The problem of sentential unity

“A succession of nouns only is not a sentence, any more than of verbs without nouns.”159 Why this is so, is the problem of sentential unity.

A sentence is a sequence of words, but not a list of proper names. In order for a sequence of words to be a sentence, i.e. to express a thought, one of the words has to be a verb. It is an obvious point to make that ‘Brutus killed Caesar’ is a sentence while, say, ‘Cato Brutus Caesar’ is not because the latter lacks a predicate. The question is in virtue of what is a word a predicate rather than a proper name: in this case, what makes ‘killed’ not a proper name.

To say that ‘Brutus’ is a proper name because is denotes an object while ‘killed’ is a verb because is denotes a concept (or an action, as Plato would say), would still not answer the question, which would reappear under the guise, What makes a word denote a concept rather than an object? Thus the problem of sentential unity has also been termed the problem of the expressiveness of the proposition.160

Again, it would be spurious to appeal to grammatical rules in this connection. It could be argued that a sequence of words is a sentence if it is well formed. Whether a word may occur as a verb or as a noun, is dictated by its grammar, or rules of combination. But then a similar question could be asked concerning the relation between grammar and words. What features does grammar endow a word with in order for it to be a verb rather than a name, i.e. to denote an object rather than a concept? The problem could indeed be expressed in Kantian terms, as concerning the conditions of the possibility of syntax.

In Fregean terms, the question is, In virtue of what is an expression a function- name, i.e. a sign for a function, rather than a proper name, i.e. a sign for an object? Peter Geach finds in Frege’s writings a definitive answer to the problem of sentential unity based on the notion of a linguistic function. Function-names denote functions and proper names objects, because they are themselves functions and objects respectively.

According to Geach linguistic functions are what symbolize numerical or other functions.161 A concept-word must therefore be a linguistic function. In ‘Raleigh smokes’, the two words have “different modes of significance.” ‘Raleigh’ denotes a man by being its name; but ‘smokes’ denotes a concept, if anything, not by being a “bare word”, but by the fact that ‘Raleigh smokes’ instantiates the pattern name- followed-by-‘smokes’.162 In general, the occurrence of a predicate is not the presence of

159

Sophist. 160

Potter 2008: 111-5. The problem of sentential unity does indeed bear a close kinship to Bradley’s regress, but unlike Potter I reserve the latter term to the problem discussed at the beginning of chapter 3. 161

Geach 1961: 144. 162

a “quotable part of a sentence”, but the fact that the sentence shares a pattern with other sentences. Geach’s wording does indeed suggest expressing the point in Wittgenstein’s terms. It is not the complex of signs ‘Fa’ that is expressive, but it is rather the fact about this complex that F can be applied to different names, or that ‘Fa’ shares the pattern ‘Fξ’ with ‘Fb’, ‘Fc’, etc, that symbolizes that a is F.

The fact about a sentence that it instantiates a certain pattern corresponds to a rule of formation. The difference between ‘John killed Mary’ and ‘Mary killed John’ – namely, who killed who – could not be appreciated if the predicate were just the bare expression ‘killed’.163 In languages such as English, it is a fact about word order that indicates what the predicate is. We know what is the nominative and what the accusative from the fact that the nominative is written before ‘killed’, which in turn precedes the accusative. But a different grammatical rule could be used for the purpose of indicating that “the first killed the second”: instead of word order, declensions for each case could be used. What is essential is that the mode of composition of the sentence be able to express the direction of the relation.

In general, what syntax must be able to do, regardless of the particular rules it chooses for the purpose, is to show the mode of “combination into a whole” of the referents of expressions. The grammar of a proper name allows it to stand for an object only because it makes it be to a predicate what an object is to a function: an argument. The grammar for a concept-word allows it to stand for a concept by making it behave to proper names as concepts to objects, i.e. by being itself a function. Proper names and objects alike behave like arguments, and only thereby can the former stand for the latter; function-names and functions alike behave like functions and only thereby can the former stand for the latter. The role of names is to complete predicates to form sentences, and the role of predicates is to be completed by names to form sentences. When syntax describes the behaviour of a predicate, what it does is to show that it is unsaturated as a function is: indeed it is a linguistic function.

Now, this is possible only because the notions of object and function are themselves modelled upon their linguistic counterparts.164 It is the fact that proper names behave linguistically like arguments, i.e. complete expressions, that makes them suitable to denote objects, but only because the notion of an object is just that of the non-linguistic correlate of a proper name. Likewise, it is the fact that function signs behave linguistically like functions that makes them suitable to represent functions, but again only because the notion of a function is merely that of the non-linguistic correlate of an unsaturated expression, i.e. of an expression whose role in syntax is that of being completed by other expressions.165 And so that a name denotes an object follows from its behaviour as a linguistic argument; that a predicate denotes a concept follows from its behaviour as a linguistic function; that a sentence expresses what it does – an object falling under a concept, for instance – follows from these facts about complexes of signs.

It follows, in general, that what a sign can it must denote. An expression is able to denote an object if its logical behaviour is that of an argument, but if it behaves like a proper name, then it must denote an object. A sign is a symbol for a function if it is a linguistic function – its role that of being completed by names; but if it behaves like a function, then it must denote a function.

163 Geach 1975: 148. 164 See Dummett 1981: 234-48. 165

One should beware of the interplay here involved between the notions of reference as modelled on the name/bearer relation and as semantic role. See chapter 3.