Characteristic Ideas.—Such, then, is the hierarchy of science and the mutual relations of the several orders. Now, each group of sciences, as Whewell has shown, has its own characteristic fundamental idea or ideas. For example, the fundamental ideas of mathematics—the ideas underlying all its operations—are those of number and quantity. The fundamental idea of mechanical and physical sciences is that of physical force. The fundamental idea peculiar to chemistry and underlying all its distinctive phenomena is that of affinity. The fundamental idea underlying all the distinctive phenomena of biology is that of life. Subordinate ideas under these general heads we shall call, after Comte, doctrines.
Characteristic Methods.—Again, each group of sciences has also its characteristic method. The characteristic method of mathematics is that of notation. We are all familiar with the wonderful power of this method. By the use of a few figures, viz., the numeral digits, having each a value of its own and another depending on position, a few symbols, a and b, x and y, connected by signs, and and , the veriest schoolboy may quickly solve problems which would defy the unassisted efforts of the greatest genius. The characteristic method of physics and chemistry is experiment: without the use of this potent instrument these sciences could not advance a step. The characteristic method of biological sciences is the method of comparison. The use of this method we will illustrate after a while.
Now, each group, after it once enters the hierarchy, besides its own characteristic ideas and methods, uses freely and with the greatest advantage all the ideas and methods of the lower sciences, but especially those of the science immediately below, and with which, therefore, it is immediately connected. Thus chemistry uses the characteristic ideas and methods of physics and mathematics, but especially of physics. Biology, besides its own characteristic ideas and methods, uses freely the methods and ideas of chemistry—physics and mathematics—but especially those of chemistry. If there be any other still higher science, it must use with the greatest advantage the ideas and methods of all lower sciences, but especially those of biology.
Again: although the ideas and methods of the lower groups are imported into the higher groups and freely used there, yet we acquire clear conceptions of such ideas and doctrines, and expertness in the use of such methods, only in the group where they are native and characteristic. Thus, each group of sciences becomes the appropriate school for its own characteristic doctrines and methods. For example, physics uses freely the method of notation, but mathematics is the true school of this method. Biology uses experiment, but physics is the true school of this method. If there be any other still higher science which shall use the doctrines of life and the method of comparison, the cultivators of that science should first acquire clear concep-
