Not to give this lecture a too controversial tone, however, I must only advert to one more doctrine, held by a thinker of our own age and country, whose opinions are worthy of all respect, it is, that the Biological sciences differ from all others, inasmuch as in them classification takes place by type and not by definition.
It is said, in short, that a natural-history class is not capable of being defined--that the class Rosaceae, for instance, or the class of Fishes, is not accurately and absolutely definable, inasmuch as its members will present exceptions to every possible definition; and that the members of the class are united together only by the circumstance that they are all more like some imaginary average rose or average fish, than they resemble anything else.
But here, as before, I think the distinction has arisen entirely from confusing a transitory imperfection with an essential character. So long as our information concerning them is imperfect, we class all objects together according to resemblances which we feel, but cannot define; we group them round types, in short. Thus, if you ask an ordinary person what kinds of animals there are, he will probably say, beasts, birds, reptiles, fishes, insects, &c. Ask him to define a beast from a reptile, and eh cannot do it; but he says, things like a frog or a lizard are reptiles. You see he does class by type, and not by definition. But how does this classification differ from that of the scientific Zoologist? How does the meaning of the scientific class-name of "Mammalia" differ from the unscientific of "Beasts"?
Why, exactly because the former depends on a definition, the latter on a type. The class Mammalia is scientifically defined as "all animals which have a vertebrated skeleton and suckle their young." Here is no reference to type, but a definition rigorous enough for a geometrician. And such is the character which every scientific naturalist recognises as that to which his classes must aspire--knowing, as he does, that classification by type is simply an acknowledgment of ignorance and a temporary device.
[T. H. Huxley, "On the Educational Value of the Natural History Sciences," Lay Sermons, Addresses, and Reviews. Macmillan (London: 1880) 81-83.]
Huxley notes in a footnote the passage to which he is referring in Whewell's Philosophy of the Inductive Sciences. I think, however, that Huxley has misunderstood Whewell on this point; for what Huxley calls a definition, Whewell would, I think, still call a type. If, for instance, by a freak of development a filly were to be born with a complete inability to suckle her young, we would not hold that a mammal had given birth to a non-mammal. Whewell thinks biologists classify by type not because they are ignorant, but because they have to do so, given the variety of nature. They can give well-defined characters of the type, but only a type. The distinction between the resemblance that is felt and the resemblance that is defined is actually found in slightly different terms in Whewell, as well, when he distinguishes between primitive and more sophisticated attempts at natural classification. (I suspect, too, that Whewell would regard Huxley's defined class of Mammalia as an artificial classification rather than a natural grouping; as opposed to the natural group of roses. But I'd have to go back and see for sure.)