In a complicated object or general idea some of the judgments we treat as inherent may be inferences in other categories used subordinately. 'The ancient Persians had remarkably thin and weak skulls. They were good horsemen and archers, courageous and spirited in battle. They wore a tunic and trousers of leather.... They were quick and lively, keen-witted, capable of repartee, ingenious, and—for Orientals—far-sighted. They had fancy and imagination, a relish for poetry and art, and they were not without a certain power of political combination.' Some of these properties might have been perceived objectively, but not the possession of fancy and imagination, which could only be known by inference in causation—here used to complete a coherent unity. The historian employs causation as a principal category when he tells us that 'their bards did not touch the chords which rouse what is noblest and highest in our nature.' The thought implied in touching chords—the notion of will directing action—is a different judgment from the perception of an inherent permanent attribute.
The argument in this category consists in ideally completing an imperfect object by comparison with a similar object, or the idea of a similar object. Suppose we have studied thoroughly one or more rhubarb plants, and then see a plant with broadly cordate leaves, footstalks long, thick, and fleshy, and having a channel above. In the time at our disposal we cannot ascertain if its growth is exceedingly rapid, but we are justified in inferring that it is, and that the plant we are examining is in all other respects rhubarb. If the Egyptian obelisks we have seen were sculptured with hieroglyphics throughout their length, and we see an obelisk part of which is underground, it is a rational inference that that part also is sculptured.
We have proved that certain samples of aluminium have a specific gravity of 2·6, and then see a metal—of specific gravity unknown—which has all the other properties of aluminium: we may confidently infer that this metal also would, if tested, show a specific gravity of 2·6.
For purposes of reason it may be necessary to compare things that cannot be brought physically together. When this happens we generally compare them in idea, or the idea of one with the other as object. When great accuracy is required and the idea—which is always rather vague—cannot be relied on, we have recourse to mediate comparison. Standards are employed. These are manageable or portable objects with which principal things are separately compared by way of effecting indirectly a comparison between them. Standards can only mediate comparisons between abstract properties, for if they contained all the concrete properties of the compared objects they would, by supposition, be as unmanageable as the latter. We have standards for length in rules, scales, tapes, chains; the balance is a standard for weight. There are also scales for pitch of sound, varieties of colour, degree of light, heat, atmospheric pressure, and probably some others for special purposes.
Indirect comparison is not in itself inference; or if inference it is subordinate and preparatory to some more important conclusion. A coin is weighed and concluded to be light, but this is only a datum in determining the more important question whether it is a forged coin or not.
XXIII—ASSOCIATION
In this category we widen the attention so as to include several objects in one act of perception.
The first result of this diffusion of attention is to lessen the brilliancy of objects. Our attention is a light which is intensified when narrowed and concentrated—enfeebled when dispersed over several objects. The observation of a group amounts practically to observing the objects in rapid succession. At a given moment we perceive only one thing well, or it may be only a small part of a thing, but we have a dull sense of other things adjacent, which we have just seen and may immediately see again in any order we please. That is all that is meant by perception of a group.
To distinguish this category properly from the next we must consider the group of objects as divested of depth or distance outwards. It is to be regarded as a flat surface standing a few feet from us, the objects in it having absolutely the dimensions they appear to have. This is in fact their real magnitude, for the supposed real magnitude is a matter of theory, and means the perceptual magnitude taken under certain conditions of observation. The real magnitude is constantly changing, so for practical convenience in determining size, etc., we refer all objects to one condition of observation—that in which they can be touched as well as seen.