clearness the slight curvature of that portion of the sea’s surface which lies before us. But when we seek in imagination to follow out this curved surface as it actually exists, slowly bending round until all its meridians meet in a point eight thousand miles below our feet, we find ourselves utterly baffled. We cannot conceive in its real form and magnitude even that small segment of our globe which extends a hundred miles on every side of us; much less the globe as a whole. The piece of rock on which we stand can be mentally represented with something like completeness: we find ourselves able to think of its top, its sides, and its under surface at the same time; or so nearly at the same time that they seem all present in consciousness together; and so we can form what we call a conception of the rock. But to do the like with the Earth we find impossible. If even to imagine the antipodes as at that distant place in space which it actually occupies, is beyond our power; much more beyond our power must it be at the same time to imagine all other remote points on the Earth’s surface as in their actual places. Yet we habitually speak as though we had an idea of the Earth – as though we could think of it in the same way that we think of minor objects.
What conception, then, do we form of it? the reader may ask. That its name calls up in us some state of consciousness is unquestionable; and if this state of consciousness is not a conception, properly so called, what is it? The answer seems to be this: – We have learnt by indirect methods that the Earth is a sphere; we have formed models approximately representing its shape and the distribution of its parts; generally when the Earth is referred to, we either think of an indefinitely extended mass beneath our feet, or else, leaving out the actual Earth, we think of a body like a terrestrial globe; but when we seek to imagine the Earth as it really is, we join these two ideas as well as we can – such perception as our eyes give us of the Earth’s surface we couple with the conception of a sphere. And thus we form of the Earth, not a conception properly so called, but only a symbolic conception.6
A large proportion of our conceptions, including all those of much generality, are of this order. Great magnitudes, great durations, great numbers, are none of them actually conceived, but are all of them conceived more or less symbolically; and so, too, are all those classes of objects of which we predicate some common fact. When mention is made of any individual man, a tolerably complete idea of him is formed. If the family he belongs to be spoken of, probably but a part of it will be represented in thought: under the necessity of attending to that which is said about the family, we realize in imagination only its most important or familiar members, and pass over the rest with a nascent consciousness which we know could, if requisite, be made complete. Should something be remarked of the class, say farmers, to which this family belongs, we neither enumerate in thought all the individuals contained in the class, nor believe that we could do so if required; but we are content with taking some few samples of it, and remembering that these could be indefinitely multiplied. Supposing the subject of which something is predicated be Englishmen, the answering state of consciousness is a still more inadequate representative of the reality. Yet more remote is the likeness of the thought to the thing, if reference be made to Europeans or to human beings. And when we come to propositions concerning the mammalia, or concerning the whole of the vertebrata, or concerning animals in general, or concerning all organic beings, the unlikeness of our conceptions to the objects named reaches its extreme. Throughout which series of instances we see, that as the number of objects grouped together in thought increases, the concept, formed of a few typical samples joined with the notion of multiplicity, becomes more and more a mere symbol; not only because it gradually ceases to represent the size of the group, but also because as the group grows more heterogeneous, the typical samples thought of are less like the average objects which the group contains.
This formation of symbolic conceptions, which inevitably arises as we pass from small and concrete objects to large and to discrete ones, is mostly a very useful, and indeed necessary, process. When, instead of things whose attributes can be tolerably well united in a single state of consciousness, we have to deal with things whose attributes are too vast or numerous to be so united, we must either drop in thought part of their attributes, or else not think of them at all – either form a more or less symbolic conception, or no conception. We must predicate nothing of objects too great or too multitudinous to be mentally represented; or we must make our predications by the help of extremely inadequate representations of such objects – mere symbols of them.
But while by this process alone we are enabled to form general propositions, and so to reach general conclusions, we are by this process perpetually led into danger, and very often into error. We habitually mistake our symbolic conceptions for real ones; and so are betrayed into countless false inferences. Not only is it that in proportion as the concept we form of any thing or class of things, misrepresents the reality, we are apt to be wrong in any assertion we make respecting the reality; but it is that we are led to suppose we have truly conceived a great variety of things which we have conceived only in this fictitious way; and further to confound with these certain things which cannot be conceived in any way. How almost unavoidably we fall into this error it will be needful here to observe.
From objects readily representable in their totality, to those of which we cannot form even an approximate representation, there is an insensible transition. Between a pebble and the entire Earth a series of magnitudes might be introduced, each of which differed from the adjacent ones so slightly that it would be impossible to say at what point in the series our conceptions of them became inadequate. Similarly, there is a gradual progression from those groups of a few individuals which we can think of as groups with tolerable completeness, to those larger and larger groups of which we can form nothing like true ideas. Whence it is manifest that we pass from actual conceptions to symbolic ones by infinitesimal steps. Note next that we are led to deal with our symbolic conceptions as though they were actual ones, not only because we cannot clearly separate the two, but also because, in the great majority of cases, the first serve our purposes nearly or quite as well as the last – are simply the abbreviated signs we substitute for those more elaborate signs which are our equivalents for real objects. Those very imperfect representations of ordinary things which we habitually make in thinking, we know can be developed into adequate ones if needful. Those concepts of larger magnitudes and more extensive classes which we cannot make adequate, we still find can be verified by some indirect process of measurement or enumeration. And even in the case of such an utterly inconceivable object as the Solar System, we yet, through the fulfilment of predictions founded on our symbolic conception of it, gain the conviction that this symbolic conception stands for an actual existence, and, in a sense, truly expresses certain of its constituent relations. Thus our symbolic conceptions being in the majority of cases capable of development into complete ones, and in most other cases serving as steps to conclusions which are proved valid by their correspondence with observation, we acquire a confirmed habit of dealing with them as true conceptions – as real representations of actualities. Learning by long experience that they can, if needful, be verified, we are led habitually to accept them without verification. And thus we open the door to some which profess to stand for known things, but which really stand for things that cannot be known in any way.
To sum up, we must say of conceptions in general, that they are complete only when the attributes of the object conceived are of such number and kind that they can be represented in consciousness so nearly at the same time as to seem all present together; that as the objects conceived become larger and more complex, some of the attributes first thought of fade from consciousness before the rest have been represented, and the conception thus becomes imperfect; that when the size, complexity, or discreteness of the object conceived becomes very great, only a small portion of its attributes can be thought of at once, and the conception formed of it thus becomes so inadequate as to be a mere symbol; that nevertheless such symbolic conceptions, which are indispensable in general thinking, are legitimate, provided that by some cumulative or indirect process of thought, or by the fulfilment of predictions based on them, we can assure ourselves that they stand for actualities; but that when our symbolic conceptions are such that no cumulative or indirect processes of thought can enable us to ascertain that there are corresponding actualities, nor any predictions be made whose fulfilment can prove this, then they are altogether vicious and illusive, and in no way distinguishable from pure fictions.
§ 10. And now to consider the bearings of this general truth on our immediate topic –