Background

In his Essay concerning Human Understanding, John Locke had described a kind of idea which he called "general" or "abstract." An idea is general when it divides objects into sorts or kinds and can represent many individuals as belonging to that sort. General words, in turn, are signs of general ideas. So the word 'horse' is general, standing for a general idea of a kind of thing. Insofar as individual objects (horses) conform to that general idea, it is said to belong to that kind. General ideas are not innate, but are formed from particular ideas through a process of abstraction. One begins with a complex idea, such as that of the horse Bucephalus. From this and other complex ideas, a "new and distinct complex idea" (e.g., the idea of a horse) arises (Book 3, Chapter 3, Section 9). Such an idea is "partial," in that it removes from the original complex ideas those circumstances in which they differ and retains only what is common to them all. This is what enables the abstract idea to refer to many individuals. Further, if the abstract idea is stripped down even further, a new abstract idea with greater generality is generated, as in the formation of the idea of an animal. In summary:

Words become general by being made the signs of general ideas: and ideas become general, by separating from them the circumstances of time and place, and any other ideas that may determine them to this or that particular existence. By this way of abstraction they are made capable of representing more individuals than one; each of which having in it a conformity to that abstract idea, is (as we call it), of that sort. (An Essay concerning Human Understanding, Book3, Chapter 3, Section 6)

It is not at all clear why Locke deviated from his description of abstract ideas as partial ideas and described them instead as consisting of contradictory elements. The general idea of a triangle would seem to apply to equilateral and scalene triangles because what it does contain is something the two have in common. Why must being equilateral and scalene be included in the general idea?

At any rate, Berkeley found the second account of general ideas to be totally implausible. He invited his readers to look into their own thoughts and see whether he can find an idea of a triangle matching Locke's description. Of course, the notion that the abstract idea has both all and none of a set of conflicting qualities is easy to dismiss. But even the more modest claim that the abstract idea merely has none of these qualities comes under attack by Berkeley. On his view, there can be no such thing as a "partial" idea. The reason is that ideas can only be sensed or imagined, and every such idea comes fully equipped, as it were, with properties. "The idea of man that I frame to myself 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" (Principles of Human Knowledge, Introduction, Section 10). Berkeley held that particular ideas are made general by standing as representatives for other ideas that resemble them. Berkeley specifically stated that "an idea which, considered in itself, is particluar, becomes general by being made to represent or stand for all other particular ideas of the same sort" (Principles of Human Knowledge, Introduction, Section 12.)

The Treatise

1. The author begins by raising the question of whether abstract or general ideas are "general or particular in the mind's conception of them." [To make sense of this question, note first that a general idea is one that refers to a number of objects indifferently. The question is the means by which an idea attains this generality. Are ideas with general reference particular ideas, or are they a special kind of idea that is not particular, but rather is a partial or reduced idea that excludes some of the specific qualities found in particular ideas?] Berkeley has disputed the "receiv'd opinion" [that general ideas are not particular, but are partial, ideas]. According to Berkeley, general ideas are particular ideas that are used in a general way by being attached to general words. This attachment allows the words to refer to many individuals, and it allows us to think of these individuals when the general term is used. The author regards this criticism of the received view by Berkeley to have been "one of the greatest and most valuable discoveries that has been made of late years." He sets out to "confirm it by some arguments, which I hope will put it beyond all doubt and controversy."

2. The author grants two claims as being "evident," and notes that they form the basis of an argument in favor of there being a special class of non-particular general ideas. The first is that in the formation of most, if not all, of our general ideas, "we abstract from every particular degree of quantity and quality." [Our general idea of a triangle does not specify exactly how big a triangle must be, or what the extent of its angles must be, in order for it to be a triangle.] The second evident principle is that small changes in properties such as extension and duration are not enough to disqualify an object from being of a certain kind. [A triangular body formed by sticks does not cease to become a triangle if the sticks are re-positioned in certain ways.] These considerations seem to lead to "a plain dilemma," whose conclusion is that the received doctrine of abstract general ideas is correct. Suppose that there is an abstract idea of a man. This idea is to represent all men, "of all sizes and all qualities." There are two ways in which this representation might take place.

1. The idea represents all the possible quantities and qualities.
2. The idea represents none of the possible quantities or qualities.

3. The first proposition to be proved is that "the mind cannot form any notion of quantity or quality without forming a precise notion of the degrees of each," which undermines the second alternative. The proof is to be found in three arguments, which span several paragraphs. The first focuses on the nature of ideas, the second on that of impressions, and the third on objects in the world. The first argument is designed to show that there can be no separation between a quantity or quality and the degrees of that quantity or quality. The received view is that in the process of abstraction, we are supposed to separate the "essential parts" of things from their "particular circumstances." The reason this cannot be done is that if there can be a separation, then there is a difference between the two things separated. The general principle is that "whatever objects are separable are also distinguishable, and whatever objects are distinguishable are also different." The author does not advance an argument for this general principle, but only asks rhetorically how it could not be true. He also notes that it is the converse (or "inverse") of a principle observed earlier (Section 3), that "whatever objects are different are distinguishable, and that whatever objects are distinguishable are separable by the thought and imagination." But there is no difference between a quantity or quality and its degrees, so the two are inseparable. And if they are inseparable, abstraction (as described by the received view) is impossible. Before examining the argument more closely, we can adapt one of the author's examples to illustrate it. We can take length to be a quantity and one foot to be a degree of length. Moreover, we can say that an "essential part" of being a line is having length. So the question is whether one can have an idea of a line without its being an idea as well as a line of a precise length, such as one foot. Clearly, we cannot separate the idea of the length of the line from that of the line itself, so the only way to separate the precise length of a line from the idea of the line would be to separate the length from the precise length. To do so would require that there be a difference between the length and the precise length. This the author cannot find. The author concludes that the two are inseparable, and hence that the idea of a line cannot be separated from a particular length. If there is to be any abstract idea of a line, its precise length must be a part of that idea. Abstraction, in that case, does not imply separation. Now since the process of abstraction does not produce separation, "the general idea of a line, notwithstanding all our abstractions and refinements, has in its appearance in the mind a precise degree of quantity and quality; however, it may be made to represent others, which have different degrees of both."

4. The author turns to a consideration of impressions in second argument to the conclusion that the mind can only form an idea of quantity or quality if that quantity or quality is given a precise degree. Every object that "can appear to the senses," or (equivalently) every impression that can become present to the mind is "determin'd in its degrees of both quantity and quality." Where precision is lacking ("the confusion, in which impressions are sometimes involv'd") is due only to the faintness and unsteadiness of the impression, and "not from any capacity in the mind to receive any impression, which in its real existence has no particular degree nor proportion." The author claims that to say otherwise would be "the flattest of contradictions, viz. that 'tis possible for the same thing to be and not to be."

5. Now the copy principle is invoked. If it is true that impressions are fully determined in degrees of quantity and quality, it is also true that ideas, their copies, are also fully determined. "Impressions and ideas differ only in their strength and vivacity." The variation in strength and vivacity has no effect on the determination of degrees of quantity and quality.

6. The third argument for the fully determinate character of ideas appeals to the character of things in nature. A principle that is generally accepted in philosophy is that all natural things are individual, "and that 'tis utterly absurd to suppose a triangle really existent, which has no precise proportion of sides and angles." What is absurd in fact and reality must also be absurd in idea, "since nothing of which we can form a clear and distinct idea is absurd and impossible." Just as we cannot form an idea of an indeterminate object ("one that is possest of quantity and quality, and yet is possest of no precise degree of it"), we cannot form an indeterminate idea. The author concludes that because objects in nature are individual, abstract ideas are also individual, "however they may become general in their representatin." In our mind there is an image only of a particular object, "tho' the application of it in our reasoning be the same, as if it were universal."

7. The author moves now to the second proposition he wishes to prove. Despite the fact that the mind's capacity is not infinite, we are still able, in an imperfect way that is good enough for the purposes of life, to represent all the possible quantities and qualities of individuals to which a general idea refers. The process proceeds as follows. When we experience a resemblance among various objects, the same name is applied to all of them, "whatever differences we may observe in the degrees of their quantity and quality, and whatever other differences may appear among them." The custom of applying the same name to different but resembling objects leads us to "revive" the fully determinate idea of some one of those objects when we hear the name again. But then how is the name related to all the other, differing objects, the experience of which led to its use? Generally, they cannot all be revived at once. The author answers with a metaphor, the word "only touches the soul, if I may be allow'd so to speak, and revives that custom, which we have acquir'd by surveying them." The ideas of the other objects are thus present not in fact, "but only in power." More concretely, the occasion of hearing the word puts us into a state of "readiness to survey any of" the objects, should our needs or plans require it. "The word raises up an individual idea, along with a certain custom; and that custom produces any other individual one, for which we may have occasion." Because in most cases it is impossible to produce all the ideas to which the name applies, "we abridge that work by a more partial consideration, and find but few inconveniencies to arise in our reasoning from that abridgement."

Appendix. The hypothesis of the author depends on our ability to bring ideas which resemble one another under a single general term. Here, the author elaborates on the nature of resemblance. In the examples given by the author in this Section, complex ideas resemble one another (e.g., the way two triangles do). The author here treats of the resemblance of simple ideas. He claims that it is "evident" that different simple ideas do resemble one another. Indeed, they may resemble one another with respect to the very circumstance in which they differ. For example, blue and green are different in color, but they resemble each other in a way that blue and red do not. Sounds, tastes, and smells "admit of infinte resemblances upon the general appearance and comparison, without having any common circumstances the same." More generally, the "very abstract terms simple idea" also make the point. All simple ideas resemble one another in their very simplicity. Yet because the ideas are simple ("from their very nature, which excludes all composition"), there is nothing separable in them, and so they have nothing in them that can be separated from their simplicity. The same holds in the case of degrees of quality (for example, degrees of heat). Ideas of heat of two different temperatures resemble each other, but the degree of heat is not distinct (and therefore separable) from the heat itself.

8. The author now cites "one of the most extraordinary circumstances in the present affair." Consider a piece of reasoning that begins with the word 'triangle.' According to the author's account in the previous paragraph, this "general or abstract term," given that a custom has been established, "revives the idea of one of these objects, and makes the imagination conceive it with all its particular circumstances and proportions" (paragraph 7). We then reason about that idea, for example, a particular equilateral triangle. Because our reasoning is confined to the particular idea, we might draw the conclusion "that the three angles of a triangle are equal to each other." At this point, the custom leads us to think of other ideas which do not agree with it, such as scalene and isosceles triangles. While we were reasoning about the equilateral triangle, these ideas were "overlook'd, at first," but after the conclusion has been drawn, they "immediately crowd in upon us, and make us perceive the falsehood of this proposition, tho' it be true with relation to that idea [i.e., of the equilateral triangle], which we had form'd." So why does the mind "readily suggest" these conflicting ideas? Before answering this question, the author notes that if the conflicting ideas are not suggested to the mind, it is due to "some imperfection in its faculties." Indeed, this defect is "often the source of false reasoning and sophistry." The failure occurs "principally" with ideas that are "abstruse and compounded." With more clear and simple ideas, the custom does its work almost without exception, and as a result, in these cases we "seldom run into such errors."

9. The custom of correcting our faulty generalizations is "so entire" that there is no danger of error even if we associate a single idea with several different words, and use the idea in a number of different instances of reasoning. An example of the former case is that of an equilateral triangle one inch from its base to its vertex. The following terms may be applied to it: figure, rectilinear figure, regular figure (all sides being equal), triangle, and equilateral triangle. Because these words apply more or less widely (all equilateral triangles are triangles, but some are not), even when they call up the same idea, the specific habit each word triggers keeps the mind ready to correct any tendency to use the idea in a way that does not apply to other ideas that might be associated with that word.

10. It may take some practice for the habit to become sufficiently strong as to keep us from error. Before the habit is perfected, the mind may wish not to confine itself to a single idea, but to "run over several, in orde to comprehend its own meaning, and the compass of that collection, which it intends to express by the general term." For example, when learning to use the word "figure," "we may revolve in our minds the ideas of circles, squares, parallelograms, triangles of different sizes and proportions, and may not rest on one image or idea." Whether or not this is what happens, the author insists on the following points of being certain, that:

• we form the idea of individuals whenever we use general terms,
• we seldom or never form at one time all the ideas of the individuals that might under the terms,
• the ideas of which we do not form on using the term are represented only by means of the habit by which we recall them when required on relevant occasions.

11. It has not yet been explained exactly how it is that the custom operates. Why does it recall just those ideas that are needed at a particular moment? Why does the custom respond to words or sounds that are general terms by producing the ideas that are associated with it. The author asserts, without giving a reason, that it is impossible to "explain the ultimate causes of our mental actions." What should properly be done is to produce other mental phenomena that are analogous to the present one, and to produce other principles that facilitate the operation of that phenomenon.

12. The first point is this. The imperfection in our "universal ideas," i.e., the fact that it produces only one or a few particular ideas when a general term is used, is like the imperfection in our thinking about large numbers. The mind initially has no particular idea of, say, one thousand, but it does have the power to produce such an idea because of its mathematical skills. The fact that our comprehension of the number lies in a power, and not a particular idea, does not make any difference in our reasoning.

13. The second point is that there are other occasions on which the mind produces ideas at the mere mention of a word. If a person has memorized a speech or a poem, a single word may be enough to trigger the memory of all its words.

14. The third point concerns our reasoning in cases where we cannot associate with words "distinct and complete ideas," omitting many simple ideas of which the complex idea is formed. This is the case, for example, with our ideas of government, church, negotiation, and conquest, which are much less distinct and complete than the idea of triangle, for example. But even though we are imperfect in this way, we still can reason cogently using these ideas and "avoid talking nonsense on these subjects." The mechanism is the same as already described. If one were to say something nonsensical, such as that in war, the weaker party can always conquer the stronger, our habit which associates the words with ideas, will make us "immediately perceive the absurdity of that proposition." We then change what we say, and assert that in war, the weaker party can always negotiate with the stronger. This is analogous to the account of general terms, in which the habit allows us to use one particular idea to reason about others that are quite different from it in some respects.

15. The fourth and final point brings in another principle that is relevant to the habit under discussion. This is the principle, discussed in Section 4, that resemblance is a natural relation that helps bring about the transition from idea to idea. The reason that we place various different ideas under a general term is because of their resemblance. And "this relation must facilitate their entrance in the imaginatinon, and make them be suggested more readily upon occasion." When we look at how conversation or reflection in common life, we find that the mind is able to move from one idea to another just when the situation calls for it. "The fancy runs from one end of the universe to the other in collecting those ideas, which belong to any subject. One wou'd think the whole intellectual world of ideas was at once subjected to our view, and that we did nothing but pick out such as were most proper for our purpose." What we call "genius" is the ability to move from an idea to another that is perfectly appropriate for the occasion. This is "a kind of magical faculty in the soul," but "is inexplicable by the utmost efforts of human understanding."

16. The author thinks that these four considerations might "help to remove all difficulties to the hypothesis I have propos'd concerning abstract ideas," a hypothesis that is "so contrary to that, which has hiterto prevail'd in philosophy." But the burden of the proof falls on the negative argument, given in sections 3 through 6, that the common method of explaining our use of general terms by partially determined ideas is impossible because every idea must be fully determined. We need another "system" to explain how we use general terms, and "there is plainly none beside what I have propos'd." The author then summarizes the system in a sentence: "If ideas be particular in their nature, and at the same time finite in their number, 'tis only by custom they can become general in their representation, and contain an infinite number of other ideas under them."

17. Having finished his exposition of the system, the author concludes this section by applying it to well-known philosophical technique. Some philosophers, most notably Descartes, claim that what does not exist separately may still be distinguished by a distinction of reason. For example, the figure of a body may be distinguished by reason from the body that has the figure. The problem, which is overlooked by those who claim that there are distinctions of reason, is that it is undermined by the author's principle that "all ideas, which are different, are separable." If there really is a distinction of reason, then what is distinguished must be something that can exist separately: "if the figure be different from the body, their ideas must be separable as well as distinguishable." So the task is to undertand what a distinction of reason could be, in a way that does not run afoul of the principle of the separability of what is different.

18. The solution is this. A body and its figure are not distinguishable or separable. The reason we think they are is because "even in this simplicity there might be contain'd many different resemblances and relations." An example is a globe of white marble, which gives rise to an impression when presented to the senses. We have the impression of "a white colour dispos'd in a certain form." The white color and the spherical form cannot be separated in the idea. However, when we see a globe of black marble and a cube of white marble, we may make comparisons between those ideas and the idea of a globe of white marble. In that case, there are "two separate resemblances," even though globe of white marble is inseparable. With practice, we can then make a "distinction of reason," in the sense that we can view the figure and color "in different aspects." "When we wou'd consider only the figure of the globe of white marble, we form in reality an idea both of the figure and colour, but tacitly carry our eye to its resemblance with the globe of black marble." The same procedure works for the color: we observe the resemblance with the cube of white marble. "By this means, we accompany our ideas with a kind of reflection, of which custom renders us, in a great measure, insensible." If one wants to think about the color of a globe, one must consider the color and figure together, "but still keep in our eye the resemblance to the globe of black marble, or that to any other globe of whatever colour or substance."