As regards these relations, they are conceptions of the second degree, as one might say, and their birthplace is the mind itself.In Chapter XXVIII
I shall at considerable length defend the mind's claim to originality and fertility in bringing them forth.But no single one of the mind's conceptions is fertile of itself , as the opinion which I criticise pretends.
When the several notes of a chord are sounded together, we get a new feeling from their combination.This feeling is due to the mind reacting upon that group of sounds in that determinate way, and no one would think of saying of any single note of the chord that it 'developed' of itself into the other notes or into the feeling of harmony.So of Conceptions.
No one of them develops into any other.But if two of them are thought at once, their relation may come to consciousness, and form matter for a third conception.
Take 'thirteen' for example, which is said to develop into 'prime.'
What really happens is that we compare the utterly changeless conception of thirteen with various other conceptions, those of the different multiples of two, three, four, five, and six, and ascertain that it differs from them all.Such difference is a freshly ascertained relation.It is only for mere brevity's sake that we call it a property of the original thirteen, the property of being prime.We shall see in the next chapter that (if we count out æsthetic and moral relations between things) the only important relations of which the mere inspection of conceptions makes us aware are relations of comparison, that is, of difference and no-difference, between them.The judgment 6 + 7 = 13 expresses the relation of equality between two ideal objects, 13 on the one hand and 6 + 7 on the other, successively conceived and compared.The judgments 6 + 7 > 12, or 6 + 7 < 14, express in like manner relations of in equality between ideal objects.But if it be unfair to say that the conception of 6 + 7 generates that of 12
or of 14, surely it is as unfair to say that it generates that of 13.
The conceptions of 12, 13, and 14 are each and all generated by individual acts of the mind, playing with its materials.When, comparing two ideal objects, we find them equal, the conception of one of them may be that of a whole and of the other that of all its parts.This particular case is, it seems to me, the only case which makes the notion of one conception evolving into another sound plausible.But even in this case the conception, as such, of the whole does not evolve into the conception, as such, of the parts.Let the conception of some object as a whole be given first.
To begin with, it points to and identifies for future thought a certain that.The 'whole' in question might be one of those mechanical puzzles of which the difficulty is to un- lock the parts.In this case, nobody would pretend that the richer and more elaborate conception which we gain of the puzzle after solving it came directly out of our first crude conception of it, for it is notoriously the outcome of experimenting with our hands.It is true that, as they both mean that same puzzle , our earlier thought and our later thought have one conceptual function, are vehicles of one conception.But in addition to being the vehicle of this bald unchanging conception, 'that same puzzle,' the later thought is the vehicle of all those other conceptions which it took the manual experimentation to acquire.Now, it is just the same where the whole is mathematical instead of being mechanical.Let it be a polygonal space, which we cut into triangles, and of which we then affirm that it is those triangles.Here the experimentation (although usually done by a pencil in the hands) may be done by the unaided imagination.We hold the space, first conceived as polygonal simply, in our mind's eye until our attention wandering to and fro within it has carved it into the triangles.The triangles are a new conception, the result of this new operation.Having once conceived them, however, and compared them with the old polygon which we originally conceived and which we have never ceased conceiving, we judge them to fit exactly into its area.The earlier and later conceptions, we say, are of one and the same space.But this relation between triangles and polygon which the mind cannot help finding if it compares them at all, is very badly expressed by saying that the old conception has developed into the new.New conceptions come from new sensations, new movements, new emotions, new associations, new acts of attention, and new comparisons of old conceptions, and not in other ways, Endogenous prolification is not a mode of growth to which conceptions can lay claim.
I hope, therefore, that I shall not be accused of huddling mysteries out of sight, when I insist that the psychology of conception is not the place in which to treat of those of continuity and change.Conceptions form the one class of entities that cannot under any circumstances change.
They can cease to be, altogether; or they can stay, as what they severally are; but there is for them no middle way.They form an essentially discontinuous system, and translate the process of our perceptual experience, which is naturally a flux, into a set of stagnant and petrified terms.
The very conception of flux itself is an absolutely changeless meaning in the mind: it signifies just that one thing, flux, immovably.- And, with this, the doctrine of the flux of the concept may be dismissed, and need not occupy our attention again. 'ABSTRACT' IDEAS.We have now to pass to a less excusable mistake.There are philosophers who deny that associated things can be broken asunder at all, even provisionally, by the conceiving mind.The opinion known as Nominalism says that we really never frame any conception of the partial elements of an experience, but are compelled, whenever we think it, to think it in its totality, just as it came.
