40. The power of abstraction is bestowed upon man, for the purposes solely of reasoning. It tends greatly to the facility as well as clearness of any process of reasoning, that, withdrawing from every other circumstance, we can confine our attention to the single property we desire to investigate.
41. Abstract ideas, may, I think, be distinguished into three different kinds, all equally subservient to the reasoning faculty. Individuals appear to have no end; and did we not possess the faculty of distributing them into classes, the mind would be lost in an endless variety, and no progress be made in knowledge. It is by the faculty of abstraction that we distribute beings into _genera_ and _species_: finding a number of individuals connected by certain qualities common to all, we give a name to these individuals considered as thus connected; which name, by gathering them together into one class, serves in a curt manner to express the whole of these individuals as distinct from others. Thus the word _animal_ serves to denote every being which hath self-motion; and the words _man_, _horse_, _lion_, &_c._ answer similar purposes. This is the first and most common sort of abstraction; and it is of the most extensive use, by enabling us to comprehend in our reasoning whole kinds and sorts, instead of individuals without end. The next sort of abstract ideas and terms comprehends a number of individual objects considered as connected by some occasional relation. A great number of persons collected together in one place, without any other relation but merely that of contiguity, are denominated _a crowd_: in forming this term, we abstract from sex, from age, from condition, from dress, &_c._ A number of persons connected by being subjected to the same laws and to the same government, are termed _a nation_; and a number of men subjected to the same military command, are termed _an army_. A third sort of abstraction is, where a single property or part, which may be common to many individuals, is selected to be the subject of our contemplation; for example, whiteness, heat, beauty, length, roundness, head, arm.
42. Abstract terms are a happy invention: it is by their means chiefly, that the particulars which we make the subject of our reasoning, are brought into close union, and separated from all others however naturally connected. Without the aid of such terms, the mind could never be kept steady to its proper subject, but would perpetually be in hazard of assuming foreign circumstances or neglecting what are essential. In a word, a general term denotes in a curt manner certain objects occasionally combined. We can, without the aid of language, compare real objects by intuition, when these objects are present; and, when absent, we can compare them by means of the ideas we have of them: but when we advance farther, and attempt to make inferences, and draw conclusions, we always employ abstract terms, even in thinking. It would be as difficult to reason without them, as to perform operations in algebra without signs: for there is scarce any reasoning without some degree of abstraction; and we cannot abstract to purpose without making use of general terms. Hence it follows, that without language man would scarce be a rational being.