Locke and Berkeley on Abstract Ideas: From the Point of View of the Theory of Reference

In the Essay Locke argues abstract ideas within the framework of the descriptivist theory of reference. For him, abstract ideas are, in many cases, conceptual ideas that play the role of “descriptions” or “descriptive contents,” determining general terms’ referents. In contrast, in the introduction of the Principles, Berkeley denies Lockean abstract ideas adamantly from an imagistic point of view, and he offers his own theory of reference seemingly consisting of referring expressions and their referents alone. However, interestingly, he mentions a general term’s “definition” and suggests that it determines the scope of the term’s referents. For example, he takes up the definition of a triangle as “a plain Surface comprehended by three right Lines” and suggests that just as Locke’s general idea of a triangle does, the definition determines the referents of the general term “triangle.” His definition reminds us of the fact that as Descartes grasps the content of the general idea of a triangle as “a figure enclosed by three lines,” so Locke grasps the abstract idea of a triangle as “a Figure including a Space between three Lines,” and so on. That is, since Berkeley is an imagist, he does not acknowledge Locke’s conceptual abstract ideas as “ideas,” but although he verbally denies “abstract ideas,” his theory of reference also actually has the same descriptivist framework consisting of referring expressions, their descriptive contents, and their referents. Thus, we understand the real reason why Berkeley’s criticism of Locke seems beside the point.


Introduction
Nowadays it is well known that Locke's theory of reference in the Essay has two aspects: one is "descriptivist" and the other "causal." It has long been known that according to Locke, things are classified into species by means of "general ideas," "abstract ideas," or "nominal essences," and that the referents, which are referred to by a "general name" or a "general term," are determined by whether or not they agree with the content of a general idea or an abstract idea, or a nominal essence that the name or the term signifies (see, e.g., Schwartz, 1977, Introduction, p. 16). In contrast, since Mackie made it clear that Locke had also shown a sort of causal theory of reference in Book III, Chapter x in the Essay (Mackie, 1974), which is one of the chapters often deleted in the abbreviated editions of the Essay, the situation of the interpretation of Locke's theory of reference has noticeably changed. If we bear in mind the fact that in the Essay, Locke considers various subjects within the corpuscularian framework that has a dual structure consisting of two different sorts of objects-"things themselves" on the one hand, and what I call "experiential objects" (see Tomida, 1995, pp. 75-93;2001a;2014) on the other, it is not surprising that his theory of reference has such two aspects. Originally, Donnellan's and Kripke's causal theory of reference (or "historical explanation theory" [Donnellan, 1974, p. 3]) was treated as a theory opposed to Frege-Strawson-Searlean descriptivism, but mainly due to Searle's responses to the causal theory (e.g., Searle, 1979;1983, Chap. 9; see also Rorty, 1976;Tomida, 2007, Chap. 3), the tension between the two were appreciably lessened. Moreover, the theory of reference concerning natural kind terms, which at around the same time Putnam proposed (Putnam, 1970(Putnam, , 1975(Putnam, , 1983, was the one that, unintentionally, reconfirms the consistency of Locke's theory of reference consisting of the two seemingly conflicting aspects (Tomida, 2001b).
When we bear in mind the classical controversy on the theory of reference among Searle, Donnellan, Kripke, Putnam, and Rorty and look anew at Locke's theory of reference from such a point of view, Berkeley's argument against Locke's theory of abstract ideas comes to seem different. The purpose of this paper is to reexamine the validity of Berkeley's argument from the viewpoint of the theory of reference. 1 As a corpuscularian, Locke hypothetically posits the world of "Things themselves" that we cannot immediately perceive. In this conjunction, he positions the things that we are familiar with every day and perceive immediately (which I call "experiential objects") as "ideas" produced in the mind by things themselves' affecting our senses. However, because in everyday life, experiential objects are "things," in the Essay Locke often treats them as "things." But when he speaks strictly, he clearly distinguishes between things themselves on the one hand and experiential objects qua ideas in the mind on the other (see Tomida, 1995, pp. 75-93;2001a;2014 2 ). Therefore, if we want to understand Locke correctly, we must bear this distinction in mind. It is as to those "experiential objects" that Locke shows his descriptivist theory of reference; his causal theory of reference is mainly concerned with "things themselves." In Locke's descriptivist view, which is mainly applied to experiential objects, abstract general ideas express "descriptive contents." 3 According to Locke, in the case of the abstract idea of man, for example, its content is "a solid extended Substance, having Life, Sense, spontaneous Motion, and the Faculty of Reasoning" (Locke, 1975, III. iii. 10, p. 413) and in the case of a triangle, it is "a Figure, with three sides meeting at three Angles" (II. xxxi. 3, p. 376), "three Lines, including a Space" (II. xxxi. 6,p. 379;II. xxxii. 24,p. 393), or "a Figure including a Space between three Lines" (III. iii. 18,p. 418). When things (experiential objects) agree with an abstract idea, they are called by the term or name that "signifies" the abstract idea. We find such a situation not only regarding sensed experiential objects, but also regarding the experiential objects produced in the mind as mental images. Whether they be sensations or mental images, if they agree with the content of a certain abstract idea, they are called by the name that is annexed to the abstract idea. 4 In contrast, Berkeley wholly denies Locke's abstract ideas. Berkeley treats them as nonexistents. Thus, whereas Locke grasps the reference as a phenomenon that consists of three terms: a referring expression, a descriptive content that the referring expression possesses, and a referent or referents of the referring expression, Berkeley constructs his theory of reference, seemingly 5 only from two terms: a referring expression and its referents. Namely, whereas Locke thinks that "Words become general, by being made the signs of general Ideas" (Locke, 1975, III. iii. 6, pp. 410-411), Berkeley explains that "a Word becomes general by being made the Sign, not of an abstract general Idea but, of several particular Ideas, any one of which it indifferently suggests to the Mind" (Berkeley, 1734, Introduction, XI, p. 15;1949, Introduction, § 11, p. 31). According to him, the generality of referring expressions is based on their ability to refer to their referents "indifferently." Needless to say, however, this is a queer view. For, as far as the relation between a general referring term and its referents is concerned, the situation that Berkeley points out-that is, the situation to the effect that a general referring term refers to various particular referents indifferently-is a matter of course in Locke's case too. In the case of Locke, when we call to mind an experiential object qua a mental image that is referred to by a general term, for example, of "man," it may be a mental image of Peter, or that of James, or that of Mary, or that of Jane; that is, we may picture to ourselves a mental image of a certain particular person "indifferently." Therefore, as far as this point is concerned, we find nothing new in Berkeley's view; this is just a basic fact of general referring expressions. However, Berkeley thinks that it is this indifference of a general term's referents that explains the term's generality. According to him, a general term is general not because it signifies an inexistent abstract general idea but because it can suggest various particular ideas indifferently.
If so, however, the problem comes down to the old one of how Berkeley's particular ideas, which are referred to by a general term indifferently, are treated as of the same kind. Unlike Locke, Berkeley does not grapple squarely with this problem. In his argument against abstract ideas, he, from the beginning, presupposes that particular ideas qua referents are already classified into various sorts. By this presupposition he puts out of sight some important problems that the theory of reference must address, but this is not the only defect in his theory. Whereas Berkeley totally denies Locke's abstract ideas, he himself mentions the importance of a "definition" and suggests that if the definition of a general name is not fixed, the scope of the particular ideas that it stands for fluctuates.
We know that Descartes, who introduced modern "idea" language, often treated concepts as ideas. Further, we know that contrary to Berkeley's interpretation, Locke treated, like Descartes, ideas qua concepts in many cases. From Locke's point of view, the "definition" that Berkeley mentions corresponds to the abstract idea that a general term signifies, but Berkeley the imagist does not admit that it is an idea. 6 If he understands, however, that Locke refers to Berkeley's "definition" as an "abstract idea," then he will know that in the case of himself too, definitions interpose themselves between general names and the particular ideas that general names indifferently suggest, and that the result is the same as Locke's. In short, although Berkeley too admits the importance of the role of Lockean abstract ideas, he does not refer to his definitions as abstract ideas, and he asserts, without justifiable grounds, that only by the relations between the remaining two terms-that is, only by the general terms and the particular ideas indifferently signified by them-he solves the problem that Locke failed to solve.
To show this, I start from reconfirming what the abstract ideas, which Berkeley took up as his targets, are. 7

Three Sorts of Abstracts Ideas qua Berkeley's Targets
In the Introduction, § § 7-9 of the Principles, Berkeley takes up three sorts of abstract ideas and explains them as follows: (1) As the extension, the color, and the motion in "an Object extended, coloured, and moved" (Berkeley, 1734, Introduction, VII, p. 8;1949, Introduction, § 7, p. 27) show, "the Qualities or Modes of things do never really exist each of them apart by it self, and separated from all others, but are mix'd, as it were, and blended together, several in the same Object" (Introduction, VII, p. 7; Introduction, § 7, p. 27). However, some people say that "the Mind being able to consider each Quality singly, or 6 As is well known, in the second edition of the Principles Berkeley emphasizes the special role of "notions" in an interesting manner, but when he criticizes Locke, he does it exclusively from the imagistic point of view. For Berkeley's usage of "notion," see, e.g., Adams (1973), Beal (1971), Davis (1959), Flage (1985Flage ( , 1987, Furlong (1968), Kupfer (1973), Park (1972), Rome (1946), Winkler (2005), and Woozley (1976). For my interpretation of Berkeley's non-imagist thinking, see Tomida (2003, esp. pp. 81-86). 7 In this paper I do not discuss the relation between Locke's theory of ideas and Berkeley's immaterialism. For this issue, see Tomida (2002Tomida ( , 2003Tomida ( , 2010Tomida ( , 2011 abstracted from those other Qualities with which it is united, does by that means frame to it self abstract Ideas" (Introduction,VII,p. 8;Introduction,§ 7,p. 27). That is, according to them, "the mind resolve[s the mix'd or compound Idea] into its Simple, constituent Parts, and view[s] each by it self, exclusive of the rest" (Introduction, VII,p. 8;Introduction,§ 7,, and in such a manner it "frame[s, for example,] the abstract Ideas of Extension, Colour, and Motion" (Introduction, VII, p. 8; Introduction, § 7, p. 28).
(2) The abstract ideas of the second sort are more abstract. For example, particular extensions respectively have "some […] things peculiar, as this or that Figure or Magnitude, which distinguish them one from another" (Berkeley, 1734, Introduction, VIII, p. 8;1949, Introduction, § 8, p. 28). At the same time, they also have "something common and alike in all" (Introduction, VIII, p. 8; Introduction, § 8, p. 28). The mind "considers apart or singles out by it self that which is common, making thereof a most abstract Idea of Extension, which is neither Line, Surface, nor Solid, nor has any Figure or Magnitude but is an Idea intirely prescinded from all these" (Introduction, VIII, p. 8; Introduction, § 8, p. 28). As to color too, the situation is the same. The mind "by leaving out of the particular Colours perceived by Sense, that which distinguishes them one from another, and retaining that only which is common to all, makes an Idea of Colour in abstract which is neither Red, nor Blue, nor White, nor any other determinate Colour" (Introduction, VIII, pp. 8-9; Introduction, § 8, p. 28). In the same manner, "by considering Motion abstractedly not only from the Body moved, but likewise from the Figure it describes, and all particular Directions and Velocities, the abstract Idea of Motion is framed" (Introduction, VIII, p. 9; Introduction, § 8, p. 28). In short, the abstract ideas of "extension," "color," and "motion" of this sort are ideas of extension in general, color in general, and motion in general.
(3) The abstract ideas of the third sort are those of "the more compounded Beings, which include several coexistent Qualities" (Berkeley, 1734, Introduction, IX, p. 9;1949, Introduction, § 9, p. 28). These abstract ideas too have the same characteristic as those of the second sort. That is, the mind finds, for example, in particular men "that which is peculiar to each" (Introduction, IX, p. 9; Introduction, § 9, p. 28) and "what is common to all" (Introduction, IX, p. 9; Introduction, § 9, p. 28), and by "retaining only what is common to all" (Introduction, IX, p. 9; Introduction, § 9, p. 28) it makes an abstract idea of man. Furthermore, the mind finds in "all the living Creatures" (Introduction, IX, p. 10; Introduction, § 9, p. 29) including human beings, some characteristics that are common to them all, and by "retaining those only which are common to all the living Creatures" (Introduction, IX, p. 10; Introduction, § 9, p. 29), the mind frames the abstract idea of animal consisting of "Body, Life, Sense, and Spontaneous Motion" (Introduction, IX, p. 10; Introduction, § 9, p. 29). In this case, as in the case of the abstract ideas of the second sort, "By Body is meant, Body without any particular Shape or Figure" (Introduction, IX, p. 10; Introduction, § 9, p. 29). Further, "the spontaneous Motion must be neither Walking, nor Flying, nor Creeping" (Introduction, IX, p. 11; Introduction, § 9, p. 29). Thus, the abstract ideas of this sort differ from the second sort in their complexity, but both of them are the same in the point that the mind leaves out peculiar parts and "retain[s] those only which are common" (Introduction, IX, p. 10; Introduction, § 9, p. 29).

3 3 Locke's Views on Abstract Ideas
As Berkeley's words in the introduction of the Principles clearly show, when he argues against abstract ideas, he does not bear in mind only Locke's theory of abstract ideas. 8 However, judging from the commonality of Locke's and Berkeley's wordings, there is no doubt that when Berkeley takes up three sorts of abstract ideas, as far as the third sort is concerned, he bears in mind Locke's explanations in Book III, Chapter iii of the Essay. As to the first sort, since when Locke discusses the "abstraction" in Book II, he takes up the "whiteness" qua an appearance, as an example, there is a possibility that Berkeley bears in mind Locke's abstract idea of whiteness as a concrete example. In contrast, as to the second sort of abstract ideas, it is difficult to find passages in the Essay that immediately correspond to Berkeley's explanations. However, many simple ideas that Locke discusses in the Essay virtually correspond to the second sort of abstract ideas.

On the First Sort of Abstract Ideas
As I have just mentioned, in Book II, Chapter xi of the Essay, Locke seems to deal with the first sort of abstract ideas. Regarding "abstraction," he says: The use of Words then being to stand as outward Marks of our internal Ideas, and those Ideas being taken from particular things, if every particular Idea that we take in, should have a distinct Name, Names must be endless. To prevent this, the Mind makes the particular Ideas, received from particular Objects, to become general; which is done by considering them as they are in the Mind such Appearances, separate from all other Existences, and the circumstances of real Existence, as Time, Place, or any other concomitant Ideas. This is called ABSTRACTION, whereby Ideas taken from particular Being, become general Representatives of all of the same kind; and their Names general Names, applicable to whatever exists conformable to such abstract Ideas. Such precise, naked Appearances in the Mind, without considering, how, whence, or with what others they came there, the Understanding lays up (with Names commonly annexed to them) as the Standards to rank real Existences into sorts, as they agree with these Patterns, and to denominate them accordingly. (Locke, 1975, II. xi. 9, p. 159) Then, citing a concrete example, he continues: Thus the same Colour being observed to day in Chalk or Snow, which the Mind yesterday received from Milk, it considers that Appearance alone, makes it a representative of all of that kind; and having given it the name Whiteness, it by that sound signifies the same quality wheresoever to be imagin'd or met with; and thus Universals, whether Ideas or Terms, are made. (Locke, 1975, II. xi. 9, p. 159) In this passage he takes up "Whiteness" qua an "Appearance" as an example. Therefore, it is certain that Locke is treating an idea qua a mental image as an abstract idea. He says that "Thus the same Colour being observed to day in Chalk or Snow, which the Mind yesterday received from Milk, it considers that Appearance alone." In this consideration of "that Appearance alone," several significant mental operations are involved. One of them is to deal with the appearance "without considering, how, whence, or with what others [it] came there." This operation has an implicit premise; that is, the premise that when such an appearance of whiteness appears, it is already accompanied by various determinations that make it particular. His words "without considering, how, whence, or with what others [it] came there" means that we do not consider the way the appearance is being given, its temporal and local determinations, and various other concomitants. Thus, according to Locke's explanation, when the "same" idea qua a certain appearance appears, it is already accompanied by various conceptual determinations, and by the mind's not "considering" those determinations that make the idea qua an appearance particular, the appearance becomes "a representative of all of that kinds." That is, the idea becomes one of "the Standards to rank real Existences into sorts, as they agree with these Patterns, and to denominate them accordingly." In the case of whiteness, the name "Whiteness" given to the appearance becomes a general name, and becomes "applicable to whatever exists conformable to" the appearance.
In this case, the mental image that appears as a standard must be the one accompanied by nothing, that is, it must be a "precise, naked Appearance." However, as Berkeley points out, a color always appears along with a certain extension. Therefore, even if the mind visualizes a white color as a "precise, naked appearance," the white color does not always act as a representative of white colors; it always has a possibility of being treated as the representative of various extensions.
Locke well understands that colors are always accompanied by extensions. He takes "Scarlet-colour" as an example and says: 'Tis true, Solidity cannot exist without Extension, neither can Scarlet-Colour exist without Extension; but this hinders not, but that they are distinct Ideas. (Locke, 1975, II. xiii. 11, p. 172) Here, although Locke acknowledges that "neither can Scarlet-Colour exist without Extension," he says that "this hinders not, but that they are distinct Ideas." In visual sensations or visual mental images, colors and extensions always appear at the same time. However, since nevertheless he says that "they are distinct Ideas," we may think that he bears in mind our power that makes us grasp the same extended color, in some cases as a sample of a color, and in other cases as a sample of extension. In the case of the abstract idea of "Whiteness" above, the mental image that we call to mind as a representative of whiteness is certainly accompanied by an extension, but our minds grasp it only as whiteness. The extension that the appearance of the white-ness possesses is, in this case, not "considered," and the appearance acts only as a representative of the white colors.
If so, in the passage cited above, certainly the appearance of whiteness qua a particular whiteness (that is, a particular sensible idea) is treated as an abstract idea, but we must admit that there Locke takes for an important factor our mental operation of "considering" that is not a mere sense-perception; that is, according to him, we attempt not to "consider" the various conceptual determinations given to it in advance and to "consider" it only as "whiteness." 9 The fact that abstract ideas qua mental images are framed on the basis of our conceptual operations is very important to examine Locke's view on abstract ideas. In addition, we must take notice of one more fact: that is, Locke's argument about abstraction in Book II, Chapter xi is already placed in the context of the quasi-descriptivist theory of reference. Here, although the abstract ideas are not pure descriptions, the three terms of the descriptivism are already lined up: that is, "general Names," the abstract ideas qua "the Standards to rank real Existences into sorts," and "all of the same kind" signified by general names (that is, the referents of the general names). The fact that Locke's theory of abstract ideas is indivisibly united with his descriptivist theory of reference is more explicit in the third sort of abstract ideas that I look at below.

On the Second Sort of Abstract Ideas
As I suggested above, Locke does not explicitly argue the second sort of abstract ideas as such. However, we must not forget that Locke's simple ideas themselves already qualify as abstract ideas.
Locke mentions "perception" and "discerning" as "the first Act of the Mind" (Locke, 1975, IV. i. 4, p. 525; see also Tomida, 1995, pp. 18-21). The "discerning" is the act of distinguishing one idea from another. When we receive ideas from experience (sensation and reflection), we receive them as a manifold. However, we do not receive such a manifold merely as a manifold; by the act of discerning we can distinguish its component elements and try to receive one element alone. Locke's simple ideas are not given as something simple from the start, but based on our discerning faculty we receive each idea as something simple, which is distinguished from others by the mind.
Moreover, as I have already discussed on many occasions (see, e.g., Tomida, 1995, pp. 15-28;2004), among Locke's ideas there are not only sensible ideas (that is, sensations and mental images), but also intelligible ones (that is, concepts). In fact, when Locke argues important simple ideas, whereas he admits that they are based on certain sensations, he often explains their contents from a conceptual viewpoint. For example, the idea of "solidity" is, for Locke, a very important idea that is an ingredient of his idea of body, and he explains it by saying that "it arises from the resistance which we find in Body, to the entrance of any other Body into the Place it possesses, till it has left it" (Locke, 1975, II. iv. 1, pp. 122-123). Certainly, Locke says that to acquire this idea, we must actually feel the resistance. However, the solidity itself is not something that we only sense or recollect by memory. In his explanation of the solidity that I cited above, Locke has already conceptually grasped the tactual sensation qua the origin of the idea, as "the resistance which we find in Body, to the entrance of any other Body into the Place it possesses, till it has left it." Furthermore, in the same section, after saying that "the Bodies which we daily handle, make us perceive, that whilst they remain between them, they do by an insurmountable Force, hinder the approach of the parts of our Hands that press them" (II. iv. 1, p. 123), he states that "That which thus hinders the approach of two Bodies, when they are moving one towards another, I call Solidity" (II. iv. 1, p. 123). Without doubt, in this passage he shows us the content of his idea of solidity verbally; he expresses it as "That which thus hinders the approach of two Bodies, when they are moving one towards another." Thus, it is clear that Locke not only treats the idea of solidity as a certain sort of sensation or a mental image, but also that he conceptually grasps it at the same time.
We can recognize the same characteristic in the case of the idea of extension, too. We cannot deny that the idea of extension, which Locke says is received "both by seeing and feeling" (II. v, p. 127), is originally acquired as a kind of sensation. This is clear from the fact that Locke considers "the least Particle of Matter or Space we can discern" (II. xv. 9, p. 203) to be the simple idea qua the smallest unit of extension (or space), calls it "a sensible Point" (II. xv. 9, p. 203), and says that it "is ordinarily about a Minute, and to the sharpest eyes seldom less than thirty Seconds of a Circle, whereof the Eye is the centre" (II. xv. 9, p. 203). However, as to the idea of extension too, Locke grasps it conceptually and gives it several conceptual determinations. This appears most noticeably in his arguments against the Cartesian view of body. In the Cartesian view, a body and an extension are identified with each other. With a view to refuting this, Locke presents the conceptual determinations of body and extension and tries to clarify the absurdity of the equation of extension with body, as follows: If therefore they mean by Body and Extension the same, that other People do, viz. by Body something that is solid, and extended, whose parts are separable and movable different ways; and by Extension, only the Space that lies between the Extremities of those solid coherent Parts, and which is possessed by them, they confound very different Ideas one with another. For I appeal to every Man's own Thoughts, whether the Idea of Space be not as distinct from that of Solidity, as it is from the Idea of Scarlet-Colour? (II. xiii. 11, Here, Locke presents the conceptual determination of body as "something that is solid, and extended, whose parts are separable and movable different ways," and that of extension as "the Space that lies between the Extremities of those solid coherent Parts, and which is possessed by them," and thereby tries to make us clearly recognize the difference between the two conceptual determinations.
The conceptual determinations of extension explicitly appear in the following passage too.
By this Idea of Solidity, is the Extension of Body distinguished from the Extension of Space. The extension of Body being nothing, but the cohesion or continuity of solid, separable, moveable Parts; and the Extension of Space, the continuity of unsolid, inseparable, and immoveable Parts. (II. iv. 5,p. 126) In this passage, he gives extension two different conceptual determinations: to the extension of body, "the cohesion or continuity of solid, separable, moveable Parts," and to the extension of space, "the continuity of unsolid, inseparable, and immoveable Parts," and by comparing those conceptual determinations, Locke tries to show that body and space are different.
Whether it be the simple idea of solidity or the simple idea of extension, when we acquire it, we must receive some kind of sensation. However, for Locke, the acquired ideas of solidity and extension are not mere sensations or mental images. They are conceptually determined, and their conceptual determinations play important roles in the arguments of his philosophy of science. Such simple ideas qua conceptual ideas do not contain the determinations that make them particular. Therefore, they are fully qualified to be abstract ideas. In the case of the idea of solidity, the conceptual determination of "That which thus hinders the approach of two Bodies, when they are moving one towards another" contains no determination of particular circumstances. In the same manner, after saying that the space "considered barely in length between any two Beings, without considering any thing else between them, is called Distance" (II. xiii. 3, p. 167) and that "If considered in Length, Breadth, and Thickness, I think, it may be called Capacity" (II. xiii. 3, p. 167), Locke asserts that "The term Extension is usually applied to it, in what manner soever considered" (II. xiii. 3, p. 167). That is, for Locke, the idea of extension functions as a conceptual determination of a high degree of abstraction that is not specified to lines, planes, or solids.
As to the "color," which Berkeley takes up as one more example of the second sort of abstract ideas, Locke says as follows: There is nothing can be left out of the idea of White and Red, to make them agree in one common appearance, and so have one general name; as Rationality being left out of the complex Idea of Man, makes it agree with Brute, in the more general Idea and name of Animal. And therefore when to avoid unpleasant enumerations, Men would comprehend both White and Red, and several other such simple Ideas, under one general name; they have been fain to do it by a Word, which denotes only the way they get into the Mind. For when White, Red, and Yellow, are all comprehended under the Genus or name Colour, it signifies no more, but such Ideas, as are produced in the Mind only by the Sight, and have entrance only through the Eyes. (III,iv. 16, Thus, according to Locke, the word "color" "denotes only the way [various colors] get into the Mind." That is, if we may use the phrase "abstract idea" in this case too, the content of the abstract idea of color is: "such [an] Idea [,] as [is] produced in the Mind only by the Sight, and [has] entrance only through the Eyes." Incidentally, as to the idea of "motion," Locke only argues its indefinability (III. iv. 8-9, pp. 422-423) and does not delve into it.

On the Third Sort of Abstract Ideas
As I mentioned above, when Berkeley explains the third sort of abstract ideas, he bears in mind, without doubt, Locke's explanation of the general ideas of man and animal in Book III, Chapter iii, Sects. 7-8 of the Essay. As to the particular ideas that act as the starting point in the formation of the general idea of man, Locke says: the Ideas of the Persons Children converse with, (to instance in them alone,) are like the Persons themselves, only particular. The Ideas of the Nurse, and the Mother, are well framed in their Minds; and, like Pictures of them there, represent only those Individuals. The Names they first give to them, are confined to those Individuals; and the Names of Nurse and Mamma, the Child uses, determine themselves to those Persons. (Locke, 1975, III. iii. 7, p. 411) We must take notice of the point that Locke distinguishes "The Ideas of the Nurse, and the Mother" from "Pictures of them [in Children's Minds]" and says that both of them "represent only those Individuals." It is without question that "Pictures of them [in Children's Minds]" are the nurse's and the mother's mental images. In contrast, as to"The Ideas of the Nurse, and the Mother" qua particular ideas, we have no choice but to see them as some kind of concepts. That is, we cannot but look upon them as accumulations of the conceptual determinations, the contents of which are concrete experiences concerning the persons in question. For there is no objective reason to believe that "The Ideas of the Nurse, and the Mother," which are distinguished from their mental images, are another set of mental images.
There is one more reason why we must see "The Ideas of the Nurse, and the Mother" in this passage as accumulations of conceptual determinations. It is because Locke continues his explanation of the acquisition of the general idea of man as follows: Afterwards, when time and a larger Acquaintance has made them observe, that there are a great many other Things in the World, that in some common agreements of Shape, and several other Qualities, resemble their Father and Mother, and those Persons they have been used to, they frame an Idea, which they find those many Particulars do partake in; and to that they give, with others, the name Man, for Example. (III. iii. 7, p. 411) He mentions "some common agreements of Shape, and several other Qualities." Maybe, "having Life" and "having Sense" will be among concrete examples of the "common agreements." These characteristics are found as common elements in the particular ideas of the nurse and the mother qua accumulations of conceptual determinations. Locke says that by taking out those common parts from various particular ideas, "they frame an Idea, which they find those many Particulars do partake in." Unless the particular ideas of individual human beings are accumulations of conceptual determinations, we cannot seem to draw out common parts from them and frame the idea of "a solid extended Substance, having Life, Sense, spontaneous Motion, and the Faculty of Reasoning" (III. iii. 10, p. 413). If we ignore the point that we confirmed above and if we take what Locke refers to as "The Ideas of the Nurse, and the Mother" for mental images of the nurse and the mother, then (as we see later, without being told by Berkeley) it is impossible to draw out common parts and frame a common idea of man from them.
In fact, if the particular ideas of the nurse and the mother that Locke discusses in the passage cited above are conceptual ideas, then we can easily understand what he states at the end of the passage. He says: Wherein they make nothing new, but only leave out of the complex Idea they had of Peter and James, Mary and Jane, that which is peculiar to each, and retain only what is common to them all. (III. iii. 7,p. 411) "The complex Idea they had of Peter and James, Mary and Jane" that Locke mentions here is the particular idea of an individual human being that plays the part of the starting point, and according to our interpretation, Locke treats it as an accumulation of conceptual determinations. The children find in the concrete conceptual determinations of Peter, Mary, and so on, some common parts such as "having Life" and "having Sense," and they "retain only what is common to them all." As I pointed out earlier, Locke discusses the abstract ideas of the first sort in the context of the descriptivist theory of reference. The context appears more explicitly in his arguments concerning the third sort of abstract ideas.
In Book III, Chapter iii of the Essay, Locke explains his descriptivist theory of reference. He states that the abstract idea that a general term signifies determines the extension of the general term, as follows: each of [the Individuals], having in it a conformity to that abstract Idea [that the general name signifies], is (as we call it) of that sort. (III. iii. 6,p. 411) as Things existing are found to agree [with an abstract Idea in the mind that a general Term signifies], so they come to be ranked under that name; or which is all one, be of that sort. (III. iii. 11,p. 414) it [is] evident, that Things are ranked under Names into sorts of Species, only as they agree to certain abstract Ideas, to which we have annexed those Names […]. (III. iii. 15,p. 417) Thus, Locke says that general terms signify general abstract ideas that express sorts, and that when things agree with the general abstract ideas, they are considered to be of the sorts and are called by the general terms. That is, according to him, the abstract ideas signified by general names express the descriptivist "descriptions" or "descriptive contents," and the things that correspond with the descriptive contents are referred to by the general terms.
Locke's explanation of the general idea of man, which is one of the targets of Berkeley's argument against abstract ideas, appears in this descriptivist context of Book III, Chapter, iii. Therefore, to understand Locke's explanation adequately, we must bear in mind the fact that the general idea of man expresses the "descriptive content" that plays an essential role in the descriptivist theory of reference. Locke concretely expresses the descriptive content of "man" in the same chapter as "a solid extended Substance, having Life, Sense, spontaneous Motion, and the Faculty of Reasoning" (III. iii. 10, p. 413). The individuals that agree with this content are referred to by the word "man." As to the general idea of animal that Berkeley treats as one more target, Locke explains it in the same manner: observing, that several Things that differ from their Idea of Man, and cannot therefore be comprehended under that Name, have yet certain Qualities, wherein they agree with Man, by retaining only those Qualities, and uniting them into one Idea, they have again another and a more general Idea […]. Which new Idea is made, not by any new addition, but only, as before, by leaving out the shape, and some other Properties signified by the name Man, and retaining only a Body, with Life, Sense, and spontaneous Motion, comprehended under the Name Animal. (III. iii. 8, If the general idea of man is a kind of accumulation of conceptual determinations and the general ideas of other animals also are such accumulations, then we can without problem understand Locke's view that we extract only "a Body," "Life, Sense, and spontaneous Motion" that are found in common in such conceptual determinations, and make the general idea of animal from them. 10 As to the second sort of abstract ideas, although Locke does not explicitly assert that simple ideas are at the same time abstract ideas, his simple ideas already qualify as abstract ideas, and Locke often treats them as conceptual ideas.
As to the complex abstract ideas of the third sort, for certain reasons, including that they take on the role of the "descriptive contents" or "descriptions" in the descriptivist theory of reference, we must see them as conceptual ideas.
If we bear those points in mind, we cannot accept Berkeley's imagistic criticism of Locke. Regarding abstraction, Berkeley says: Whether others have this wonderful Faculty of Abstracting their Ideas, they best can tell: For my self I find indeed I have a Faculty of imagining, or representing to myself the Ideas of those particular things I have perceived and of variously compounding and dividing them.
[…] But then whatever Hand or Eye I imagine, it must have some particular Shape and Colour. Likewise the Idea of Man that I frame to my self, must be either of a White, or a Black, or a Tawny, a Straight, or a Crooked, a Tall, or a Low, or a Middle-sized Man. I cannot by any effort of Thought conceive the abstract Idea above described. (Berkeley, 1734, Introduction, X, pp. 11-12;1949, Introduction, § 10, p. 29) This is unmistakably the story when we operate ideas qua mental images. We know that in Part I of the Principles Berkeley treats, aside from ideas of reflexion, only "Ideas of Sense" (sensations) and "Ideas of Imagination" (mental images) as "ideas." If we bear in mind such an imagistic viewpoint of Berkeley's, we can barely understand his view that since abstract ideas are ideas, they must be mental images. However, as to his seeing Locke's abstract ideas as mental images without giving any reason, and concluding that all sorts of abstract ideas cannot exist, we must say that he is being extremely unfair. In any case, as far as abstract ideas are mental images, it is impossible for us to separate extension, color, and motion and make them an abstract idea respectively (his negation of the first sort of abstract ideas).
Further, there cannot be any mental image of extension that "is neither Line, Surface, nor Solid, nor has any Figure or Magnitude but is an Idea intirely prescinded from all these" (Introduction, VIII, p. 8; Introduction, § 8, p. 28), and there cannot be any mental image of color that "is neither Red, nor Blue, nor White, nor any other determinate Colour" (Introduction, VIII, p. 9; Introduction, § 8, p. 28), and there cannot be any mental idea of motion that is considered "abstractedly not only from the Body moved, but likewise from the Figure it describes, and all particular Directions and Velocities" (Introduction, VIII, p. 9; Introduction, § 8, p. 28) (his negation of the second sort of abstract ideas).
Furthermore, there cannot be a mental image of a human being whose color is "neither White, nor Black, nor any particular Colour" (Introduction, IX, p. 10; Introduction, § 9, pp. 28-29), and whose stature is "neither Tall Stature nor Low Stature, nor yet Middle Stature, but something abstracted from all these" (Introduction, IX, p. 10; Introduction, § 9, p. 29), and there cannot be any mental image of animal "without Covering, either of Hair or Feathers, or Scales, &c. nor yet Naked" (Introduction, IX, p. 11; Introduction, § 9, p. 29), nor any mental image of animal whose "spontane-ous Motion must be neither Walking, nor Flying, nor Creeping" (Introduction, IX, p. 11; Introduction, § 9, p. 29) (his negation of the third sort of abstract ideas).
Berkeley repeats such arguments, and asserts that abstract ideas of the first, the second, and the third sorts cannot exist.

Descartes's "Idea"
If Berkeley changes the usage of the word "idea" and reads the same word that others (especially Locke) use, in his imagistic manner, he must specify it, but he never does so. From the beginning he takes his imagistic usage for granted. However, when we look at the usage of Descartes, who introduced modern "idea" language, and that of Locke, whose Essay Berkeley studied in his alma mater, Trinity College, it is clear that Berkeley's imagistic "idea" language is very different from theirs.
For example, in the case of Descartes, his "ideas" are, in many cases, not mental images but concepts.
In the "Reasons Proving the Existence of God and the Distinction between the Soul and the Body, Set Out in Geometrical Fashion," which was added to "The Second Reply" in his Meditations, Descartes explains "idea" in the following manner: By the term idea I understand the form, of any thought whatever, by the immediate perception of which I am conscious of the same thought itself; so that I cannot express anything in words (understanding what I am saying), without its being certain, for this very reason, that there is in me the idea of the thing that is signified by those words. And therefore I do not confine the term "ideas" only to the mental pictures depicted in the imagination […]. (Descartes, 1983, p. 160; English translation is from: Descartes, 2008, p. 102) The "form" (forma) that he identifies here with "idea" 11 is the "essence of a thing" (rei essentia [Descartes, 1983, p. 371]) or the "nature of a thing" (rei natura [Descartes, 1983, p. 166]), and he also says that "an idea […] represents the essence of a thing" (Descartes, 1983, p. 371; English translation is mine). Thus, the idea of a triangle is "the nature of a triangle" (natura Trianguli [Descartes, 1983, p. 163]) and its content is "a figure enclosed by three lines" (figura tribus lineis comprehensa [Descartes, 1983, p. 73, p. 368; English translation is mine]). Further, in order for me to be able to "express[, for example, a triangle] in words (understanding what I am saying)," the idea of a triangle must be "in me." That is, the idea is also the meaning of a word. In addition, Descartes rephrases "the nature of a thing" as "concept" (conceptus [Descartes, 1983, p. 162, p. 166]) and identifies "idea" with "concept" by the phrase "idea or concept" (idea sive conceptus [Descartes, 1983, p. 166]). In short, judging from such explanations and wordings, Descartes's idea is not a sensation or a mental image but a "concept." Needless to say, as his words "I do not confine the term 'ideas' only to the mental pictures depicted in the imagination" suggest, it is not the case that Descartes only refers to concepts or meanings as "ideas." We can clearly see that he also refers to sensations and mental images as "ideas" from the following passage: the ideas perceived by the senses were much more vivid and emphatic, and in their own way more distinct, than any of the ideas that I deliberately and knowingly formed by myself in my meditations, or that I found engraved upon my memory […]. (Descartes, 1983, p. 75;2008, p. 53) 12 It is well-known that Descartes repeatedly emphasizes the difference between the operation of understanding (intellectio) and the operation of imagination (imaginatio). 13 This distinction between operations corresponds to the distinction between mental objects. That is, while he refers to all mental objects as "ideas," he clearly distinguishes concepts from sensations and mental images.
In contrast, according to the responses that Descartes adds to the Meditations, Hobbes "intends the term 'idea' to be taken purely in the sense of the images of material things that are depicted in the bodily imagination" (Descartes, 1983, p. 181;2008, p. 113) and Gassendi "equat[es] 'idea' with 'mental image'" (Descartes, 1983, pp. 363-364;2008, p. 190). As far as this issue is concerned, Berkeley's understanding of "ideas" follows Hobbes's and Gassendi's, and is remote from Descartes's. 14 6 Berkeley's "Definition" Unlike Descartes and Locke, Berkeley understands "ideas" from an imagist point of view; from the same viewpoint he mistakes all of Locke's abstract ideas for mental images, and based on such an imagistic understanding of ideas he asserts that Locke's abstract ideas cannot exist. His typical attack ("the killing blow" [Berkeley, 1948, # 687, p. 84]) on Locke is, needless to say, found in his argument against Locke's abstract idea of a triangle. However, since Aaron pointed out its invalidity (see Aaron, 1933, pp. 175-176;1971, pp. 196-197), there has been much literature concerning it (e.g. Jolley, 1999, pp. 52-53;Tomida, 2004, pp. 79-86). Therefore, here I do not reargue it. Instead, I take up one more important point.
As I showed above, Descartes mentions "the nature of a triangle," that is, "a figure enclosed by three lines" (Descartes, 1983, p. 73, p. 368), and in the introduction of this paper I showed that Locke expresses the content of the abstract idea of a triangle as "a Figure, with three sides meeting at three Angles" (Locke, 1975, II. xxxi. 3, p. 376), "three Lines, including a Space" (II. xxxi. 6,p. 379;II. xxxii. 24,p. 393), and "a Figure including a Space between three Lines" (III. iii. 18,p. 418). Those conceptual ideas play the role of "descriptive content" or a "description" that determines the referents of a general term, in this case, "triangle." Interestingly, whereas Berkeley denies Locke's abstract idea of a triangle (Berkeley, 1734, XIII, pp. 17-19;1949, § 13, pp. 32-33), he assigns an important role to a "definition" that has the same content. He says: To this it will be objected, that every Name that has a Definition, is thereby restrained to one certain Signification. For Example, a Triangle is defined to be a plain Surface comprehended by three right Lines; by which that Name is limited to denote one certain Idea and no other. To which I answer, that in the Definition it is not said whether the Surface be Great or Small, Black or White, nor whether the Sides are Long or Short, Equal or Unequal, nor with what Angles they are inclined to each other; in all which there may be great Variety, and consequently there is no one settled Idea which limits the Signification of the word Triangle. 'Tis one thing for to keep a Name constantly to the same Definition, and another to make it stand every where for the same Idea: the one is necessary, the other useless and impracticable. (Berkeley, 1734, Introduction, XVIII, p. 26;1949, Introduction, § 18, p. 36) In this passage Berkeley takes up, as the definition of the word "triangle," "a plain Surface comprehended by three right Lines." It is almost the same as the content of what Descartes took up as the "nature" or "idea" of a triangle, and the content of Locke's abstract idea of a triangle. Further, he says that since this definition lacks concrete determinations of sides, angles, and so on, "there is no one settled Idea which limits the Signification of the word Triangle." That is, he implicitly acknowledges that the definition determines the scope of the term's referents. Thus, Berkeley, too, proves to be arguing in the context of the descriptivist theory of reference. He makes the "definition" play the role that Locke makes an abstract idea play. He only changes the wording, and he, too, is thinking within the same framework as a theory of reference consisting of three terms: referring expressions, descriptive contents, and referents. 15 His mention of the definition is crucially important in the interpretation of Berkeley's theory of reference. In the case of Locke, since the abstract idea, which expresses the descriptive content of a general term, does not contain such conceptual determinations that limit its referent to a certain particular individual, we may call all individual figures that agree with the abstract idea of a triangle, for example, by the name "triangle." Berkeley's definition of a triangle too, has substantially the same content that Locke's abstract idea of a triangle has. Therefore, the general name "triangle" that possesses that definition can refer to various triangles "indifferently." When we bear this fact in mind, we can understand why Berkeley's counterproposal to Locke's theory of abstract ideas is unexciting.

Berkeley's Counterproposal
I cite Berkeley's counterproposal once more: [Locke asks,] "Since all things that exist are only Particulars, how come we by general Terms? His Answer is, Words become general by being made the Signs of general Ideas." […] But it seems that a Word becomes general by being made the Sign, not of an abstract general Idea but, of several particular Ideas, any one of which it indifferently suggests to the Mind. (Berkeley, 1734, Introduction, XI, p. 15;1949, Introduction, § 11, p. 31) Berkeley says that "a Word becomes general by being made the Sign, not of an abstract general Idea but, of several particular Ideas, any one of which it indifferently suggests to the Mind." If this assertion is the main part of the counterproposal that he offers to Locke's theory of language, it creates a critical problem.
As is well known, in the case of Locke, for a mere articulate sound to operate as a meaningful word, generally it must signify a certain idea (see Locke, 1975, III. i. 1-2, p. 402), and in the case of a general term, he considers the idea that it signifies to be a general abstract idea. In contrast, Berkeley asserts that Locke's abstract ideas do not exist and that a general term "indifferently suggests [one of several particular Ideas] to the Mind." However, if Berkeley acknowledges Locke's basic view of language to the effect that generally, signifying an idea is a necessary condition for the meaningfulness of a word, according to Berkeley's theory, there follows the possibility that the meaning of a word may fluctuate depending on which particular idea it suggests. For, according to Berkeley, a general term suggests one of several particular ideas "indifferently." However, he does not think that there is any problem. Maybe we will find the reason in the fact that in Berkeley's case, the definition of a general term plays the role of determining the scope of its referents instead of Locke's abstract idea.
However, there still remains a problem. As to meaningfulness of words, Berkeley says: Now if we will annex a meaning to our Words, and speak only of what we can conceive, I believe we shall acknowledge, that an Idea, which considered in it self is particular, becomes general, by being made to represent or stand for all other particular Ideas of the same sort. (Berkeley, 1734, Introduction, XII, p. 16;1949, Introduction, § 12, pp. 31-32) And he explains this with an example: To make this plain by an Example, suppose a Geometrician is demonstrating the Method, of cutting a Line in two equal Parts. He draws, for Instance, a Black Line of an Inch in Length, this which in it self is a particular Line is nevertheless with regard to its signification General, since as it is there used, it represents all particular Lines whatsoever; so that what is demonstrated of it, is demonstrated of all Lines, or, in other Words, of a Line in General. And as that particular Line becomes General, by being made a Sign, so the name Line which taken absolutely is particular, by being a Sign is made General. And as the former owes its Generality, not to its being the Sign of an abstract or general Line, but of all particular right Lines that may possibly exist, so the latter must be thought to derive its Generality from the same Cause, namely, the various particular Lines which it indifferently denotes. (Introduction,XII,Introduction,§ 12,p. 32) We must pay attention to the clause "if we will annex a meaning to our Words." Although Berkeley rejects Locke's theory of abstract ideas, his own theory of general ideas too is concerned with "annex[ing] a meaning to our Words." According to Berkeley, for a general term to be meaningful it must be a sign of a certain particular idea, and the particular idea "becomes general, by being made to represent or stand for all other particular Ideas of the same sort." If so, however, as I pointed out above, since the particular idea in question can be different each time, if no further explanation is added, we must acknowledge the possibility that the meaning of the word may change. A black line of an inch in length and a black line of two inches in length are not the same, and a black line of an inch in length and a red line of an inch in length are not the same, either. If Berkeley says that even if the particular idea that a general term signifies is different each time, the meaning is the same, he must explain the reason by some conceptual device other than a set of particular ideas that he thinks the general term indifferently suggests; but Berkeley just mentions the term's "definition," and he does nothing more. If he allows his "definition" to be called "general idea," the problem of the fluctuation of meaning will be dissolved, but his theory of reference will become almost the same as Locke's. This is the reason why I think Berkeley's counterproposal is unstimulating and his criticism of Locke is beside the mark.
Incidentally, as we see in the passage cited above, Berkeley takes up the geometrical method that uses a particular idea of a line as a representative of other particular lines and thereby shows that how a particular idea becomes general. 16 However, when we consider this method, we must not forget that the particular idea as a representative is one of a general name's referents, and his explanation is not one that shows how the particular idea in question is referred to by the general term and comes to be treated as one of the referents of the same sort. The question is begged. 17 Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/ licenses/by/4.0/.