Philosophy as forgetting, and index characters

I was talking to a friend, Damian Cox, yesterday, and we were discussing how many of the ideas of, say, a Wittgenstein had been a rediscovery or reformulation of what had been commonly held over a century before. Damian made the comment that philosophy is a process of forgetting what we previously had worked out, so that ideas like Wittgenstein’s strike us as novel and important.

This was in the context of discussions about natural kinds. It is my contention that until the late nineteenth century, with a couple of exceptions, “kind” in philosophy, and “natural kind” in Venn’s Logic of Chance (1866), in which the term is coined, meant something like this: a kind is natural if it has a common cause that gives all instances some set of properties, of which the majority are sufficient to license generalities of inference. Or, in simpler terms, natural kinds make things similar enough that we know something about all of them if we know something about one of them.

But we do not know exactly the same things about all of them if we know one. That is, it doesn’t license a deductive inference of the sort: X is a member of A, X has property P, therefore all members of A have P. This is the notion of “class” kind introduced, I think, by John Stuart Mill in his A System of Logic (1843, Vol 1 and Vol 2):

We form our groups round certain selected Kinds, each of which serves as a sort of exemplar of its group. But though the groups are suggested by types, I cannot think that a group when formed is determined by the type; that in deciding whether a species belongs to the group, a reference is made to the type, and not to the characters; that the characters “cannot be expressed in words.” This assertion is inconsistent with Dr. Whewell’s own statement of the fundamental principle of classification, namely, that “general assertions shall be possible.” If the class did not possess any characters in common, what general assertions would be possible respecting it? Except that they all resemble each other more than they resemble anything else, nothing whatever could be predicated of the class. [System of Logic IV.vii.4 ]

But earlier, Whewell, to whom Mill is responding in part, had previously used a different notion of generalisation:

But it may be asked, if we cannot define a word, or a class of things which a word denotes, how can we distinguish what it does mean from what it does not mean? How can we say that it signifies one thing rather than another, except we declare what is its signification? The answer to this question involves the general principle of a natural method of classification which has already been stated and need not here be again dwelt on. It has been shown that names of kinds of things (genera) associate them according to total resemblances, not partial characters. The principle which connects a group of objects in natural history is not a definition but a type. Thus we take as the type of the Rose family, it may be the common wild rose; all species which resemble this flower more than they resemble any other group of species are also roses, and form one genus. All genera which resemble Roses more than they resemble any other group of genera are of the same family. And thus the Rose family is collected about some one species which is the type or central point of the group.

In such an arrangement, it may readily be conceived that though the nucleus of each group may cohere firmly together, the outskirts of contiguous groups may approach, and may even be intermingled, so that some species may doubtfully adhere to one group or another. Yet this uncertainty does not at all affect the truths which we find ourselves enabled to assert with regard to the general mass of each group. And thus we are taught that there may be very important differences between two groups of objects, although we are unable to tell where the one group ends and where the other begins; and that there may be propositions of indisputable truth, in which it is impossible to give unexceptionable definitions of the terms employed.

15. These lessons are of the highest value with regard to all employments [sic] of the human mind; for the mode in which words in common use acquire their meaning, approaches far more nearly to the Method of Type than to the method of definition. [Whewell, Philosophy of the Inductive Sciences, 1840: vol 2: 517–519]

We may further observe, that in order that Natural History may produce such an effect [to correct “the belief that definitions are essential to substantial truth”], it must be studied by inspection of the objects themselves, and not by the reading of books only. Its lesson is, that we must in all cases of doubt or obscurity refer, not to words or definitions, but to things. The Book of Nature is its dictionary: it is there that the natural historian looks, to find the meaning of the words which he uses … . So long as a plant, in its most essential parts, is more like a rose than anything else, it is a rose. He knows no other definition. [pp519-520]

Whoa. Did Whewell just say that what we do with kinds is arrange them around a type, and that definitions are irrelevant? Did he just, in other words, posit a Family Resemblance Predicate? Yes he did. What appears to have happened is that Mill changed the subject. Before, natural kinds were devised as cluster concepts. Definition was arid and uninformative (because one cannot make inductive generalisations from a definition). With Mill, we now have the modern notion of a Kind:

When the infima species, or proximate Kind, to which an individual belongs, has been ascertained, the properties common to that Kind include necessarily the whole of the common properties of every other real Kind to which the individual can be referrible. Let the individual, for example, be Socrates, and the proximate Kind, man. Animal, or living creature, is also a real Kind, and includes Socrates; but, since it likewise includes man, or in other words, since all men are animals, the properties common to animals form a portion of the common properties of the sub-class, man. And if there be any class which includes Socrates without including man, that class is not a real Kind.

And in Bk IV, ch iv, sect iii and iv he says:

For, in order to give a connotation to a name, consistently with its denoting certain objects, we have to make our selection from among the various attributes in which those objects agree. To ascertain in what they do agree is, therefore,the first logical operation requisite. When this has been done as far as is necessary or practicable, the question arises, which of these common attributes shall be selected to be associated with the name. For if the class which the name denotes be a Kind, the common properties are innumerable; and even ff not, they are often extremely numerous. Our choice is first limited by the preference to be given to properties which are well known, and familiarly predicated of the class; but even these are often too numerous to be all included in the definition, and, besides, the properties most generally known may not be those which serve best to mark out the class from all others. We should therefore select from among the common properties, (if among them any such are to be found,) those on which it has been ascertained by experience, or proved by deduction, that many others depend; or at least which are sure marks of them, and from whence, therefore, many others will follow by inference. We thus see that to frame a good definition of a name already in use, is not a matter of choice but of discussion, and discussion not merely respecting the usage of language, but respecting the properties of things, and even the origin of those properties. And hence every enlargement of our knowledge of the objects to which the name is applied, is liable to suggest an improvement in the definition. It is impossible to frame a perfect set of definitions on any subject, until the theory of the subject is perfect: and as science makes progress, its definitions are also progressive. … [sect iii]

By a Kind, it will be remembered, we mean one of those classes which are distinguished from all others not by one or a few definite properties, but by an unknown multitude of them: the combination of properties on which the class is grounded, being a mere index to an indefinite number of other distinctive attributes. [ sect iv, Emphasis added]

Mill’s notion of a “real Kind” is one of causality, and he takes the old scholastic notion of definition and makes all class concepts depend on a set of necessary and sufficient causal properties. The identification of kinds is done by characters that are a “mere index” to the whole. So Mill is not exactly an essentialist in the older sense, but he is in the sense that there are properties and their origins that make classes “real”.

This view of natural kinds enters the modern debates around the time of the Principia Mathematica, but not in that work, I think. The problem as bequeathed to us from this tradition, of which such classics as Quine’s 1969 essay by that title are the exemplars, is in effect to have changed the subject from the older notion of types. Mill’s Ciceronian definitional account claims to aid our induction, but unlike Whewell’s type-based view, it actually is at best only deductive. While if the class actually is based on a “real kind” inferences based on the index characters may generalise, in fact all we know about a Millian class is that it is constructed by some set of necessary and sufficient properties. All we are warranted in inferring from that is whatever the definienda are that were used to construct the class. For inductively projectible classes or kinds, we need some warrant that the “unseen” properties actually do travel with the index properties. For that we need to construct our classes based on a large, and relatively arbitrary, but informative, set of characters. And for that we need to use types, not necessary and sufficient classes.