seems to be no reason at all to prefer a result in accord with ‘+’ (i.e. 125) rather than one in accord with Å (i.e. 5) given my past behaviour – even granted that I have perfect knowledge of all my past actions and internal mental states. But if this is correct, there can of course be no fact about which function I meant, and if there can be no fact about which particular function I meant in the past, there can be none in the present either. Kripke takes this contentious assertion to argue that language based solely on rule following is devoid of meaning since even a solitary speaker using a private language cannot justify his own choices of usage. Even I cannot know what I mean since I cannot unambiguously identify the ‘rule’ I am using to ascribe meaning to my sentences. The challenge thus presented asks us to find a fact (hereafter called a meaning-fact) that can legitimise our justification of meaning and hence our language. Note that this is different from saying that we do not know which of several competing hypotheses we are using since, as Kripke admits, we almost certainly are using the ‘normal’ rule – but there is no fact of the matter which allows us to safely justify this.

This paradox, if accepted, raises serious questions about the possibility of both teaching someone to use a new function and our own ability to be sure we have learned a particular function. Given the sceptic’s argument, how can any teacher be sure that he is teaching his student to ‘add’ rather than to ’quadd’? Furthermore, what compels the student to take the instruction s/he is given in one way rather than another? There are after all an infinity of possible rules we could be described as learning given that our instruction consists in a finite number of examples of its use. This then makes an appeal to some disposition we may have to behave in one way rather than another rather weak – surely we will find the worm of a deviant interpretation of our actions in every bite of the apple?

From another viewpoint, teaching might be seen as instructing the student simultaneously in the whole infinite set of functions { +, Å, … etc.} which share the same extension. But surely then the only answer to the challenge of the sceptic is to reply in accord with the whole set of functions ( i.e. 125 and 5)! Our experience however clearly shows us that in cases where the answers for + and Å differ (as in 57+68) we are immediately able to know which of the two functions we "ought" to mean.

Notice also that Kripke’s sceptic is using an inductive argument in asserting that since there is no such fact in the past then there cannot be such a fact in the present. This is perhaps a potentially unsafe inference - surely we should be allowed to assume that the present allows us access to facts, linguistic behaviour and dispositions which were not available to us in the past and which now enable us to legitimise our answers.

Given the carefully prepared ground and the clear exposition of the argument, we must though tend to agree with the sceptic that there is no fact that renders our answers non-arbitrary. But clearly, it does not necessarily follow that our answers are arbitrary. Although Kripke’s sceptic wants to move from the lack of facts that legitimate our meaning to the nonsensicalness of language itself, such a move is not justified.

Kripke himself proposes a ‘sceptical solution’ wherein our choices can be rendered non-arbitrary despite the explicit acceptance that there are indeed no meaning-facts that render them non-arbitrary. Any ‘straight solution’ to the problem would need to establish the reality of the elusive meaning-facts. Kripke proposes that we abandon the search for non-existent truth conditions which establish meaning in the verificationist tradition – i.e. there are no facts by virtue of which sentences can be established true or false. Instead we should talk in terms of assertability conditions – the set of circumstances under which our particular linguistic statements can safely be asserted and justified. This reduces to some form of value judgement by some entity that the relevant assertability conditions have in fact been satisfied and that the statement(s) uttered under these conditions then have meaning ascribed according to convention. But who is in a position to make such judgements? Kripke argues that no isolated individual can make such a judgement about himself; he can only assert that “I believe I mean ‘+’ and not Å” rather than a justified “I mean ‘+’ and not Å” (although these have the same truth value). Such a statement is then just as much subject to the sceptical challenge as any other statement by the same individual and hence, as Kripke sees it, no isolated individual can meaningfully use language (i.e. no private language is possible).

Kripke proposes a ‘community solution’ wherein meaning is ascribed to statements by virtue of their being in accord with the accepted use (assertability-conditions) as agreed between members of the linguistic community. This allows the community to successfully differentiate between the assertions that "X believes he is using ‘+’” and “X is using ‘+’” – the latter being determined by the assertability conditions of the community being met. The community then underwrites the ascription of meaning by setting and validating the assertability conditions for the public language by which members of the community understand each other.

So how valid is Kripke’s sceptical solution? He attempts to show that an isolated individual cannot be a rule-follower but a community-member can be by virtue of the community. The problem is however that Kripke appears to weaken the satisfaction conditions for successful rule following as he moves from the isolated individual to community member. The individual cannot be a rule-follower because of the supposedly watertight sceptical argument while all a community member would seem to need to do is to appear to be a rule follower by conforming to a community-validated rule. The sceptical argument in its full force form applies just as much to the community member and yet by virtue of his place within a self-validating community his linguistic utterances can be justifiably ascribed meaning.

What now of possible ‘straight’ solutions to the paradox which attempt to derive some fact than allows the individual in isolation to justify the assertion of that s/he means X and not Y? One response might be to say that meaning is an intrinsic component of our internal intentional states of mind (our propositional attitudes) which is not then subject to some reductive analysis. What then is the relationship between linguistic meaning and mental content – do we explain one in terms of the other or are they irreducibly intertwined? The problem here is that Kripke’s sceptical argument can be applied just as devastatingly to beliefs about our mental content as to ascriptions about our meaning – one is a facet of the other.

Ultimately though, is not Kripke’s paradox just an interesting restatement of a trivial truth? While it is undoubtedly true that we are never in a position to rule out all competing hypotheses about what someone means by their words, this in no way threatens our ability to apply valid justifications to our actual interpretation of their words. Having said this, how reasonable is it to suppose that someone might mean Å rather than the ‘+’ they believe they were taught when they have never encountered the concept of Å (or any of the other infinite number of possible functions)? Clearly though, we are still able to make conditional statements about meaning; for example: "If X means plus by '+' then X ought (indeed, is compelled) to say that 68 + 57 is 125 rather than 5". Similarly we can say: "Granted that X said that 68 + 57 is 5, it is clear that he does not mean simple addition by '+'".

As individuals though we must ask ourselves which potential conception of plus is "the right one". Suppose given the same question: “What is 68+57?” I answer 125 while my wife answers 5. Our arithmetical disagreement can be resolved by one of us adopting a new term to denote their respective interpretation of the ‘+’ symbol - suppose I use “plus” and my wife uses “quus”. A third party giving the answer 125 would then lend weight to my justification that ‘+’ means ‘plus’ and not ‘quus’. The key point is that we easily recognise that we are referring to different functions by virtue of our differing answers. Surely this indicates the way that community consensus validates correct usage of language and shapes the publicly adopted meaning of terms? If we can't recognize such differences then language really would be impossible.

To adopt a purely pragmatic approach, as human society inevitably must, then we can argue that it does not matter which candidate rule we follow providing that it provides results in accord with the general consensus of its acceptable extension within the problem space of language. Providing the set of use cases encompasses a sufficiently large proportion of human experience both in the past and likely projection into the future (ignoring the danger of induction here), then surely this will guarantee that any of the rules we use which conform to this use case set can ensure understanding between any two parties who share the same use cases (through cultural inheritance etc.) If I believe I use rule A while your observation of my behaviour convinces you I am using rule B, then providing rules A and B have identical extensions in the domain of our shared experience then there will be sufficient overlap for us to validate and understand each other’s statements. To make an astronomical analogy, suppose the planets are in fact conforming to a gravitational equivalent to ‘quus’ rather than to Einstein’s general relativity theory of gravity (equivalent to ‘plus’). Providing the shared domain of these functions encompasses the past and future history of the universe then our space probes can continue to be launched based on Einsteinian calculations rather than astro-quadditional calculations.

The question then arises as to whether in reality we are all using our own individually crafted rules (as Chomsky proposes, we all talk a different language) or whether Kripke’s community solution ensures that we really are all using the same rules.

To conclude then, I believe we are driven to accept the validity of Kripke’s sceptical challenge but that this in no way undermines the justifiable ascription of meaning to statements made by either individuals in isolation or by full-fledged community members. Meaning does indeed arrive as a result of association with the conditions under which a statement may be justifably made. It is the nature of this justification though which differs between the individual and the community: one appeals merely to his/her own internal mental states and dispositions governed by past experience while the other appeals to the community at large to set out the ground rules. Kripke fails I think to fully discredit the possibility of private language – if I think I mean X then, provided I operate as an individual in isolation, surely I do mean X? Of course the sceptical argument proves that this cannot be the case in any absolute sense but surely we must appeal to pragmatism – the linguistic castaway can have perfectly satisfactory conversations with himself. Only when I move into the community of others do my statements need validating by the mass consensus.

Language is a meandering river through which the tide of meaning flows between banks constantly re-shaped by dynamic cultural and technological forces. Regretably, in their attempt to analyse the nature of meaning reductively in terms of its constitutive water molecules, many have drowned.


1. Alex Miller, Philosophy of Language, 1998
2. Saul Kripke, Wittgenstein on Rules and Private Language, 1982
3. Ludwig Wittgenstein, Philosophical Investigations, 1953
4. Matt Ridley, The Red Queen, 1993