the animal world is that which occurs in ruminating animals, and which
could not be better stated than in the following extract from the
classical work of Cuvier:[565]
[565] *Ossemens Fossiles*, 4th edit. vol. i. p. 164. Quoted by
Huxley, *Lectures*, &c., p. 5.
“I doubt if any one would have divined, if untaught by observation,
that all ruminants have the foot cleft, and that they alone have it. I
doubt if any one would have divined that there are frontal horns only
in this class: that those among them which have sharp canines for the
most part lack horns.
“However, since these relations are constant, they must have some
sufficient cause; but since we are ignorant of it, we must make good
the defect of the theory by means of observation: it enables us to
establish empirical laws which become almost as certain as rational
laws when they rest on sufficiently repeated observations; so that
now whoso sees merely the print of a cleft foot may conclude that the
animal which left this impression ruminated, and this conclusion is as
certain as any other in physics or morals. This footprint alone then,
yields, to him who observes it, the form of the teeth, the form of the
jaws, the form of the vertebræ, the form of all the bones of the legs,
of the thighs, of the shoulders, and of the pelvis of the animal which
has passed by: it is a surer mark than all those of Zadig.”
We meet with a good instance of the purely empirical correlation
of circumstances when we classify the planets according to their
densities and periods of axial rotation.[566] If we examine a table
specifying the usual astronomical elements of the solar system, we find
that four planets resemble each other very closely in the period of
axial rotation, and the same four planets are all found to have high
densities, thus:--
[566] Chambers, *Descriptive Astronomy*, 1st edit. p. 23.
Name of Period of Axial
Planet. Rotation. Density.
Mercury 24 hours 5 minutes 7·94
Venus 23 " 21 " 5·33
Earth 23 " 56 " 5·67
Mars 24 " 37 " 5·84
A similar table for the other larger planets, is as follows:--
Jupiter 9 hours 55 minutes 1·36
Saturn 10 " 29 " ·74
Uranus 9 " 30 " ·97
Neptune -- " -- 1·02
It will be observed that in neither group is the equality of the
rotational period or the density more than rudely approximate;
nevertheless the difference of the numbers in the first and second
group is so very well marked, the periods of the first being at least
double and the densities four or five times those of the second, that
the coincidence cannot be attributed to accident. The reader will
also notice that the first group consists of the planets nearest to
the sun; that with the exception of the earth none of them possess
satellites; and that they are all comparatively small. The second group
are furthest from the sun, and all of them possess several satellites,
and are comparatively great. Therefore, with but slight exceptions, the
following correlations hold true:--
Interior planets. Long period. Small size. High Density. No satellites.
Exterior " Short " Great " Low " Many "
These coincidences point with much probability to a difference in the
origin of the two groups, but no further explanation of the matter is
yet possible.
The classification of comets according to their periods by Mr.
Hind and Mr. A. S. Davies, tends to establish the conclusion that
distinct groups of comets have been brought into the solar system
by the attractive powers of Jupiter, Uranus, or other planets.[567]
The classification of nebulæ as commenced by the two Herschels, and
continued by Lord Rosse, Mr. Huggins, and others, will probably lead
at some future time to the discovery of important empirical laws
concerning the constitution of the universe. The minute examination and
classification of meteorites, as carried on by Mr. Sorby and others,
seems likely to afford us an insight into the formation of the heavenly
bodies.
[567] *Philosophical Magazine*, 4th Series, vol. xxxix. p. 396;
vol. xl. p. 183; vol. xli. p. 44. See also Proctor, *Popular Science
Review*, October 1874, p. 350.
We should never fail to remember the slightest and most inexplicable
correlations, for they may prove of importance in the future.
Discoveries begin when we are least expecting them. It is a significant
fact, for instance, that the greater number of variable stars are of
a reddish colour. Not all variable stars are red, nor all red stars
variable; but considering that only a small fraction of the observed
stars are known to be variable, and only a small fraction are red, the
number which fall into both classes is too great to be accidental.[568]
It is also remarkable that the greater number of stars possessing great
proper motion are double stars, the star 61 Cygni being especially
noticeable in this respect.[569] The correlation in these cases is
not without exception, but the preponderance is so great as to point
to some natural connexion, the exact nature of which must be a matter
for future investigation. Herschel remarked that the two double stars
61 Cygni and α Centauri of which the orbits were well ascertained,
evidently belonged to the same family or genus.[570]
[568] Humboldt, *Cosmos* (Bohn), vol. iii. p. 224.
[569] Baily, British *Association Catalogue*, p. 48.
[570] *Outlines of Astronomy*, § 850, 4th edit. p. 578.
*Classification in Crystallography.*
Perhaps the most perfect and instructive instance of classification
which we can find is furnished by the science of crystallography
(p. 133). The system of arrangement now generally adopted is
conspicuously natural, and is even mathematically perfect. A crystal
consists in every part of similar molecules similarly related to the
adjoining molecules, and connected with them by forces the nature of
which we can only learn by their apparent effects. But these forces
are exerted in space of three dimensions, so that there is a limited
number of suppositions which can be entertained as to the relations of
these forces. In one case each molecule will be similarly related to
all those which are next to it; in a second case, it will be similarly
related to those in a certain plane, but differently related to those
not in that plane. In the simpler cases the arrangement of molecules is
rectangular; in the remaining cases oblique either in one or two planes.
In order to simplify the explanation and conception of the complicated
phenomena which crystals exhibit, an hypothesis has been invented which
is an excellent instance of the Descriptive Hypotheses before mentioned
(p. 522). Crystallographers imagine that there are within each crystal
certain axes, or lines of direction, by the comparative length and the
mutual inclination of which the nature of the crystal is determined.
In one class of crystals there are three such axes lying in one plane,
and a fourth perpendicular to that plane; but in all the other classes
there are imagined to be only three axes. Now these axes can be varied
in three ways as regards length: they may be (1) all equal, or (2) two
equal and one unequal, or (3) all unequal. They may also be varied in
four ways as regards direction: (1) they may be all at right angles
to each other; (2) two axes may be oblique to each other and at right
angles to the third; (3) two axes may be at right angles to each other
and the third oblique to both; (4) the three axes may be all oblique.
Now, if all the variations as regards length were combined with those
regarding direction, it would seem to be possible to have twelve
classes of crystals in all, the enumeration being then logically and
geometrically complete. But as a matter of empirical observation, many
of these classes are not found to occur, oblique axes being seldom or
never equal. There remain seven recognised classes of crystals, but
even of these one class is not positively known to be represented in
nature.
The first class of crystals is defined by possessing three equal
rectangular axes, and equal elasticity in all directions. The primary
or simple form of the crystals is the cube, but by the removal of the
corners of the cube by planes variously inclined to the axes, we have
the regular octohedron, the dodecahedron, and various combinations of
these forms. Now it is a law of this class of crystals that as each
axis is exactly like each other axis, every modification of any corner
of a crystal must be repeated symmetrically with regard to the other
axes; thus the forms produced are symmetrical or regular, and the
class is called the *Regular System* of crystals. It includes a great
variety of substances, some of them being elements, such as carbon in
the form of diamond, others more or less complex compounds, such as
rock-salt, potassium iodide and bromide, the several kinds of alum,
fluor-spar, iron bisulphide, garnet, spinelle, &c. No correlation
then is apparent between the form of crystallisation and the chemical
composition. But what we have to notice is that the physical properties
of the crystallised substances with regard to light, heat, electricity,
&c., are closely similar. Light and heat undulations, wherever they
enter a crystal of the regular system, spread with equal rapidity in
all directions, just as they would in a uniform fluid. Crystals of the
regular system accordingly do not in any case exhibit the phenomena
of double refraction, unless by mechanical compression we alter the
conditions of elasticity. These crystals, again, expand equally in all
directions when heated, and if we could cut a sufficiently large plate
from a cubical crystal, and examine the sound vibrations of which it
is capable, we should find that they indicated an equal elasticity
in every direction. Thus we see that a great number of important
properties are correlated with that of crystallisation in the regular
system, and as soon as we know that the primary form of a substance
is the cube, we are able to infer with approximate certainty that it
possesses all these properties. The class of regular crystals is then
an eminently natural class, one disclosing many general laws connecting
together the physical and mechanical properties of the substances
classified.
In the second class of crystals, called the dimetric, square prismatic,
or pyramidal system, there are also three axes at right angles to each
other; two of the axes are equal, but the third or principal axis is
unequal, being either greater or less than either of the other two. In
such crystals accordingly the elasticity and other properties are alike
in all directions perpendicular to the principal axis, but vary in all
other directions. If a point within a crystal of this system be heated,
the heat spreads with equal rapidity in planes perpendicular to the
principal axis, but more or less rapidly in the direction of this axis,
so that the isothermal surface is an ellipsoid of revolution round that
axis.
Nearly the same statement may be made concerning the third or hexagonal
or rhombohedral system of crystals, in which there are three axes lying
in one plane and meeting at angles of 60°, while the fourth axis is
perpendicular to the other three. The hexagonal prism and rhombohedron
are the commonest forms assumed by crystals of this system, and in
ice, quartz, and calc-spar, we have abundance of beautiful specimens
of the various shapes produced by the modification of the primitive
form. Calc-spar alone is said to crystallise in at least 700 varieties
of form. Now of all the crystals belonging both to this and the
dimetric class, we know that a ray of light passing in the direction
of the principal axis will be refracted singly as in a crystal of the
regular system; but in every other direction the light will suffer
double refraction being separated into two rays, one of which obeys
the ordinary law of refraction, but the other a much more complicated
law. The other physical properties vary in an analogous manner. Thus
calc-spar expands by heat in the direction of the principal axis, but
contracts a little in directions perpendicular to it. So closely are
the physical properties correlated that Mitscherlich, having observed
the law of expansion in calc-spar, was enabled to predict that the
double refracting power of the substance would be decreased by a rise
of temperature, as was proved by experiment to be the case.
In the fourth system, called the trimetric, rhombic, or right prismatic
system, there are three axes, at right angles, but all unequal in
length. It may be asserted in general terms that the mechanical
properties vary in such crystals in every direction, and heat spreads
so that the isothermal surface is an ellipsoid with three unequal axes.
In the remaining three classes, called the monoclinic, diclinic, and
triclinic, the axes are more or less oblique, and at the same time
unequal. The complication of phenomena is therefore greatly increased,
and it need only be stated that there are always two directions in
which a ray is singly refracted, but that in all other directions
double refraction takes place. The conduction of heat is unequal in
all directions, the isothermal surface being an ellipsoid of three
unequal axes. The relations of such crystals to other phenomena are
often very complicated, and hardly yet reduced to law. Some crystals,
called pyro-electric, manifest vitreous electricity at some points of
their surface, and resinous electricity at other points when rising in
temperature, the character of the electricity being changed when the
temperature sinks again. This production of electricity is believed to
be connected with the hemihedral character of the crystals exhibiting
it. The crystalline structure of a substance again influences its
magnetic behaviour, the general law being that the direction in which
the molecules of a crystal are most approximated tends to place itself
axially or equatorially between the poles of a magnet, respectively
as the body is magnetic or diamagnetic. Further questions arise if we
apply pressure to crystals. Thus doubly refracting crystals with one
principal axis acquire two axes when the pressure is perpendicular in
direction to the principal axis.
All the phenomena peculiar to crystalline bodies are thus closely
correlated with the formation of the crystal, or will almost
certainly be found to be so as investigation proceeds. It is upon
empirical observation indeed that the laws of connexion are in the
first place founded, but the simple hypothesis that the elasticity
and approximation of the particles vary in the directions of the
crystalline axes allows of the application of deductive reasoning. The
whole of the phenomena are gradually being proved to be consistent with
this hypothesis, so that we have in this subject of crystallography
a beautiful instance of successful classification, connected with
a nearly perfect physical hypothesis. Moreover this hypothesis was
verified experimentally as regards the mechanical vibrations of sound
by Savart, who found that the vibrations in a plate of biaxial crystal
indicated the existence of varying elasticity in varying directions.
*Classification an Inverse and Tentative Operation.*
If attempts at so-called natural classification are really attempts
at perfect induction, it follows that they are subject to the remarks
which were made upon the inverse character of the inductive process,
and upon the difficulty of every inverse operation (pp. 11, 12, 122,
&c.). There will be no royal road to the discovery of the best system,
and it will even be impossible to lay down rules of procedure to
assist those who are in search of a good arrangement. The only logical
rule would be as follows:--Having given certain objects, group them
in every way in which they can be grouped, and then observe in which
method of grouping the correlation of properties is most conspicuously
manifested. But this method of exhaustive classification will in almost
every case be impracticable, owing to the immensely great number of
modes in which a comparatively small number of objects may be grouped
together. About sixty-three elements have been classified by chemists
in six principal groups as monad, dyad, triad, &c., elements, the
numbers in the classes varying from three to twenty elements. Now if we
were to calculate the whole number of ways in which sixty-three objects
can be arranged in six groups, we should find the number to be so great
that the life of the longest lived man would be wholly inadequate
to enable him to go through these possible groupings. The rule of
exhaustive arrangement, then, is absolutely impracticable. It follows
that mere haphazard trial cannot as a general rule give any useful
result. If we were to write the names of the elements in succession
upon sixty-three cards, throw them into a ballot-box, and draw them
out haphazard in six handfuls time after time, the probability is
excessively small that we should take them out in a specified order,
that for instance at present adopted by chemists.
The usual mode in which an investigator proceeds to form a
classification of a new group of objects seems to consist in
tentatively arranging them according to their most obvious
similarities. Any two objects which present a close resemblance to
each other will be joined and formed into the rudiment of a class, the
definition of which will at first include all the apparent points of
resemblance. Other objects as they come to our notice will be gradually
assigned to those groups with which they present the greatest number
of points of resemblance, and the definition of a class will often
have to be altered in order to admit them. The early chemists could
hardly avoid classing together the common metals, gold, silver, copper,
lead, and iron, which present such conspicuous points of similarity as
regards density, metallic lustre, malleability, &c. With the progress
of discovery, however, difficulties began to present themselves in such
a grouping. Antimony, bismuth, and arsenic are distinctly metallic
as regards lustre, density, and some chemical properties, but are
wanting in malleability. The recently discovered tellurium presents
greater difficulties, for it has many of the physical properties of
metal, and yet all its chemical properties are analogous to those of
sulphur and selenium, which have never been regarded as metals. Great
chemical differences again are discovered by degrees between the
five metals mentioned; and the class, if it is to have any chemical
validity, must be made to include other elements, having none of the
original properties on which the class was founded. Hydrogen is a
transparent colourless gas, and the least dense of all substances; yet
in its chemical analogies it is a metal, as suggested by Faraday[571]
in 1838, and almost proved by Graham;[572] it must be placed in the
same class as silver. In this way it comes to pass that almost every
classification which is proposed in the early stages of a science will
be found to break down as the deeper similarities of the objects come
to be detected. The most obvious points of difference will have to be
neglected. Chlorine is a gas, bromine a liquid, and iodine a solid,
and at first sight these might have seemed formidable circumstances to
overlook; but in chemical analogy the substances are closely united.
The progress of organic chemistry, again, has yielded wholly new ideas
of the similarities of compounds. Who, for instance, would recognise
without extensive research a close similarity between glycerine and
alcohol, or between fatty substances and ether? The class of paraffins
contains three substances gaseous at ordinary temperatures, several
liquids, and some crystalline solids. It required much insight to
detect the analogy which exists between such apparently different
substances.
[571] *Life of Faraday*, vol. ii. p. 87.
[572] *Proceedings of the Royal Society*, vol. xvii. p. 212.
*Chemical and Physical Researches*, reprint, by Young and Angus
Smith, p. 290.
The science of chemistry now depends to a great extent on a correct
classification of the elements, as will be learnt by consulting
the able article on Classification by Professor G. C. Foster in
Watts’ *Dictionary of Chemistry*. But the present system of chemical
classification was not reached until at least three previous false
systems had been long entertained. And though there is much reason to
believe that the present mode of classification according to atomicity
is substantially correct, errors may yet be discovered in the details
of the grouping.
*Symbolic Statement of the Theory of Classification.*
The theory of classification can be explained in the most complete
and general manner, by reverting for a time to the use of the Logical
Alphabet, which was found to be of supreme importance in Formal Logic.
That form expresses the necessary classification of all objects and
ideas as depending on the laws of thought, and there is no point
concerning the purpose and methods of classification which may not
be stated precisely by the use of letter combinations, the only
inconvenience being the abstract form in which the subject is thus
represented.
If we pay regard only to three qualities in which things may resemble
each other, namely, the qualities A, B, C, there are according to
the laws of thought eight possible classes of objects, shown in the
fourth column of the Logical Alphabet (p. 94). If there exist objects
belonging to all these eight classes, it follows that the qualities A,
B, C, are subject to no conditions except the primary laws of thought
and things (p. 5). There is then no special law of nature to discover,
and, if we arrange the objects in any one order rather than another, it
must be for the purpose of showing that the combinations are logically
complete.
Suppose, however, that there are but four kinds of objects possessing
the qualities A, B, C, and that these kinds are represented by the
combinations ABC, A*b*C, *a*B*c*, *abc*. The order of arrangement will
now be of importance; for if we place them in the order
{ ABC { A*b*C
{ *a*B*c* { *abc*
placing the B’s first and those which are *b*’s last, we shall perhaps
overlook the law of correlation of properties involved. But if we
arrange the combinations as follows
{ ABC { *a*B*c*
{ A*b*C { *abc*
it becomes apparent at once that where A is, and only where A is, the
property C is to be found, B being indifferently present and absent.
The second arrangement then would be called a natural one, as rendering
manifest the conditions under which the combinations exist.
As a further instance, let us suppose that eight objects are presented
to us for classification, which exhibit combinations of the five
properties, A, B, C, D, E, in the following manner:--
ABC*d*E *a*BC*d*E
AB*cde* *a*B*cde*
A*b*CDE *ab*CDE
A*bc*D*e* *abc*D*e*
They are now classified, so that those containing A stand first, and
those devoid of A second, but no other property seems to be correlated
with A. Let us alter this arrangement and group the combinations thus:--
ABC*d*E A*b*CDE
AB*cde* A*bc*D*e*
*a*BC*d*E *ab*CDE
*a*B*cde* *abc*D*e*
It requires little examination to discover that in the first group B is
always present and D absent, whereas in the second group, B is always
absent and D present. This is the result which follows from a law of
the form B = d (p. 136), so that in this mode of arrangement we readily
discover correlation between two letters. Altering the groups again as
follows:--
ABC*d*E AB*cde*
*a*BC*d*E *a*B*cde*
A*b*CDE A*bc*D*e*
*ab*CDE *abc*D*e*,
we discover another evident correlation between C and E. Between A and
the other letters, or between the two pairs of letters B, D and C, E,
there is no logical connexion.
This example may seem tedious, but it will be found instructive in this
way. We are classifying only eight objects or combinations, in each
of which only five qualities are considered. There are only two laws
of correlation between four of those five qualities, and those laws
are of the simplest logical character. Yet the reader would hardly
discover what those laws are, and confidently assign them by rapid
contemplation of the combinations, as given in the first group. Several
tentative classifications must probably be made before we can resolve
the question. Let us now suppose that instead of eight objects and five
qualities, we have, say, five hundred objects and fifty qualities. If
we were to attempt the same method of exhaustive grouping which we
before employed, we should have to arrange the five hundred objects in
fifty different ways, before we could be sure that we had discovered
even the simpler laws of correlation. But even the successive
grouping of all those possessing each of the fifty properties would
not necessarily give us all the laws. There might exist complicated
relations between several properties simultaneously, for the detection
of which no rule of procedure whatever can be given.
*Bifurcate Classification.*
Every system of classification ought to be formed on the principles of
the Logical Alphabet. Each superior class should be divided into two
inferior classes, distinguished by the possession and non-possession
of a single specified difference. Each of these minor classes, again,
is divisible by any other quality whatever which can be suggested,
and thus every classification logically consists of an infinitely
extended series of subaltern genera and species. The classifications
which we form are in reality very small fragments of those which would
correctly and fully represent the relations of existing things. But if
we take more than four or five qualities into account, the number of
subdivisions grows impracticably large. Our finite minds are unable to
treat any complex group exhaustively, and we are obliged to simplify
and generalise scientific problems, often at the risk of overlooking
particular conditions and exceptions.
Every system of classes displayed in the manner of the Logical Alphabet
may be called *bifurcate*, because every class branches out at each
step into two minor classes, existent or imaginary. It would be a
great mistake to regard this arrangement as in any way a peculiar or
special method; it is not only a natural and important one, but it is
the inevitable and only system which is logically perfect, according
to the fundamental laws of thought. All other arrangements of classes
correspond to the bifurcate arrangement, with the implication that
some of the minor classes are not represented among existing things.
If we take the genus A and divide it into the species AB and AC, we
imply two propositions, namely that in the class A, the properties of B
and C never occur together, and that they are never both absent; these
propositions are logically equivalent to one, namely AB = A*c*. Our
classification is then identical with the following bifurcate one:--
A
|
+----------+----------+
| |
AB A*b*
| |
+------+------+ +------+------+
| | | |
ABC = 0 AB*c* A*b*C A*bc* = 0
If, again, we divide the genus A into three species, AB, AC, AD, we
are either logically in error, or else we must be understood to imply
that, as regards the other letters, there exist only three combinations
containing A, namely AB*cd*, A*b*C*d*, and A*bc*D.
The logical necessity of bifurcate classification has been clearly and
correctly stated in the *Outline of a New System of Logic* by George
Bentham, the eminent botanist, a work of which the logical value has
been quite overlooked until lately. Mr. Bentham points out, in p. 113,
that every classification must be essentially bifurcate, and takes, as
an example, the division of vertebrate animals into four sub-classes,
as follows:--
Mammifera--endowed with mammæ and lungs.
Birds without mammæ but with lungs and wings.
Fish deprived of lungs.
Reptiles deprived of mammæ and wings but with lungs.
We have, then, as Mr. Bentham says, three bifid divisions, thus
represented:--
Vertebrata
|
+-----------+-----------+
| |
Endowed with lungs deprived of lungs
| = Fish.
+--------+----------------+
| |
Endowed with deprived of
mammæ mammæ
= Mammifera. |
+------+------+
| |
with wings without wings
= Birds. = Reptiles.
It is quite evident that according to the laws of thought even this
arrangement is incomplete. The sub-class mammifera must either have
wings or be deprived of them; we must either subdivide this class, or
assume that none of the mammifera have wings, which is, as a matter of
fact, the case, the wings of bats not being true wings in the meaning
of the term as applied to birds. Fish, again, ought to be considered
with regard to the possession of mammæ and wings; and in leaving them
undivided we really imply that they never have mammæ nor wings, the
wings of the flying-fish, again, being no exception. If we resort to
the use of our letters and define them as follows--
A = vertebrata,
B = having lungs,
C = having mammæ,
D = having wings,
then there are four existent classes of vertebrata which appear to be
thus described--
ABC AB*c*D AB*cd* A*b*.
But in reality the combinations are implied to be
ABC*d* = Mammifera,
AB*c*D = Birds,
AB*cd* = Reptiles,
A*bcd* = Fish,
and we imply at the same time that the other four conceivable
combinations containing B, C, or D, namely ABCD, A*b*CD, A*b*C*d*, and
A*bc*D, do not exist in nature.
Mr. Bentham points out[573] that it is really this method of
classification which was employed by Lamarck and De Candolle in their
so-called analytical arrangement of the French Flora. He gives as an
example a table of the principal classes of De Candolle’s system, as
also a bifurcate arrangement of animals after the method proposed
by Duméril in his *Zoologie Analytique*, this naturalist being
distinguished by his clear perception of the logical importance of the
method. A bifurcate classification of the animal kingdom may also be
found in Professor Reay Greene’s *Manual of the Cœlenterata*, p. 18.
[573] *Essai sur la Nomenclature et la Classification*, Paris, 1823,
pp. 107, 108.
The bifurcate form of classification seems to be needless when the
quality according to which we classify any group of things admits
of numerical discrimination. It would seem absurd to arrange things
according as they have one degree of the quality or not one degree,
two degrees or not two degrees, and so on. The elements are classified
according as the atom of each saturates one, two, three, or more atoms
of a monad element, such as chlorine, and they are called accordingly
monad, dyad, triad, tetrad elements, and so on. It would be useless to
apply the bifid arrangement, thus:--
Element
|
+-----+-------+
| |
Monad not-Monad
|
+---------+---------+
| |
Dyad not-Dyad
|
+---------+---------+
| |
Triad not-Triad
|
+---------+--------+
| |
Tetrad not-Tetrad.
The reason of this is that, by the nature of number (p. 157) every
number is logically discriminated from every other number. There can
thus be no logical confusion in a numerical arrangement, and the series
of numbers indefinitely extended is also exhaustive. Every thing
admitting of a quality expressible in numbers must find its place
somewhere in the series of numbers. The chords in music correspond to
the simpler numerical ratios and must admit of complete exhaustive
classification in respect to the complexity of the ratios forming
them. Plane rectilinear figures may be classified according to the
numbers of their sides, as triangles, quadrilateral figures, pentagons,
hexagons, heptagons, &c. The bifurcate arrangement is not false when
applied to such series of objects; it is even necessarily involved in
the arrangement which we do apply, so that its formal statement is
needless and tedious. The same may be said of the division of portions
of space. Reid and Kames endeavoured to cast ridicule on the bifurcate
arrangement[574] by proposing to classify the parts of England into
Middlesex and what is not Middlesex, dividing the latter again into
Kent and what is not Kent, Sussex and what is not Sussex; and so on.
This is so far, however, from being an absurd proceeding that it is
requisite to assure us that we have made an exhaustive enumeration of
the parts of England.
[574] George Bentham, *Outline of a New System of Logic*, p. 115.
*The Five Predicables.*
As a rule it is highly desirable to consign to oblivion the ancient
logical names and expressions, which have infested the science for
many centuries past. If logic is ever to be a useful and progressive
science, logicians must distinguish between logic and the history of
logic. As in the case of any other science it may be desirable to
examine the course of thought by which logic has, before or since the
time of Aristotle, been brought to its present state; the history of a
science is always instructive as giving instances of the mode in which
discoveries take place. But at the same time we ought carefully to
disencumber the statement of the science itself of all names and other
vestiges of antiquity which are not actually useful at the present day.
Among the ancient expressions which may well be excepted from such
considerations and retained in use, are the “Five Words” or “Five
Predicables” which were described by Porphyry in his introduction to
Aristotle’s Organum. Two of them, *Genus* and *Species*, are the most
venerable names in philosophy, having probably been first employed
in their present logical meanings by Socrates. In the present day it
requires some mental effort, as remarked by Grote, to see anything
important in the invention of notions now so familiar as those of Genus
and Species. But in reality the introduction of such terms showed the
rise of the first germs of logic and scientific method; it showed that
men were beginning to analyse their processes of thought.
The Five Predicables are Genus, Species, Difference, Property, and
Accident, or in the original Greek, γένος, εἶδος, διαφορά, ἴδιον,
συμβεβηκός. Of these, Genus may be taken to mean any class of objects
which is regarded as broken up into two minor classes, which form
Species of it. The genus is defined by a certain number of qualities or
circumstances which belong to all objects included in the class, and
which are sufficient to mark out these objects from all others which
we do not intend to include. Interpreted as regards intension, then,
the genus is a group of qualities; interpreted as regards extension, it
is a group of objects possessing those qualities. If another quality
be taken into account which is possessed by some of the objects and
not by the others, this quality becomes a difference which divides
the genus into two species. We may interpret the species either in
intension or extension; in the former respect it is more than the genus
as containing one more quality, the difference: in the latter respect
it is less than the genus as containing only a portion of the group
constituting the genus. We may say, then, with Aristotle, that in one
sense the genus is in the species, namely in intension, and in another
sense the species is in the genus, namely in extension. The difference,
it is evident, can be interpreted in intension only.
A Property is a quality which belongs to the whole of a class, but does
not enter into the definition of that class. A generic property belongs
to every individual object contained in the genus. It is a property
of the genus parallelogram that the opposite angles are equal. If we
regard a rectangle as a species of parallelogram, the difference being
that *one* angle is a right angle, it follows as a specific property
that all the angles are right angles. Though a property in the strict
logical sense must belong to each of the objects included in the class
of which it is a property, it may or may not belong to other objects.
The property of having the opposite angles equal may belong to many
figures besides parallelograms, for instance, regular hexagons. It is a
property of the circle that all triangles constructed upon the diameter
with the apex upon the circumference are right-angled triangles, and
*vice versâ*, all curves of which this is true must be circles. A
property which thus belongs to the whole of a class and only to that
class, corresponds to the ἴδιον of Aristotle and Porphyry; we might
conveniently call it *a peculiar property*. Every such property enables
us to make a statement in the form of a simple identity (p. 37). Thus
we know it to be a peculiar property of the circle that for a given
length of perimeter it encloses a greater area than any other possible
curve; hence we may say--
Curve of equal curvature = curve of greatest area.
It is a peculiar property of equilateral triangles that they are
equiangular, and *vice versâ*, it is a peculiar property of equiangular
triangles that they are equilateral. It is a property of crystals
of the regular system that they are devoid of the power of double
refraction, but this is not a property peculiar to them, because
liquids and gases are devoid of the same property.
An Accident, the fifth and last of the Predicables, is any quality
which may or may not belong to certain objects, and which has no
connexion with the classification adopted. The particular size of
a crystal does not in the slightest degree affect the form of the
crystal, nor does the manner in which it is grouped with other
crystals; these, then, are accidents as regards a crystallographic
classification. With respect to the chemical composition of a
substance, again, it is an accident whether the substance be
crystallised or not, or whether it be organised or not. As regards
botanical classification the absolute size of a plant is an accident.
Thus we see that a logical accident is any quality or circumstance
which is not known to be correlated with those qualities or
circumstances forming the definition of the species.
The meanings of the Predicables can be clearly explained by our
symbols. Let A be any definite group of qualities and B another quality
or group of qualities; then A will constitute a genus, and AB, A*b*
will be species of it, B being the difference. Let C, D and E be other
qualities or groups of qualities, and on examining the combinations in
which A, B, C, D, E occur let them be as follows:--
ABCDE A*b*C*d*E
ABCD*e* A*b*C*de*.
Here we see that wherever A is we also find C, so that C is a generic
property; D occurs always with B, so that it constitutes a specific
property, while E is indifferently present and absent, so as not to be
related to any other letter; it represents, therefore, an accident. It
will now be seen that the Logical Alphabet represents an interminable
series of subordinate genera and species; it is but a concise symbolic
statement of what was involved in the ancient doctrine of the
Predicables.
*Summum Genus and Infima Species.*
As a genus means any class whatever which is regarded as composed
of minor classes or species, it follows that the same class will be
a genus in one point of view and a species in another. Metal is a
genus as regards alkaline metal, a species as regards element, and
any extensive system of classes consists of a series of subordinate,
or as they are technically called, *subaltern* genera and species.
The question, however, arises, whether such a chain of classes
has a definite termination at either end. The doctrine of the old
logicians was to the effect that it terminated upwards in a *genus
generalissimum* or *summum genus*, which was not a species of any
wider class. Some very general notion, such as substance, object, or
thing, was supposed to be so comprehensive as to include all thinkable
objects, and for all practical purposes this might be so. But as I
have already explained (p. 74), we cannot really think of any object
or class without thereby separating it from what is not that object or
class. All thinking is relative, and implies discrimination, so that
every class and every logical notion must have its negative. If so,
there is no such thing as a *summum genus*; for we cannot frame the
requisite notion of a class forming it without implying the existence
of another class discriminated from it; add this new negative class to
the supposed *summum genus*, and we form a still higher genus, which is
absurd.
Although there is no absolute summum genus, nevertheless relatively to
any branch of knowledge or any particular argument, there is always
some class or notion which bounds our horizon as it were. The chemist
restricts his view to material substances and the forces manifested
in them; the mathematician extends his view so as to comprehend all
notions capable of numerical discrimination. The biologist, on the
other hand, has a narrower sphere containing only organised bodies, and
of these the botanist and the zoologist take parts. In other subjects
there may be a still narrower summum genus, as when the lawyer regards
only reasoning beings of his own country together with their property.
In the description of the Logical Alphabet it was pointed out (p. 93)
that every series of combinations is really the development of a
single class, denoted by X, which letter was accordingly placed in the
first column of the table on p. 94. This is the formal acknowledgment
of the principle clearly stated by De Morgan, that all reasoning
proceeds within an assumed summum genus. But at the same time the fact
that X as a logical term must have its negative *x*, shows that it
cannot be an absolute summum genus.
There arises, again, the question whether there be any such thing as
an *infima species*, which cannot be divided into minor species. The
ancient logicians were of opinion that there always was some assignable
class which could only be divided into individuals, but this doctrine
appears to be theoretically incorrect, as Mr. George Bentham long ago
stated.[575] We may put an arbitrary limit to the subdivision of our
classes at any point convenient to our purpose. The crystallographer
would not generally treat as different species crystalline forms which
differ only in the degree of development of the faces. The naturalist
overlooks innumerable slight differences between animals which he
refers to the same species. But in a strictly logical point of view
classification might be carried on as long as there is a difference,
however minute, between two objects, and we might thus go on until we
arrive at individual objects which are numerically distinct in the
logical sense attributed to that expression in the chapter upon Number.
Either, then, we must call the individual the *infima species* or allow
that there is no such thing at all.
[575] *Outline of a New System of Logic*, 1827, p. 117.
*The Tree of Porphyry.*
Both Aristotle and Plato were acquainted with the value of bifurcate
classification, which they occasionally employed in an explicit manner.
It is impossible too that Aristotle should state the laws of thought,
and employ the predicables without implicitly recognising the logical
necessity of that method. It is, however, in Porphyry’s remarkable
and in many respects excellent *Introduction to the Categories of
Aristotle* that we find the most distinct account of it. Porphyry not
only fully and accurately describes the Predicables, but incidentally
introduces an example for illustrating those predicables, which
constitutes a good specimen of bifurcate classification. Translating
his words[576] freely we may say that he takes Substance as the genus
to be divided, under which are successively placed as Species--Body,
Animated Body, Animal, Rational Animal, and Man. Under Man, again,
come Socrates, Plato, and other particular men. Now of these notions
Substance is the genus generalissimum, and is a genus only, not a
species. Man, on the other hand, is the species specialissima (infima
species), and is a species only, not a genus. Body is a species of
substance, but a genus of animated body, which, again, is a species of
body but a genus of animal. Animal is a species of animated body, but
a genus of rational animal, which, again, is a species of animal, but
a genus of man. Finally, man is a species of rational animal, but is a
species merely and not a genus, being divisible only into particular
men.
[576] *Porphyrii Isagoge*, Caput ii. 24.
Porphyry proceeds at some length to employ his example in further
illustration of the predicables. We do not find in Porphyry’s own
work any scheme or diagram exhibiting this curious specimen of
classification, but some of the earlier commentators and epitome
writers drew what has long been called the Tree of Porphyry. This
diagram, which may be found in most elementary works on Logic,[577] is
also called the Ramean Tree, because Ramus insisted much upon the value
of Dichotomy. With the exception of Jeremy Bentham[578] and George
Bentham, hardly any modern logicians have shown an appreciation of the
value of bifurcate classification. The latter author has treated the
subject, both in his *Outline of a New System of Logic* (pp. 105–118),
and in his earlier work entitled *Essai sur la Nomenclature et la
Classification des Principales Branches d’Art-et-Science* (Paris,
1823), which consists of a free translation or improved version of his
uncle’s Essay on Classification in the *Chrestomathia*. Some interest
attaches to the history of the Tree of Porphyry and Ramus, because
it is the prototype of the Logical Alphabet which lies at the basis
of logical method. Jeremy Bentham speaks truly of “the matchless
beauty of the Ramean Tree.” After fully showing its logical value as
an exhaustive method of classification, and refuting the objections
of Reid and Kames, on a wrong ground, as I think, he proceeds to
inquire to what length it may be carried. He correctly points out two
objections to the extensive use of bifid arrangements, (1) that they
soon become impracticably extensive and unwieldy, and (2) that they
are uneconomical. In his day the recorded number of different species
of plants was 40,000, and he leaves the reader to estimate the immense
number of branches and the enormous area of a bifurcate table which
should exhibit all these species in one scheme. He also points out the
apparent loss of labour in making any large bifurcate classification;
but this he considers to be fully recompensed by the logical value of
the result, and the logical training acquired in its execution. Jeremy
Bentham, then, fully recognises the value of the Logical Alphabet under
another name, though he apprehends also the limit to its use placed by
the finiteness of our mental and manual powers.
[577] Jevons, *Elementary Lessons in Logic*, p. 104.
[578] *Chrestomathia; being a Collection of Papers, &c.* London,
1816, Appendix V.
*Does Abstraction imply Generalisation?*
Before we can acquire a sound comprehension of the subject of
classification we must answer the very difficult question whether
logical abstraction does or does not imply generalisation. It comes to
exactly the same thing if we ask whether a species may be coextensive
with its genus, or whether, on the other hand, the genus must contain
more than the species. To abstract logically is (p. 27), to overlook or
withdraw our notice from some point of difference. Whenever we form a
class we abstract, for the time being, the differences of the objects
so united in respect of some common quality. If we class together a
great number of objects as dwelling-houses, we overlook the fact that
some dwelling-houses are constructed of stone, others of brick, wood,
iron, &c. Often at least the abstraction of a circumstance increases
the number of objects included under a class according to the law of
the inverse relation of the quantities of extension and intension
(p. 26). Dwelling-house is a wider term than brick-dwelling-house.
House is more general than dwelling-house. But the question before
us is, whether abstraction *always* increases the number of objects
included in a class, which amounts to asking whether the law of
the inverse relation of logical quantities is *always* true. The
interest of the question partly arises from the fact, that so high
a philosophical authority as Mr. Herbert Spencer has denied that
generalisation is implied in abstraction,[579] making this doctrine
the ground for rejecting previous methods of classifying the sciences,
and for forming an ingenious but peculiar method of his own. The
question is also a fundamental one of the highest logical importance,
and involves subtle difficulties which have made me long hesitate in
forming a decisive opinion.
[579] *The Classification of the Sciences*, &c., 3rd edit. p. 7.
*Essays: Scientific, Political, and Speculative*, vol. iii. p. 13.
Let us attempt to answer the question by examination of a few examples.
Compare the two classes *gun* and *iron gun*. It is certain that there
are many guns which are not made of iron, so that abstraction of the
circumstance “made of iron” increases the extent of the notion. Next
compare *gun* and *metallic gun*. All guns made at the present day
consist of metal, so that the two notions seem to be coextensive;
but guns were at first made of pieces of wood bound together like
a tub, and as the logical term gun takes no account of time, it
must include all guns that have ever existed. Here again extension
increases as intension decreases. Compare once more “steam-locomotive
engine” and “locomotive engine.” In the present day, as far as I am
aware, all locomotives are worked by steam, so that the omission of
that qualification might seem not to widen the term; but it is quite
possible that in some future age a different motive power may be used
in locomotives; and as there is no limitation of time in the use of
logical terms, we must certainly assume that there is a class of
locomotives not worked by steam, as well as a class that is worked by
steam. When the natural class of Euphorbiaceæ was originally formed,
all the plants known to belong to it were devoid of corollas; it
would have seemed therefore that the two classes “Euphorbiaceæ,” and
“Euphorbiaceæ devoid of Corollas,” were of equal extent. Subsequently
a number of plants plainly belonging to the same class were found in
tropical countries, and they possessed bright coloured corollas.
Naturalists believe with the utmost confidence that “Ruminants” and
“Ruminants with cleft feet” are identical terms, because no ruminant
has yet been discovered without cleft feet. But we can see no
impossibility in the conjunction of rumination with uncleft feet, and
it would be too great an assumption to say that we are certain that an
example of it will never be met with. Instances can be quoted, without
end, of objects being ultimately discovered combining properties which
had never before been seen together. In the animal kingdom the Black
Swan, the Ornithorhynchus Paradoxus, and more recently the singular
fish called Ceratodus Forsteri, all discovered in Australia, have
united characters never previously known to coexist. At the present
time deep-sea dredging is bringing to light many animals of an
unprecedented nature. Singular exceptional discoveries may certainly
occur in other branches of science. When Davy first discovered metallic
potassium, it was a well established empirical law that all metallic
substances possessed a high specific gravity, the least dense of the
metals then known being zinc, of which the specific gravity is 7·1. Yet
to the surprise of chemists, potassium was found to be an undoubted
metal of less density than water, its specific gravity being 0·865.
It is hardly requisite to prove by further examples that our knowledge
of nature is incomplete, so that we cannot safely assume the
non-existence of new combinations. Logically speaking, we ought to
leave a place open for animals which ruminate but are without cleft
feet, and for every possible intermediate form of animal, plant, or
mineral. A purely logical classification must take account not only of
what certainly does exist, but of what may in after ages be found to
exist.
I will go a step further, and say that we must have places in our
scientific classifications for purely imaginary existences. A large
proportion of the mathematical functions which are conceivable have no
application to the circumstances of this world. Physicists certainly do
investigate the nature and consequences of forces which nowhere exist.
Newton’s *Principia* is full of such investigations. In one chapter of
his *Mécanique Céleste* Laplace indulges in a remarkable speculation
as to what the laws of motion would have been if momentum, instead of
varying simply as the velocity, had been a more complicated function
of it. I have already mentioned (p. 223) that Airy contemplated the
existence of a world in which the laws of force should be such that
a perpetual motion would be possible, and the Law of Conservation of
Energy would not hold true.
Thought is not bound down to the limits of what is materially existent,
but is circumscribed only by those Fundamental Laws of Identity,
Contradiction and Duality, which were laid down at the outset. This
is the point at which I should differ from Mr. Spencer. He appears
to suppose that a classification is complete if it has a place for
every existing object, and this may perhaps seem to be practically
sufficient; but it is subject to two profound objections. Firstly, we
do not know all that exists, and therefore in limiting our classes we
are erroneously omitting multitudes of objects of unknown form and
nature which may exist either on this earth or in other parts of space.
Secondly, as I have explained, the powers of thought are not limited by
material existences, and we may, or, for some purposes, must imagine
objects which probably do not exist, and if we imagine them we ought to
find places for them in the classifications of science.
The chief difficulty of this subject, however, consists in the fact
that mathematical or other certain laws may entirely forbid the
existence of some combinations. The circle may be defined as a plane
curve of equal curvature, and it is a property of the circle that it
contains the greatest area within the least possible perimeter. May we
then contemplate mentally a circle not a figure of greatest possible
area? Or, to take a still simpler example, a parallelogram possesses
the property of having the opposite angles equal. May we then mentally
divide parallelograms into two classes according as they do or do
not have their opposite angles equal? It might seem absurd to do so,
because we know that one of the two species of parallelogram would be
non-existent. But, then, unless the student had previously contemplated
the existence of both species as possible, what is the meaning of the
thirty-fourth proposition of Euclid’s first book? We cannot deny or
disprove the existence of a certain combination without thereby in a
certain way recognising that combination as an object of thought.
The conclusion at which I arrive is in opposition to that of Mr.
Spencer. I think that whenever we abstract a quality or circumstance we
do generalise or widen the notion from which we abstract. Whatever the
terms A, B, and C may be, I hold that in strict logic AB is mentally
a wider term than ABC, because AB includes the two species ABC and
AB*c*. The term A is wider still, for it includes the four species
ABC, AB*c*, A*b*C, A*bc*. The Logical Alphabet, in short, is the only
limit of the classes of objects which we must contemplate in a purely
logical point of view. Whatever notions be brought before us, we must
mentally combine them in all the ways sanctioned by the laws of thought
and exhibited in the Logical Alphabet, and it is a matter for after
consideration to determine how many of these combinations exist in
outward nature, or how many are actually forbidden by the conditions of
space. A classification is essentially a mental, not a material thing.
*Discovery of Marks or Characteristics.*
Although the chief purpose of classification is to disclose the
deepest and most general resemblances of the objects classified, yet
the practical value of a system will depend partly upon the ease with
which we can refer an object to its proper class, and thus infer
concerning it all that is known generally of that class. This operation
of discovering to which class of a system a certain specimen or case
belongs, is generally called *Diagnosis*, a technical term familiarly
used by physicians, who constantly require to diagnose or determine
the nature of the disease from which a patient is suffering. Now every
class is defined by certain specified qualities or circumstances, the
whole of which are present in every object contained in the class,
and *not all present* in any object excluded from it. These defining
circumstances ought to consist of the deepest and most important
circumstances, by which we vaguely mean those probably forming the
conditions with which the minor circumstances are correlated. But it
will often happen that the so-called important points of an object
are not those which can most readily be observed. Thus the two great
classes of phanerogamous plants are defined respectively by the
possession of two cotyledons or seed-leaves, and one cotyledon. But
when a plant comes to our notice and we want to refer it to the right
class, it will often happen that we have no seed at all to examine, in
order to discover whether there be one seed-leaf or two in the germ.
Even if we have a seed it will often be small, and a careful dissection
under the microscope will be requisite to ascertain the number of
cotyledons. Occasionally the examination of the germ would mislead us,
for the cotyledons may be obsolete, as in Cuscuta, or united together,
as in Clintonia. Botanists therefore seldom actually refer to the
seed for such information. Certain other characters of a plant are
correlated with the number of seed-leaves; thus monocotyledonous plants
almost always possess leaves with parallel veins like those of grass,
while dicotyledonous plants have leaves with reticulated veins like
those of an oak leaf. In monocotyledonous plants, too, the parts of the
flower are most often three or some multiple of three in number, while
in dicotyledonous plants the numbers four and five and their multiples
prevail. Botanists, therefore, by a glance at the leaves and flowers
can almost certainly refer a plant to its right class, and can infer
not only the number of cotyledons which would be found in the seed
or young plant, but also the structure of the stem and other general
characters.
Any conspicuous and easily discriminated property which we thus
select for the purpose of deciding to which class an object belongs,
may be called a *characteristic*. The logical conditions of a good
characteristic mark are very simple, namely, that it should be
possessed by all objects entering into a certain class, and by none
others. Every characteristic should enable us to assert a simple
identity; if A is a characteristic, and B, viewed intensively, the
class of objects of which it is the mark, then A = B ought to be
true. The characteristic may consist either of a single quality or
circumstance, or of a group of such, provided that they all be constant
and easily detected. Thus in the classification of mammals the teeth
are of the greatest assistance, not because a slight variation in the
number and form of the teeth is of importance in the general economy
of the animal, but because such variations are proved by empirical
observation to coincide with most important differences in the general
affinities. It is found that the minor classes and genera of mammals
can be discriminated accurately by their teeth, especially by the
foremost molars and the hindmost pre-molars. Some teeth, indeed, are
occasionally missing, so that zoologists prefer to trust to those
characteristic teeth which are most constant,[580] and to infer from
them not only the arrangement of the other teeth, but the whole
conformation of the animal.
[580] Owen, *Essay on the Classification and Geographical
Distribution of the Mammalia*, p. 20.
It is a very difficult matter to mark out a boundary-line between the
animal and vegetable kingdoms, and it may even be doubted whether
a rigorous boundary can be established. The most fundamental and
important difference of a vegetable as compared with an animal
substance probably consists in the absence of nitrogen from the
constituent membranes. Supposing this to be the case, the difficulty
arises that in examining minute organisms we cannot ascertain directly
whether they contain nitrogen or not. Some minor but easily detected
circumstance is therefore needed to discriminate between animals and
vegetables, and this is furnished to some extent by the fact that the
production of starch granules is restricted to the vegetable kingdom.
Thus the Desmidiaceæ may be safely assigned to the vegetable kingdom,
because they contain starch. But we must not employ this characteristic
negatively; the Diatomaceæ are probably vegetables, though they do not
produce starch.
*Diagnostic Systems of Classification.*
We have seen that diagnosis is the process of discovering the place in
any system of classes, to which an object has been referred by some
previous investigation, the object being to avail ourselves of the
information relating to such an object which has been accumulated and
recorded. It is obvious that this is a matter of great importance,
for, unless we can recognise, from time to time, objects or substances
which have been investigated, recorded discoveries would lose their
value. Even a single investigator must have means of recording and
systematising his observations of any large groups of objects like the
vegetable and animal kingdoms.
Now whenever a class has been properly formed, a definition must have
been laid down, stating the qualities and circumstances possessed by
all the objects which are intended to be included in the class, and
not possessed *completely* by any other objects. Diagnosis, therefore,
consists in comparing the qualities of a certain object with the
definitions of a series of classes; the absence in the object of any
one quality stated in the definition excludes it from the class thus
defined; whereas, if we find every point of a definition exactly
fulfilled in the specimen, we may at once assign it to the class in
question. It is of course by no means certain that everything which has
been affirmed of a class is true of all objects afterwards referred
to the class; for this would be a case of imperfect inference, which
is never more than matter of probability. A definition can only make
known a finite number of the qualities of an object, and it always
remains possible that objects agreeing in those assigned qualities will
differ in others. *An individual cannot be defined*, and can only be
made known by the exhibition of the individual itself, or by a material
specimen exactly representing it. But this and other questions relating
to definition must be treated when I am able to take up the subject of
language in another work.
Diagnostic systems of classification should, as a general rule, be
arranged on the bifurcate method explicitly. Any quality may be chosen
which divides the whole group of objects into two distinct parts,
and each part may be sub-divided successively by any prominent and
well-marked circumstance which is present in a large part of the genus
and not in the other. To refer an object to its proper place in such an
arrangement we have only to note whether it does or does not possess
the successive critical differentiæ. Dana devised a classification of
this kind[581] by which to refer a crystal to its place in the series
of six or seven classes already described. If a crystal has all its
edges modified alike or the angles replaced by three or six similar
planes, it belongs to the monometric system; if not, we observe
whether the number of similar planes at the extremity of the crystal
is three or some multiple of three, in which case it is a crystal
of the hexagonal system; and so we proceed with further successive
discriminations. To ascertain the name of a mineral by examination with
the blow-pipe, an arrangement more or less evidently on the bifurcate
plan, has been laid down by Von Kobell.[582] Minerals are divided
according as they possess or do not possess metallic lustre; as they
are fusible or not fusible, according as they do or do not on charcoal
give a metallic bead, and so on.
[581] Dana’s *Mineralogy*, vol. i. p. 123; quoted in Watts’
*Dictionary of Chemistry*, vol. ii. p. 166.
[582] *Instructions for the Discrimination of Minerals by Simple
Chemical Experiments*, by Franz von Kobell, translated from the
German by R. C. Campbell. Glasgow, 1841.
Perhaps the best example to be found of an arrangement devised simply
for the purpose of diagnosis, is Mr. George Bentham’s *Analytical Key
to the Natural Orders and Anomalous Genera of the British Flora*, given
in his *Handbook of the British Flora*.[583] In this scheme, the great
composite family of plants, together with the closely approximate
genus Jasione, are first separated from all other flowering plants
by the compound character of their flowers. The remaining plants are
sub-divided according as the perianth is double or single. Since no
plants are yet known in which the perianth can be said to have three
or more distinct rings, this division becomes practically the same as
one into double and not-double. Flowers with a double perianth are
next discriminated according as the corolla does or does not consist
of one piece; according as the ovary is free or not free; as it is
simple or not simple; as the corolla is regular or irregular; and so
on. On looking over this arrangement, it will be found that numerical
discriminations often occur, the numbers of petals, stamens, capsules,
or other parts being the criteria, in which cases, as already explained
(p. 697), the actual exhibition of the bifid division would be tedious.
[583] Edition of 1866, p. lxiii.
Linnæus appears to have been perfectly acquainted with the nature and
uses of diagnostic classification, which he describes under the name
of Synopsis, saying:[584]--“Synopsis tradit Divisiones arbitrarias,
longiores aut breviores, plures aut pauciores: a Botanicis in genere
non agnoscenda. Synopsis est dichotomia arbitraria, quæ instar viæ ad
Botanicem ducit. Limites autem non determinat.”
[584] *Philosophia Botanica* (1770), § 154, p. 98.
The rules and tables drawn out by chemists to facilitate the discovery
of the nature of a substance in qualitative analysis are usually
arranged on the bifurcate method, and form excellent examples of
diagnostic classification, the qualities of the substances produced
in testing being in most cases merely characteristic properties of
little importance in other respects. The chemist does not detect
potassium by reducing it to the state of metallic potassium, and
then observing whether it has all the principal qualities belonging
to potassium. He selects from among the whole number of compounds of
potassium that salt, namely the compound of platinum tetra-chloride,
and potassium chloride, which has the most distinctive appearance,
as it is comparatively insoluble and produces a peculiar yellow and
highly crystalline precipitate. Accordingly, potassium is present
whenever this precipitate can be produced by adding platinum chloride
to a solution. The fine purple or violet colour which potassium
salts communicate to the blowpipe flame, had long been used as a
characteristic mark. Some other elements were readily detected by the
colouring of the blowpipe flame, barium giving a pale yellowish green,
and salts of strontium a bright red. By the use of the spectroscope
the coloured light given off by an incandescent vapour is made to give
perfectly characteristic marks of the elements contained in the vapour.
Diagnosis seems to be identical with the process termed by the ancient
logicians *abscissio infiniti*, the cutting off of the infinite or
negative part of a genus when we discover by observation that an
object possesses a particular difference. At every step in a bifurcate
division, some objects possessing the difference will fall into
the affirmative part or species; all the remaining objects in the
world fall into the negative part, which will be infinite in extent.
Diagnosis consists in the successive rejection from further notice of
those infinite classes with which the specimen in question does not
agree.
*Index Classifications.*
Under classification we may include all arrangements of objects or
names, which we make for saving labour in the discovery of an object.
Even alphabetical indices are real classifications. No such arrangement
can be of use unless it involves some correlation of circumstances, so
that knowing one thing we learn another. If we merely arrange letters
in the pigeon-holes of a secretaire we establish a correlation, for all
letters in the first hole will be written by persons, for instance,
whose names begin with A, and so on. Knowing then the initial letter of
the writer’s name, we know also the place of the letter, and the labour
of search is thus reduced to one twenty-sixth part of what it would be
without arrangement.
Now the purpose of a catalogue is to discover the place in which an
object is to be found; but the art of cataloguing involves logical
considerations of some importance. We want to establish a correlation
between the place of an object and some circumstance about the object
which shall enable us readily to refer to it; this circumstance
therefore should be that which will most readily dwell in the memory
of the searcher. A piece of poetry will be best remembered by the
first line of the piece, and the name of the author will be the next
most definite circumstance; a catalogue of poetry should therefore be
arranged alphabetically according to the first word of the piece, or
the name of the author, or, still better, in both ways. It would be
impossible to arrange poems according to their subjects, so vague and
mixed are these found to be when the attempt is made.
It is a matter of considerable literary importance to decide upon the
best mode of cataloguing books, so that any required book in a library
shall be most readily found. Books may be classified in a great number
of ways, according to subject, language, date, or place of publication,
size, the initial words of the text or title-page, or colophon, the
author’s name, the publisher’s name, the printer’s name, the character
of the type, and so on. Every one of these modes of arrangement may be
useful, for we may happen to remember one circumstance about a book
when we have forgotten all others; but as we cannot usually go to the
expense of forming more than two or three indices, we must select
those circumstances which will lead to the discovery of a book most
frequently. Many of the criteria mentioned are evidently inapplicable.
The language in which a book is written is definite enough, provided
that the whole book is written in the same language; but it is obvious
that language gives no means for the subdivision and arrangement of
the literature of any one people. Classification by subjects would be
an exceedingly useful method if it were practicable, but experience
shows it to be a logical absurdity. It is a very difficult matter to
classify the sciences, so complicated are the relations between them.
But with books the complication is vastly greater, since the same book
may treat of different sciences, or it may discuss a problem involving
many branches of knowledge. A good account of the steam-engine will be
antiquarian, so far as it traces out the earliest efforts at discovery;
purely scientific, as regards the principles of thermodynamics
involved; technical, as regards the mechanical means of applying
those principles; economical, as regards the industrial results of
the invention; biographical, as regards the lives of the inventors.
A history of Westminster Abbey might belong either to the history of
architecture, the history of the Church, or the history of England.
If we abandon the attempt to carry out an arrangement according to
the natural classification of the sciences, and form comprehensive
practical groups, we shall be continually perplexed by the occurrence
of intermediate cases, and opinions will differ *ad infinitum* as to
the details. If, to avoid the difficulty about Westminster Abbey, we
form a class of books devoted to the History of Buildings, the question
will then arise whether Stonehenge is a building, and if so, whether
cromlechs, mounds, and monoliths are so. We shall be uncertain whether
to include lighthouses, monuments, bridges, &c. In regard to literary
works, rigorous classification is still less possible. The same work
may partake of the nature of poetry, biography, history, philosophy,
or if we form a comprehensive class of Belles-lettres, nobody can say
exactly what does or does not come under the term.
My own experience entirely bears out the opinion of De Morgan, that
classification according to the name of the author is the only one
practicable in a large library, and this method has been admirably
carried out in the great catalogue of the British Museum. The name
of the author is the most precise circumstance concerning a book,
which usually dwells in the memory. It is a better characteristic of
the book than anything else. In an alphabetical arrangement we have
an exhaustive classification, including a place for every name. The
following remarks[585] of De Morgan seem therefore to be entirely
correct. “From much, almost daily use, of catalogues for many years,
I am perfectly satisfied that a classed catalogue is more difficult
to use than to make. It is one man’s theory of the subdivision of
knowledge, and the chances are against its suiting any other man. Even
if all doubtful works were entered under several different heads, the
frontier of the dubious region would itself be a mere matter of doubt.
I never turn from a classed catalogue to an alphabetical one without
a feeling of relief and security. With the latter I can always, by
taking proper pains, make a library yield its utmost; with the former
I can never be satisfied that I have taken proper pains, until I have
made it, in fact, as many different catalogues as there are different
headings, with separate trouble for each. Those to whom bibliographical
research is familiar, know that they have much more frequently to
hunt an author than a subject: they know also that in searching for a
subject, it is never safe to take another person’s view, however good,
of the limits of that subject with reference to their own particular
purposes.”
[585] *Philosophical Magazine*, 3rd Series (1845), vol. xxvi. p. 522.
See also De Morgan’s evidence before the Royal Commission on the
British Museum in 1849, Report (1850), Questions, 5704*-5815*,
6481–6513. This evidence should be studied by every person who wishes
to understand the elements of Bibliography.
It is often desirable, however, that a name catalogue should be
accompanied by a subordinate subject catalogue, but in this case
no attempt should be made to devise a theoretically complete
classification. Every principal subject treated in a book should
be entered separately in an alphabetical list, under the name most
likely to occur to the searcher, or under several names. This method
was partially carried out in Watts’ *Bibliotheca Britannica*, but
it was excellently applied in the admirable subject index to the
*British Catalogue of Books*, and equally well in the *Catalogue
of the Manchester Free Library* at Campfield, drawn up under the
direction of Mr. Crestadoro, this latter being the most perfect model
of a printed catalogue with which I am acquainted. The Catalogue of
the London Library is also in the right form, and has a useful index
of subjects, though it is too much condensed and abbreviated. The
public catalogue of the British Museum is arranged as far as possible
according to the alphabetical order of the authors’ names, but in
writing the titles for this catalogue several copies are simultaneously
produced by a manifold writer, so that a catalogue according to the
order of the books on the shelves, and another according to the first
words of the title-page, are created by a mere rearrangement of the
spare copies. In the *English Cyclopædia* it is suggested that twenty
copies of the book titles might readily have been utilised in forming
additional catalogues, arranged according to the place of publication,
the language of the book, the general nature of the subject, and so
forth.[586] An excellent suggestion has also been made to the effect
that each book when published should have a fly-leaf containing half
a dozen printed copies of the title, drawn up in a form suitable for
insertion in catalogues. Every owner of a library could then easily
make accurate printed catalogues to suit his own purposes, by merely
cutting out these titles and pasting them in books in any desirable
order.
[586] *English Cyclopædia, Arts and Sciences*, vol. v. p. 233.
It will hardly be a digression to point out the enormous saving of
labour, or, what comes to the same thing, the enormous increase in our
available knowledge, both literary and scientific, which arises from
the formation of extensive indices. The “State Papers,” containing
the whole history of the nation, were practically sealed to literary
inquirers until the Government undertook the task of calendaring and
indexing them. The British Museum Catalogue is another national work,
of which the importance in advancing knowledge cannot be overrated.
The Royal Society is doing great service in publishing a complete
catalogue of memoirs upon physical science. The time will perhaps
come when our views upon this subject will be extended, and either
Government or some public society will undertake the systematic
cataloguing and indexing of masses of historical and scientific
information which are now almost closed against inquiry.
*Classification in the Biological Sciences.*
The great generalisations established in the works of Herbert Spencer
and Charles Darwin have thrown much light upon other sciences, and
have removed several difficulties out of the way of the logician. The
subject of classification has long been studied in almost exclusive
reference to the arrangement of animals and plants. Systematic botany
and zoology have been commonly known as the Classificatory Sciences,
and scientific men seemed to suppose that the methods of arrangement,
which were suitable for living creatures, must be the best for all
other classes of objects. Several mineralogists, especially Mohs, have
attempted to arrange minerals in genera and species, just as if they
had been animals capable of reproducing their kind with variations.
This confusion of ideas between the relationship of living forms and
the logical relationship of things in general prevailed from the
earliest times, as manifested in the etymology of words. We familiarly
speak of a *kind* of things meaning a class of things, and the kind
consists of those things which are *akin*, or come of the same race.
When Socrates and his followers wanted a name for a class regarded in a
philosophical light, they adopted the analogy in question, and called
it a γένος, or race, the root γεν- being connected with the notion of
generation.
So long as species of plants and animals were believed to proceed from
distinct acts of Creation, there was no apparent reason why methods of
classification suitable to them should not be treated as a guide to
the classification of other objects generally. But when once we regard
these resemblances as hereditary in their origin, we see that the
sciences of systematic botany and zoology have a special character of
their own. There is no reason to suppose that the same kind of natural
classification which is best in biology will apply also in mineralogy,
in chemistry, or in astronomy. The logical principles which underlie
all classification are of course the same in natural history as in the
sciences of lifeless matter, but the special resemblances which arise
from the relation of parent and offspring will not be found to prevail
between different kinds of crystals or mineral bodies.
The genealogical view of the relations of animals and plants leads us
to discard all notions of a regular progression of living forms, or
any theory as to their symmetrical relations. It was at one time a
question whether the ultimate scheme of natural classification would
lead to arrangement in a simple line, or a circle, or a combination
of circles. Macleay’s once celebrated system was a circular one, and
each class-circle was composed of five order-circles, each of which was
composed again of five tribe-circles, and so on, the subdivision being
at each step into five minor circles. Macleay held that in the animal
kingdom there are five sub-kingdoms--the Vertebrata, Annulosa, Radiata,
Acrita, and Mollusca. Each of these was again divided into five--the
Vertebrata, consisting of Mammalia, Reptilia, Pisces, Amphibia, and
Aves.[587] It is evident that in such a symmetrical system the animals
were made to suit themselves to the classes instead of the classes
being suited to the animals.
[587] Swainson, “Treatise on the Geography and Classification of
Animals,” *Cabinet Cyclopædia*, p. 201.
We now perceive that the ultimate system will have the form of an
immensely extended genealogical tree, which will be capable of
representation by lines on a plane surface of sufficient extent.
Strictly speaking, this genealogical tree ought to represent the
descent of each individual living form now existing or which has
existed. It should be as personal and minute in its detail of
relations, as the Stemma of the Kings of England. We must not assume
that any two forms are exactly alike, and in any case they are
numerically distinct. Every parent then must be represented at the apex
of a series of divergent lines, representing the generation of so many
children. Any complete system of classification must regard individuals
as the infimæ species. But as in the lower races of animals and
plants the differences between individuals are slight and apparently
unimportant, while the numbers of such individuals are immensely
great, beyond all possibility of separate treatment, scientific men
have always stopped at some convenient but arbitrary point, and have
assumed that forms so closely resembling each other as to present no
constant difference were all of one kind. They have, in short, fixed
their attention entirely upon the main features of family difference.
In the genealogical tree which they have been unconsciously aiming to
construct, diverging lines meant races diverging in character, and the
purpose of all efforts at so-called natural classification was to trace
out the descents between existing groups of plants or animals.
Now it is evident that hereditary descent may have in different
cases produced very different results as regards the problem of
classification. In some cases the differentiation of characters may
have been very frequent, and specimens of all the characters produced
may have been transmitted to the present time. A living form will then
have, as it were, an almost infinite number of cousins of various
degrees, and there will be an immense number of forms finely graduated
in their resemblances. Exact and distinct classification will then
be almost impossible, and the wisest course will be not to attempt
arbitrarily to distinguish forms closely related in nature, but to
allow that there exist transitional forms of every degree, to mark
out if possible the extreme limits of the family relationship, and
perhaps to select the most generalised form, or that which presents the
greatest number of close resemblances to others of the family, as the
*type* of the whole.
Mr. Darwin, in his most interesting work upon Orchids, points out
that the tribe of Malaxeæ are distinguished from Epidendreæ by the
absence of a caudicle to the pollinia; but as some of the Malaxeæ
have a minute caudicle, the division really breaks down in the most
essential point. “This is a misfortune,” he remarks,[588] “which every
naturalist encounters in attempting to classify a largely developed
or so-called natural group, in which, relatively to other groups,
there has been little extinction. In order that the naturalist may be
enabled to give precise and clear definitions of his divisions, whole
ranks of intermediate or gradational forms must have been utterly swept
away: if here and there a member of the intermediate ranks has escaped
annihilation, it puts an effectual bar to any absolutely distinct
definition.”
[588] Darwin, *Fertilisation of Orchids*, p. 159.
In other cases a particular plant or animal may perhaps have
transmitted its form from generation to generation almost unchanged,
or, what comes to the same result, those forms which diverged in
character from the parent stock may have proved unsuitable to their
circumstances, and perished. We shall then find a particular form
standing apart from all others, and marked by many distinct characters.
Occasionally we may meet with specimens of a race which was formerly
far more common but is now undergoing extinction, and is nearly the
last of its kind. Thus we explain the occurrence of exceptional forms
such as are found in the Amphioxus. The Equisetaceæ perplex botanists
by their want of affinity to other orders of Acrogenous plants. This
doubtless indicates that their genealogical connection with other
plants must be sought for in the most distant ages of geological
development.
Constancy of character, as Mr. Darwin has said,[589] is what is chiefly
valued and sought after by naturalists; that is to say, naturalists
wish to find some distinct family mark, or group of characters, by
which they may clearly recognise the relationship of descent between a
large group of living forms. It is accordingly a great relief to the
mind of the naturalist when he comes upon a definitely marked group,
such as the Diatomaceæ, which are clearly separated from their nearest
neighbours the Desmidiaceæ by their siliceous framework and the absence
of chlorophyll. But we must no longer think that because we fail in
detecting constancy of character the fault is in our classificatory
sciences. Where gradation of character really exists, we must devote
ourselves to defining and registering the degrees and limits of that
gradation. The ultimate natural arrangement will often be devoid of
strong lines of demarcation.
[589] *Descent of Man*, vol. i. p. 214.
Let naturalists, too, form their systems of natural classification
with all care they can, yet it will certainly happen from time to
time that new and exceptional forms of animals or vegetables will be
discovered and will require the modification of the system. A natural
system is directed, as we have seen, to the discovery of empirical laws
of correlation, but these laws being purely empirical will frequently
be falsified by more extensive investigation. From time to time the
notions of naturalists have been greatly widened, especially in the
case of Australian animals and plants, by the discovery of unexpected
combinations of organs, and such events must often happen in the
future. If indeed the time shall come when all the forms of plants are
discovered and accurately described, the science of Systematic Botany
will then be placed in a new and more favourable position, as remarked
by Alphonse Decandolle.[590]
[590] *Laws of Botanical Nomenclature*, p. 16.
It ought to be remembered that though the genealogical classification
of plants or animals is doubtless the most instructive of all, it is
not necessarily the best for all purposes. There may be correlations
of properties important for medicinal, or other practical purposes,
which do not correspond to the correlations of descent. We must regard
the bamboo as a tree rather than a grass, although it is botanically
a grass. For legal purposes we may continue with advantage to treat
the whale, seal, and other cetaceæ, as fish. We must also class plants
according as they belong to arctic, alpine, temperate, sub-tropical or
tropical regions. There are causes of likeness apart from hereditary
relationship, and *we must not attribute exclusive excellence to any
one method of classification*.
*Classification by Types.*
Perplexed by the difficulties arising in natural history from the
discovery of intermediate forms, naturalists have resorted to what they
call classification by types. Instead of forming one distinct class
defined by the invariable possession of certain assigned properties,
and rigidly including or excluding objects according as they do or
do not possess all these properties, naturalists select a typical
specimen, and they group around it all other specimens which resemble
this type more than any other selected type. “The type of each genus,”
we are told,[591] “should be that species in which the characters
of its group are best exhibited and most evenly balanced.” It would
usually consist of those descendants of a form which had undergone
little alteration, while other descendants had suffered slight
differentiation in various directions.
[591] Waterhouse, quoted by Woodward in his *Rudimentary Treatise of
Recent and Fossil Shells*, p. 61.
It would be a great mistake to suppose that this classification by
types is a logically distinct method. It is either not a real method
of classification at all, or it is merely an abbreviated mode of
representing a complicated system of arrangement. A class must be
defined by the invariable presence of certain common properties. If,
then, we include an individual in which one of these properties does
not appear, we either fall into logical contradiction, or else we form
a new class with a new definition. Even a single exception constitutes
a new class by itself, and by calling it an exception we merely imply
that this new class closely resembles that from which it diverges in
one or two points only. Thus in the definition of the natural order
of Rosaceæ, we find that the seeds are one or two in each carpel, but
that in the genus Spiræa there are three or four; this must mean either
that the number of seeds is not a part of the fixed definition of the
class, or else that Spiræa does not belong to that class, though it
may closely approximate to it. Naturalists continually find themselves
between two horns of a dilemma; if they restrict the number of marks
specified in a definition so that every form intended to come within
the class shall possess all those marks, it will then be usually found
to include too many forms; if the definition be made more particular,
the result is to produce so-called anomalous genera, which, while they
are held to belong to the class, do not in all respects conform to its
definition. The practice has hence arisen of allowing considerable
latitude in the definition of natural orders. The family of Cruciferæ,
for instance, forms an exceedingly well-marked natural order, and among
its characters we find it specified that the fruit is a pod, divided
into two cells by a thin partition, from which the valves generally
separate at maturity; but we are also informed that, in a few genera,
the pod is one-celled, or indehiscent, or separates transversely into
several joints.[592] Now this must either mean that the formation of
the pod is not an essential point in the definition of the family, or
that there are several closely associated families.
[592] Bentham’s *Handbook of the British Flora* (1866), p. 25.
The same holds true of typical classification. The type itself is
an individual, not a class, and no other object can be exactly like
the type. But as soon as we abstract the individual peculiarities
of the type and thus specify a finite number of qualities in which
other objects may resemble the type, we immediately constitute
a class. If some objects resemble the type in some points, and
others in other points, then each definite collection of points of
resemblance constitutes intensively a separate class. The very notion
of classification by types is in fact erroneous in a logical point of
view. The naturalist is constantly occupied in endeavouring to mark
out definite groups of living forms, where the forms themselves do not
in many cases admit of such rigorous lines of demarcation. A certain
laxity of logical method is thus apt to creep in, the only remedy for
which will be the frank recognition of the fact, that, according to the
theory of hereditary descent, gradation of characters is probably the
rule, and precise demarcation between groups the exception.
*Natural Genera and Species.*
One important result of the establishment of the theory of evolution
is to explode all notions about natural groups constituting separate
creations. Naturalists long held that every plant belongs to some
species, marked out by invariable characters, which do not change by
difference of soil, climate, cross-breeding, or other circumstances.
They were unable to deny the existence of such things as sub-species,
varieties, and hybrids, so that a species of plants was often
subdivided and classified within itself. But then the differences upon
which this sub-classification depended were supposed to be variable,
and thus distinguished from the invariable characters imposed upon the
whole species at its creation. Similarly a natural genus was a group of
species, and was marked out from other genera by eternal differences of
still greater importance.
We now, however, perceive that the existence of any such groups as
genera and species is an arbitrary creation of the naturalist’s
mind. All resemblances of plants are natural so far as they express
hereditary affinities; but this applies as well to the variations
within the species as to the species itself, or to the larger groups.
All is a matter of degree. The deeper differences between plants have
been produced by the differentiating action of circumstances during
millions of years, so that it would naturally require millions of
years to undo this result, and prove experimentally that the forms can
be approximated again. Sub-species may sometimes have arisen within
historical times, and varieties approaching to sub-species may often
be produced by the horticulturist in a few years. Such varieties can
easily be brought back to their original forms, or, if placed in the
original circumstances, will themselves revert to those forms; but
according to Darwin’s views all forms are capable of unlimited change,
and it might possibly be, unlimited reversion if suitable circumstances
and sufficient time be granted.
Many fruitless attempts have been made to establish a rigorous
criterion of specific and generic difference, so that these classes
might have a definite value and rank in all branches of biology.
Linnæus adopted the view that the species was to be defined as a
distinct creation, saying,[593] “Species tot numeramus, quot diversæ
formæ in principio sunt creatæ;” or again, “Species tot sunt, quot
diversas formas ab initio produxit Infinitum Ens; quæ formæ, secundum
generationis inditas leges, produxere plures, at sibi semper similes.”
Of genera he also says,[594] “Genus omne est naturale, in primordio
tale creatum.” It was a common doctrine added to and essential to that
of distinct creation that these species could not produce intermediate
and variable forms, so that we find Linnæus obliged by the ascertained
existence of hybrids to take a different view in another work; he
says,[595] “Novas species immo et genera ex copula diversarum specierum
in regno vegetabilium oriri primo intuitu paradoxum videtur; interim
observationes sic fieri non ita dissuadent.” Even supposing in the
present day that we could assent to the notion of a certain number of
distinct creational acts, this notion would not help us in the theory
of classification. Naturalists have never pointed out any method of
deciding what are the results of distinct creations, and what are
not. As Darwin says,[596] “the definition must not include an element
which cannot possibly be ascertained, such as an act of creation.”
It is, in fact, by investigation of forms and classification that we
should ascertain what were distinct creations and what were not; this
information would be a result and not a means of classification.
[593] *Philosophia Botanica* (1770), § 157, p. 99.
[594] *Ibid.* § 159, p. 100.
[595] *Amœnitates Academicæ* (1744), vol. i. p. 70. Quoted in
*Edinburgh Review*, October 1868, vol. cxxviii. pp. 416, 417.
[596] *Descent of Man*, vol. i. p. 228.
Agassiz seemed to consider that he had discovered an important
principle, to the effect that general plan or structure is the true
ground for the discrimination of the great classes of animals, which
may be called branches of the animal kingdom.[597] He also thought that
genera are definite and natural groups. “Genera,” he says,[598] “are
most closely allied groups of animals, differing neither in form, nor
in complication of structure, but simply in the ultimate structural
peculiarities of some of their parts; and this is, I believe, the best
definition which can be given of genera.” But it is surely apparent
that there are endless degrees both of structural peculiarity and of
complication of structure. It is impossible to define the amount of
structural peculiarity which constitutes the genus as distinguished
from the species.
[597] Agassiz, *Essay on Classification*, p. 219.
[598] *Ibid.* p. 249.
The form which any classification of plants or animals tends to take is
that of an unlimited series of subaltern classes. Originally botanists
confined themselves for the most part to a small number of such
classes. Linnæus adopted Class, Order, Genus, Species, and Variety, and
even seemed to think that there was something essentially natural in a
five-fold arrangement of groups.[599]
[599] *Philosophia Botanica*, § 155, p. 98.
With the progress of botany intermediate and additional groups
have gradually been introduced. According to the Laws of Botanical
Nomenclature adopted by the International Botanical Congress, held at
Paris[600] in August 1867, no less than twenty-one names of classes
are recognised--namely, Kingdom, Division, Sub-division, Class,
Sub-class, Cohort, Sub-cohort, Order, Sub-order, Tribe, Sub-tribe,
Genus, Sub-genus, Section, Sub-section, Species, Sub-species, Variety,
Sub-variety, Variation, Sub-variation. It is allowed by the authors of
this scheme, that the rank or degree of importance to be attributed
to any of these divisions may vary in a certain degree according to
individual opinion. The only point on which botanists are not allowed
discretion is as to the order of the successive sub-divisions; any
inversion of the arrangement, such as division of a genus into tribes,
or of a tribe into orders, is quite inadmissible. There is no reason
to suppose that even the above list is complete and inextensible. The
Botanical Congress itself recognised the distinction between variations
according as they are Seedlings, Half-breeds, or *Lusus Naturæ*.
The complication of the inferior classes is increased again by the
existence of *hybrids*, arising from the fertilisation of one species
by another deemed a distinct species, nor can we place any limit to the
minuteness of discrimination of degrees of breeding short of an actual
pedigree of individuals.
[600] *Laws of Botanical Nomenclature*, by Alphonse Decandolle,
translated from the French, 1868, p. 19.
It will be evident to the reader that in the remarks upon
classification as applied to the Natural Sciences, given in this
and the preceding sections, I have not in the least attempted to
treat the subject in a manner adequate to its extent and importance.
A volume would be insufficient for tracing out the principles of
scientific method specially applicable to these branches of science.
What more I may be able to say upon the subject will be better said,
if ever, when I am able to take up the closely-connected subjects of
Scientific Nomenclature, Terminology, and Descriptive Representation.
In the meantime, I have wished to show, in a negative point of
view, that natural classification in the animal and vegetable
kingdoms is a special problem, and that the particular methods and
difficulties to which it gives rise are not those common to all cases
of classification, as so many physicists have supposed. Genealogical
resemblances are only a special case of resemblances in general.
*Unique or Exceptional Objects.*
In framing a system of classification in almost any branch of science,
we must expect to meet with unique or peculiar objects, which stand
alone, having comparatively few analogies with other objects. They may
also be said to be *sui generis*, each unique object forming, as it
were, a genus by itself; or they are called *nondescript*, because from
thus standing apart it is difficult to find terms in which to describe
their properties. The rings of Saturn, for instance, form a unique
object among the celestial bodies. We have indeed considered this and
many other instances of unique objects in the preceding chapter on
Exceptional Phenomena. Apparent, Singular, and Divergent Exceptions
especially, are analogous to unique objects.
In the classification of the elements, Carbon stands apart as a
substance entirely unique in its powers of producing compounds. It is
considered to be a quadrivalent element, and it obeys all the ordinary
laws of chemical combination. Yet it manifests powers of affinity in
such an exalted degree that the substances in which it appears are
more numerous than all the other compounds known to chemists. Almost
the whole of the substances which have been called organic contain
carbon, and are probably held together by the carbon atoms, so that
many chemists are now inclined to abandon the name Organic Chemistry,
and substitute the name Chemistry of the Carbon Compounds. It used to
be believed that the production of organic compounds could be effected
only by the action of vital force, or of some inexplicable cause
involved in the phenomena of life; but it is now found that chemists
are able to commence with the elementary materials, pure carbon,
hydrogen, and oxygen, and by strictly chemical operations to combine
these so as to form complicated organic compounds. So many substances
have already been formed that we might be inclined to generalise and
infer that all organic compounds might ultimately be produced without
the agency of living beings. Thus the distinction between the organic
and the inorganic kingdoms seems to be breaking down, but our wonder at
the peculiar powers of carbon must increase at the same time.
In considering generalisation, the law of continuity was applied
chiefly to physical properties capable of mathematical treatment. But
in the classificatory sciences, also, the same important principle
is often beautifully exemplified. Many objects or events seem to be
entirely exceptional and abnormal, and in regard to degree or magnitude
they may be so termed; but it is often easy to show that they are
connected by intermediate links with ordinary cases. In the organic
kingdoms there is a common groundwork of similarity running through
all classes, but particular actions and processes present themselves
conspicuously in particular families and classes. Tenacity of life
is most marked in the Rotifera, and some other kinds of microscopic
organisms, which can be dried and boiled without loss of life. Reptiles
are distinguished by torpidity, and the length of time they can live
without food. Birds, on the contrary, exhibit ceaseless activity and
high muscular power. The ant is as conspicuous for intelligence and
size of brain among insects as the quadrumana and man among vertebrata.
Among plants the Leguminosæ are distinguished by a tendency to sleep,
folding their leaves at the approach of night. In the genus Mimosa,
especially the Mimosa pudica, commonly called the sensitive plant,
the same tendency is magnified into an extreme irritability, almost
resembling voluntary motion. More or less of the same irritability
probably belongs to vegetable forms of every kind, but it is of course
to be investigated with special ease in such an extreme case. In the
Gymnotus and Torpedo, we find that organic structures can act like
galvanic batteries. Are we to suppose that such animals are entirely
anomalous exceptions; or may we not justly expect to find less intense
manifestations of electric action in all animals?
Some extraordinary differences between the modes of reproduction
of animals have been shown to be far less than was at first sight
apparent. The lower animals seem to differ entirely from the higher
ones in the power of reproducing lost limbs. A kind of crab has the
habit of casting portions of its claws when much frightened, but
they soon grow again. There are multitudes of smaller animals which,
like the Hydra, may be cut in two and yet live and develop into new
complete individuals. No mammalian animal can reproduce a limb, and
in appearance there is no analogy. But it was suggested by Blumenbach
that the healing of a wound in the higher animals really represents in
a lower degree the power of reproducing a limb. That this is true may
be shown by adducing a multitude of intermediate cases, each adjoining
pair of which are clearly analogous, so that we pass gradually from one
extreme to the other. Darwin holds, moreover, that any such restoration
of parts is closely connected with that perpetual replacement of
the particles which causes every organised body to be after a time
entirely new as regards its constituent substance. In short, we
approach to a great generalisation under which all the phenomena of
growth, restoration, and maintenance of organs are effects of one and
the same power.[601] It is perhaps still more surprising to find that
the complicated process of reproduction in the higher animals may be
gradually traced down to a simpler and simpler form, which at last
becomes undistinguishable from the budding out of one plant from the
stem of another. By a great generalisation we may regard all the modes
of reproduction of organic life as alike in their nature, and varying
only in complexity of development.[602]
[601] Darwin, *The Variation of Animals and Plants*, vol. ii.
pp. 293, 359, &c.; quoting Paget, *Lectures on Pathology*, 1853,
pp. 152, 164.
[602] *Ibid.* vol. ii. p. 372.
*Limits of Classification.*
Science can extend only so far as the power of accurate classification
extends. If we cannot detect resemblances, and assign their exact
character and amount, we cannot have that generalised knowledge which
constitutes science; we cannot infer from case to case. Classification
is the opposite process to discrimination. If we feel that two tastes
differ, the tastes of two kinds of wine for instance, the mere fact of
difference existing prevents inference. The detection of the difference
saves us, indeed, from false inference, because so far as difference
exists, inference is impossible. But classification consists in
detecting resemblances of all degrees of generality, and ascertaining
exactly how far such resemblances extend, while assigning precisely the
points at which difference begins. It enables us, then, to generalise,
and make inferences where it is possible, and it saves us at the same
time from going too far. A full classification constitutes a complete
record of all our knowledge of the objects or events classified,
and the limits of exact knowledge are identical with the limits of
classification.
It must by no means be supposed that every group of natural objects
will be found capable of rigorous classification. There may be
substances which vary by insensible degrees, consisting, for instance,
in varying mixtures of simpler substances. Granite is a mixture of
quartz, felspar, and mica, but there are hardly two specimens in which
the proportions of these three constituents are alike, and it would
be impossible to lay down definitions of distinct species of granite
without finding an infinite variety of intermediate species. The
only true classification of granites, then, would be founded on the
proportions of the constituents present, and a chemical or microscopic
analysis would be requisite, in order that we might assign a specimen
to its true position in the series. Granites vary, again, by insensible
degrees, as regards the magnitude of the crystals of felspar and mica.
Precisely similar remarks might be made concerning the classification
of other plutonic rocks, such as syenite, basalt, pumice-stone, lava.
The nature of a ray of homogeneous light is strictly defined, either
by its place in the spectrum or by the corresponding wave-length, but
a ray of mixed light admits of no simple classification; any of the
infinitely numerous rays of the continuous spectrum may be present or
absent, or present in various intensities, so that we can only class
and define a mixed colour by defining the intensity and wave-length
of each ray of homogeneous light which is present in it. Complete
spectroscopic analysis and the determination of the intensity of
every part of the spectrum yielded by a mixed ray is requisite for
its accurate classification. Nearly the same may be said of complex
sounds. A simple sound undulation, if we could meet with such a sound,
would admit of precise and exhaustive classification as regards pitch,
the length of wave, or the number of waves reaching the ear per
second being a sufficient criterion. But almost all ordinary sounds,
even those of musical instruments, consist of complex aggregates of
undulations of different pitches, and in order to classify the sound
we should have to measure the intensities of each of the constituent
sounds, a work which has been partially accomplished by Helmholtz, as
regards the vowel sounds. The different tones of voice distinctive
of different individuals must also be due to the intermixture of
minute waves of various pitch, which are yet quite beyond the range
of experimental investigation. We cannot, then, at present attempt to
classify the different kinds or *timbres* of sound.
The difficulties of classification are still greater when a varying
phenomenon cannot be shown to be a mixture of simpler phenomena. If
we attempt to classify tastes, we may rudely group them according as
they are sweet, bitter, saline, alkaline, acid, astringent or fiery;
but it is evident that these groups are bounded by no sharp lines
of definition. Tastes of mixed or intermediate character may exist
almost *ad infinitum*, and what is still more troublesome, the tastes
clearly united within one class may differ more or less from each
other, without our being able to arrange them in subordinate genera and
species. The same remarks may be made concerning the classification of
odours, which may be roughly grouped according to the arrangement of
Linnæus as, aromatic, fragrant, ambrosiac, alliaceous, fetid, virulent,
nauseous. Within each of these vague classes, however, there would be
infinite shades of variety, and each class would graduate into other
classes. The odours which can be discriminated by an acute nose are
infinite; every rock, stone, plant, or animal has some slight smell,
and it is well known that dogs, or even blind men, can discriminate
persons by a slight distinctive odour which usually passes unnoticed.
Similar remarks may be made concerning the feelings of the human mind,
called emotions. We know what is anger, grief, fear, hatred, love;
and many systems for classifying these feelings have been proposed.
They may be roughly distinguished according as they are pleasurable
or painful, prospective or retrospective, selfish or sympathetic,
active or passive, and possibly in many other ways; but each mode of
arrangement will be indefinite and unsatisfactory when followed into
details. As a general rule, the emotional state of the mind at any
moment will be neither pure anger nor pure fear, nor any one pure
feeling, but an indefinite and complex aggregate of feelings. It may
be that the state of mind is really a sum of several distinct modes
of agitation, just as a mixed colour is the sum of the several rays
of the spectrum. In this case there may be more hope of some method
of analysis being successfully applied at a future time. But it may
be found that states of mind really graduate into each other so that
rigorous classification would be hopeless.
A little reflection will show that there are whole worlds of
existences which in like manner are incapable of logical analysis and
classification. One friend may be able to single out and identify
another friend by his countenance among a million other countenances.
Faces are capable of infinite discrimination, but who shall classify
and define them, or say by what particular shades of feature he does
judge? There are of course certain distinct types of face, but each
type is connected with each other type by infinite intermediate
specimens. We may classify melodies according to the major or minor
key, the character of the time, and some other distinct points;
but every melody has, independently of such circumstances, its
own distinctive character and effect upon the mind. We can detect
differences between the styles of literary, musical, or artistic
compositions. We can even in some cases assign a picture to its
painter, or a symphony to its composer, by a subtle feeling of
resemblances or differences which may be felt, but cannot be described.
Finally, it is apparent that in human character there is unfathomable
and inexhaustible diversity. Every mind is more or less like every
other mind; there is always a basis of similarity, but there is a
superstructure of feelings, impulses, and motives which is distinctive
for each person. We can sometimes predict the general character of the
feelings and actions which will be produced by a given external event
in an individual well known to us; but we also know that we are often
inexplicably at fault in our inferences. No one can safely generalise
upon the subtle variations of temper and emotion which may arise even
in a person of ordinary character. As human knowledge and civilisation
progress, these characteristic differences tend to develop and multiply
themselves, rather than decrease. Character grows more many-sided. Two
well educated Englishmen are far better distinguished from each other
than two common labourers, and these are better distinguished than two
Australian aborigines. The complexities of existing phenomena probably
develop themselves more rapidly than scientific method can overtake
them. In spite of all the boasted powers of science, we cannot really
apply scientific method to our own minds and characters, which are more
important to us than all the stars and nebulæ.
BOOK VI.
CHAPTER XXXI.