Notes on Hume's Treatise

by G. J. Mattey

Book 1
Of the UNDERSTANDING
PART 1
Of ideas, their origin, composition, connexion, abstraction, &c.

Sect. 5. Of relations.

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

The first sense is that which is always used "in common language." The "manner above-explained" is by the principles of the association of ideas. For example, resemblance is a quality connecting the ideas of a picture of a person and of the person himself. Having an idea of the picture naturally introduces the idea of the person into the mind. The second sense is used only in philosophical discourse. It is an extension of the first sense, in which two ideas are connected together by a certain quality, without there having to be any principle that naturally moves the mind to connect them. [If there is a connecting principle, then the relation is both natural and philosophical.] For example, we acquire an idea of the relation of distance by comparing objects [that are not contiguous with one another, since contiguity is a natural relation]. The author points out the disparity between the language of the philosopher and the common language in the case of distance. For the philosopher, distance is a "true relation," while we commonly speak as if distance and relation are incompatible, as in the expression, nothing can be more distant than such and such things from each other, nothing can have less relation.

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 1st 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 condtion 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 2nd 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 3rd 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 4th 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 5th 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 6th 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 7th 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.]

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