The Concept. We have already explained what are the grounds, on which Logic takes cognizance of the Concept. Considered in isolation, the concept is not an act by which the mind attains truth. It can neither be termed true nor false. But concepts are the material of which our mental acts, true and false, consist.

Every judgment of necessity contains two concepts. Hence the treatment of the concept is fundamental in the science of Logic. And in every science it is of vital importance that the primary notions should be accurately grasped. There is truth in that saying of Aristotle's, which in the middle ages had passed into a proverb : "What is at the beginning but a small error, swells to huge proportions at the close." ¹

In the first place it is necessary to distinguish carefully between the Concept or intellectual idea properly so called, and the Phantasm or Mental picture.

Whenever I think of an object, I simultaneously form a sensible picture of it in my imagination. If for instance I judge that fishes are vertebrate, or that the sun is round, I cannot do so without imagining to myself a sensible representation of a fish, or of the sun. Sometimes, indeed, as when I think of some abstract subject, such as ‘virtue’, the image of the mere word 'virtue’ will serve my purpose: but some image is requisite, nor does the intellect ever operate save in connection with a phantasm.²

This mental picture is however very different from the concept. This will be easily understood, if we notice that to judge "The sun is round", I must in thought have separated the attribute of roundness from the thing I term "the sun". No sensible image can effect such a separation. It can only picture the single object "a round sun". If again I say, "This glass is transparent", I have in thought separated the attribute "transparency" from the thing "glass". This power of separation requires a higher faculty than that of the imagination, namely the faculty of thought or intelligence. It is the intellect alone that has this wonderful power of distinguishing two things which in nature are inseparably conjoined, of severing its roundness from the sun, its transparency from the glass.

Thus I can look at a single object, e.g., the paper I am using, and consider separately its whiteness, its smoothness, its oblong shape, its opacity, etc.

The mind's power of thus separating in thought things which in the real order are one, is known as its power of abstraction.

Abstraction: The characteristic feature by which the Concept differs from the Phantasm, is its universality. A Concept is equally representative of all objects of the same character. Thus if I see a circle drawn on a chalk-board, the concept which I form of that geometrical figure will express not merely the individual circle before me, but all circles. The figure I see is of a definite size, and is in a particular place. But my mind by an act of abstraction omits these individual characteristics, and forms the concept of a circle as it is enunciated in Euclid's definition.

This concept is applicable to every circle that ever was drawn.

When however I form the phantasm of a circle, my phantasm must necessarily represent a figure of particular dimensions. In other words the concept of the circle is universal: the phantasm is singular. Similarly, if I form a concept of 'man', my concept is applicable to all men. But a phantasm of a man must represent him as possessed of a certain height, with certain features, with hair of a definite colour, etc.

We have only to consider any object to see that all the concepts which we can form of it have this universal character. Thus, glancing out of the window, I see a garden-roller. My mind conceives it as a roller, as cylindrical, as iron, as dusty, cold and so on. Every one of these concepts is universal, and thus applicable to any other thing which resembles the roller in that one attribute, no matter how much it may differ from it in others.

The concept of 'roller' is equally applicable to the ponderous machine with which the county-council repairs the highways: that of 'cylindrical' expresses perfectly the shape of the candle on my mantel-piece while the concept of 'cold' is appropriate to the water in the neighbouring fountain. These various concepts are not, of course, so many isolated units in the mind. They unite to form a single composite concept. But that composite concept is a universal, and would express all similar rollers.³

It must not be thought that the intellect has no means of knowing individuals. It knows the individual by advertence to the phantasm from which the universal idea is abstracted* But the work of the intellect, as distinct from that of sense, is to express the individual object of sense-perception in a series of universal concepts. Thus it is the intellectual faculty which enables us to conceive the individual Socrates as a 'man,' or as a 'vertebrate,' or as a ' father.'
 
 

Repugnant Concepts. Concepts are said to be repugnant, when, as mutually exclusive, they cannot be united in one composite concept.

It is not all concepts which can be brought together to form a composite concept such as those described in the last section. There are some which are incompatible, so that the one necessarily postulates the exclusion of the other. These are known as repugnant concepts. Thus it is impossible to form the concept of 'a thinking stone': for the concept of 'a stone' expresses lifeless matter, and the concept 'thinking' expresses living intelligence. Just as in the real order a thing cannot both live and not live, so in the order of thought such a thing is inconceivable.

The difference between what is inconceivable and what is unimaginable should be carefully noted. There are many things, that cannot be represented in our imagination, which nevertheless contain no repugnance — as for instance, colour to the blind from birth. On the other hand, some things are quite inconceivable, and hence impossible, of which I can form some kind of image. Perhaps, it is possible to imagine a thinking stone.

Adequate, Clear and Obscure Concepts. A concept is said to be adequate when it represents distinctly all the notes which go to make up an object. It is plain that in regard to individual things such concepts are impossible. We cannot form a concept representing every characteristic of even the smallest flower. We can however have adequate concepts of mathematical figures in their universal aspect.

Euclid's definitions express adequate concepts of the figures with which they deal. A concept is clear when, although it does not represent all the notes of an object, it yet contains a sufficient number to distinguish that object from any other. Thus our knowledge of nature may be very limited, but our concepts of the chief tribes of animals have a degree of definiteness amply sufficient to enable us accurately to distinguish one from another. A concept is obscure when our knowledge is insufficient to distinguish the object of thought from other things. Thus a man may have a general idea of what is meant by prudence and by fortitude and may nevertheless be incapable of distinguishing prudence from timidity, fortitude from rashness.