Frege makes a distinction between concept and predicate. If the predicate is ‘red’, as in
The ball is red.
Here ‘red’ is used as a predicate of the ball, whereas redness is the extension of the predicate ‘red’.
Redness is not a predicate. For example, we cannot say ‘This ball is redness’. Instead it is a concept. It is not as easy to predicate a concept. For example
Redness is a colour.
wouldn’t quite work. It should be
Red is a colour.
where red is itself a concept but not a predicate.The concept ‘redness’ has an extension: redness or the class of all red things.
A concept is applied to something. It is ‘predicative’. On the other hand, a ‘proper name’, say, ‘John’, cannot be used as a predicate. For example, ‘This hat is John’. We can say that something is ‘Alexander the Great’, or that something is ‘green’. But these two examples are not logically equivalent.
…is a mammal.
or
…is green.
are both copula. That is, ‘is’ is used as a sign of predication. By saying that something ‘is green’ we are saying that
….this cabbage has greenness as a predicate.
or that we predicate ‘mammal’ of a whale. ‘Green’ and ‘mammal’ are concept-words. ‘Cabbage’ and ‘whale’ will ‘fall under’ the concepts ‘green’ and ‘mammal’.
On the other hand, ‘is’ in the example
The Morning Star is Venus.
is used as ‘equal to’ – the sign of equality. With regard to
The Morning Star is a planet.
‘planet’ is a ‘concept-word’ that Venus ‘falls under’ (24) as a proper name.
The Morning Star is white.
and
The Morning Star is a planet.
are not logically equivalent. The former ‘white’ is a predicate whereas the latter ‘planet’ is a concept-word. The first example is descriptive, whereas the latter is telling us what the Morning Star is – what concept it falls under.
Concepts are essentially predicative. For example, the concept [red] is used predicatively in the sentence
The ball is red.
That is, ‘is red’ is the predicate and [red] is the concept.However, a proper name like ‘Tony Blair’ cannot, according to Frege, be used predicatively. We cannot write ‘The ball is Tony Blair’. That is because proper names are not concepts; they are proper names that are used essentially to refer to objects, either abstract or concrete. This simply means that proper names don’t really say anything. If they are used predicatively of, say, ‘The ball’, then a proper name predicate cannot say anything about the ball in question.The predicate ‘is red’ can sometimes be used as the subject of a sentence. For example,
Red is a beautiful colour.
Here we could say that we have a second-order predicate, ‘beautiful’, being applied to a first-order predicate, ‘Red’. Or, alternatively, a second-order concept [beautiful] is applied to a first-order concept [red]. In addition, we can have proper names that function predicatively. For example
This town is no Vienna.
Here the proper name ‘Vienna’ is being used predicatively of the subject ‘This town’. But we can say that it this case the proper name ‘Vienna’ does not function entirely as a proper name. In this instance, ‘Vienna’ has a definite sense, which could be, a beautiful city. If it were just used referentially, then it would not work as a predicate of a sentence or as a second-order concept.However, isn’t it always the case that proper names have a sense? Even when a proper name is used as a subject in a sentence, that proper name, say ‘Vienna’, will still have a sense. Even in that case a predicate will be being applied to a subject that has itself a sense. Or a predicate will be being applied to something that itself has a predicative value or can used use as a concept of another concept.
Concepts Applied to Concepts
In
All mammals have red blood.
we appear to have a sentence with two concepts or two predicates. Both ‘mammals’ and ‘have red blood’ could be used conceptually or predicatively. We don’t appear to have a proper name or a proper subject in this sentence. What we have, instead, is a statement about two concepts that are related to each other. The proper Fregean formulation would be:
Whatever is a mammal is red-blooded.
This means that a certain set of objects falls under two separate concepts: [mammals] and [red-blooded]. We can also say that the class red-blooded animals is more primary or is bigger than the class mammals. We can conclude that the secondary class, mammals, could be used predicatively of the primary class, red-blooded animals. And, indeed, this is what Frege argues. We have the subject-term of this sentence, ‘mammals’, being used predicatively. The ‘mammals’ is being predicated of ‘is red-blooded’. After the analysis of its logical grammar, we can see that this is not a typical subject-predicate sentence because the subject-term is in fact the predicate. Couldn’t we also see it as an identity statement? Such as:
Mammalian animals are identical to red-blooded animals.
However, we couldn’t because the class of red-blooded animals is larger than the class of mammals. This would effectively mean that there are red-blooded animals that are not mammals. And if that’s the case, then it cannot function as a genuine identity statement because they do not refer to the same class or the same set of objects or animals.
In
The ball is red.
the predicate is ‘red’. In
Red is beautiful.
the word ‘red’ is a concept-word. In that sentence a predicate is applied to a predicate. If that is the case, then the predicated predicate becomes a concept-word and ‘beautiful’ is a second-order concept. That is, a predicate applied to a predicate.
A second-order concept is applied to a first-order concept. The concept [mammals] can be applied to the concept [red-blooded animals]. We are tempted to say here that we are really referring to the extension of the concept [mammals], not to the concept itself. It is mammals that are really red-blooded; it is not the concept [mammals] that is itself red-blooded. Can we escape from concepts when we are intending to get to the various extensions of concepts?Take this example of a second-order concept being applied to a first-order concept:
The concept [round square] is empty.
In this instance the second-order concept [empty] is being applied to the first-order concept [round square]. Both the subject and predicate certainly appear to be concepts of some description. However, if extensions are important, if they determine reference and predication, then the concept [round square] has no extension. As the sentence says, the concept “is empty”. In this instance we cannot be relying on the extension of [round square]. In addition, as Frege said, the concept [empty] has a number as a synonym – viz., 0. This is the zero class. However, numbers can only be applied to concepts, not directly to objects. So even if the concept [round square] were not an empty class, the predicate “is empty”, or the number 0, can only be applied to the concept [round square], not to the extension of that concept. The conclusion seems to be that we cannot dispense with concepts even when we are talking about extensions or references.
That’s the important point here. Concepts are applied to concepts, not the extensions of the concepts. We are either saying something about the concept itself, or the extension of the concept. This seems to result in a kind of conceptual idealism. And perhaps this is one reason why Quine, for one, wanted extensions too to be important and why Frege himself distinguished ‘the concept horse’ and ‘horse’.
When Concepts Become Objects: The Concept Horse
The singular definite article ‘the’ indicates an object. As in:
The horse over there.
The indefinite article ‘a’ indicates a concept word, as in:
Is that a horse?
Here ‘…a horse’ is a concept-word, signifying the ‘universal horse’. ‘The horse…’ is defining a singular object.
When we use the word ‘the’ we are referring to a single definite object. When we use ‘a’, on the other hand, we are referring to a concept-word. We are not referring to a single definite object, but a kind. That is
Is that a horse?
can be translated into:
Is that thing an example of the horse kind?
That means we are referring to a concept, [horse], rather than a particular individual that may well fall under the concept or kind.
So Frege makes the counterintuitive claim that in
The concept horse is a familiar one.
the subject, ‘the concept horse’, is not the name of a concept, but the name of an object. This is the case, Frege argues, because the subject term is prefixed by the definite article ‘the’. Usually when we refer to a concept we use the indefinite article. For example, ‘a mammal’, ‘a whale’ or ‘a man’.When we use the definite article ‘the’ we are referring to a specific thing. This is not the case with ‘a’. If ‘The concept horse’ is a definite thing, rather than, say, a collection or an extension, then it must be being used as an object and not a concept.In ‘the evening star’ and ‘the capital of Australia’ we use the definite article ‘the’. Therefore we must be referring to a specific object rather than a class or an extension. The second-order concept [is a familiar one] is being applied to a first-order concept [the concept horse] that has become an object instead. In ‘The concept horse’ we are not referring to the concept [horse] directly, and therefore its extension, but to the concept itself [the concept horse]. When we say that “This is a horse’ we use the indefinite ‘a’ because we are referring to a second-order concept that has a certain extension. In ‘The concept horse’ we are referring to the concept [horse] and not its extension. In that instance, it is the concept that ‘is a familiar one’, not its extensional meaning. Usually we refer to concepts as a means to get at the reference or extension. In the case of ‘The concept horse’ we are referring to the concept that is applied to horses, not to the class of horses itself. If we use the definite article ‘the’ in a seeminglypredicative sentence, then the second-order concept, [is a familiar one], is referring to the concept as object – viz., ‘the concept horse’ rather than [horse].
The obvious point here is that we need to distinguish when we are referring to a concept itself, or the concept’s extension. Are we referring to the concept of a horse or to horse itself? This simply means that we can say things of horses that we cannot say of the concept [horse]. For example, we can say:
The concept horse is an abstract object that many people use.
Or:
Horses have long tails and hooves.
Clearly the concept horse does not have a long tail or hooves, just as horses are not abstract objects that many people use.
When we talk of a concept, or predicate properties of that concept, then that concept becomes an object or a concept-object. We are predicating the concept itself, rather than, say, the extensions of that concept.We can have two similar expressions. 1):
The city of Berlin.
2):
The concept horse.
On the surface they seem like similar expressions. They both begin with the definite article ‘the’. However, the first expression is about a concrete object – the city Berlin. The second expression, on the other hand, is about an abstract object – the concept horse. In that case Frege italicises the word ‘horse’ in ‘The concept horse’, but he does not italicise the word ‘Berlin’ in ‘The city of Berlin’. ‘Horse’ and ‘Berlin’ are both objects. The italicised ‘horse’ is an object or a concept-object.
It certainly seems counter intuitively to say that the concept horse is not a concept. Why refer to it as a ‘concept’? When we say that ‘The city of Berlin is a city’ we don’t also say that ‘The city Berlin is not a city’. What differentiates these two examples? Frege simply says that whereas the horse in ‘the concept horse’ is italicised, the Berlin in ‘The city of Berlin’ is not italicised. The italicising must therefore turn the concept into an object. Or the concept [horse] becomes the object horse. An object, when it is also a concept, must be italicised in order to make it clear that it has this double function. How does the italicising alone solve Frege’s puzzles? I don’t see how it can. Perhaps it all boils down to the fact that ‘The concept horse’ is being used as a subject-term in ‘The concept horse is a familiar one’. That is, the predicate concept [is a familiar one] is predicated of the subject ‘The concept horse’. Consequently, a concept or predicate can only be applied to an object, not another concept. It is still the case that ‘the concept horse’ is neither an object nor a predicate/concept, but an object-concept or a subject-predicate.
Reference to the Concept of an Object, Reference to an Object, and Concept-Objects
Frege is clearly trying to distinguish references to objects and references to concepts. If we get the two things mixed up, then we may end up talking nonsense. Take the sentence
There is at least one square root of 4.
This is clearly a reference to an object – viz., the square root of 4. There is no mention here of concepts.However, what if we say
The concept square root of 4.
Here we are referring to a concept, even if that concept is [square root of four]. It is not referring to what is the square root of 4, that is an object, but it is referring to the concept [square root of 4] not what is the result of the square root of 4. The concept of the object and the object are, therefore, two very different things. Concepts have certain attributes that objects don’t have. We must make sure whether or not we are referring to the concept of an object or the object itself. That is, the object 4 may not be familiar, but the concept [4] may well be familiar.
We cannot say that the concept [square root of 4] has as it result a certain number, it is the object the square root of 4 that has as its result a number. Concepts in and of themselves cannot have square roots, only the objects we call ‘numbers’ have square roots. However, it is indeed the case that the result of the square root of 4 can be used as a concept, but the concept would still be different to the number that is the square root of 4. The concept [square root of 4] is something we use to get at the square root of 4; it does not tell what the square root of 4 actually is. Therefore, according to Frege, ‘the concept square root of 4’ cannot be used as the argument in a sentence precisely because it is a reference to a concept, not an object. On the other hand, ‘the concept square root of 4’ can be used predicatively or as a function in a sentence, as in
That inscription is the concept square root of 4.
Here the concept is used predicatively of the subject-term ‘inscription’. And so on. So, again, concepts can only be subjects if they are used as a concept-subject, not just as a concept. That is, ‘the concept horse’ is a concept-object, whereas [horse] is just a concept.
It is clear from all this that Frege thought that it is vitally important to distinguish talking about a concept from just using a concept (i.e., to refer to an object). When we talk about a concept itself, then that concept effectively becomes an object, or an object-concept. When used predicatively, the concept is simply a concept and not an object. In ‘The concept horse’ we are talking about a concept therefore the concept becomes an object. In ‘Jasper is a horse’ the concept [horse] is used predicatively and therefore cannot be an object. To put it simply, we will say different things about an object than we would say about the/a concept of that object.
Fregean Individual Concepts
There is a lone history of quantification over concepts. For example, it was Frege’s idea that predicates ‘denoted’ concepts rather than objects. Or perhaps we should say that in a Fregean scheme we quantify over “senses” rather than concepts:
… in Frege, that in opaque contexts, names refer to something other than their ordinary referents such as the senses of names. (Marcus, 1978)
In the following scheme it is not just predicates that denote concepts, but names and singular descriptions do so too. So that whereas in certain schemes in the sentence
Tony Blair is wise.
only the predicate ‘is wise’ denotes a concept, but in the following scheme the name ‘Tony Blair’ also “refers” to a concept or to concepts. In the Fregean scheme the name ‘Tony Blair’ also has a ‘sense’ as well as a referent. For Frege the sense of the name ‘Tony Blair’ was not the same as a concept as the term is used in the following.
I would like to make another quick note here about the relation between concepts and objects. Frege himself has been the object of such criticisms. Take Forbes’s interpretation of what may be a possible account of the Fregean scheme:
Echoing Church, a traditional Fregean could point out that it is not part of her theory that… ‘Lex Luthor is afraid of the concept of Superman’, and that the relation holding between [Luthor] and the concept of [Superman] is not quite that of [being afraid of]…surely one’s current perceptual beliefs about x can prompt fear of x directly, without a detour through fearing* [the concept of x]. Indeed, I doubt that we can explain what fearing* a way of thinking of x is except in terms of fearing x. (Forbes, 1996)
I hope that Forbes’s distinction of “fearing” a concept and fearing anobject is not feasible. However, Forbes himself says later that the object itself is not feared or admired because such an object is feared or admired only with a name attached to it. And, if the object has a name attached to it, it will also have concepts attached to it :
Thus ‘Superman is Lois’s hero’ is interpretable as ‘Superman, so labelled, is Lois’s hero’, in which there is a three-place relation x is a hero of y under mode of presentation m. (Forbes, 1996)
Forbes in the above brings in the notion of a “mode of presentation” of x. The thing that was feared in the earlier extract, is in fact feared
under a mode of presentation.
If that is the case, perhaps Forbes was incorrect to distinguish “fearing* a way of thinking of x” from simply “fearing x”. And, again, “modes of presentation” bring in concepts even if the object isconceptually separable from particular “modes of presentation”. However, Forbes again sees problems with the “Fregean account”:
…[we are in] the unfortunate position of having to find something for [the name] ‘Superman’ to denote…other than Clark Kent – that is, Superman. A traditional Fregean proposal would be that ‘Superman’ refers to an individual concept…but this is the sort of view to which Davidsonian incredulity is an entirely appropriate response: it is not a concept that Luthor is afraid of, it is the man himself…
But then we get this passage again:
Lois Lane admires Superman, so labelled…
Lex Luthor is afraid of Superman, so labelled… (Forbes, 1996)
Forbes makes a distinction between being afraid of a Fregean “individual concept” and being afraid of “the man himself”. But if Luthor is afraid of “the man himself” (i.e., Superman), he has already applied the sortal concept man to Superman. No one, however, fears a concept as such, but an object seen through the spectacles that are concepts, as it were. It depends, of course, on the metaphysics and epistemology of concepts, which is not the concern of this essay. No one fears a concept qua concept. For example, say concepts are seen as tools of individuation. Then no one would fear tools of individuation. Or say that concepts are defined in terms of the roles they play within mental economies. In that case, no one would fear something that simply plays a role in a mental economy. Davidson’s “incredulity” is understandable if the notion of a concept is torn free from the objects of concepts. If concepts were torn asunder from their objects, then this would indeed be an example of what I have called “conceptual idealism” (or even of “conceptual relativism”). However, just after such protestations on Forbes’s part, he again talks about Superman “so labelled”. And, as I’ve said, a name brings along with it concepts, especially if the object of the concepts is “feared” or “admired”. With fearing and admiring now brought on board we go much further than the Kripkean practice of simple naming and causal contact with an object or referent. We fear an object because of our conceptual mediation of an object; except, perhaps, if we are talking about some kind of pure and instantaneous physiological fear-response to an object (but that sort of physiological fear would not be fear of Superman “so labelled”).
References
Forbes. G.(1996) ‘Substitutivity and the Coherence of Quantifying In’, in The Philosophical Review, 105
Marcus. R.B. (1978) ‘Nominalism and the Substitutional Quantifier’, in The Monist 61
