A sentence is made out of words. Words fall into different grammatical types or classes – syntactical categories. To these categories correspond different semantical categories – categories of meaning. According to the classifications of traditional grammar, these include proper names, nouns, pronouns, verbs, adjectives, definite and indefinite articles, adverbs, prepositions, quantifiers and more. Those classifications have been partly superseded in modern linguistics, largely because that discipline has a firmer grasp of what such classifications are for. For our purposes, the purposes of the philosophy of language, many of these distinctions don’t matter; we’ll carve up language in slightly different and in some respects cruder ways – ways, primarily, that in the first instance directly affect the truth-conditions of statements. Also, the individual words are sometimes best treated not as semantically significant parts in themselves but only as parts of parts that do have meaning (as ‘syncategorematic’). What all this means will be much easier to see once we get going.
Singular terms
Consider:
- (1) Mars is red.
- (2) Mars orbits the sun.
Both (1) and (2) contain the name ‘Mars’. ‘Mars’ is a name, a proper name, of Mars. It stands for it, names it, picks it out, denotes it, designates it. According to a decision announced in the Introduction, we say that it refers to it; Mars, the actual planet Mars with all its red dust, is its referent, i.e. the thing it refers to. It is customary to call ‘Mars’ a singular term. We will also formulate naïve principle 2 (naïve principle 1 will be introduced shortly):
(NP2) The meaning of a singular term is its referent.
We are not going to try to give a precise definition of ‘singular term’. It is too hard. But our intuitive classification is sufficiently reliable: we are thinking simply of words whose role, whose function, is to stand for an object, a certain individual – a person, a city, a planet (so all these things are objects, in an extended but philosophically standard sense of ‘object’). ‘Dog’, by contrast, is not singular term because there are many dogs for which it stands.
Thus ‘the sun’, as it occurs in (2), is also a singular term. It refers to the sun. Here are more singular terms:
- (3) Jupiter
- (4) Prince Charles’ mother
- (5) the river that runs through Prague
- (6) the fastest mammal
(3) is a proper name, but (4) and (5) are not (though (4) and (5) contain proper names or titles as parts). As you can see, singular terms may be simple (containing no expressions as parts), as in the case of (3), or complex, as in the case of (5).
Predicates I: syntax
If we remove the name ‘Mars’ from (1) and (2), we get:
- (7) ____ is red.
- (8) ____ orbits the sun.
These, in the logical sense of the word, are predicates. In general: the result of removing a singular term from a sentence is a predicate. This is a point of syntax, for we expressed it without speaking of the semantics of predicates, of their meaning.
In writing down (7) and (8) we used underlining to indicate blanks or gaps – the places vacated by the singular terms we removed. It is convenient to refine this practice, using Greek letters to indicate the gaps:
- (9) α is red.
- (10) β orbits the sun.
The Greek letters do not mean anything. They are not variables, either (as we use in logic to express quantification, or in algebra to speak of numbers in general, as in ‘2(x + y) = 2x + 2y)’. They are just there to mark the gaps, the places in predicates where names can be inserted (if this were a hard-core course in logic we would take care to distinguish these from ‘open sentences’, which become closed sentences when the blanks are filled with suitable expressions). We call this procedure predicate extraction.
We can attach any singular term to a predicate such as (9) or (10), and the result is a sentence. In particular we can make a sentence in this way by replacing the Greek letter with a singular term. Thus we can attach (4) to (10), yielding the sentence:
- (11) Prince Charles’ mother orbits the sun.
It’s not likely that anyone would ever say this, but nevertheless there is nothing grammatically wrong with it as a sentence.
The predicate (10), you may observe, contains a singular term. The sentence (2), from which we derived (10) by deleting a singular term, contains two singular terms, not just one. If we now delete the remaining singular term from (10), inserting another Greek letter in the vacated space, we extract:
- (12) α orbits β.
This too is a predicate. But unlike (9) and (10), which are one-place predicates, or monadic predicates, (12) is a two-place, or binary predicate.
To construct another sentence from (12), we can replace both Greek letters with singular terms (either different ones or the same one used twice). There are also three-place predicates, such as:
- (13) α gave β to χ.
There is in principle a predicate of n places for any finite n, no matter how large.
Unlike (10), no further predicates can be extracted from (12) or (13) by removing singular terms. (12) and (13) are what we shall call pure predicates, by which we mean that not only are they without singular terms as parts, they also do not contain sentential connectives such as ‘and’ and ‘or’, or quantifier-words such as ‘something’ or ‘everything’. We shall consider sentential connectives and quantifiers later in the chapter. We will also set aside adverbs such as ‘quickly’ (although the presence of an adverb does not disqualify a predicate from being a pure predicate).
We adopt a rule governing our use of Greek letters: when replacing Greek letters with names (or, later, with variables) to form a sentence, always replace every occurrence of each Greek letter with the same name (or variable). For example, we regard the following as different predicates:
Thus ‘Jones killed Jones’ is correctly obtained from either of these predicates, but ‘Jones killed Smith’ cannot be obtained correctly from the second one. This reflects the fact that the concept of suicide could be defined in terms of the concept of killing (one commits suicide just in case one kills oneself), but that of killing could not be defined in terms of suicide.
Such sentences as (1), (2) and (11) are the simplest sentences: each is constructed from a pure predicate and the requisite number of singular terms, and contains nothing else, no other kind of expression. Indeed, any such sentence contains exactly one (pure) predicate. Sentences of this kind are called atomic sentences.
An atomic sentence is a sentence comprising nothing besides one n-place pure predicate and n singular terms.