From the ALWS archives: A selection of papers from the International Wittgenstein Symposia in Kirchberg am Wechsel

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This paper is an examination and defence of Wittgenstein's thesis that language itself promotes an Augustinian picture of its workings. Let us define Augustinianism as the thesis that the meaning of an expression is its referent, and distinguish a strong variant that restricts the referents of expressions to ostensively indicatable material objects. In this paper I will argue that if Wittgenstein is correct about reference talk, linguistic practice tempts us to (incorrectly) adopt both positions. I shall begin by describing a naïve notion of reference. Then I will examine the role of reference in contemporary meaning theories and draw parallels with Wittgenstein's own account in order to elucidate the latter. Finally I will explain why the resulting practices can lead us to accept both forms of Augustinianism, and why these positions are mistaken.

At first blush, Wittgenstein's ‘meaning is use’ thesis seems to offer a simple account of reference. As he noted at PI 10:

What is supposed to shew what [words] signify, if not the kind of use they have?

I take Wittgenstein to accept that, in one sense of ‘refers’ or ‘signifies’, the referential link between a sign and its referent lies in the fact that the rules for some signs use are such that their correct use intimately involves (a) particular ostensively indicatable material entity/entities which are thereby the referent(s) of the sign. It is this sense that captures what I shall term ‘naïve referential practice’.

But, Wittgenstein points out, it is not this sense of reference that motivates the question of what the expressions of his simple language refer to. Since he had explained the use of the expressions he was at that point dealing with, in its naïve sense the question is already answered. Thus, Wittgenstein continues, the question must be a request ‘for the expression “This word signifies this” to be made part of the description’ of the expressions use. There must, alongside our naïve referential talk, be a sophisticated variant wherein the uses of expressions are explicated via referential claims. Certainly, even in ordinary language, ‘refers’ has a much broader role than the naïve practice allows. We talk of our expressions referring to abstract objects like numbers, fictional objects like Sherlock Holmes, properties like blue, and many other things besides. The only hypothesis here seems to be that this broader use of ‘refers’ is involved in elucidating the use of expressions. For the purposes of this paper I shall assume this is correct. For what I wish to argue is that it is the way Wittgenstein believed that expressions such as ‘This word signifies this’ and ‘This word refers to this’ are made part of the description of words’ uses that leads to the conclusion that language itself tempts us to understand it in an Augustinian fashion.

To explain this, let us begin by turning to the role of reference in formal meaning theories. Presuming a Fregean syntax and ignoring complications required to deal with quantifiers, a typical meaning theory attributes semantic values to names and treats predicates as functions from names to the semantic value of sentences – where an expression’s semantic value is that which indicates the contribution the expressions make to the meanings of the sentences it can be part of, whilst a sentence’s semantic value is its meaning. The theory then gives a functional account of the logical connectives which permits the production of semantic values for complex sentences, and lastly (and most problematically) provides a theory for how the use of sentences can be deduced from the semantic values the meaning theory attributes to them. In attributing semantic values to (the sub-sentential expressions the theory parses as) names, the names are said to refer to objects, which, in a deliberately set-theoretic construal of what is going on, we can take to be grouped in the meaning-theory’s domain. The theoretical relation of reference thus introduced can be expanded such that one might also say that definite descriptions and predicates refer to the objects that satisfy them and (possibly empty) sets of objects respectively. The latter case looks very akin to saying that predicates refer to properties, and to assist this exposition let us explicitly accept that properties are sets. In this case, a set-theoretic construal of the quantifiers permits us to understand them as referring to properties (sets) of sets – taking ‘all’ to refer to the property of being identical to the universal set and ‘some’ the property of not being identical to the empty set. Importantly, the single criterion for a successful meaning theory (as a descriptive account of the meanings we do attribute to others) lies in its getting its theorems correct. In the rarefied air of theoretical semiotics, it makes no sense, Davidson pointed out, to complain that a meaning theory comes up with the right theorems time after time, but has the logical form (or deep structure) wrong. [Davidson; 1977] The objects to which an expression refers are therefore not something that can be examined directly, but are determined by the legitimacy of the theorems the referential axioms produce.

One might object that referential axioms are not so thoroughly unconstrained, for they relate singular terms to objects. Therefore only those things that actually exist are kosher referents in the theory. So, for example, since there is no object Atlantis, a meaning theory ought not to accept the axiom ‘‘Atlantis’ refers to Atlantis’. One might reply that by the criterion given above what is important is merely that the meaning theory produces the correct theorems. So whilst one could, there is neither need nor justification in restricting the axioms of a meaning theory such that one ought to include as referents only objects one is ontologically committed to. But this reply is too quick. For the objection’s motivation is likely not the given criterion for determining a correct meaning theory, but Quine’s thought that accepting any theory requires ontological commitment to the objects it quantifies over (or, since a theory may be satisfied by models with different domains, it requires existential ontological commitment to there being one such domain). Insofar as, for any singular term of a theory, t, the theory implies (∃x)(x=t), a theory’s singular terms refer to objects of its domain of quantification – to objects which we therefore ought to be ontological committed.

There are reasons to object to this claim. But I shall not pursue them here. Let us accept that a theory requires ontological commitment to the objects its quantifiers range over. In the case of a meaning theory, these objects are the semantic values of (expressions parsed as) names. But these objects have not been shown to be the middle-sized dry goods we would, in the aforementioned naïve reference talk, say are the referents of most of the mentioned expressions in the referential axioms. On the contrary, formal semantics is a mathematical discipline: First order set theory. Given the possibility of a set-theoretic construal of formal meaning theories, as well as their historical development from Tarskian model theory, we might think the same is true in their case; or more weakly, we might think it possible to interpret them in this way. If so, then although we owe ontological commitment to the members of a meaning theory’s domain, these would, or at least could, be urelements. In which case the axiom ‘‘Atlantis’ refers to Atlantis’ demands ontological commitment to nothing more than an (existent) urelement, not a (non-existent) continent.

This foray into formal meaning theories casts light on how the expression “This word signifies this” can be made part of the description’ of the word’s use. As in formal meaning theories, so in folk practice: It occurs through reference talk coming to be used to indicate at least certain aspects of the expression’s semantic role. This indication can be wider or narrower. We have, for example, numerals in our language that are characterised as referring to natural numbers. They are characterised this way both en masse, in that referring to natural numbers is what numerals do, and individually, in that each numeral has a specific natural number it refers to. Presuming the practice does not also describe complex arithmetical equations as referring to numbers (or numbers alone), to say that a person uses a particular expression to refer to a natural number is to indicate that they mean it as a numeral. To indicate that they use it to refer to a particular natural number is to indicate that they give it the same meaning as a particular numeral. Let us assume, as seems plausible, that natural language has the semantic vocabulary – expressions denoting the categories of objects, properties, relations, truth functions, properties of properties, etc, and the means to provide indefinitely many names of the individuals entities of the various categories – to allow us to think of every sub-sentential expression (as parsed in the canonical syntax, which we can assume to be Fregean) as referring to particular referents of a particular category. Let us call these the canonical referents of the language's sub-sentential expressions. This permits information about the meaning a person gives a sub-sentential expression to be expressed by the class of entity that the expression is said to refer to: to learn that someone uses a sub-sentential expression to refer to an object is to discover that they mean it as a name (or definite description), whilst to learn they use it to refer to a property is to find they mean it as a predicate, etc. Referents, via the referential relation, provide a model for language on the basis of referential claims of the form ‘‘a’ refers to b’ and ‘There is some x such that ‘A’ refers to an x’. To those familiar with the practice, this model categorises the correct use of expressions. Explaining the model a person utilises helps explain the meaning they provide their expressions. Telling others the model they ought to use helps to teach them to use language as we wish them too. Since such a model provides referents that suffice, within the practice, to entirely represent the contribution the expressions make to the meanings of the sentences they can be part of, then knowledge about what a person refers to by an expression will provide knowledge of what the person means by the expression.

It is but a short step from believing our language and canonical syntax permits such a referential practice to thinking we possess the same. Such a sophisticated referential practice would not be redundant. As well as facilitating learning, it permits translations from one language to another; indeed it permits extremely subtle translations that can elucidate the similarities and differences in structures between the two languages (cf PI 10). But when applied to one’s own language in the presence of competent users the practice idles, it produces trivial substitution instances of the schema ‘‘A’ refers to A’, or ''A' refers to the property (of) A', etc (perhaps with small amounts of declination or conjugation to produce appropriately reified canonical referents). This is harmless enough, but note that reference is simultaneously important in elucidating meaning and every expression is (given a recursive categorisation system and an ability to provide names for previously undiscussed members of categories) tautologically provided with a referent, and this referent is (also tautologically) the meaning (semantic role) of the expression.

Thus, as in formal meaning theories, saying that an expression possesses a particular referent, or possesses a referent of a particular type, provides information about the expressions’ semantic value. (And certainly, Wittgenstein exorcises any concern about the legitimacy of the used expressions on the right of reference claims. We can think of this sophisticated reference talk as a sui generis linguistic practice whose utility lies in its creation of this referential model. The objects of this model, which we arguably need to be ontologically committed to, are nothing more than other expressions of the language.) Such, I think, is Wittgenstein’s understanding of how expressions such as ‘This word refers to this’ are made part of the description of the use of words.

It is clear how such a linguistic practice lures us towards Augustinianism. For in the sophisticated practice every expression possesses a referent which is, in some sense, the expressions meaning (semantic role). Two points elucidate the lure and problems of the weak and strong Augustinian accounts respectively:

• (i) Within sophisticated referential practice, reference talk provides a model of the semantic role of expressions in that referential claims represent, to those familiar with the practice, the semantic role of expressions. It is a mistake to think that the possession of a referent in this sense causes an expression to have a semantic role.
• (ii) Within sophisticated referential practice, all expressions possess (their canonical) referents which represent their semantic role. But, as noted, we also naïvely talk about expressions referring in the sense that their correct use intimately involve (a) particular material entity/entities which are thereby their referent(s). It is a mistake to think that the fact that all expressions possess referents in the sophisticated sense entails that they possess referents in the naïve sense. It is likewise a mistake to think that the referents expressions may possess in the naive sense represent the semantic role of the expression.

The Augustinian account confuses modelling with explaining and, in its strong variety, conflates the naïve concept of reference with the sophisticated. But the ease of these mistakes is why Wittgenstein felt that, given a sophisticated referential practice, our language itself attempts to foist an Augustinian understanding upon us. In searching for what Wittgenstein described as the 'life' of our expressions we immediately confront a picture of meaning provided by a practice wherein the semantic role of expressions is given by their referents. To paraphrase his characterisation, this picture holds us captive. We cannot get outside it, for it lies in our language and languages repeats it to us inexorably. But we can equally see why the Augustinian accounts are mistaken, confusing modelling with explanation and, in the strong case, trading on ambiguity.

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