Peter Geach's distinction between logically predicative and logically attributive adjectives, first advanced just over fifty years ago, has become part of the technical apparatus of philosophers.Footnote 1 For all that, no satisfactory explanation of what an attributive adjective is has yet been provided. We argue that Geach's discussion suggests two different ways of understanding the notion. According to one, an adjective is attributive just in case predications of it in combination with a noun fail to behave in inferences like a logical conjunction of two separate predications. According to the other, an adjective is attributive just in case it cannot be applied in a truth-value-yielding fashion unless combined with a noun. We argue that the latter way of understanding the notion yields both a more defensible version of Geach's arguments that ‘good’ and ‘bad’ are attributive and a more satisfactory explanation of attributivity.
1. Inferential Irregularity
Geach introduces the terms ‘logically predicative adjective’ and ‘logically attributive adjective’ as follows:Footnote 2
I shall say that in a phrase ‘an A B’ (‘A’ being an adjective and ‘B’ being a noun) ‘A’ is a (logically) predicative adjective if the predication ‘is an A B’ splits up logically into a pair of predications ‘is a B’ and ‘is A’; otherwise I shall say that ‘A’ is a (logically) attributive adjective.
Before we examine this passage, a few points of terminology are in order. First, following Geach, we shall hereafter omit the qualification ‘logically’ from the terms ‘predicative’ and ‘attributive’. Second, Geach's use of the term ‘predication’ here is unusual. In other writings, he uses it to signify a sentence or a phrase in which a predicate is applied to something, and uses the word ‘predicate’ for what he here calls a ‘predication’.Footnote 3 The latter usage is more common, and it is the one that we shall follow. Finally, for the sake of brevity, we shall call predicates of the form ‘is an A B’ ‘complex predicates’.
In the quoted passage, Geach distinguishes between complex predicates that ‘split up logically’ into a pair of predicates and ones that do not so split up, and uses this distinction in turn to distinguish between predicative and attributive adjectives. According to the passage, if a complex predicate splits up logically, then the adjective in it is predicative; if it does not, the adjective is attributive.
Since Geach offers no explanation of what it means for a complex predicate to ‘split up logically’, we are left to determine the content of the notion for ourselves. An obvious way to do this is to examine the considerations by which he justifies applications of the notion. Immediately after introducing the predicative–attributive distinction, Geach observes that predications of the phrases ‘big flea’ and ‘small elephant’ do not split up logically—‘for', he says, ‘if these analyses were correct, a simple argument would show that a big flea is a big animal and a small elephant a small animal’. Geach's reasoning may be elaborated thus:
(1) The following argument is not valid:
(1.1) Whatever is a flea is an animal.
(1.2) Therefore, whatever is a big flea is big animal.Footnote 4
(2) Any argument of the following form is valid:
(2.1) Whatever is an F is an A.
(2.2) Therefore, whatever is an F and is B is an A and is B.
(3) Therefore, the first argument cannot have the same logical form as the second.
(4) Therefore, ‘is a big flea’ does not split up logically into ‘is a flea’ and ‘is big’ (and the same, mutatis mutandis, for ‘small elephant’).
The disparity in logical status between the sample argument (1.1)–(1.2) and the schematic argument (2.1)–(2.2) shows that the two do not correspond in logical form, and thus that ‘x is a big flea’ does not correspond in logical form to the conjunction of a pair of predications.Footnote 5
These examples suggest that a complex predicate ‘splits up logically’ just in case applications of it enter into inferences according to the same forms as apply to a conjunction of predications. Accordingly, a predicative adjective will be an adjective, applications of whose complex predicates license inferences in the fashion of logical conjunctions, and an attributive adjective will be an adjective, applications of whose complex predicates fail to license inferences in this fashion. For convenience, we shall describe complex predicates whose applications do not behave in the manner of logical conjunctions as inferentially irregular.
The examples also suggest that one way to show that an adjective is attributive is to provide a sample argument using the adjective in such a way that (i) the argument itself is invalid, and (ii) the schema that one gets by treating all applications of complex predicates with the adjective in the original argument as conjunctions is valid. For convenience, we shall call the latter the predicative counterpart of the original argument.
This understanding allows us to make sense of Geach's rather cursory account of two more examples—‘putative' and ‘forged’:
Again, the sort of adjective that the mediaevals called alienans is attributive; ‘x is a forged banknote’ does not split up logically into ‘x is a banknote’ and ‘x is forged’, nor ‘x is the putative father of y’ into ‘x is the father of y’ and ‘x is putative’.
Although Geach offers no argument for this assertion, the notion of inferential irregularity indicates where to look for one. For it is evident that from ‘x is a forged banknote’, one cannot validly infer ‘x is a banknote’, and from ‘x is the putative father of y’, one cannot validly infer ‘x is the father of y’. (This invalidation of the inference from ‘x is an A B’ to ‘x is a B’ seems to be what Geach means by calling an adjective ‘alienans’.)Footnote 6
One further clarification: It is obvious that, when Geach uses the letters ‘A’ and ‘B’ as proxies for an adjective and a noun, respectively, each stands, in a given substitution, for the same adjective or noun in all occurrences. What may not be obvious is that the sameness is not merely in respect of spelling, pronunciation, and etymology, but also sense. Thus, e.g., the fact that ‘x is a red herring’ (the idiom, not the description of a fish of a certain colour), does not license the same inferences as ‘x is red and x is a herring’ does not show ‘red’ to be attributive.Footnote 7 With respect to sense, ‘red’ is no more a component of the idiom ‘red herring’ than are the words ‘her’ and ‘ring’.
The explanation of attributivity in terms of inferential irregularity has several virtues: it makes sense of Geach's treatment of the examples that he gives of attributive adjectives; it yields a natural account of his claim that alienans adjectives are attributive; and it seems to afford at least a semi-rigorous way of proving that a given adjective is attributive—‘semi-rigorous' in that we can appeal to canonical forms of inference to show that an argument of a given form is valid or invalid, even if the claim that a given argument in natural language has this or that logical form is not itself amenable to rigourous proof.
2. Difficulties with Inferential Irregularity
However, the notion of inferential irregularity is much less helpful when we turn to Geach's arguments that ‘good’ and ‘bad’ are attributive. Indeed, if his arguments are taken to rely on that notion, they seem to fail entirely.
Geach's arguments for the attributivity of ‘good’ and ‘bad’ are both presented very briefly. Here is the pertinent passage on ‘good’:
I could ascertain that a distant object is a red car because I can see it is red and a keener-sighted but colour-blind friend can see it is a car; there is no such possibility of ascertaining that a thing is a good car by pooling independent information that it is good and that it is a car. This sort of example shows that ‘good’ … is essentially an attributive adjective.
If we try to understand this passage in terms of inferential irregularity, we immediately run into difficulties. For the only argument that it suggests is one on the following lines:Footnote 8
(1) That distant object is good.
(2) That (same) distant object is a car.
(3) Therefore, that (same) distant object is a good car.
If this argument is to show the inferential irregularity of ‘good car’, then, as has been noted, (i) it must be invalid, and (ii) its predicative counterpart must be valid. But, on the assumption that every one of the sentences (1)–(3) is logically well-formed, one could hold their sequence to meet the first condition only by supposing that some expression in them, presumably ‘good’, is employed equivocally; and if that were the case then the predicative counterpart of the argument would have to use more than one predicate letter to stand for different occurrences of the supposedly equivocal word. It would therefore also be invalid, and the original argument would consequently fail to meet the second condition. Thus, the example fails to reveal inferential irregularity.
One faces even greater difficulties in finding a proof of attributivity in the passage about ‘bad’. Geach writes:
[That ‘bad’ is attributive] is fairly clear … because ‘bad’ is something like an alienans adjective; we cannot safely predicate of a bad A what we predicate of an A, any more than we can predicate of a forged banknote or a putative father what we predicate of a banknote or a father. We actually call forged money ‘bad’; and we cannot infer e.g. that because food supports life bad food supports life.
For a start, it is not clear how one is to take Geach's point about ‘bad’ being ‘something like’ an alienans adjective. One may be tempted to construe it as implying the following argument: alienans adjectives are attributive; ‘bad’ is ‘something like’ an alienans adjective; therefore, ‘bad’ is attributive. Such an argument would be a miserable non sequitur; for without a specification of the respect in which ‘bad’ is like an alienans adjective, and a proof that the respect in question is what makes alienans adjectives attributive, the conclusion does not follow.Footnote 9
But perhaps the likening of ‘bad’ to alienans adjectives is merely an expository device. The nerve of the argument would then be the claim that, when ‘bad’ is applied to some object in combination with some substantive ‘A’ (e.g., ‘food’), we cannot make those predications of the object which we otherwise make of an A (e.g., ‘supports life’). That would be the respect in which ‘bad’ is like an alienans adjective. So understood, the passage at least does not fall flat on its face argumentatively; but there remains the question how this fact about ‘bad’ is supposed to show that it is attributive. The difficulty this time is that the statement ‘Food supports life’ must figure as a premiss and yet has no determinate logical quantity. Should it be understood as a strictly universal statement, ‘All food supports life’, or as a merely general one, such as ‘Most food supports life’? Neither option gets us what we are after.
To see this, suppose that we take the premiss to be a universal statement. We then get the argument: ‘All food supports life; therefore, bad food supports life’. Obviously, the argument rests on a false premiss: some food presumably does not support life, namely some bad food.Footnote 10 But if it were true that all food supports life, the conclusion would follow without a hitch. The argument is therefore valid (even though not sound) and accordingly provides no evidence that ‘bad’ is attributive.
The other option is to take the premiss to be a rough generalization, such as ‘Most food supports life’. We then get the argument: ‘Most food supports life; therefore, bad food supports life.’ This is certainly an invalid argument; but it is not an argument whose predicative counterpart is valid: from ‘Most F is G’ one cannot infer ‘Such and such F is G’.Footnote 11 Again, the argument does not show that ‘bad’ is attributive.
Thus, so long as Geach's examples with ‘good’ and ‘bad’ are interpreted in terms of inferential irregularity, they manifestly fail to show that those adjectives are attributive.
3. Substantive-dependence
But suppose that, instead of assuming that inferential irregularity is the key to understanding Geach's arguments that ‘good’ and ‘bad’ are attributive, we ask what conception of attributivity his arguments require. If we do so, we find that, in these cases, what makes an adjective attributive is the fact that it cannot be used to make a logically complete predication unless it modifies some substantive expression.Footnote 12 For convenience, we shall say that, according to this conception, an adjective is attributive just in case it is substantive-dependent.Footnote 13
Consider, again, the point about ‘good’. If Jones can see that the speck in the distance is red, and keen-eyed but colour-blind Smith tells him that it is a car, Jones can conclude that the thing in question is a red car: so why can there not be a corresponding case with ‘good’—one in which Jones supplies the judgment that that thing is good, Smith tells him that it is a car, and Jones concludes that it is a good car? The obvious answer is that there is no such thing as ‘judging that a thing is good when one does not know what the thing is’. To say, ‘That thing in the distance, whatever it is, is good’, is to talk vacuously. Such an utterance is not a logically complete sentence: ‘is good’, used without a substantive, either in explicit combination with it or, as Geach says, ‘supplied from the context’, is not a genuine predicate at all. The example thus appears to be an attempt to show that ‘good’ is attributive by drawing attention to its substantive-dependent character.
Geach's argument about ‘bad’ also fares better when understood along these lines. To see this, recall that Geach's main claim about ‘bad’ is that ‘we cannot safely predicate of a bad A what we predicate of an A’. Geach contrasts this point about ‘bad’ with a companion observation about ‘good’, that ‘whatever holds true of an A as such holds true of a good A’. The idea appears to be that, if one is to say of some A that it is a bad A (or simply that it is bad A, if ‘A’ is a mass term), there must be some predicates that are true of an A as such, or in kind, even though they do not hold true of every A (e.g., ‘supports life’ holds of food as such, but not of everything that is food). To say of some A that it is a bad A is to say that some such predicate (one or more) is not true of it. Now, provided that this holds for the use of ‘bad’ quite generally, and not merely for its use as a qualifier of nouns, it plainly follows that any attempt to apply ‘bad’ without applying it to qualify some particular substantive fails to constitute a genuine predication. Thus ‘bad’ is substantive-dependent, and therefore attributive.
For present purposes, it is not necessary to find these arguments for the attributivity of ‘good’ and ‘bad’ conclusive. The idea of what may ‘safely’ be predicated of an A is far from perspicuous, and it may not be taken for granted that ‘good’ and ‘bad’ have only the sort of use that Geach describes. But this should not obscure the fact that neither argument is the non-starter it has struck critics as being. Our point is merely that Geach's treatment of ‘good’ and ‘bad’ rests on the understanding of attributive adjectives as substantive-dependent adjectives, rather than as adjectives, complex predicates with which are inferentially irregular.
4. So What Is an Attributive Adjective?
At this point we appear to have on our hands two different accounts of what an attributive adjective is. According to the one suggested by Geach's treatment of ‘big’, ‘small’, ‘forged’, and ‘putative’, an attributive adjective is an adjective that when combined with a noun forms an inferentially irregular predicate. According to the other account, suggested by Geach's treatment of ‘good’ and ‘bad’, an attributive adjective is a substantive-dependent adjective. We shall argue that, of the two, only the latter identifies a genuine logical characteristic of adjectives. The inferential irregularity of complex predicates using a given adjective is better regarded as a manifestation of attributivity than as a defining mark of it.
If attributivity is to be defined in terms of inferential irregularity, there are two ways of accomplishing the task. One is to say that an adjective is attributive just in case some complex predicate with it is inferentially irregular. Such a definition follows Geach's own formulation, according to which an adjective is predicative just in case some complex predicate with it fails to ‘split up logically’. But it is easily seen that on this definition an adjective can be counted as ‘attributive’ for reasons that have nothing to do with its logical character; for it is conceivable that, just as there are substantive-dependent adjectives, there could be adjective-dependent nouns. Imagine, for example, a noun ‘nort’ that works by negating the adjective with which it is combined; or a noun ‘bleve’ that indicates that the adjective with which it is combined is believed to hold of that of which the adjective–noun combination is predicated. Thus, to say, e.g., ‘That book is a red nort’ would be as much as to say ‘That book is not red’, and to say ‘Jones is a dead bleve’ would be equivalent to saying, ‘Jones is believed dead’. Clearly, predicates formed of such nouns would be inferentially irregular: from ‘That book is a red nort’ one could not infer ‘That book is red’, nor from ‘Jones is a dead bleve’ could one infer ‘Jones is dead’. If the English language contained such nouns, it would be possible to form an inferentially irregular predicate from any adjective that could be intelligibly combined with them. In such a scenario, the class of adjectives that can be made to count as ‘attributive’ by the given definition threatens to extend over all adjectives in the language. It may well be that no adjective-dependent nouns exist in English, or in any other natural language. But the conceivability of such nouns shows that the proposed definition is capable of classifying adjectives as ‘attributive’ regardless of their logical character.
The other option is to say that an adjective is attributive just in case every complex predicate with it is inferentially irregular. Such a definition will not have the problem just mentioned, for if an adjective forms an inferentially irregular complex predicate with any noun with which it can be intelligibly combined, whether the noun is adjective-dependent or not, then it must have a distinctive logical character by which it does so. The definition, however, does not tell us what this logical character is. It specifies which adjectives are attributive, but gives no account of what makes them so.
We can solve both problems by identifying attributivity with substantive-dependence. An attributive adjective may be defined as an adjective that cannot be used to make a logically complete predication unless it modifies some substantive; or, in slightly different phrasing, as an adjective that forms predicable terms through, and only through, combination with substantives.Footnote 14
It may clarify the meaning of this definition to return to the contrast with predicative adjectives. A predicative adjective may be applied either by itself or in combination with a noun. In the latter case, adjective and noun form a compound term, the truth-value of an application of which is determined by those of the applications of the component terms. E.g., ‘That is a red car’ is true just in case ‘That is red’ and ‘That is a car’ are both true of the object in question. An attributive adjective, by contrast, can be applied only in combination with a noun. A term thus formed—‘good car', ‘putative father’, ‘big flea’, etc.—is complex, but not compound:Footnote 15 its sense is a function of the senses of each of the component expressions, but the truth-value of an application of the complex term cannot be determined by applying the two component expressions separately; for one of them, namely the adjective, has no truth- or falsehood-yielding application by itself.
This definition also makes possible a straightforward account of the connection between attributivity and inferential irregularity; for it is easily shown that any complex predicate with a substantive-dependent adjective is necessarily inferentially irregular. Suppose, for instance, that ‘A’ is a substantive-dependent adjective, ‘B’ a noun with which it may be combined, and ‘s’ a possible subject of predication. Since ‘A’ is substantive-dependent, ‘s is A’ has no truth-value: it therefore cannot be inferred from ‘s is an A B’. Thus, applications of ‘is an A B’ deviate in at least one respect from the forms that govern logical conjunctions. In general terms, any complex predicate using an attributive adjective must be inferentially irregular in at least the specified respect. It follows that the proposed definition is compatible with the use of sample arguments to prove the attributivity of adjectives, provided that none of the nouns used in the arguments are adjective-dependent ones. (The specified condition will be otiose if there are no such nouns in the language.)
To be sure, the impossibility of inference from ‘s is an A B’ to ‘s is A’ is not the only variety of inferential irregularity that complex predicates using attributive adjectives can exhibit: it is merely the one variety that necessarily attends every such adjective. Other varieties are easily found. E.g., from ‘Smith is an alleged thief’ one cannot infer ‘Smith is a thief’, and from ‘Daisy is a small elephant’ and ‘Every elephant is an animal’ one cannot infer ‘Daisy is a small animal’, although one can infer ‘Daisy is an elephant’. On the other hand, complex predicates using certain attributive adjectives do not exhibit any form of inferential irregularity beyond the kind that marks all complex predicates using attributive adjectives. E.g., from ‘This is a real banknote’ one can draw exactly those conclusions which one can draw from ‘This is a banknote’. The variety of ways in which attributive adjectives manifest inferential irregularity owes to the variety of ways in which such adjectives logically depend on the nouns with which they combine. There is no way to investigate these varieties without examining in detail the adjectives concerned. But there is no way to begin that task without first getting clear on what it means for an adjective to be attributive. We leave the former task for another occasion, but we believe that we have accomplished the latter.
