Context

Having described the three principles of association which relate simple ideas with one another, the author investigates the kinds of relations which result from the action of those principles, as well as of relations which arise in some other manner.

Background

According to Locke, ideas of relations are one of the three kinds of complex ideas made by the mind. In Book II, Chapter 25 of the Essay, Locke gives a general account of ideas of relation, which is followed by a chapter on cause and effect and other relations, and a chapter on the relations of identity and diversity. Here we will sketch Locke’s general account of relations.

Ideas of relation are the result of the comparison of ideas with one another.

The understanding, in the consideration of anything, is not confined to that precise object: it can carry any idea as it were beyond itself, or at least look beyond it, to see how it stands in conformity to any other. When the mind so considers one thing, that it does as it were bring to it, and set it by another, and carries its view from one to the other—this is, as the words import, relation and respect; and the denominations given to positive things, intimating that respect, and serving as marks to lead the thoughts beyond the subject itself denominated, to something distinct from it, are what we call relatives; and the things so brought together, related. (Essay, Book II, Chapter 25)

Locke goes on to discuss various aspects of relations, including the principles that if one of the relata ceases to exist, so does the relation, and that the relata must be “either in themselves really separate, or considered as distinct.” He notes the vast number of relations into which anything stands, and he claims that the ideas of relations themselves may be much clearer than the ideas of what is related. Finally, he claims that (as with any other complex idea), the ideas of any relations “all terminate in, and are concerned about those simple ideas, either of sensation or reflection, which I think to be the whole material of all our knowledge.” This he undertakes to prove in the course of his account of some specific relations in the next two chapters.

The Treatise

1. There are two commonly used senses of the word 'relation,’ each “considerably different” from the other.

• Natural: “that quality, by which two ideas are connected together in the imagination, and the one naturally introduces the other, after the manner above-explained.”
• Philosophical: “that particular circumstance, in which, even upon the arbitrary union of two ideas in the fancy, we may think proper to compare them.”

2. Although it may seem that the task of listing all the qualities that can give rise to philosophical relations is endless, in fact it turns out, upon diligent inquiry, that they can easily be grouped into seven different headings, each of which describes a type of philosophical relation. These qualities can then be seen as “the sources of all philosophical relations.”

3. The first quality on which a philosophical relation may be based is resemblance. [Note that the author describes resemblance as a relation at this point.] Resemblance plays a special role, in that it is the fundamental basis for all comparison of objects: “no objects will admit of comparison, but what have some degree of resemblance.” On the other hand, resemblance is not a sufficient condition for the comparison of ideas of objects to take place. When the resemblance “becomes very general, and is common to a great many individuals,” the mind is not led directly to any one of them. Too great a choice is present, which prevents the imagination from “fixing on any single object.” [For example, all animals resemble one another in a general way. Having an idea of a particular animal, just as being an animal, does not lead me to think of any other particular animal.]

4. The second quality is identity, which is now called a “species of relation.” It is applied “in the strictest sense” to objects which are “constant and unchangeable.” The author puts off a discussion of personal identity until Part 4 of Book 1. Every being stands in a relation of identity to itself, so long as it endures for any period of time. [That is, the object at one time is identical to itself at the later time.] This makes identity “the most universal” of all relations.

5. The third species of relation is that of relations in space and time. These are the most universal after the relation of identity. Space and time themselves are “the sources of an infinite number of comparisons, such as distant, contiguous, above, below, after &c.”

6. The fourth source of relations, which is “very fertile” is the quantity and number of objects. [For example, one house has three bedrooms while another has four.]

7. The fifth species of relation is based on the quality which an object might have. When two objects share a quality (such as weight), the degree of that quality may be compared. Another example is two objects which share a color: they may be compared with respect to the shade of that color [e.g., one is a deeper blue than the other].

8. The sixth kind of relation is that of contrariety, or being contrary to one another. The only two ideas that are contrary “in themselves” are the ideas of existence and non-existence. Both ideas are ideas of an object. The idea of a non-existent object is one which “excludes the object from all times and places, in which it is supposed not to exist.” [Thus I exclude existence of Abraham Lincoln in Scotland in 1741 from my idea of him.] Because the contrary ideas of the objects [Lincoln in the United States in 1864 and Lincoln in Scotland in 1741] have in common the object itself, there is a resemblance between them. Moreover, ideas which are not contrary in themselves have resemblance, [as, for example, there are many points of resemblance between my idea of Lincoln and that of my refrigerator]. Thus the relation of contrariety is not an exception to the rule that no relation of any kind can subsist without some degree of resemblance, though at first sight it may seem to be an exception.

9. The seventh and final type of relation is that of cause and effect. The relation of cause and effect is the basis for some relations of contrariety. Fire is contrary to water, because as experience (and experience alone) shows, pouring water on a fire is the cause of its being extinguished. Resemblance is a factor in the relation of cause and effect, but it will not be shown how until later. [Like resemblance and contiguity,] the relation of cause and effect is a natural relation.

10. It is natural to expect that difference is a philosophical relation. The author considers it instead to be “the negation of relation,” rather than “any thing real or positive.” There are two kinds of difference. Negation of identity is called [numerical difference, or] difference in number. [I say that there are two different people in the room, not one person.] Negation of resemblance is called difference in kind. [I say that dogs and cats are different in kind, because they do not resemble one another in various respects.]

In Part 3, Section 1, the author will return to this list of seven kinds of relation, considering each of the relations with respect to whether they can be known to exist, or whether their existence is merely probable.

The Enquiry

There is no general discussion of relations in the Enquiry. This is not to say that ideas relations do not play an important role in that book, as the idea of the relation of cause and effect plays the leading role there.