On the whole, from the discussion of probabilities there emerge four principal cautions as to their use:  Not to make a pedantic parade of numerical probability, where the numbers have not been ascertained; Not to trust to our feeling of what is likely, if statistics can be obtained; Not to apply an average probability to special classes or individuals without inquiring whether they correspond to the average type; and Not to trust to the empirical probability of events, if their causes can be discovered and made the basis of reasoning which the empirical probability may be used to verify.

The reader who wishes to pursue this subject further should read a work to which the foregoing chapter is greatly indebted, Dr. Venn’s Logic of Chance.

CHAPTER XXI

DIVISION AND CLASSIFICATION

Sec. 1.  Classification, in its widest sense, is a mental grouping of facts or phenomena according to their resemblances and differences, so as best to serve some purpose.  A “mental grouping”:  for although in museums we often see the things themselves arranged in classes, yet such an arrangement only contains specimens representing a classification.  The classification itself may extend to innumerable objects most of which have never been seen at all.  Extinct animals, for example, are classified from what we know of their fossils; and some of the fossils may be seen arranged in a museum; but the animals themselves have disappeared for many ages.

Again, things are classed according to their resemblances and differences:  that is to say, those that most closely resemble one another are classed together on that ground; and those that differ from one another in important ways, are distributed into other classes.  The more the things differ, the wider apart are their classes both in thought and in the arrangements of a museum.  If their differences are very great, as with animals, vegetables and minerals, the classing of them falls to different departments of thought or science, and is often represented in different museums, zoological, botanical, mineralogical.

We must not, however, suppose that there is only one way of classifying things.  The same objects may be classed in various ways according to the purpose in view.  For gardening, we are usually content to classify plants into trees, shrubs, flowers, grasses and weeds; the ordinary crops of English agriculture are distinguished, in settling their rotation, into white and green; the botanist divides the higher plants into gymnosperms and angiosperms, and the latter into monocotyledons and dicotyledons.  The principle of resemblance and difference is recognised in all these cases; but what resemblances or differences are important depends upon the purpose to be served.