Nevertheless, the concept which he has formed is an extremely simple one—amounting, in fact, to nothing more than the naming of one among the most habitual of his recepts. But it is of the nature of concepts that, when once formed, they admit of being intentionally compared; and thus there arises a new possibility in the way of grouping ideas—namely, no longer by means of sensuous associations, but by means of symbolic representations. The names of recepts now serve as symbols of the recepts themselves, and so admit of being grouped without reference to the sensuous perceptions out of which they originally sprang. No longer restricted to time, place, circumstance, or occasion, ideas may now be called up and manipulated at pleasure; for in this new method of ideation the mind has, as it were, acquired an _algebra of recepts_: it is no longer necessary that the actual recepts themselves should be present to sensuous perception, or even to representative imagination. And as concepts are thus symbols of recepts, they admit, as I have said, of being compared and combined without reference to the recepts which they serve to symbolize. Thus we become able, as it were, to calculate in concepts in a way and to an extent that would be quite impossible in the merely perceptual medium of recepts. Now, it is in this algebra of the imagination that all the higher work of ideation is accomplished; and as the result of long and elaborate syntheses of concepts we turn out mental products of enormous intricacy—which, nevertheless, may be embodied in single words. Such words, for example, as Virtue, Government, Mechanical Equivalent, stand for immensely more elaborated concepts than the words Solid or Fluid—seeing that to the former there are no possible equivalents in the way of recepts. Hence I say we must begin by recognizing the great reach of intellectual territory which is covered by what are called concepts. At the lowest level they are nothing more than named recepts; beyond that level they become the names of other concepts; and eventually they become the named products of the highest and most complex co-ordinations of concepts which have been achieved by the human mind. By the term _Lower Concepts_, then, I will understand those which are nothing more than named recepts, while by the term _Higher Concepts_ I will understand those which are compounded of other concepts. * * * * *