Chapter II

Mill's Logic

I. Intuitionism and Empiricism

    Mill's System of Logic may be regarded as the most important
manifesto of Utilitarian philosophy. It lays down explicitly and
in their ripest form the principles implicitly assumed by Bentham
and the elder Mill. It modifies as well as expounds. It
represents the process by which J. S. Mill, on becoming aware of
certain defects in the Utilitarians' philosophy, endeavoured to
restate the first principles so as to avoid the erroneous
conclusions. The coincidence with his predecessors remains far
closer than the divergence. The fundamental tenets are developed
rather than withdrawn. The Logic thus most distinctly raises the
ultimate issues. It has the impressiveness which belongs in some
degree to every genuine exertion of a powerful mind. Mill is
struggling with real difficulties; not trying to bolster up a
theory commended to him by extraneous considerations. He is doing
his best to give an answer to his problem; not to hide an
evasion. His honourable candour incidentally reveals the weakness
as frankly as the strength of his position. He neither shirks nor
hides difficulties, and if we are forced to admit that some of
his reasoning is fallacious, the admission scarcely adds to the
statement that he is writing a treatise upon philosophical
problems. His frankness has made the task of critics
comparatively easy. It takes so many volumes to settle what some
philosophers have meant that we scarcely reach the question
whether their meaning, or rather any of their many possible
meanings, was right. In the case of Mill, that preparatory labour
is not required. His book, too, has been sufficiently tested by
time to enable us to mark the points at which his structure has
failed to stand the wear and tear of general discussion. I must
try to bring out the vital points of the doctrine.
    Mill, I have said, had a very definite purpose beyond the
purely philosophical. 'Bad institutions,' he says,(1*) are
supported by false philosophy. The false philosophy to which he
refers is that of the so-called 'intuitionist school.' Its
'stronghold,' he thought, lay in appeals to the mathematical and
physical sciences. To drive it from this position was to deprive
it of 'speculative support'; and, though it could still appeal to
prejudice, the destruction of this support was an indispenSable
step to complete victory. Mill wished to provide a logical
armoury for all assailants of established dogmatism, and his
success as a propagandist surprised him. The book was read, to
his astonishment, even in the universities. Indeed, I can testify
from personal observation that it became a kind of sacred book
for students who claimed to be genuine Liberals. It gave the
philosophical creed of an important section of the rising
generation, partly biassed, it may be, by the application to 'bad
institutions.' Mill's logic, that is, fell in with the one main
current of political opinion. His readings in logic with Grote
and other friends enabled him to fashion the weapons needed for
the assault. Thus in its origin and by its execution the task was
in fact an attempt to give an organised statement of sound
philosophy in a form applicable to social and political
speculations.
    Mill considered that the school of metaphysicians which he
attacked had long predominated in this country.(2*) When Taine
called his view specially English, Mill protested. The Scottish
reaction against Hume, he said, which 'assumed long ago the
German form,' had ended by 'prevailing universally' in this
country. When he first wrote he was almost alone in his opinions,
and there were still 'twenty a priori and spiritualist
philosophers for every partisan of the doctrine of
Experience.'(3*) The philosophical world, he says elsewhere,(4*)
is 'bisected' by the line between the 'Intuitional' and the
'Experiential' schools. Mill's conviction that a majority of
Englishmen were really 'intuitionists' in any shape is
significant, I think, of his isolated position. Undoubtedly most
Englishmen disliked Utilitarians, and respectable professors of
philosophy were anxious to disavow sympathy with covert atheism.
Yet the general tendency of thought was, I suspect, far more
congenial to Mill's doctrine than he admitted. Englishmen were
practically, if not avowedly, predisposed to empiricism. In any
case, he was carrying on the tradition which Taine rightly, as I
should say, regarded as specifically English. Its adherents
traced its origin back through James Mill to Hartley, Hume,
Locke, Hobbes, and Francis Bacon, and perhaps it might even count
among its remoter ancestors such men as William of Ockham and
Roger Bacon. The series of names suggests some permanent
congeniality to the national character.(5*) Although, more over,
this tradition had in later times been broken by Reid and his
followers, their condemnation did not really imply so fundamental
an antithesis of thought as Mill supposed. They and the
empiricists had, in their own opinion at least, a common ancestor
in Bacon, if not in Locke. But, however this may be, the Scottish
school had maintained the positions which Mill thought himself
concerned to attack; and for him represented the rejection of
'experience.'
    Experience is a word which requires exposition; but in a
general way the aim of the Utilitarians is abundantly clear. They
attacked 'intuitions' as Locke had attacked 'innate ideas.' The
great error of philosophy, according to them, as according to
Locke, has been the attempt to transcend the limits of human
intelligence, and so to wander into the regions of mysticism; to
seek knowledge by spinning logical structures which, having no
base in fact, ended in mere scholastic logomachy; or to override
experience by claiming absolute authority for theories which
dispense with further proof for the simple reason that no proof
of them can be given. To limit speculation and to make it
fruitful by forcing it from the first to deal with facts; to
trace all its evidence to experience or the observation of facts;
and to insist upon its verification by comparison with facts, is
the main and surely the legitimate purpose of the Utilitarians as
of all their philosophical congeners. The gulf between the world
of speculation and the world of fact is the great opprobrium of
philosophy. The necessity for finding a basis of fact was
emphasised at this time by the rapid development of the sciences
which may be called purely empirical, and which had sprung, in
any case, from methods of direct observation. This development
suggested the elaborate treatise written from a different point
of view by Whewell. The great ambition of the Benthamites had
been to apply scientific methods to all the problems of
legislation, jurisprudence, economics, ethics, and philosophy.
Mill could now show, with the involuntary help of Whewell, what
those methods really implied The questions remain: What are
facts? and, What is experience? and, What are the consequent
conditions of reasoning about facts? Admitting that, somehow or
other, a vast and rapidly growing body of knowledge has been
attained in the physical sciences, we may ask how it has been
gained, and proceed to apply the methods in what have been called
the moral sciences. Kant's famous problem was, How is a priori
synthetic knowledge possible? Mill denies that any such knowledge
exists. His problem is therefore, How can knowledge be explained
without a priori elements? When this can be satisfactorily done,
we shall be able to show how both moral and physical science can
be fairly based upon experience.
    Mill's view of the proper limits of his inquiry is
characteristic. He accepts Bacon's account of logic. It, is the
ars artium, the science of science itself.'(6*) It implies an
investigation into the processes of inference generally. It is
not limited to the old formal logic, but includes every operation
by which knowledge is extended. It is thus, as he afterwards puts
it, the 'theory of proof.'(7*) The book, indeed, owes its
interest to the width of the field covered. It has not the
repulsive dryness of formal logic, but would lead to a natural
history of the whole growth of knowledge, and makes constant
reference to the actual development of thought. On the other
hand, Mill gives notice that he has no more to do with
metaphysics than with any of the special sciences. Logic, he
declares, is common ground for all schools of philosophy. It is,
he says, the office of metaphysics to decide what are ultimate
facts, but for the logician it is needless to go into this
analysis.(8*) Accordingly, he often in the course of the book
considers himself entitled to hand over various problems to the
metaphysicians.(9*) The possibility of really keeping to this
distinction is doubtful. Since Mill's very aim is to show that
all knowledge comes from observation of 'facts,' it is apparently
relevant to inquire what are these 'ultimate facts.' Indeed, his
statement, though made in all sincerity, almost suggests a
controversial artifice. Logic, as Mill of course admits, affects
metaphysics as it affects all sciences; but in one way it affects
them very differently. It justifies astronomy, but it apparently
makes metaphysics superfluous. Inquiry into the 'ultimate facts'
turns out to be either hopeless or meaningless. Mill does not
directly assert that all 'ontological' speculations are merely
cobwebs of the brain. But he tries to show that, whatever they
may be, they are strictly irrelevant in reasoning. All
metaphysicians are expected to grant him certain postulates.
These once granted, he will be able to account for the whole
structure of knowledge. 'Intuitions,' transcendental
speculations, and ontology will then be deprived of the whole
conditions under which they thrive. I do not now assert, he
virtually says, that your doctrine is wrong, but I shall show
that it is thrown away. It is a pretence of explaining something
which lies altogether beyond the limits of real knowledge, and
therefore admits of no explanation.
    Mill starts from the classification given in old logical
textbooks, to which, different as are his conclusions, he
attached a very high value.(10*) The schoolmen had by their
elaborate acuteness established a whole system of logical
distinctions and definitions which are both important and
accurate, however sterile the inquiries in which they were used.
The machinery was excellent, though its contrivers forgot that a
mill cannot grind out flour if you put in no grain. Mill begins
accordingly by classifying the various kinds of words in the
light afforded by previous logical systems.
    He is to give a theory of proof. That which is to be proved
is a proposition; and a proposition deals with names, and
moreover with the names of 'things,' not merely with the names
'of our ideas of things.'(11*) That, in some sense, reasoning has
to do with things is of course his essential principle; and the
problem consequently arises, What are empirical 'things'?(12*)
Though we cannot ask what are 'ultimate things,' the logician
must enumerate the various kinds of things to which reference may
be made in predication. Mill makes out a classification which he
proposes to substitute, provisionally at any rate, for the
Aristotelian categories.(13*) The first and simplest class of
nameable things corresponds to things 'in the mind,' that is,
'feelings,' or 'states of consciousness,' sensations, emotions,
thoughts, and volitions. The second class corresponds to things
'external to the mind'.(14*) and these are either 'substances' or
'attributes.' Here our task is lightened by a welcome discovery.
All philosophers, it appears, are now agreed upon one point. Sir
W. Hamilton, Cousin, Kant, nay, according to Hamilton -- though
that is too good to be true -- nearly all previous philosophers
admit one truth.(15*) We know, as they agree, nothing about
'objects' except the sensations which they give us and the order
of those sensations. Hence the two 'substances,' body and mind,
remain unknowable 'in themselves.' Body is the 'hidden external
cause' to which we refer our sensations;(16*) and as body is the
'mysterious something which excites the mind to feel, so mind is
the mysterious something which feels and thinks.' The mind is, as
he says in language quoted from his father, 'a thread of
consciousness,' a series of 'feelings': it is the 'myself' which
is conceived as distinct from the feelings but of which I can yet
know nothing except that it has the feelings.
    Thus, although we know nothing of minds and of bodies 'in
themselves,' we do know their existence. That is essential to his
position. The 'thread of consciousness' is a 'final
inexplicability' with him, but it corresponds to some real
entity. And, on the other side, we must believe, in some sense,
in things. The thing, though known only through the sensations
which it excites, must be something more than a mere sensation,
for the whole of his logic defends the thesis that in some way or
other thought has to conform to facts or to the relations between
'things.' Knowledge, however, is confined entirely to the
sensations and the attributes; and the two are at bottom one. The
'verbal' distinction between a property of things and the
sensation which we receive from it, is made, he says, for
convenience of discourse rather than from any difference in the
nature of the thing denoted.(17*) This brings us to a critical
point. Attributes, he says, following the old distribution, are
of Quality, Quantity, and Relation. Now Quality and Quantity mean
simply the sensations excited by bodies. To say that snow is
white, or that there is a gallon of water, means simply that
certain sensations of colour or size are excited in us by snow or
a volume of water. The attribute called 'Relation' introduces a
different order of feelings. A 'relation' supposes that two
things are involved in some one fact or series of facts.(18*) But
it is still an 'attribute' or a 'state of consciousness.' It is a
feeling different from other feelings by the circumstance that
two 'things' instead of one are involved. This is the explanation
which, as we have seen, he praises so warmly in his father's
Analysis, and now adopts for his own purposes. It enables him to
classify predications. All predication is either an assertion of
simple existence or an assertion of 'relations.' By classifying
the possible relations, therefore, we obtain the possible forms
of predication. It turns out accordingly that we can make five
possible predications: we can predicate, first, simple existence;
or secondly, 'coexistence'; or thirdly, 'sequence' (these two
being equivalent, as he adds, to 'order in place' and 'order in
time'); or fourthly, we may predicate 'resemblance'; or fifthly,
and this is only to be stated provisionally, we may predicate
'causation.'(19*)
    So far, Mill's view corresponds to the psychology of the
Analysis, which gives a similar account of the various terms
employed. J. S. Mill has now the standing ground from which he
can explain the whole development of knowledge. At this point,
however, he has to diverge from his father's extreme nominalism.
Predication, according to the elder, is a process of naming. A
predicate is a name of the same thing of which the subject is a
name; and to predicate is simply to assert this identity of
names. This doctrine, as Mill thinks, is equally implied in the
dictum de omni et nullo which is taken as the explanation of the
syllogism. We have arbitrarily put a number of things in a class,
and to 'reason' is simply to repeat of each what we have said of
all. This is to put the cart before the horse, or to assume that
the classification precedes the reason for classification, though
probably the theory, thus nakedly stated, would not be granted by
any one.(20*) What, then, is the true theory? That is explained
by the distinction between 'connotation' and 'denotation,' which
Mill accepted (though inverting the use of the words) from his
father. A general name such as 'man' denotes John, Thomas, and
other individuals. It connotes certain 'attributes,' such as
rationality and a certain shape. When, therefore, I say that John
is a man, I say that he has the attributes 'connoted'; and when I
say that all men are mortal, I assert that along with the other
attributes of man goes the attribute of mortality.(21*)
Predication, then, in general, involves the attribute of
'relation.' We may assert the simple existence of a 'quality,'
or, which is the same thing, of a 'sensation'; but to say that
John is a man. or that men are mortal, or to make any of the
general propositions which constitute knowledge, is to assert
some of those 'relations' which are perceived when we consider
two or more things together.
    'Things,' then, so far as knowable are clusters (in Hartley's
language) of 'attributes'; and the attributes may be equally
regarded as 'feelings.' To predicate is to refer a thing to one
of the clusters, and therefore to assert its possession of the
attributes connoted. I will only note in passing that by
declining to go into the metaphysical question as to the
difference between 'attributes' and 'sensations,' or thoughts and
things, Mill leaves an obscurity at the foundation of his
philosophy. But leaving this for the present, it is enough to say
that we have our five possible types of predication.(22*) All
propositions may be reduced to one of the forms. Things exist or
coexist or follow or resemble or are cause or effect.(23*) The
next problem, therefore, is, How are these propositions to be
proved? or, by what tests is our belief to be justified.
    What may be the nature of belief itself is a question which
Mill leaves to the analytical psychologist,(24*) who, as he
admits, will probably find it puzzling, if not hopeless. But as
we all agree that somehow or other we attain knowledge, we may
inquire what is implied in the process. Now, some part of our
knowledge obviously depends upon 'experience.' We know of any
particular fact from the testimony of our senses. We know that
London Bridge exists because we have seen and touched it; and it
would be obviously hopeless to try to deduce ts existence from
the principle of the excluded middle. London Bridge would then be
something independent of time and place. But do we not want
something more than bare experience when we lay down a general
rule is a law of nature? Then we not only say 'is,' but 'must
be'; and this, according to the Intuitionist, marks the
introduction of something more than an appeal to 'experience.'
There are truths, he says, which represent 'laws of thought';
which are self-evident, or perceived by 'intuition'; or the
contrary of which is 'inconceivable.' Without some such laws, we
could not bind together the shifting data of experience, or
advance from 'is' to 'must be,' or even to 'will be.' We lose all
certainty, and fall into the scepticism of Hume, which makes
belief a mere 'custom,' regards all things as distinct atoms
conjoined but not connected, and holds that 'anything may be the
cause of anything.' Mill's aim is to explode the intuitions
without falling into the scepticism. Necessary truths, he holds,
are mere figments. All knowledge whatever is of the empirical
type. 'This has been' justifies 'this will be.' Empirical truths
clearly exist, and are held undoubtingly, although they have no
foundation except experience. Nobody ever doubted that all men
die; yet no 'proof' of the fact could be ever suggested, before
physiology was created, except the bare fact that all men have
died. If physiology has made the necessity more evident, it has
not appreciably strengthened the conviction. We all believe even
now that thunder will follow lightning, though nobody has been
able to show why it should follow. The ultimate proof in
countless cases, if not in all, is simply that some connection
has been observed, and, in many such cases, the belief reaches a
pitch which excludes all perceptible doubt. As a fact, then,
belief of the strongest kind can be generated from simple
experience. The burthen of proof is upon those who assume
different origins for different classes of truth.(25*)

 II. SYLLOGISM AND DEFINITION

    This main thesis leads to two lines of argument. First of
all, Mill seeks to show that the methods of proof expounded by
his adversaries do not really take us beyond experience; and,
secondly, he seeks to show that experience gives us a sufficient
basis of knowledge. Let us first notice, then, how the ground is
cleared by examining previous accounts of the process of
inference. The old theory of reasoning depends upon the
syllogism. That gives the type of the whole process by which
knowledge is extended. All men are mortal; Socrates is a man,
therefore Socrates is mortal. Stewart and Brown had both attacked
the syllogism on the familiar ground that it is tautologous. The
major has already asserted the minor. To say that one man is
mortal when you have already said that all men are mortal, is
merely to repeat yourself. There can be no real inference, and no
advance to new knowledge. So long as the syllogism is to be
explained on the old terms, Mill thinks this criticism fatal; but
he holds, too, that by a different interpretation we may assign a
real and vitally important meaning to this venerable form of
argument. In several places(26*) he gives a view which seems to
be much to the purpose. The syllogism, it would seem, corresponds
really, not to a mode of reasoning, but to a system of arguing.
When a disputant bases some statement upon an inference, we may
challenge either the truth of the rule or the statement of fact.
The cogency of the argument depends upon the applicability of the
rule to the fact. If men be not mortal, or, again, if Socrates be
not a man, the inference is not valid; and these two distinct
issues, the issue of law and the issue of fact, may be raised in
any case.(27*) The value of the syllogism is that it raises these
issues distinctly. The argument is thus put in such a form as to
be absolutely conclusive if the premises be themselves granted.
It therefore provides a test of the validity of the logic.
Granting the premises, a denial of the inference must involve a
contradiction. That is the only test in pure logic. The syllogism
must, therefore, be in a sense tautologous, for otherwise it
could not be conclusive. Acceptance o£ the premises must be shown
from the form of statement to necessitate the admission of the
inference. This follows, and the logical link is complete and
irrefragable, if the middle term be identical in both premises,
and not otherwise. This is what Mill indicates by saying that
'the rules of the syllogism are rules for compelling a person to
be aware of the whole of what he must undertake to defend if he
persists in maintaining his conclusion.'(28*) Ratiocination, as
he sums up his view elsewhere, 'does not consist of syllogisms';
but the syllogism is a useful formula into which it can
'translate its reasonings,' and so guarantee their
correctness.(29*) If this be granted, we must consider the
essential step of inference to be embodied in, but not created
by, the syllogism. Correct reasoning can always be thrown into
this form. The syllogism emerges when the reasoning is complete.
'The use of the syllogism is no other,' says Mill, 'than the use
of general propositions in reasoning.' It is a security for
correct generalisation.(30*) We have, then, still to ask what is
the reasoning process for which the syllogism provides a test.
Generalisation implies classification. Our general rule or major
premise states some property of a class to which the individual
belongs. The question is how this reference to a class enables us
to draw inferences which we could not draw from the individual
case. To this Mill gives a simple answer, which is already
implied in his theory of predication. When I say that Socrates is
a man, I say that he has the attributes connoted by the name. He
is a rational, featherless biped, for example. But I already know
by observation that with these attributes goes the attribute of
mortality. The essence of the reasoning process is therefore
that, from the possession of certain attributes, I infer the
possession of another attribute which has coexisted with them
previously. That I do, in fact, reason in this way in countless
cases is undeniable. I know that a certain quality, say
malleability, goes along with other qualities of colour, shape,
and so forth, by which I recognise a substance as gold. I can, it
may be, give no other reason for believing the future conjunction
of those qualities than the fact of their previous conjunction.
The belief, that is, is as a matter of fact generated simply by
the previous coincidence or corresponds to constant association.
Whether this exhausts the whole logical significance may still be
disputed; but, at any rate, upon these terms we can escape from
the charge of tautology. The rule in the major premise registers
a number of previous experiences of coexistence. When we notice
some of the attributes in a given case, we make an addition to
our knowledge by applying the rule, that is, by inferring that
another attribute may be added to the observed attributes. This,
then, gives a rational account of the advance in knowledge made
through the syllogism in the case where the class can be defined
as a simple sum of attributes.
    But is this an adequate account of the reasoning process in
general? There is another view which suggested difficulties to
Mill. His solution of these difficulties, marked, as we learn
from the Autobiography, an essential stage in the development of
his doctrine. Reference to a class is, upon his interpretation,
implied in the syllogism; and classification implies definition.
A class means all things which have a certain list of attributes
stated in the definition. May we not then infer other properties
from the definition? May not mortality, for example, be deducible
from the other attributes of man? The assumption that we can do
so is connected with the fallacy most characteristic of the
misuse of the syllogism. It is plain that we may create as many
classes as we please, and make names for combinations of
attributes which have no actual, or even no possible, existence.
Any inferences which we make on the strength of such
classification must be nugatory or simply tautologous. I show
that a certain proposition follows from my definition; but that
gives no guarantee for its conformity to the realities behind the
definition. Your 'proof' that a man is mortal means simply that
if he is not mortal you don't call him a man. The syllogism
treated on that system becomes simply an elaborate series of
devices for begging the question. From such methods arise all the
futilities of scholasticism, and the doctrine of essences which,
though Locke confuted it,(31*) has 'never ceased to poison
philosophy.'(32*) It may, I suppose, be taken for granted that
the syllogism was constantly applied to cover such fallacies, and
so far Mill is on safe ground. The theory, however, leads him to
a characteristic point. Already in the early review (January
1828), he had criticised Whately's account of definition. A 'real
definition,' as Whately had said, 'explains and unfolds "the
nature" of the thing defined, whereas a "nominal definition" only
explains the name.' Whately goes on to point out that the only
real definitions in this sense are the mathematical definitions.
It is impossible to discover the properties of a thing, a man, or
a plant from the definition. If it were possible, we might
proceed to 'evolve a camel from the depths of our consciousness,'
and nobody now professes to be equal to that feat. When, however,
we 'define' a circle or a line and so forth, we make assertions
from which we can deduce the whole theory of geometry. A
geometrical figure represents a vast complex of truths, mutually
implying each other, and all deducible from a few simple
definitions. The middle term is not the name of a simple thing,
or of a thing which has a certain set of coexisting attributes,
but a word expressive of a whole system of reciprocal relations.
If one property entitles me to say that a certain figure is a
circle, I am virtually declaring that it has innumerable other
properties, and I am thus able to make inferences which, although
implicitly given, are not perceived till explicitly stated. By
assigning a thing to a class, I say in this case that I may make
any one of an indefinite number of propositions about it, all
mutually implying each other, and requiring the highest faculties
for combining and evolving. Pure mathematics give the one great
example of a vast body of truths reached by purely deductive
processes. They appear to be evolved from certain simple and
self-evident truths. Can they, then, be explained as simply
empirical? Do we know the properties of a circle as we know the
properties of gold, simply by combining records of previous
experience? Or can we admit that this great system of truth is
all evolved out of 'definitions'?
    Mill scents in Whately's doctrine a taint of a priori
assumption, and accordingly meets it by a direct contradiction. A
geometrical definition, he says, is no more a 'real' definition
than the definition of a camel. No definition whatever can
'unfold the nature' of a thing. He states this in his review,
though it was at a later period,(33*) when meditating upon a
passage of Dugald Stewart, that he perceived the full
consequences of his own position. In answering Whately, he had
said that all definitions were 'nominal.' A 'real definition'
means that to the definition proper we add the statement that
there is a thing corresponding to the name.(34*) The definition
itself is a 'mere identical proposition,' from which we can learn
nothing as to facts. But it may be accompanied by a postulate
which 'covertly asserts a fact,' and from the fact may follow
consequences of any degree of importance. This distinction
between the definition and the postulate may be exhibited, as he
remarks, by substituting 'means' for 'is.' If we say: a centaur
'means' a being half man and half horse, we give a pure
definition. If we say: a man 'is' a featherless biped, our
statement includes the definition -- man 'means' featherless
biped; but if we said no more, no inference could be made as to
facts. If we are really to increase our knowledge by using this
definition, we must add the 'covert' assertion that such
featherless bipeds exist. The mathematical case is identical,
Stewart had argued that geometrical propositions followed, not
from the axioms but, from the definitions. From the bare axiom
that if equals be added to equals the wholes are equal, you can
infer nothing. You must also perceive the particular figures
which are compared. Of course the truth of the axioms must be
admitted; but they do not specify the first principles from which
geometry is evolved. In other words, geometry implies
'intuition,' not the a priori 'intuitions' to which Mill
objected, but the direct perception of the spatial relations. We
must see the figure as well as admit the self-evident axiom.
Mill, on considering this argument, thought that Stewart had
stopped at a half truth.(35*) He ought to have got rid of the
definitions as well as the axioms. Every demonstration in Euclid,
says Mill, might be carried on without them. When we argue from a
diagram in which there is a circle, we do not really refer to
circles in general, but only to the particular circle before us.
If its radii be equal or approximately equal, the conclusions are
true. We afterwards extend our reasoning to similar cases; but
only one instance is demonstrated. The definition is merely a
'notice to ourselves and others,' stating what assumptions we
think ourselves entitled to make; and in this way it resembles
the major in the syllogism. The demonstration does not 'depend
upon' it, though if we deny it, the demonstration fails. By this
argument, Mill conceives that the case of mathematics is put on a
level with other cases. We always argue from facts, and moreover
from 'particular facts,' not from definitions. We start from an
observation of this particular circle -- a sensible 'thing' or
object, as in arguing about natural history we start from
observation of the camel. Hence we may lay down the general
proposition, applicable to geometry as well as to all ordinary
observation, that, all inference is from particulars to
particulars.'(36*) This is the 'foundation' both of Induction,
which is 'popularly said' to reason from particulars to generals,
and of Deduction, which is supposed to reason from generals to
particulars.(37*) This sums up Mill's characteristic position.

 III. MATHEMATICAL TRUTHS

    This attempt to bring all reasoning to the same type forces
Mill to ignore what to others seems to be of the essence of the
case. There are, he says, two statements: 'There may exist a
figure bounded by three straight lines'; that is the fruitful
statement of facts. 'This figure is called a triangle'; that is
the merely nominal definition or explanation of words. Moreover,
as he says, we may drop the definition by substituting the
equivalent words or simply looking at the thing. It does not
follow that we can dispense with the mode of apprehension implied
by the definition. Whether we use the word triangle, or the
words, 'three lines enclosing a space,' or no words at all, we
must equally have the conceptions or intuitions of lines and
space. All demonstration in geometry consists in mentally
rearranging a combination of lines and angles so as to show that
one figure may be made to coincide absolutely with another
figure. The original fact remains unaltered, but the ways of
apprehending the fact are innumerable. Newton and his dog Diamond
might both see the same circular thing; but to Diamond the circle
was a simple round object; to Newton it was also a complex system
of related lines, capable of being so regarded as to embody a
vast variety of elaborate formulae.(38*) Geometry, as Mill
undeniably says, deals with facts. Newton and Diamond have
precisely the same fact before them. It remains the same, whether
we stop at the simplest stage or proceed to the most complex
evolution of geometry. The difference between the observers is
not that Newton has seen new facts, but that he sees more in the
same fact. The change is not in the things but in the mind,
which, by grouping the things in the way pointed out by the
definitions, is able to discover countless new relations involved
in the same perception. This again may suggest that even the fact
revealed to simple perception is not a bare 'fact,' something, as
Mill puts it, 'external to the mind,' but is in some sense itself
constituted by the faculty of perception. It contains already the
germ of the whole intellectual evolution. The change is not in
the thing perceived, but in the mode of perceiving. And,
therefore, again, we do not acquire new knowledge, as we acquire
it in the physical sciences, by observing new facts, discovering
resemblances and differences, and generalising from the
properties common to all; but by contemplating the same fact. All
geometry is in any particular space -- if only we can find it. We
do not proceed by comparing a number of different regions of
spaces, and inquire whether French triangles have the same
properties as English triangles. To Mill, however, the statement
that geometry deals with fact leads to another conclusion. We
must deal with these facts as with other facts, and follow the
method of other natural sciences. We really proceed in the same
way whether we are investigating the properties of an ellipse or
a camel. In either case we must discover truth by experience.
    What, then, is really implied in the doctrine that all
knowledge rests upon experience? One of Mill's intellectual
ancestors lays down the fundamental principle. It is absurd, says
Hume,(39*) to try to demonstrate matter of fact by a priori
arguments. 'Nothing is demonstrable unless the contrary implies a
contradiction. Nothing that is distinctly conceivable implies a
contradiction. Whatever we conceive as existent we can also
conceive as non-existent. There is no being, therefore, whoa
non-existence implies a contradiction.' 'Matter of fact,' then,
must be proved by experience; but, given a 'fact' we may deduce
necessary consequences. All necessity may be hypothetical; there
is an 'if' to every 'must,' but remembering the 'if' the 'must'
will be harmless. It can never take us beyond experience. The
existence of space itself cannot be called necessary; but space
once given, all geometry may 'necessarily' follow, and imply
relations running through the whole fabric of scientific
knowledge. Mill agrees that a 'hypothetical' necessity of this
kind belongs to geometry; and adds, that in any science whatever,
we might, by making hypotheses, arrive at an equal
necessity.(40*) But then, he goes on to urge, the hypotheses of
geometry are not 'absolute truths,' but 'generalisations from
observation,' or 'inductions from the evidence of our
senses,'(41*) which, therefore, are not necessarily true. This
led to his keenest controversies, and, in my opinion, to his
least successful answers. He especially claims credit in his
Autobiography for having attacked the 'stronghold' of the
intuitionists by upsetting belief in the a priori certainty of
mathematical aphorisms. In fact, his opponents constantly
appealed to the case of mathematics, and Mill assumes that they
can be met only by reducing such truths to the case of purely
empirical truths. He argues boldly that the 'character of
necessity ascribed to the truths of mathematics' is 'an
illusion.'(42*) Geometry and arithmetic are both founded upon
experience or observation. He goes indeed still further at times.
At one place he even holds that the principle of contradiction
itself is simply, one of our first and most familiar
generalisations from experience.' We know, 'by the simplest
observation of our own minds,' that belief and disbelief exclude
each other, and that when light is present darkness is
absent.(43*) Mill thought himself bound, we see, to refer to
experience not only our knowledge of facts, but even the
capacities, which are said by another school to be the conditions
of perceiving and thus acquiring experience. If he had studied
Kant, he might have reached a better version of his own view. As
it was, he was led to accepting paradoxes which he was not really
concerned to maintain. He had to choose between a theory of
'intuitions' -- so understood as to entitle us to assert matter
of fact independently of experience -- and a theory which seems
to make even the primary intellectual operations mere statements
of empirical fact. Since necessary statements about matters of
fact must be impossible, he argues that we cannot even draw
necessary inferences from observed fact. Not content with saying
that all necessity is hypothetical, he argues that all necessity,
even the logical necessity of contradiction, is a figment. If he
does not carry out a theory which would seem to make all
reasoning unsatisfactory, he maintains, at least, that the
hypotheses or assumptions involved in geometry, and even in
arithmetic, are generalised from experience, and 'seldom, if
ever, exactly true.' If the assumptions are inaccurate or
uncertain, the whole superstructure of science must also be
uncertain.
    The nature of his argument follows from his previous
positions. He treats space and number as somehow qualities of the
'things,' or as attributes which we observe without in any sense
supplying them. His argument upon geometry begins by asserting
that there are no such 'real things' as points or lines or
circles. Nay, they are not even possible, so far as we can see,
consistently with the actual constitution of the universe. It is
'customary' to answer that such lines only exist in our minds,
and have therefore nothing to do with outward experience.(44*)
This, however, is incorrect psychologically, because our ideas
are copies of the realities. A line without breadth is
'inconceivable,' and therefore does not exist even in the mind.
Hence we must suppose that geometry deals either with
'non-entities' or with 'natural objects.'(45*) Arithmetic fares
little better. When we say that two and one make three, we assert
that the same pebbles may, 'by an alteration of place and
arrangement' -- that is, by being formed into one parcel or two
-- be made to produce either set of sensations.(46*) Each of the
numbers, 2, 3, 4, etc., he says elsewhere, 'denotes physical
phenomena and connotes a physical property of those
phenomena.'(47*) Arithmetic owes its position to the 'fortunate
applicability' to it of the 'inductive truth' that the sums of
equals 'are equal.'(48*) It is obvious to remark that this is
only true of certain applications of arithmetic. When we speak of
the numbers of a population, we imply, as Mill admits, no
equality except that each person is a unit.(49*) We may speak
with equal propriety of a number of syllogisms or of metaphors,
in which we have nothing to do with 'equality' or 'physical
properties' at all. Further, as he observes,(50*) it is the
peculiarity of the case that counting one thing is to count all
things. When I see that four pebbles are two pairs of pebbles, I
see the same truth for all cases, including, for example,
syllogisms. Mill admits, accordingly, that 'in questions of pure
number' -- though only in such questions -- the assumptions are
'exactly true,' and apparently holds that we may deduce exactly
true conclusions. That ought to have been enough for him. He had
really no sufficient reason for depriving us of our arithmetical
faith. He can himself point out its harmlessness. As he truly
says, 'from laws of spare and number alone nothing can be deduced
but laws of spare and number.'(51*) We ran never get outside of
the world of experience and observation by applying them. If we
count, we do not say that there must be four things, but that
wherever there are four things there are also two pairs of
things. The unlucky 'pebble' argument illustrates one confusion.
'Two and two are four' is changed into 'two and two make four.'
The statement of a constant relation is made into a statement of
an event. Two pebbles added to two might produce a fifth, but the
original two pairs would still be four. The space-problem
suggests greater difficulties. Space, he argues, must either be a
property of things or an idea in our minds, and therefore a
'non-entity.' If we consider it, however, to be a form of
perception, the disjunction ceases to be valid. The
space-perceptions mark the border-line between 'object' and
'subject,' and we cannot place its product in either sphere
exclusively. The space-relations are 'subjective,' because they
imply perception by the mind, but objective because they imply
the action of the mind as mind, and do not vary from one person
or 'subject' to another. To say whether they were objective or
subjective absolutely we should have to get outside of our minds
altogether -- which is an impossible feat. Therefore, again, it
is not really to the purpose to allege that such a 'thing' as a
straight line or a perfect circle never exists. Whether we say
that a curve deviates from or conforms to perfect circularity, we
equally admit the existence of a perfect circle. We may be unable
to mark it with finger or micrometer, but it is there. If no two
lines are exactly equal, that must be because one has more spare
than the other. Mill's argument seems to involve the confusion
between the statement that things differ in space and the
statement, which would be surely nonsense, that the spare itself
differs. It is to transfer the difference from the things
measured to the measure itself. It is just the peculiarity of
space that it can only be measured by space; and that to say one
space is greater than another, is simply to say, 'there is more
space.' As in the case of number, he is really making an
illegitimate transfer from one sphere to another. A straight line
is a symmetrical division of space, which must be taken to exist,
though we cannot make a perfectly straight line. Our inability
does not tend to prove that the 'space' itself is variable. In
applying a measure we necessarily assume its constancy; and it is
difficult even to understand what 'variability' means, unless it
is variability in reference to some assumed standard. If, as Mill
seems to think, space is a property of things, varying like other
properties, we have to ask, In what, then, does it vary? All
other properties vary in respect of their space-relations; but,
if space itself be variable, we seem to be reduced to hopeless
incoherence.
    Thus, to ascribe necessity to geometry as well as to
arithmetic is not to ascribe 'necessity' to propositions (to use
Hume's language again) about 'matters of fact.' The 'necessity'
is implied in a peculiarity which Mill himself puts very
forcibly,(52*) and which seems to be all that is wanted. An
arithmetical formula of the simplest or most complex kind is an
assertion that two ways of considering a fact are identical. When
I say that two and two make four, or lay down some algebraical
formula, such as Taylor's theorem, I am asserting the precise
equivalence of two processes. I do not even say that two and two
must make four, but that, if they make four, they cannot also or
ever make five. The number is the same in whatever order we
count, so long as we count all the units, and count them
correctly. So much is implied in Mill's observation that counting
one set of things is counting all things. The concrete
circumstances make no difference. The same is true of geometry.
The complex figure may be also regarded as a combination of
simpler figures. It remains precisely the same, though we
perceive that besides being one figure it is also a combination
of figures. This runs through all mathematical truths, and, I
think, indicates Mill's precise difficulty. He says quite truly
that to know the existence of a fact you must always have
something given by observation or experience. The most complex
mathematical formulae may still be regarded as equating different
statements of the same experience. The difference is only that
the experience is evolved into more complex forms, not by any
change in the data supplied, but by an intellectual operation
which consists essentially in organising the data in various
ways. The reasoner does not for an instant desert fact; he only
perceives that it may be contemplated in different ways, and that
very different statements assert the very same fact or facts. Our
experience may be increased, either by the entrance of new
objects into our field of observation, or by the different
methods of contemplation. The mathematician deals with
propositions which remain equally true if we suppose no change
whatever to take place in the world, or, as Mill puts it, 'if all
the objects of the universe were unchangeably fixed.'(53*) His
theories, in short, construct a map on which he can afterwards
lay down the changes which involve time. The filling up of the
map depends entirely upon observation and experience; but to make
the map itself a mere bundle of accidental coexistences is to
destroy the conditions of experience. The map is our own faculty
of perception.
    'There is something which seems to require explanation,' says
Mill,(54*) 'in the fact that an immense multitude of mathematical
truths... can be elicited from so small a number of elementary
laws.' It is puzzling when you identify Newton with Diamond on
the ground that they both see the same 'fact.' But it is no more
puzzling than anything else, as indeed Mill proceeds to show,
when we observe the method by which in arithmetic, for example,
an indefinite number of relations is implied by the simple
process of counting. The fact is the same for all observers, in
so far as they have the same data; but to perceive the data
already implies the germ of thought from which all the
demonstrative sciences are evolved. The knowledge can be
transformed and complicated to an indefinite degree by simply
identifying different ways of combining the data. Mill, in his
anxiety to adhere to facts and experience, fails to recognise
adequately the process by which simple observation is evolved
into countless modifications. The difficulty appears in its
extreme form in the curious suggestion that even the principle of
contradiction is a product of experience. Mill is so resolved to
leave nothing for the mind to do, that he supposes a primitive
mind which is not even able to distinguish 'is not' from 'is.' It
is hard to understand how such a 'mind,' if it were a 'mind,'
could ever acquire any 'experience' at all. So when Mill says
that the burthen of proof rests with the intuitionist, he is, no
doubt, quite right in throwing the burthen of proof upon thinkers
who suppose particular doctrines to have been somehow inserted
into the fabric of knowledge without any relation to other
truths; but it is surely not a gratuitous assumption that the
mind which combines experience must have some kind of properties
as well as the things combined. If it knows no 'truths' except
from experience, it is at least possible that it may in some way
react upon the given experience. This, at any rate, should be
Mill's view, who takes 'mind' and 'body' to be unknowable, and
all knowledge of fact to be a combination of 'sensations.' He
only requires to admit that knowledge may be increased either by
varying the data or by varying the mind's action upon fixed data.
In neither case do we get beyond 'experience.' In many places,
Mill seems to interpret his view in consistency with this
doctrine. His invariable candour leads him to make admissions,
some of which I have noticed. Yet his prepossessions lead him to
the superfluous paradoxes which, for the rest, he maintains with
remarkable vigour and ingenuity.
    One other device of the enemy raised the troublesome question
of inconceivability as a test of truth, which brought Mill into
conflict not only with Whewell and Hamilton, but with Mr Herbert
Spencer. I will only notice the curious illustration which it
affords of Mill's tendency to confound statements of fact with
the purely logical assertion that two modes of stating a fact are
precisely equivalent. The existence of Antipodeans, in his
favourite illustration,(55*) was declared to be 'inconceivable.'
Disbelief in their existence involved the statement of fact:
gravity acts here and at the Antipodes in the same direction.
That statement could of course be disproved by evidence; and
there is no reason to suppose that the truth, once suggested,
would be less 'conceivable' to Augustine or, say, to Archimedes,
than to Newton. It also involved the assertion: men (if the
direction of gravity were constant) would drop off the earth at
the Antipodes as they here drop off the ceiling. The denial of
that statement is still 'inconceivable,' though the statement
ceases to be applicable. Mill, however, infers that, as an
'inconceivability' has been surmounted, 'inconceivability' in
general is no test of truth. 'There is,' he says,(56*) 'no
proposition of which it can be asserted that every human mind
must eternally and irrevocably believe it,' and he tries, as I
have said, to apply this even to the principle of contradiction.
In other words, because our logic requires a basis in fact, and
the fact must be given by experience, the logic is itself
dependent upon experience. If 'inconceivable' be limited, as I
think it should be limited in logic, to the contradictory, an
inconceivable proposition is incredible because it is really no
proposition at all. We may, no doubt, believe statements which
are implicitly contradictory. but when the contradiction is made
explicit, the belief becomes impossible. Similarly we may
disbelieve statements which appear to be contradictory; and when
the error is exposed, we may believe what was once
'inconceivable.' That only shows that our thoughts are often in a
great muddle, and in great need of logical unification. It does
not prove any incoherence in the logical process itself.

 IV. CAUSATION

    We can now proceed to what may be called the constructive
part of the logic. We have got rid of proofs from intuitions,
from definitions, and from inconceivabilities, and the question
remains how we can prove anything. All knowledge is inductive. It
is all derived from facts; it proceeds from particulars to
particulars; the previous coexistence of sequences which have
been observed constitute our whole raw material. What, then,
serves to bind facts together? or how are we to know that facts
are bound together, or that any two given facts have this
relation? The fundamental postulate of science is the so-called
'uniformity of nature.' But Nature, as it is seen by the
unscientific mind, is anything but uniform. There are, it is
true, certain simple uniformities which frequently recur. Fire
burns, water drowns, stones thrown up fall down; and such
observations are the germs of what we afterwards call scientific
'laws.' But things are constantly happening of which we can give
no account. Catastrophes occur without any assignable
'antecedent'; storm and sunshine seem to come at random; and the
same combination of events never recurs in all its details.
Variety is as manifest as uniformity. How can cosmos be made out
of chaos? How do we come to trace regularity in this bewildering
world of irregularities? From any fact taken by itself, as Hume
had fully shown, we can deduce no necessity for any other fact.
The question is, whether we are to account for the belief in
uniformity by an 'intuition' or by James Mill's universal solvent
of 'association of ideas.' J. S. Mill was fully convinced of the
efficacy of this panacea, but he sees difficulties over which his
father had passed. If association explains everything, the tie
between ideas ought to be stronger, it might be supposed, in
proportion to the frequency of their association. The oftener two
facts have been joined, the more confidently we should expect a
junction hereafter. But this does not hold true universally. A
chemist, as Mill observes, analyses a substance; and assuming the
accuracy of his results, we at once infer a general law of nature
from 'a single instance.' But if any one from the beginning of
the world has seen that crows are black, and a single credible
witness says that he has seen a grey crow, we abandon at once a
conjunction which seemed to rest upon invariable and
superabundant evidence. Why is a 'single instance' sufficient in
one case, and any number of instances insufficient in the other?
'Whoever can answer this question,' says Mill, 'knows more of the
philosophy of logic than the wisest of the ancients, and has
solved the problem of induction.'(57*)
    Here Mill again professes to set metaphysics aside. He has
nothing to do with 'ontology.' He deals with 'physical,' not
'efficient,' causes. He does not ask whether there be or be not a
'mysterious' tie lying behind the phenomena and actually
producing them.(58*) He is content to lay down as his statement
of the 'law of causation' that there is an invariable succession
between 'every fact in nature' and 'some other fact which has
preceded it.' This, he assumes, is a truth, whatever be the
nature of things in themselves. The true account is rather that
he will show that 'ontology' is a set of meaningless phrases. He
can answer his problem without it. Causation is, in fact,
conceived by him as it was conceived by all the psychologists,
including Brown; and he has simply to show that Brown's supposed
'intuition' is a superfluity. His treatment of the question gives
the really critical part of his philosophy. It leads to some of
the results which have been most highly and, as I think, most
deservedly praised. It also leads to some of his greatest errors,
and shows the weak point of his method.
    Mathematical knowledge, as Mill remarks, has nothing to do
with causation. Every geometrical or arithmetical formula is true
without supposing change. One theorem does not 'cause' the
others; it 'implies' them. The most complex and the most simple
are mutually involved in the single perception, though our
knowledge of one may be the cause of our knowing the others.
Their necessity is another way of stating this implication. We
can show that to deny one theorem while admitting another is to
be contradictory. The whole of physical science, however, from
first to last, is a process of stating the changes of phenomena
in terms of time and place, and therefore brings them all within
the range of mathematical methods. Science is not fully
constituted till it becomes quantitative or can speak in terms of
definite relations of magnitudes. How, then, are its laws
necessary? It is contradictory to say that the same thing has
different space-relations at the same time; but there is no
contradiction in saying that it is here now and somewhere else
to-morrow. The formula of the 'uniformity of nature,' whatever
may be its warrant, transfers the necessity of the geometrical
theorem to the laws of phenomena. We assume that things are
continuous or retain identity in change. We are no more permitted
to say that the combination of the same elements may produce a
compound of different properties, than to say that the product of
two numbers may sometimes give one result and sometimes another.
Every change is regarded as regular, or as having a 'sufficient
reason.' The same series of changes therefore must take place
under the same conditions, or every difference implies a
difference in the conditions. So far as we carry out this
assumption, we resolve the shifting and apparently irregular
panorama into a system of uniform laws. Each law may be, and if
it be really a law must be, absolutely true, not in the sense
that it states a fact unconditionally, but that it is stated so
that the conditions under. which it is absolutely true are fully
specified. If we could reach a complete science of all physical
phenomena, we should have a system of connected laws as
infallible and mutually consistent as those of geometry or
arithmetic. But in order thus to organise our knowledge, we have
to alter -- not the facts -- but the order of grouping and
conceiving them. We have to see identities where there were
apparent differences, and differences in apparent identities, and
to regard the whole order of nature from a fresh point of view.
The fact remains just as it was; but the laws -- that is, the
formulae which express them -- are grouped upon a new system. The
questions remain, What is the precise nature of the scientific
view? and What is our guarantee for a postulate which it
everywhere implies?
    The chapter upon causation(59*) is a vigorous assertion of
Mill's position. He accepts the traditional view of his school,
that cause means invariable sequence; but he makes two very
important amendments to the previous statements. A simple
sequence of two events is not a sufficient indication, however
often repeated, that they are cause and effect. We speak, he
says, of a particular dish 'causing' death; but to be accurate we
must also include, as part of the cause, all the other phenomena
present, the man as well as the food, the man's state of health
at the time, and possibly even the state of the atmosphere or the
planet. The real cause must include all the relevant phenomena.
The cause, therefore, is, 'philosophically speaking,' the 'sum
total of the conditions,' positive and negative, 'taken together,
the whole of the contingencies of every description, which, being
realised, the consequent invariably follows.'(60*) Mill's second
amendment is made by saying that the cause does not signify
simply 'invariable antecedence,' but also 'unconditional'
sequence. There may be 'invariable' sequences, such as day and
night -- a case often alleged by Reid and others, which are not
'unconditional.' The sun, for anything we can say, might not
rise, and then day would not follow night. The real condition,
therefore, is the presence of a luminous body without the
interposition of an opaque screen.(61*) These are undoubtedly
material improvements upon previous statements; and this view
being admitted, it follows, as Mill says, that the state of the
whole universe is the consequence of its state at the previous
instant. Knowing all the facts and all the laws at any time we
could predict all the future history of the universe.(62*) Some
curious confusions, it must be noticed, result apparently from
Mill's use of popular language. The most singular is implied in
his discussion of the question whether cause and effect can ever
be simultaneous. Some 'causes,' he says, leave permanent effects;
a sword runs a man through, but it need not remain in his body in
order that he may 'continue dead.'(63*) The 'cause' here is taken
to mean the 'thing' which was once a part of a set of things, and
has clearly ceased to mean the sum of all the conditions. 'Most
things,' he continues, once produced, remain as they are till
something changes them. Other things require the continual
presence of the agencies which produced them. But since all
change, according to him, supposes a cause, it is clear that not
only 'most things' but all things must remain as they are till
something changes them. Persistence is implied in causation as
much as change, for it is merely the other side of the same
principle. Inertia is as much assumed in mechanics as mobility;
for it is the same thing to say that a body remains in one place
when there is no moving force, as to say that whenever it ceases
to remain there is a moving force. The difference which Mill
means to point out is that some changes alter permanent
conditions of other changes, as when a man cuts his throat and
all vital processes cease; while sometimes the change leaves
permanent conditions unaffected, as when a man shaves himself,
and his vital processes continue. But in no case is the effect
produced, as he says, after the cause has ceased; it is always
produced through the actually present conditions, which may have
come into their present state through a change at some more or
less remote period. Each link in a chain, according to the common
metaphor, depends upon all the previous links and may be said to
hang from them; but the distant link can only act through the
intermediate links.
    These slips imply a vagueness which leads to more serious
results. Mill's aim is to construct a kind of logical machinery
-- a sieve, if I may say so, through which we pass all the
phenomenal of the universe in order to find out which are really
loose and which are connected by the ties of causation. We are
unweaving the complex web of nature by discovering what is the
hidden system of connections in virtue of which one event or
thing is somehow fastened to another. Everything, we may say,
which appears is called up by something else -- the thunder by
the lightning, the death by the poison, and so forth. In every
case we can reduce a statement of causation to the form of an
assertion of sequence or coexistence. Here, as he observes, we
meet one difficulty. Everything is connected with some other
thing. But then it may or must be also connected with a third.
The two connections may interfere, and we have to consider how
they can be disentangled. This leads to a distinction to which he
attaches, very rightly, I think, the highest importance. In some
cases, the correct version of the facts can be obtained by simply
superposing the laws of simpler cases. A body moves to the north
under certain conditions; but other conditions force it to move
also east or south. We then have only to combine the two 'laws,'
and to say that it is moving both north and east, that is,
north-east, or perhaps to interpret rest as an equal movement to
both north and south. This, as he remarks, represents the general
case in regard to mechanical phenomena. We have simply to combine
two rules to get what is called in dynamics 'the composition of
forces'; and, in accordance with this phase, he uses the general
phrase, 'the composition of causes.'(64*) But, as he observes,
this principle is in many cases not applicable. In chemical
combinations, in particular, we cannot infer the properties of
the compound from the properties of the components. The laws of
simple substances will not give us the laws of the product, and
we can only learn these derivative laws by experiment. This
holds, still more conspicuously, of organised bodies. From
considering the properties of its chemical constituents
separately you cannot deduce the properties of the human body. We
thus come to a kind of knot in the web; we are at a deadlock,
because the laws from which we start are superseded by an
entirely different set of laws. Mill marks this by speaking of
'heteropathic laws.'(65*) Such laws are not analysable into
simple laws. He thinks, indeed, that 'heteropathic laws' are --
at least 'in some cases may be derived from the separate laws,
according to a fixed principle.' The fact to which he calls
attention is undeniable. We discover countless laws as to the
properties of bodies which it is impossible at present either to
resolve into simpler laws, or to deduce from the laws of the
constituent elements. Such laws are properly 'empirical.' The
observation of the facts asserted is the sole guarantee for our
belief in their truth; and they can he reduced under no more
general formula. Is this, however, simply a challenge to the man
of science to inquire further, or does it oppose an insuperable
obstacle to further scientific researches? Mill avowedly limits
himself to 'our present state of knowledge.' He recognised that
Grove, in his Correlation of Forces,(66*) made out a strong,
though still only a probable, case for believing that a
'heteropathic law' may represent a complete transformation of one
set of forces into another. Heat, light, and magnetism may be all
different manifestations of a single force -- not so much causes
of one another as 'convertible into one another.'(67*) Grove, as
Mill adds, is not, as might be supposed, deviating into ontology,
but giving a strictly philosophical statement. Mill is here
speaking of a great principle, imperfectly known at the time,
which has been accepted by modern science, and he is quite ready
to welcome it. It is, however, noticeable that he still guards
himself against admitting any intrusion of 'necessity.' He will
not allow that the dependence of the properties of compounds upon
these elements must result in all cases 'according to a fixed
principle.' The meaning of this may appear from his later assault
upon the doctrine that 'like produces like.' This he reckons
among the fallacies which he discovers in all manner of pestilent
a priori philosophising. Descartes, Spinoza, Leibniz, and
Coleridge have all been guilty of it in various forms.(68*) We
are therefore under no obligation to go further when we come to
totally disparate phenomena in our series. We have unravelled our
web sufficiently when we find laws disappearing and being
superseded by a totally different set of laws, not describable
even in the same language. That we may be forced to be content
with such a result is undeniable. But it is equally true that one
main end of scientific theorists is to get round this difficulty.
Without inquiring in what sense the axiom that 'like produces
like' may be fallacious, we must at least admit that to give a
scientific law -- that is, a rule by which one set of events is
deducible from another -- we must be able to express it in terms
of some single measure. Til I we can get such a statement, we
have not the complete formula. There is a breach of continuity in
our theories, which we try to remove by reducing all the forces
to measures assignable in terms of space and number. The
hypothesis of an ether and vibrating atoms enables us to regard
phenomena as corresponding in some way to the laws which, as Mill
says, can be compounded by simple superposition, without
introducing heterogeneous terms. Though he does not condemn this
hypothesis, Mill regards it with a certain suspicion as an
attempt to wander into ontology, and the search for what is in
its nature inaccessible.(69*) At any rate, it does not appear to
him that further inquiry is necessary when we come to an
irreducible breach of continuity. to a case in which one set of
phenomena is simply superseded by another, instead of being
transformable into it. If a compound is made of certain elements
exclusively, a physicist would clearly infer that its properties
must be a result of the properties of the elements according to
'some fixed principle.' Mill is only prepared to admit that this
may be the case. The physicist, again, seeks for a mode of
stating the principle in theorems capable of being combined and
superposed, whereas Mill holds that our knowledge may have come
to an ultimate insuperable end.

 V. PLURALITY OF CAUSES

    It is in the applications of this view that we come to what
must be regarded as downright fallacies. If, as Mill holds, an
effect may be something absolutely disparate from the cause -- a
new thing which starts into existence when its antecedent occurs
-- we are led to another result. There is, then, no apparent
reason why the same thing should not spring up in answer to
different summonses. Not only is this possible, but, as Mill
thinks, it constantly occurs. This is his doctrine of the
'Plurality of Causes.' A given cause, he holds, can only produce
one effect. But a given effect may follow various causes. So long
as the relation is merely one of arbitrary succession, not of
continuity, this is obviously possible. The fully scientific
view, I take it, would be that when we speak of 'cause and
effect' we are really thinking of a single process regarded in
different ways. We may analyse the process differently for
different purposes, and infer the past from the future or the
future from the past; but we assume that, if we could perfectly
understand the whole process, there would be thorough continuity,
and no abrupt supersession of one thing or one set of 'laws' by
another. This continuity is precisely what Mill systematically
denies. A cause, he holds, means an absolute beginning of a new
effect.(70*) The process becomes a series of distinct terms -- a
set of 'links' in a chain, not a flow of a stream. One remarkable
case is enough to illustrate the point. When Bacon's claims to
have founded a truly scientific theory are considered, it is
generally said that his guess as to the nature of heat is a point
in his favour.(71*) Mill, however, takes this particular case as
an instance of Bacon's errors. Bacon, he says,(72*) 'entirely
overlooked the Plurality of Causes. All his rules imply the
assumption, so contrary to what we now know of nature, that a
phenomenon cannot have more than one cause.' Bacon was misguided
enough to apply this to heat. Now, as Mill had already argued,
heat may have several causes: the 'sun,' or 'friction,' or
'percussion,' or 'electricity,' or 'chemical action.'(73*)
Consequently, the attempt to find a single cause is doomed to
failure. We shall find, not that one antecedent but, that one of
several antecedents is always present. Clearly the 'sun' is not
'friction,' nor is 'percussion' 'electricity.' Each of those
phrases indicates concrete facts involving various processes.
Heat, as a 'mode of motion,' occurs in them all, because all
involve particular phases of movement. From the 'raw' fact, as it
presents itself -- 'This body is hot' -- I cannot say which of
various laws represents the true antecedents in that case. The
heat may have been caused by exposure to fire or by friction. In
that sense, undoubtedly, one effect may really have any number of
'causes.' But replace all the conditions, and it is evident that
there can be only one true analysis of the whole process.
    Mill's insistence upon this imaginary 'plurality of causes'
is significant. It indicates the precise stage in the development
of the idea of cause to which his doctrine corresponds. Taking
what we may call the popular sense of causation, the 'plurality'
expresses an obvious truth; and we can understand its
plausibility. We take, in fact, two concrete events which follow
each other, and call them cause and effect. We use a tool -- a
knife to cut bread, for example; we are forced to attend to the
fact that every difference in the knife will have an effect on
the result. The work is better or worse, as the knife is sharper
or blunter. If we did not recognise this in every purposeful
action, all action would be intrinsically uncertain. We are,
therefore, impressed with the necessity of admitting that the
effect is determined by the cause. But, on the other hand, the
knife is there. It may have been made by fifty different methods,
and yet be the same. The handle may have been first made and then
the blade, or vice versa, and so forth. therefore we believe, and
in this sense of cause believe correctly, that one effect may be
the product of any number of different 'causes.' In order to
reach the more scientific sense of causation, we have to take
into account all that we have neglected. The knife is one product
of an indefinite multitude of processes, and is therefore not the
total 'effect' of the concrete antecedent, but only a part of it
arbitrarily singled out. We do not attend to all these collateral
results, because for us at the moment they have no interest; but
when we systematically carry out the 'uniformity of nature'
principle, it is obvious that they must be taken into account. We
then see that although precisely similar products appear in an
infinite variety of concrete processes, they correspond only to a
part of those processes, and may always be analysed into
identical elements. The effect can no more have two causes than a
cause two effects, for cause and effect are distinguished by
observing the same process in a different order. It was just
because men of science held that the one effect must have one
cause that they could make a coherent theory of heat. Mill,
however goes a step further. Bacon's error was the assumption
that there was only one 'form' of heat. Now it is specially
futile, says Mill, to seek for the causes of 'sensible qualities
of objects.... In regard to scarcely any of them has it been
found possible to trace any unity of cause.' Bacon, therefore,
was seeking for 'what did not exist,' and to this Mill adds the
surprising statement that 'the phenomenon of which he sought for
the one cause has oftenest no cause at all, and, when it has,
depends (as far as hitherto ascertained) on an unassignable
variety of causes.'(74*)
    To explain this rather startling assertion we must take one
more of Mill's theories. How from the doctrine, which he fully
admits, that every event has a cause can he reach the conclusion
that some things have 'no cause at all'? Once more we have, I
think, the misapplication of an undeniable truth. A 'law' of
causation, taken by itself, will obviously not fully account for
a single fact. It cannot lead to the conclusion: 'this fact must
exist,' but only to the conclusion: this fact must exist if
certain previous facts existed. We somewhere assume an initial
stage. However far back we can go, we may still repeat the
question. Given a single state of facts and the 'laws of
causation,' we can go indefinitely backwards or forwards in time.
Given the sun, the planets, and gravitation, we can trace the
whole past and future history of the solar system; but the facts
at some period must be 'given.' We cannot say that they must, but
only that they do exist. Mill himself puts this(75*) with all
desirable clearness. He expresses it by saying that besides
'causation' there is 'collocation,' a word, he says, suggested by
Chalmers.(76*) To know the 'collocation,' therefore, is
essential. A 'law' does not tell us that there 'must' be plums
and suet, but only that if there are such things in certain
'collocations' a plum pudding 'must' be the result. All
statements of fact have thus an empirical basis. This, however,
takes a peculiar turn in his exposition, and one which is
characteristic of a Utilitarian failing. He makes the distinction
of relations correspond to a distinction of things. Instead of
saying that both causation and collocation are implied in all
phenomena, he speaks of some 'uniformities' as dependent upon
causation and others as dependent upon collocation. He therefore
writes a chapter on 'uniformities of coexistence not dependent on
causation.'(77*) This, however, is closely connected with, and
must be explained by, another doctrine to which he attached the
highest importance. After telling us how he was started afresh by
Stewart's account of axioms, he adds that he came to
'inextricable difficulties' in regard to induction. He had come
to the 'end of his tether,' and 'could make nothing satisfactory
of the subject.' When, after five years' halt, he again set to
work, he introduced his 'theory of kinds,' which, as he
intimates, got round the difficulty. He felt, as we may
conjecture, that he had now reduced all the facts to such purely
empirical conjunctions that he did not see how to get any tie
between them. Any cause, so far as we have gone, might lead to
any effect. and even when we have seen a case of conjunction, we
can give no reason for its recurrence. Induction enables us to
predicate attributes of a class; but a logical class is itself
merely a bundle of attributes arbitrarily selected, and it
remains to see why, from a thing's possession of some of the
class attributes, we can infer that it has the others. Why should
not the same set of attributes form part of different bundles?
and if so, what is the justification for the primary logical
procedure? From featherless bipedism we infer mortality. But why
may not some class of featherless bipeds be immortal? If we admit
the possibility, all induction becomes precarious. The 'theory of
kinds' was, it seems, intended as an answer to these obvious
difficulties.

 VI. REAL KINDS

    Mill's account of 'real kinds' corresponds, as he tells us,
to the old logicians' distinction between genus and species.
Though our classification may be arbitrary and nothing properly
deducible from it, except the mere fact that we have chosen to
give names to certain clusters of attributes, there is also a
real difference. Some of our classes do not correspond to 'real
kinds,' and are mistaken for them. Others, however, correspond to
a real or natural kind. The difference is this: a 'real kind' has
an 'indeterminate multitude of properties, not derivable from
each other,' whereas an arbitrary or merely logical 'kind' may
only differ in respect of the particular attribute assigned.
Thus, to say that Newton is a man is to attribute to him the
'unknown multitude of properties' connoted by 'man.' To say that
Newton is a Christian is only to attribute to him a particular
belief and whatever consequences may follow from having that
belief.(78*) One classification, as he says, 'answers to a much
more radical distinction in the things themselves, than the other
does'; and a man may thus fairly say, if he chooses, that one
classification is made 'by Nature' and one 'by ourselves,'
provided that he means no more than to express the distinction
just drawn. Now, it is easy to understand why Mill felt that this
assertion entitled him to a 'real' bond which would keep
phenomena together in a more satisfactory way. All things had
become so loose and disconnected that it was difficult to explain
any extension of knowledge even by induction. Yet, whatever the
reason, things do stick together in coherent and many-propertied
clusters. The bond seems to be real when it is stated
'objectively,' not 'subjectively' -- as a property of the things
observed, not of the classes made by the mind itself. I take the
remark to be both true and important; and, moreover, that Mill
deserves credit for perceiving so clearly this weak joint in his
armour. His application, however, suggests, when he had hit upon
an apparent escape from his 'inextricable' difficulties, he was
too much relieved to work out its full effect upon his general
theory. The 'theory of kinds' is inserted rather than embodied in
his philosophy, and makes rents in the attempt to fill a gap. It
plays, however, so important a part in the doctrine that it
requires some further consideration.
    A real kind, we see, has two characteristics; it has
innumerable properties, and those properties are not 'derivable'
from the others. In fact, a derivative property would be merely a
modification of a primitive property. A geometrical 'kind,' a
curve of the second order, for example, has innumerable
properties, but they are all derivative from the simple
properties expressed in the axioms and definitions. They
reciprocally imply each other. But can we say the same of the
properties of a thing -- of a plant or of water or of an atom?
Here we have the distinction already noticed. The so-called
'thing' may be merely a collection of separate things, and we can
discover the 'laws' applicable to all by combining the laws
applicable to each. From a given 'collocation' we can infer past
or future 'collocations,' and one set of results can be added to
or superposed upon the other. But when we proceed to chemical or
organic compounds, we have 'heteropathic' laws. The compound may
be analysed into elements, but we cannot derive the properties of
the compounds from the properties of the elements. Hydrogen and
oxygen can be combined into the form of water; but we could not
infer the properties of water from the properties of the hydrogen
and oxygen taken apart. In organic compounds, the problem is
still more intricate. We have to consider a series of
inter-related changes taking place within the organism, and
dependent partly upon the 'environment' and partly upon the
complex constitution of the organism itself. It is a unit in so
far as all its properties manifest an organic law or a system of
organic laws. Individuals may differ from external causes as
plants, for example, in different soils, and in that case we may
regard the differences as simply derivative. Differences which
belong to the organic law itself indicate differences of kind;
and these are ultimate for us, so long as we cannot trace the way
in which they are dependent upon differences of constitution.
These, roughly stated, are the facts which Mill recognises. Now,
in any case whatever, we can only 'explain' a fact by assuming
both 'collocation' and 'causation'; or, in other words, we must
have a statement of facts and of laws. Our analysis of the
phenomena will in all cases come to showing how a given state
results from, or results in, a previous or succeeding state. If
new properties appear from the combination of simpler elements,
we should infer that they result, though we may be quite unable
in the existing state of knowledge to show how they result, from
the properties of those elements. The properties do not manifest
themselves, and are therefore not discoverable, till the
combination is formed; and are thus only known to us
'empirically.' No process of reasoning, that is, can be adduced
to show that they must result from the combination. But, in the
case supposed, we do not doubt that they do result, and we assume
that the elements had certain latent properties not previously
discoverable. This, however, is the point upon which Mill
diverges, owing, as I think, to his imperfect view of causation.
    The doctrine of 'kinds,' in fact, gives the answer to Mill's
old problem, why a single instance is sometimes conclusive,
whereas any number of instances may sometimes fail to give
certainty. It is this reciprocal connection between the
properties of a 'kind' which justifies the inference from one set
of attributes to another attribute -- the inference implied in
all induction. But Mill's interpretation of the fact seems
strangely inconsistent. His favourite instance is the black crow.
I have seen a million black crows. Can I say that the million and
oneth crow will be black? To answer this we must ask whether
blackness is a property of 'kind.'(79*) If the blackness be, 'as
it were, an accident,' or not a property of kind, it must, he
says, be a case of causation. If not a case of causation, it must
be a property of kind. Hence we have the singular result, that if
the coexistence be casual, it is caused, and if invariable, not
caused. As 'causation' means according to him simply
unconditional connection, the statement seems to be especially
paradoxical. It is, however, explicable.
    The blackness of the crow may be regarded as 'accidental,' if
it is due to the external cause. The crow, perhaps, has fallen
into a paint-pot. The blackness is 'caused,' then, by the
properties of paint and by the 'accidental' collocation. It is an
'accident' in the crow, though caused in respect of the general
arrangements of the universe. But why, if a property of 'kind,'
should it be called 'not caused'? Here we have a curious result
of Mill's view of causation. Our natural reply would be that the
colour is still caused as everything else is caused.(80*) We
assume, that is, that 'crow' implies such a constitution that
under a given environment crows will be black. Change something
outside the crow and he may turn white. Or find a white crow in
the same 'environment,' and we infer some difference in his
constitution. There is a relation, we assume, though we cannot
specify its nature, which determines the colour, and as in all
cases we have at once collocation and causation. Here is Mill's
peculiar difficulty. Causation, as he is profoundly convinced,
always means a beginning. It is only, as we have seen, concerned
with changes, not with persistence. Therefore, if two things,
like blackness and crowness, exist side by side, it is a case of
collocation, and consequently, as he supposes, not a case of
causation. He cannot recognise a reciprocal relation, although it
is clear that if one thing is found always to accompany another,
the argument is the same as though one always followed another.
Indeed, his whole theory of induction implies the possibility of
reasoning from one property or attribute to another. Make a
change in one and the other must be changed. He sees this clearly
in the case of organised bodies.(81*) In that case, he says,
there is a 'presumption' that the properties are 'derivable' and
therefore 'caused,' because there we have sequences or one
process following another. He thus seems to limit his 'natural
kinds' chiefly to chemical compounds. There we have properties
lying side by side and not 'derivable,' that is, not to be
inferred by us from the properties of the elementary
constituents. The very attempt to derive them is idle. As any
event may cause any other, however unlike, so any set of
properties may be simply stuck together. Bacon is again
reproved(82*) for assuming that 'every object has an invariable
coexistent.' The ultimate properties, so far as we can
conjecture, are 'inherently properties of many different kinds of
things, not allied in any other respect.' They simply lie side by
side, without reference to each other. Thus Mill pushes his
empiricism to assuming not only that our knowledge of properties
must rest upon direct observation, but that there is absolutely
no connection or 'cause' to be known. The 'kind' after all, which
was meant to be an essential bond, turns out to be itself a
purely arbitrary collection of attributes, and we have to ask
whether it does not lose all the significance which he attached
to it. The 'collocation' means that the attributes simply lie
side by side, and yet are always conjoined. The tie which
combines them is undiscoverable, and therefore for us
non-existent. It is, as he rightly insists, important that our
classification should correspond to natural kinds. 'Kinds,' he
says, are classes 'between which there is an impassable barrier';
the logical class is arbitrary, but the real class is an
essential fact, His illustration is remarkable. He holds that the
'species of plants are not only real kinds, but are probably all
of them real lowest kinds, infimae species,' and that further
subdivision would lead to no valuable results.(83*) The doctrine
that the species of botany must correspond to 'real kinds ' is
curious in a writer who was himself a botanist and familiar with
the difficulty of making absolute divisions between kinds. The
conflict with the conceptions implied in Darwinism is of the
highest importance.(84*) The distinction between 'kinds,'
according to Darwin, is not absolute, for it is the product of
gradual divergence from a single form. But, on the other hand,
the kinds existing at a given time are discrete. There are gaps
between them, as Mill remarks; though, in so far as they have a
common origin, not absolutely insuperable gaps. This implies that
the organism does not correspond to a mere aggregate of
disconnected attributes, so that the difference of kinds would be
simply a difference of more or less, and each type pass into the
other by imperceptible gradations. We are obliged to suppose a
system of reciprocal relations, so that any change in one organ
involves correlated changes in others; and thus species diverge
along different lines instead of remaining constant or simply
adding on new properties. Mill, it seems, has to admit of kinds
in order to account for the possibility of inference; but then,
as he wishes to avoid 'mystical bonds,' and inferences from
'definitions,' and the scholastic beggings of the question, he
declares the relation between the attributes to be 'accidental'
or 'uncaused.' Hence, though he sees the difficulty and
recognises the probability of 'causation' in organised bodies, he
really reduces the 'kind' to be a mere aggregate, and destroys
the very organic bond of which he is in need.

 VII. UNIFORMITY OF NATURE

    The effect of thus contra-distinguishing 'collocation' from
causation, and admitting that 'uncaused coexistences' cover a
large part of all observable phenomena, is to make the uniformity
of nature exceedingly precarious. Indeed, Mill denies it to be
conclusively proved. The chapter in which he sums up 'the
evidence of the law of universal causation' leads to remarkable
results. No one, he thinks, with a properly trained imagination
will find any difficulty in conceiving that in remote parts of
the universe 'events may succeed one another at random without
any fixed law'. He concludes by asserting that it would be 'folly
to affirm confidently' that the law does prevail in 'distant
parts of the stellar regions.'(85*) A truth which depends upon
locality might, for anything one sees, break down in Australia
and even at Paris as easily as at Sirius. Mill, accordingly,
reaches a thoroughly sceptical conclusion,(86*) and reduces the
evidence for universal causation to an induction per
enumerationem simplicem. The wider the generalisation, the
greater the efficacy of such induction, upon which depends not
only the law of causation but the principles of number and
geometry. If the 'subject-matter of any generalisation' be so
widely diffused that it can be tested at every time and place,
and if it 'be never found otherwise than true' its truth cannot
depend on any collocations, unless such as exist at all times and
places, nor can it be frustrated by any counteracting agencies
except such as never actually occur.'(87*) Now no exception to
the 'law of causation' has ever been found, and apparent
exceptions have only confirmed it. It is no doubt true that if a
law be universal, it will be confirmed by all our experiments;
but it hardly follows that, because all our experiments have
failed to detect an exception, it is true universally. All our
experiments have covered but a small fragment of nature, and they
do not justify us, as he expressly asserts, in reasoning about
the stellar regions. It is difficult, moreover, to see how an
'exception' could ever be proved, since, wherever we do not see a
'cause,' we can always suppose, and do in fact suppose, an
invisible cause. Finally, the theory of 'natural kinds,' as it
has now been interpreted, seems to fail us in our need. He takes
it to indicate, indeed, that there are connections in nature,
which, if known, would justify certain general inferences; but it
does not appear that we can know what are these connections, and
as, moreover, we have been carefully told that they are ultimate
or not 'derivative,' we have no right to be certain that they
will recur. We do not know, for example, whether blackness be a
property of kind. If we found a black crow among white ones, the
property would be casual, and therefore 'caused.' If we found a
race of white crows in Australia, we should simply say that there
was a kind hitherto overlooked.(88*) Such a discovery, he says,
is not at all incredible. It might be proved by the evidence of a
single credible witness. It merely supposes that there is a kind
with a different set of attributes, and as the attributes are in
no way 'derivative,' there is no improbability in this. The more
general the rule, however, the greater the probability of its
holding, because the greater the improbability of the exception
being overlooked. We should easily believe in white crows, but
not so easily in crows with a property 'at variance with any
generally recognised universal property of birds,' and still
less, if it were 'at variance with such a property of
animals.'(89*) We could hardly, that is, believe in crows with
the stomachs of wolves, or in crows without stomachs at all. But
the difficulty appears to depend upon nothing else than the
improbability that such animals, had they existed, would have
been unnoticed.
    Without trying fully to unravel this logic, we may notice one
characteristic. Mill, trying to refer everything to 'experience,'
has gone far to make experience impossible. What has dropped out
of this theory of knowledge is the constructive part. He
substitutes for organisation combinations of disparate 'things.'
He will admit of no logic, except that. of an external connection
of radically different objects. Attributes must be stuck together
without any reciprocal relations. All causation becomes in his
phrase 'collocation,' though he declares causation and
collocation to be not only different but mutually exclusive. His
one logical formula is the nota notae est nota rei ipsius.(90*)
Things are marks of each other, not implied by each other. He
forces this language even upon mathematics. Even a geometrical
'kind,' if we may use the word, an ellipse, or a curve of the
second order, is treated by the formula applicable to purely
empirical conjunctions. The equality of two straight lines, it
seems, is simply a 'mark' that if applied to each other they
would coincide; the fact that two things are sums of equals is a
'mark' that they are equal, and so forth.(91*) He would
apparently be inclined to say that a thing's existence is a mark
of its not being nothing. Thus, even the 'natural kind' becomes
merely a permanent combination. When the properties of a curve
are merely connected by 'marks,' it is no wonder that the
properties of crows should be mere bundles. If it is only on such
terms that we can thoroughly get rid of 'intuitions,' the
advantage is doubtful.
    I will venture to say another word upon the uniformity of
Nature difficulty. It is easy, says Mill, to conceive of things
happening at random. It is, indeed, in one sense perfectly easy.
'Raw' things, or unanalysed concrete events, do happen at random,
that is, without uniform antecedents. Nothing is easier than to
think of things without thinking of their causes. The primitive
mind, and even the cultivated mind, may simply watch the series
of events without trying to find any connection or indulging in
any reasoning. But this is quite different from thinking of
things as positively uncaused. A phenomenon suddenly intrudes
without warning. I may accept it without asking whence it comes,
or why. But there is no really positive meaning in the statement
that it is caused by 'nothing.' It does not imply a
contradiction, such as occurs when I put together the words
crooked and straight, round and square; but it represents no
intelligible meaning. It corresponds to a simple absence of
thought. When I speak of the uniformity of Nature, I mean simply
to indicate a condition of thinking about Nature at all. I may
cease to reason or to think; but if I think, I must think
coherently, and assume what has been called the 'Universal
Postulate.'(92*) The phrase seems to me to be inadequate; and at
any rate it is a postulate with this peculiarity, that we cannot
make any other. To deny it is to allow contradictory statements
on the most intimate tissue of our reasoning. It is as impossible
to do without it as to do without the principle of contradiction
in pure logic. It helps us to no positive statement; but it is a
warning that our statements must be coherent. Hence, we must
allow the mind to have this modest capacity for working up its
experience. If it starts from so unprejudiced a point of view as
to admit contradictions, or allow of inconsistent statements
about things, it will never be able to get anywhere, and when
Mill has reduced all our knowledge to the relations between ideas
in the mind, it is really quite inconsistent to allow the mind no
power of putting ideas together. Without such a power it is
difficult to say what is even meant by the perception of
'coexistences' and 'sequences.' The progress of knowledge, then,
must be understood as corresponding to the process by which the
chaos of impressions and ideas is gradually reduced to cosmos;
and as starting from a position in which no cause has been yet
discovered for great masses of facts, not from a position in
which 'no cause' is an equally probable alternative with 'some
cause.' To reason at all about facts is to arrange them in order
of causation, and to suppose them as having certain time- and
space-relations. To get behind that primitive germ of reasoning
is really to make logic impossible from the start. Mill's dread
of a priori intuitions and necessary results thus led him into
perfectly gratuitous difficulties. Granting the 'necessity' of
arithmetic or geometry, it is still a hypothetical necessity. It
can never take us beyond experience. Such theorems cannot tell us
of the existence of a single thing or of its nature. They can
only say that if we see things in space they will have certain
relations which are deducible from the special confirmation.
Without that power the universe would be undecipherable, but with
it our knowledge still has throughout a completely empirical
base. Not a single statement of fact can be made which is not
derived from, and justified by, experience; nor can our
experience ever get beyond saying that any given section of the
whole is developed out of, and develops into, preceding and
succeeding sections.

 VIII. THE FOUR METHODS

    I have dwelt upon these misconceptions to show why Mill was
driven in defence of experience to assume the burthen of proving
paradoxes which would be destructive to our very capacity for
obtaining experience. Mill prided himself with some reason on his
'four methods.' Although they have been severely criticised,(93*)
they have, I take it, a genuine value; and, if we ask how they
can be valuable in spite of his errors, a satisfactory answer may
perhaps be given. In the first place, his assumptions represent
one genuine 'moment' in all reasoning about facts. The primitive
intellect may be supposed to regard facts as simply conjoined,
and to be guided by 'association of ideas.' The early
generalisations of which Mill speaks -- 'fire burns,' 'water
drowns,' and so forth are really of this kind, and are apparently
formed even by dogs and monkeys. Mill is quite right, moreover,
in holding that a purely empirical element runs through the whole
fabric of knowledge. The error, I think, is in his failure to
allow for the way in which it is modified in scientific
construction. The ultimate element out of which that construction
is developed is always an observation of fact, but the fact means
a definite relation of time and space. We start from a 'fact,'
but it is not as a simple unanalysable unit, but as something
which already is the base of a relation. The unit which
corresponds to the final cell out of which tissue is composed is
not properly a fact, but a 'truth.' We do not say simply 'this
is,' but this is so and so, and has a certain order and
configuration. This is gradually elaborated into physical science
by the help of the geometrical and numerical relations already
implied. Thus, causation, or the connection between phenomena, is
not simple collocation, but supposes continuity. The
unconditional sequence which Mill identifies with 'causation'
does not, and cannot, give the 'cause,' though it does indicate
'causal connection.' So long as two things are entirely separate
and distinguishable, we cannot say, in the full sense, that one
is the cause of the other; but the connection, if proved, proves
that there is a cause which may or may not be discoverable. Brown
was right in thinking that something was still wanting, though
his mode of filling the gap by an intuition was erroneous. Mill's
answer that the 'intuition' was needless left the difficulty
where Hume had put it. Two facts are supposed to be unrelated and
yet always combined. That states a difficulty, and only
pronounces it to be insoluble. It has, in fact, to be surmounted
by scientific hypotheses. Thunder and lightning, for example, are
causally connected, but not so that lightning can be properly
called the cause of thunder. They are regarded as due to a common
cause to the processes which we call electric disturbance, and so
forth. We cannot give the 'law' or state the casual connection
adequately, but we regard them as indicating some common element,
which is continuous and capable of being described in terms of
pure number and geometry. Hence any observation, as soon as we
begin to reason, may be regarded as a particular case of some
general law, or rather, as being conceivably a case of an
indefinite number of laws. Not only so, but any law under which
it may be arranged is 'necessary' if all the conditions be
restored. The process by which we select one of the possible
formula, therefore, comes to eliminating all the formula which
are incorrect when various conditions are altered. We all along
assume that some coherent system of 'laws' is possible, or that
the rule is there if only we can discover it. If lightning goes
once with thunder, we are entitled to say not only that it may go
with thunder hereafter, but that it must go with thunder under
the same conditions. Therefore the simple inference from an
empirical conjunction is justified by the 'law of causation' or
the 'uniformity of nature.'
    Now, Mill's 'four methods' are applicable to the merely
empirical conjunctions, which form a large part of our knowledge,
and are implied in every stage. The methods do, in fact, I take
it, form an approximately accurate mode of dealing with such
knowledge. His cases are, for the most part, selected from the
sciences, chemistry in particular, where in point of fact our
knowledge is still purely empirical, and we can only assert a
collocation, or sequence, without bringing it under a more
general rule. He also observes, and the remark must be
remembered, that he is trying to give a method of proof, rather
than of discovery.(94*) If the scientific theory be true, these
purely empirical truths will hold good, although from them alone
the theory might not have been discoverable. The phenomenon which
we call the fall of a stone will be presented when an unsupported
stone is near the earth, although the law of gravitation requires
an application of methods not summed up by simple observation of
conjoined phenomena. The most unsatisfactory part of the 'four
methods' results from this view.(95*) The process of discovery is
not sufficiently represented by the case of A occurring with or
without B. The sciences which have risen to be quantitative
advance by showing how a variety of cases can be brought within
some general and precise formula, and every approximation to, or
deviation from, the law be exactly measured. Mill pays too little
attention to this essential characteristic, partly, perhaps,
because he considers mathematics as simply one part of the
'inductive' or empirical sciences.
    The final position may be shortly illustrated by Mill's
relation to his contemporaries. It will show briefly what were
the alternatives between which he had to choose, and that, if
that which he chose leads to error, there were at least equal
errors on the other side. Mill frankly states in his preface that
but for Whewell's History of the Inductive Sciences the
corresponding part of his own book 'would probably not have been
written.' He remarks with equal candour that Sir John Herschel,
in his Discourse on the Study of Natural Philosophy,(96*) had
recognised the four methods. Herschel, however, was his only
predecessor, and a more distinct and articulate exhibition of
their nature was desirable. Herschel and Whewell had graduated at
Cambridge in 1813 and 1816. Both of them were able
mathematicians, and, with their contemporary Babbage, had done
much to introduce at their university the methods of analysis
developed on the Continent. The university was gradually roused;
Herschel won a great name in astronomy, and Whewell took in
earlier life a very active part in promoting scientific studies
in England.(97*) Both of them had much closer acquaintance with
the physical sciences than Mill, for whom they provided a useful
store of materials. Herschel, though a friend of Whewell,
approximates to Mill. A 'famous' review of Whewell's two books in
the Quarterly of June 1841(98*) gives his position; but although
he seems to perceive the source of Whewell's weakness, he
scarcely comes to close quarters. It is enough for my purpose to
speak briefly of the points at issue between Mill and Whewell.
Whewell, like his most eminent contemporaries at Cambridge, was
becoming aware that German speculation could no longer be
overlooked. Herschel was son of a German; and Whewell's friends,
Julius Hare (1795-1855) and Connop Thirlwall (1797-1875) were
taking up the study of German. Their translation of Niebuhr's
History of Rome (1828-1832) marked an epoch in English
scholarship. Whewell meanwhile had read Kant, and been greatly
impressed. Especially, as he says, he accepted Kant's theories of
space, time, and, in some degree, causation, although he differed
from Kant's doctrine as to other so-called 'fundamental
ideas.'(99*) He 'gladly acknowledges,' too, his obligations to
the Scottish school.(100*) In fact, it may be said that, like Sir
W. Hamilton, he made a compromise between two modes of thought
which very rapidly diverge from each other. Whewell begins his
Philosophy of the Inductive Sciences by considering the
fundamental antithesis of philosophy, which corresponds to the
distinction between thoughts and things, necessity and
experience, object and subject, and so forth. Time and space are,
in his phrase, 'fundamental ideas,' upon which are founded the
mathematical sciences. But there are other 'fundamental ideas' --
'cause,' 'media,' 'polarity,' 'chemical affinity resemblance,'
'excitability,' and 'final cause' -- which in succession become
the foundation of various sciences.
    These fundamental ideas are, as he admits, something like
'innate ideas,' except that they can be 'developed.' They can
somehow be 'superinduced upon facts,' and are not 'generated by
experience.' I shall not attempt to explain a theory which seems
to be radically incoherent, and which made no converts. It will
be quite enough to notice two of the points of collision with
Mill. Mill and Whewell agree(101*) that the 'first law of motion'
which asserts the uniform rectilinear motion of a body not acted
upon by a force was unknown till the time of Galileo. Whewell
admits further that, 'historically speaking,' it was made 'by
means of experiment.' We have, however, attained a point of view
in which we ae that it might have been certainly known to be
true, independently of experience, Mill naturally ridicules this
doctrine, according to which we burden ourselves with 'truths
independent of experience' and yet admit that they were proved
'by (or 'by means of') experiment.' The history is admitted on
both sides. It had been observed that the motion of all bodies
ceases unless they receive a new impulse. The statement was true,
though vague, for all bodies upon the earth. But the progress of
astronomy and exact sciences required a more precise statement.
Science has not simply to recognise that motion declines, but to
show at what rate, and under what conditions it declines. Then,
as we cannot measure 'absolute motion,' or assign any fixed point
in space, we can obtain no rule as to absolute motion. If we
assume, however, that we have to account not for motion but for
change of motion, we can get a consistent 'law' which at once
gives a sufficient account of many observed phenomena. We proceed
to define force as the cause of change in motion. Then it becomes
an identical proposition that all change of motion implies force,
or that bodies not acted upon continue to move uniformly. Thus
the definition of force takes the shape of an a priori axiom as
to force. We imagine that instead of simply co-ordinating our
experience we are 'applying a fundamental idea' to it, the idea,
namely, of a 'cause' or 'force.'(102*) The axiom is not
'independent of experience.' Rightly understood, the whole
process is one of interpreting experience. Mill, however, is
hardly correct in saying that the law was proved by experiment.
We cannot observe a 'force' apart from the moving body. Force is
one of Bentham's 'fictitious entities,' a word which enables us
to state the relations of moving bodies accurately. It harmonises
our conceptions. The old belief that all motions stop is not
disproved by discovering cases in which force is absent, but by
postulating the presence of force wherever we find change of
motion. The real proof is not in direct experiment but in the
harmonising of an indefinite number of complex statements when
once the principle is systematically applied. It can reveal no
fact to us, for nothing but experience can show that there are
such things as the planets fortunately are, bodies moving freely,
so as to illustrate the law continuously. Mill puts the first law
of motion on a level with the law that the period of the earth's
rotation is uniform. Both 'inductions,' he says, are accurately
true.(103*) In fact, however, the earth's motion is not
absolutely uniform, a truth which we discover by applying the
laws of motion, though no direct experiment could exhibit the
fact. The law of motion has the authority derived from its
rendering possible a consistent interpretation of experiences,
whereas the earth's rotation is simply a particular fact which
might change if the conditions were altered. The 'law' implies,
therefore, a reconstruction of experience not given by simple
observation.
    This applies to a controversy between Mill and Whewell as to
Kepler's great discoveries. They both accept the familiar facts.
Kepler's problem was to show how a simple configuration of the
solar system would present the complex appearances which we
directly observe. The old observations gave approximately correct
statements of the movements of the planets, assuming the earth to
be fixed, or, as we may say, neglecting the consideration of its
motion. His theory shows how the apparent movements must result
if we suppose the sun to be fixed, or rather (as the sun is not
really fixed) if we measure from it as fixed. Whewell treats this
as a case of 'induction.' It illustrates what he calls the
'colligation of facts' -- a happy phrase, accepted by Mill, for
the arrangement of facts in a new order, and the application to
the facts of the appropriate conceptions; in this case, of the
theorems of conic sections and solid geometry. The argument takes
the form of a discussion as to whether this should be called
induction or an operation subsidiary to induction.(104*) Kepler,
as Mill urges, was simply describing facts. He discovered a fact
in which all the positions of the planet agreed -- namely, that
they were in an ellipse. If he had been somewhere in space, or
the planet had left a visible track, he might have actually seen
it to be an ellipse. He had only to 'piece together' his
observations, as a man who sails round an island discovers its
insularity. The only induction, then, was that as Mars had been
in an ellipse he would stay in an ellipse. Apart from the verbal
question whether the process be rightly called induction or
subsidiary to induction, the real issue is in Mill's complaint
that Whewell supposed a 'conception to be something added to the
facts.' The conception, Mill admits, is in the mind, but it must
be a conception of 'something in the facts.' The ellipse was in
the facts before Kepler saw it. He did not put it, but found it
there. Whether Kepler's process was inductive or deductive or
subsidiary, it was an essential part of scientific investigation.
The man of science must, as Mill truly says, interpret the facts,
and nothing but the facts; he must also, as Whewell truly
replies, 'colligate' or arrange the facts in a new order. The
constructive process which justifies me in saying this is an
island, or this is an ellipse, is precisely what makes scientific
knowledge possible, and involves something more than a mere
putting together of raw fact. Every fact, as Whewell sees, may be
regarded as a case of countless laws, each of which may be true
under appropriate conditions. To eliminate the irrelevant, to
organise the whole system of truths, so as to make the order of
nature (as Mill forcibly says (105*)) deducible from the smallest
possible number of general propositions, is the aim of science;
and Mill obscures this so far as he regards such operations as
Kepler's as mere observations of fact, in such a sense as to omit
the necessity of a new organisation of the data.
    I have gone into some detail in order to show what was the
essential characteristic of Mill's doctrine, which was itself, as
I have said, an explicit statement of the principles implicitly
assumed by his predecessors in the same school. To do him full
justice, it would be necessary to show what was the alternative
presented by his opponents. The Scottish writers and Whewell
brought back 'innate ideas,' or endeavoured to connect knowledge
by beliefs and intuitions arbitrarily inserted into the fabric as
a kind of supernatural revelation. To explain these intuitive
dogmas into effects of 'association' was the natural retort.
Meanwhile the transcendental school was taking the bolder line of
rejecting experience altogether, treating it with contempt as a
mere rope of sand, and inferring that the universe itself is
incarnate logic -- a complex web woven out of dialectic, and
capable of being evolved from mixing 'is' and 'is not.' To Mill
this appeared rightly, as I should say, to be mysticism and
ontology, or a chimerical attempt to get rid of the inevitable
conditions of all knowledge of reality. The real problem of
metaphysics appears to be the discovery of the right method of
statement, which will explain what appeared to be the insoluble
antithesis between empiricism and intuitionism (to take Mill's
phrase), and show that they are attempts to formulate correlative
and essential truths.

 IX. THE MORAL SCIENCES

    Happily, philosophical theories are not really important
solely as giving tenable and definitive results, but as
indications of the intellectual temperament of different schools,
and of the methods of reasoning which they find congenial.
Without further disquisition, I shall conclude by indicating
briefly Mill's application of his principles to the 'Moral
Sciences.' This is the subject of the last book of his treatise,
and represents, as we have seen, the purpose of the whole. As,
however, the full application will appear hereafter, I may here
confine myself to certain critical points. Mill begins of course
by arguing that the 'Moral Sciences' are possible, and are to be
created by applying the method of the physical sciences. This
suggests the free will difficulty. The doctrine of 'philosophical
necessity' had 'weighed on his existence like an incubus' during
his early depression.(106*) He escaped by the solution which now
forms a chapter in the Logic. He discovered that the Hume and
Brown theory removed the misleading associations with the word
'necessity.' It would be truer, he thinks, to say that matter is
free than that mind is not free.(107*) The supposed external
'tie' which binds things together is a nonentity. In practice,
however, Owen and his like had become fatalists rather than
necessitarians. Holding that character is formed by
circumstances, they had forgotten that our own desires are part
of the 'circumstances,' and therefore that the mind has the power
to co-operate in the 'formation of its own character.' This, Mill
thinks, is the ennobling belief which is completely reconcilable
with the admission that human actions are caused, although the
two doctrines had been on both sides regarded as incompatible.
Upon this endless controversy I can only suggest one hint. Mill,
I think, was right in saying that the difficulty depends on the
confusion of 'determinism' with 'fatalism'. that is, with the
belief that the will is coerced by some external force. But he
does not see that his doctrine of causation always raises the
difficulty. He orders us to think of the succession of ideas as
due simply to association, as in the external world events are to
be regarded as simply following each other; and in either case it
is impossible to avoid the impression that there must be some
connecting link which binds together entirely disparate
phenomena. We cannot help asking why 'this' should always follow
'that,' and inferring that there is something more than a bare
sequence. The real line of escape is, I think, shown by an
improved view of causation. If we hold that the theory of cause
and effect simply arises from the analysis of a single process,
we need no external force to act upon the will. There is no
'coercion' involved. Given the effect, there must have been the
cause; as given the cause, the effect must follow. 'All the
universe must exist in order that I must exist' is as true as
that 'I must exist if all the universe exists.' There is not a
man plus a law, but the law is already implied in the man; or the
distinction of cause and effect corresponds to a difference in
our way of regarding the facts, and implies no addition to the
facts. I must not, however, launch into this inquiry. I only note
that Mill's view is connected with his favourite principle of the
indefinite modifiability of character.(108*) To Mill, as to his
father, this seemed to hold out hopes for the 'unlimited
possibility' of elevating the race. If J. S. Mill denied 'the
freedom of the will,' or, rather, the existence of 'will' itself
as a separate entity, actually originating active principles, he
admitted that the desires erroneously hypostatised as 'will'
could work wonders. As the causal link between events is a
figment, so, in the sphere of mind, we are bound by no fixed
mysterious tie. He thus escapes from the painful sense of
coercion by holding that an infinite variety of results is made
possible by the infinite combinations of materials, though, in
each case, there is a necessary sequence. Association, in fact,
is omnipotent. As it can make the so-called necessary truths, it
can transform the very essence of character. Accordingly the
foundation of the moral sciences is to be found in the
psychology, for an exposition of which he refers to his father,
to Mr Bain, and to Mr Herbert Spencer.(109*) He thus drops,
consciously or not, the claim of treating metaphysical doctrine
as common ground, and assumes the truth of the association
doctrine. To pass from these principles to questions of actual
conduct requires a science not hitherto constructed -- the
science, namely, of human character, for which he proposes the
name Ethology. This, as we have seen, occupied his thoughts for
some time, till it was ultimately dropped for political economy.
The difficulty of forming such a science upon his terms is
obvious. It holds an ambiguous place between 'psychology' and the
'sociology' which he afterwards accepts from Comte; and as
Professor Bain remarks, his doctrine would not fit easily to any
such science. He has got rid of 'necessity' only too completely.
In fact, his view of the indefinite power of association, and his
strong desire to explain all differences, even those between the
sexes, as due to outward circumstances, seem to make character
too evanescent a phenomenon to be subjected to any definite
laws.(110*) Ethology, however, is taken by him to be the science
which corresponds to the 'art of education,' taken in its widest
sense, and would, if constructed, be a 'deductive science,'
consisting of corollaries from psychology, the 'experimental
science.'(111*) The utility of such a science from his point of
view is obvious. It would be a statement of the way in which
society was actually to be built up out of the clusters of
associated ideas, held together by the unit Man.
    His method in 'moral science' follows the lines now laid
down. All inference, as he has urged, consists of 'inductions'
and 'the interpretation of inductions.'(112*) Deduction is the
application to new cases of the laws observed in previous cases.
As our knowledge of such laws multiplies, science tends to become
more deductive. But the deduction is still an induction; and the
true antithesis is not between deductive and inductive but
between 'deductive and experimental.'(113*) Deductive reasoning,
that is, simply applies a previous induction; but reasoning
becomes 'experimental' when we have to interrogate nature for a
fresh rule. This has an important bearing upon the next step.
Social phenomena of all kinds are so complex that we cannot apply
his four methods. They belong to the region (in his phraseology)
of the 'intermixture of laws' and 'plurality of causes';(114*)
and though the phrases be inaccurate, the example certainly
illustrates their plausibility. Experimental reasoning is thus
impossible. We have, therefore, to fall back upon the 'deductive'
method, which, indeed, would lead to mere 'conjecture' were it
not for the essential aid of Verification.(115*) The meaning of
this is explained in two chapters really directed against
Macaulay and James Mill, and giving the theory which had been
suggested by their controversy.(116*) Macaulay used the
'chemical' method. If men in society formed a new product
differing from the individual man, as water from oxygen and
hydrogen, or, in Mill's phrase, if the social union afforded
'heteropathic' laws, we should have to study social science apart
from the science of individual human nature. But as men even in
society are still men, the social law is derivable from the laws
of individual nature. It is a case of 'composition of causes.'
Now the purely empirical reasoner neglects this obvious fact. He
reasons from immediate experience without connecting his
conclusions with psychology. He argues offhand that because the
English have flourished under the old parliamentary system,
therefore the old parliamentary system was perfect. That gives
the crude empiricism preached by Macaulay in the name of Bacon.
James Mill, on the contrary, represents the 'geometrical method.'
He argued about politics as if all constitutional questions could
be settled like a geometrical problem by appeals to a single
axiom. Therefore a doctrine applicable to the immediate question
of parliamentary reform was put forward as a general theory of
government. Mill tells us in the Autobiography(117*) that his
reflection upon this controversy led to a critical point of his
doctrine. Science must be deductive, when the effects are simply
the sum of those due to the operating causes; inductive, when
they are not the sum, that is, when 'heteropathic' laws appear.
Hence, he inferred, politics must be treated deductively, though
not as his father had done, geometrically.
    Both the criticisms are much to the purpose. Here I need only
remark one point which affects Mill's later conclusions. Was
Mill's inference correct? Is it true that the social phenomena
represent simply the sum of the individual actions? Undoubtedly,
there is a good deal to be said for it. Society does not exist
apart from the individuals of which it is constructed. Moreover,
in a great many cases, if we know the average character of an
individual, we can deduce the character of a number of
individuals. The bulk of what is called knowledge of the world is
made up from more or less shrewd conjectures as to the motives of
the average man. If we know what the average man thinks, we can
guess what will be the opinion of a majority of the House of
Commons. There are, however, two points which are taken for
granted. In the first place, if we are to deduce the social
phenomena from the individual, we must know the individual, who
is already a tolerably complex product. In Mill's language, we
require an ethology. and the name already indicates a difficulty.
Can we consider the average man to be a constant? or must we not
take into account the fact that he is also a product of society,
and varies upon our hands as society develops? And beyond this
there is the further question, whether, in so far as society can
be properly regarded as an 'organism,' we can fully explain the
laws of social combination by considering the laws of individual
character. Are not the two sets of laws so intricately combined
and blended that the analysis of a society into separate
individuals becomes necessarily illusory? Can we explain the
reciprocal actions and reactions of a social body by simply
adding together the laws of individual conduct? These questions
will meet us in considering Mill's practical application of his
theories. They amount to asking whether 'sociology' can be
constituted from a purely 'individualist' basis, and Mill's view
of sociology is a vital point in his doctrine. The name had
already been invented by Comte, and Mill at this time was greatly
influenced by Comte, and especially was kindled to enthusiasm by
the last two volumes of the Philosophie Positive, containing a
connected view of history. Although Mill had, as he says, worked
out his theory of induction before reading Comte, he owed a great
deal, as he fully acknowledges, to Comte's philosophy. The two
lines of thought, however, could never completely coalesce, and
the result appears in this part of Mill's book.
    Admitting a deductive method to be necessary, Mill
distinguishes the 'direct' and the 'inverse methods.'(118*) The
direct method is that of reasoning from one 'law of human
nature,' considering, of course, the outward circumstances. This
justifies the system of political economy, which considers men as
acting solely from the desire of wealth. He points out that
fallacies may here arise from applying to one state of society
what is true of another; but he also holds that one who knows the
political economy of England, or even of Yorkshire, knows that of
all nations, if he have good sense enough to modify his
conclusions.(119*) Mill admits fully that this method can only
give us 'tendencies' -- results which are true if certain
conditions, never fully assignable, are actually secured; and
that it therefore requires to be constantly checked by
verification, that is, by showing that the results are confirmed
by direct observation. The admission, however, that such a method
is in any case admissible separates him from Comte, who held that
we must in all cases start from historical generalisations, not
from independent 'laws of human nature.'(120*) Comte, in fact,
rejected Mill's psychology and political economy as
pseudo-sciences, and the difference is really vital. Mill,
however, was prepared to accept much of Comte's teaching, and in
particular allows the legitimacy of the 'historical method.' Upon
this he writes a chapter,(121*) which shows no want of
appreciation of Comte or of the great French writers by whom, as
his Dissertations show, he had been deeply impressed.(122*) He
complains of the English want of interest in such matters. They
know nothing in French literature except the novels of Balzac and
Eugène Sue, and are not aware that the French historians greatly
surpass even the Germans.(123*) He points out the importance of
the conception of progress and of the great modifications of
human character. Still, he charges the French with a
misconception. History can never give us a 'law of nature,' only
'empirical laws,' which are not scientific till duly based upon
psychology and 'ethology.' Comte alone has seen the necessity of
a deeper foundation; and he proceeds to give an admiring account
of some of Comte's conclusions. Especially he insists upon the
necessity of connecting the social phenomena with the
intellectual development of mankind. This Comte alone has
attempted systematically, and he ends by emphatically adhering to
the doctrine of the three stages -- theological, metaphysical,
and positive. The essential difference, however, remains. Comte
held that we must not explain humanity by man, but man by
humanity.(124*) To Mill, of course, this savoured of mysticism.
In any case, it marks the divergence of the two: Mill is a
thorough individualist. He thinks it absolutely necessary to base
sociology upon 'ethology,' that is, a theory of the individual
character, and this again must be based upon psychology.
Sympathising with Comte's general purpose, and warmly admiring
some of his results, Mill adheres to a doctrine which was sure to
bring him into conflict with his master. To create the moral
sciences, we must start from a scientific psychology. This means
that we must work on the lines of Hartley, James Mill, and his
own younger contemporaries, Professor Bain and Mr Herbert
Spencer. The corollary from psychology is ethology, or the
science of character. This view does not conflict with the
admission of the great importance of some historical method. At
present, it needs only to be said that Mill accepts that method
very cordially, subject to two conditions. First, he holds that
some social sciences -- political economy being, in fact, the
only one to be clearly specified -- can be deduced from ethology
and psychology independently of history, though requiring
verification from history. Secondly, he holds that the historical
method cannot reveal true 'laws of nature' unless it is properly
connected with psychological data. How far Mill really
appreciated the significance of the historical method, or
perceived its true relation to other departments of thought, must
be left for consideration.

NOTES:

1. Autobiography, p. 226.

2. Logic, p. 389 (bk. iii. ch. xxi, section 1). I quote from the
popular edition of 1898. Book, chapter and section are generally
applicable to former edition.

3. See letter in note to chapter upon Mill in Taine's History of
English Literature.

4. James Mill's Analysis, i. 352 n.

5. See an interesting article in G. Croom Robertson's
Philosophical Remains (1894), pp. 28-45.

6. Logic, Introduction, section 5.

7. Ibid., p. 29 (bk i, ch. iii, section 1).

8. Ibid., p. 8 section 7.

9. See John Grote's Exploratio Philosophica (1865), p. 209 n.
This book is, I think, by far the most interesting comtemporary
discussion of Mill, Hamilton, and Whewell. It was, unfortunately,
desultory and unfinished, but it is full of acute criticism, and
charmingly candid and modest. Mill's Logic is especially
discussed in chapters viii and ix. Grote holds, and I think
truly, that Mill's attempt to divide metaphysics from logic leads
to real confusion, and especially to an untenable mode of
conceiving the relation between 'things' and thoughts. I cannot
discuss Grote's views; but the book is full of interesting
suggestions though the result are rather vague. See the excellent
account of Grote by the late Croom Robertson in the History of
National Biography.

10. Mill, in his review of Whately, refers to Du Trieu (whose
treatise had been privately printed by him and his friends),
Crakenthorpe and Burgersdyk; and in the Examination of Hamilton's
Philosophy (ch. xxii) quotes also Sanderson, Wallis, Aldrich,
Keckermann, Bartholinus, and Du Hamel as the 'authorities nearest
at hand'. There is nothing, as I am told by the learned,
exceptionally interesting in Du Trieu; and the selection was
probably accidental.

11. Logic, p. 13 (bk. i, ch. ii, section 1).

12. Ibid., p. 29 (bk. i, ch. iii, section 1).

13. Ibid., p. 49 (bk. i, ch. iii, section 15).

14. Ibid., p. 35 (bk. i, ch. iv, section 6).

15. Ibid., p. 38 (bk. i, ch. iv, section 7).

16. Logic, p. 40 (bk. i, ch. iv, section 8).

17. Ibid. p. 41 (bk. i, ch. iii, section 9).

18. Logic, p. 43 (bk. i, ch. iv, section 10).

19. Ibid., p. 68 (bk. i, ch. v, section 6).

20. Logic, p. 61 (bk. i, ch. v, section 3).

21. Ibid., p. 63 (bk. i, ch. v, section 4).

22. It would be interesting to compare this part of Mill with the
corresponding part of Hume's Treatise. Hume, like Mill, begins by
accepting causation as one of the relations involved, and then
explains it as merely derivative. His treatment of relations
generally, especially the division of relations into the two
classes, which do or do not depend upon the 'ideas' themselves,
has a bearing upon Mill's doctrine too intricate to be considered
here. [Treatise of Human Nature, pt. vi. sec. 1.] I do not think
that Mill was very familiar with Hume's writings. A note to the
concluding chapter of the Examination of Hamilton seems to imply
that he was not acquainted with the Treatise; nor does he appear
from his posthumous Essays to have studied Hume's writings upon
theology. Whether T.H. Green was right in holding that Hume had a
more distinct view than his successor of some metaphysical
difficulties, I need not inquire.

23. Logic, p. 70 (bk. i, ch. v, section 7).

24. Ibid. p. 434 (bk. iv, ch. iii, section 2 n.).

25. Logic, p. 132 (bk. ii. ch. v, section 4).

26. Especially the early review of Whately.

27. This suggests a parallel to the old English system of
pleading -- as a preparatory process for bringing out the issues
really involved in a dispute -- which is said to have been
thoroughly logical, though it became excessively cumbrous and
technical.

28. Logic, p. 327 (bk. v, ch. vi, section 3). So in Examination
of Hamilton, ch. xxii., 'The syllogism is not the form in which
we necessarily reason, but a test of reasoning.'

29. James Mill's Analysis, ii. 427.

30. Logic, p. 131. (bk. ii, ch. iii, section 5).

31. Logic, p. 72 (bk. i, ch. vi, section 2).

32. Ibid. p. 113 (bk. ii, ch. ii, section 5).

33. Autobiography, p. 181. The passage to which Mill refers is
apparently that in Stewart's Works, iii, 24-36 and 113-52.
Stewart quotes a passage from Dr Beddoes' Observations on the
Nature of Demonstrative Evidence (1793), which anticipates Mill's
view that the 'mathematical sciences are sciences of experiment
and observation, founded solely on the induction of particular
facts.' Stewart professes to follow Locke (see Locke's Essay, bk.
iv, ch. xii, section 15), and gives some references to other
discussions on the questions.

34. Logic, p. 94 (bk. i, ch. viii, section 5).

35. Logic, p. 125 (bk. ii, ch. iii, section 3).

36. Logic, p. 126 (bk. ii, ch. iii, section 4).

37. Ibid. p. 107 (bk. ii, ch. i, section 3).

38. Whiston (Memoirs, i, 35) reports that Newton saw by
intuition, or previously to formal demonstration, the equality of
all parallelograms described about the conjugate diameters of an
ellipse. Most of us can only learn the fact by painful
construction.

39. Hume's Works (Grose and Green), ii, 432 and iv, 134. Hume's
statement is criticised by G.H. Lewes in his Problems, etc. i,
391, but, I think, on an erroneous interpretation.

40. Logic, p. 149 (bk. ii, ch. v. section 1).

41. Ibid. p. 151 (bk. ii. ch. v. section 4).

42. Ibid. p. 147 (bk. ii. ch. v. section 1).

43. Ibid. p. 183 (bk. ii. ch. vii section 5). In the Examination
of Hamilton he is less confident. It is 'not only inconceivable
to us, but inconceivable that it should be mad conceivable' that
the same statement should be both true and false (ch. vi. p. 67).
Afterwards (ch. xxi. p. 418) he will only decide that such laws
are now 'invincibly' laws of thought, though they may or may not
be 'capable of alteration by experience.'

44. Logic, p. 148 (bk. ii. ch. v. section 1).

45. Ibid. p. 168 (bk. ii. ch. vi. section 2).

46. Ibid. p. 400 (bk. iii. ch. xxiv. section 5).

47. Ibid. p. 401 (bk. iii. ch. xxiv. section 5).

48. Ibid. p. 170 (bk. ii. ch. vi. section 3).

49. Ibid. p. 167 (bk. ii. ch. vi. section 2).

50. Logic, p. 212 (bk. iii. ch. v. section 1).

51. Logic, p. 401 (bk. iii. ch. xxiv. section 6).

52. Logic, fourth edition, i. 356 (bk. iii. ch. v. section 1).
This phase is omitted in the last edition (p. 211), but the
meaning is apparently not altered.

53. Ibid. p. 399 (bk. iii. ch. xxiv. section 5).

54. See Logic, p. 177 (bk. ii. ch. vii. section 3), and p. 493
(bk. v. ch. ii. section 3).

55. Ibid. p. 370 (bk. ii. ch. xxi. section 1).

56. Logic, p. 206 (bk. iii. ch. iii. section 3).

57. Ibid. p. 213 (bk. iii. ch. v. section 2).

58. Logic, bk. iii. ch. v.

59. Ibid. p. 217 (bk. iii. ch. v. section 3).

60. Logic, p. 221 (bk. iii. ch. v. section 5).

61. Ibid. p. 227 (bk. iii. ch. v. section 8).

62. Ibid. p. 224 (bk. iii. ch. v. section 7).

63. Logic, p. 243 (bk. iii. ch. vi. section 1).

64. Logic, p. 245 (bk. iii. ch. vi. section 2).

65. Grove's work was first published in 1846, i.e. after the
first edition of the Logic.

66. Logic, fourth edition, p. 477 (bk. iii. ch. x. section 4). In
the eighth edition this passage was suppressed, and Mill
discusses the theory of 'conservation or persistence of force,"
as he calls it, in an earlier section. -- Logic, p. 228 (bk. iii.
ch. v. section 10).

67. Logic, p. 501 (bk. v. ch. iii. section 8).

68. See, for example, his criticism of a 'luminiferous ether' in
answer to Whewell, Logic, p. 328 (bk. iii. ch. xiv. section 6).
He agrees here with Comte (Phil. Positive, ii. 639), whom he
perhaps follows.

69. See especially the chapter on causation in the Examination of
Hamilton.

70. Tyndall, e.g., in his Heat as a Mode of Motion, quotes
Bacon's anticipation. It is summed up by Whewell (Phil. Ind. ii.,
Sciences, ii. 239) in the statement that the 'form of heat is an
expansive, restrained motion, modified in certain ways, and
exerted in the smaller particles of the body.'

71. Logic, p. 500 (bk. v. ch. iii. section 7).

72. Logic, p. 288 (bk. iii. ch. x. section 3).

73. Logic, p. 500 (bk. v. ch. iii section 7). It may be noted
that Whewell (in 1847) equally regards Bacon's theory as a
complete failure. He thinks more favourably of an 'imponderable
fluid.' Mill, therefore, had good authority as to the failure.
The modern doctrine, says Lord Kelvin (Encycl. Britannica), was
established about 1851. See Huxley on the 'Progress of Science'
(Essays, i. 86) for Whewell's treatment of Bacon's guess.

74. Logic, p. 226 (bk. iii. ch. v. section 7).

75. Logic, p. 306 (bk. iii. ch. xii. section 2). See Chalmer's
Natural Theology, bk. ii. ch. i.

76. Logic, pp. 377-85 (bk. iii. ch. xxii).

77. Logic, pp. 79-81 (bk. i. ch. vii. section 4).

78. Logic, pp. 377-86 (bk. iii. ch. xxii).

79. It has been suggested that upon Mill's principles the change
of a lobster's colour to red is 'caused' when he is boiled, but
the colour before boiling uncaused. A case in the South
Kensington Museum showing variously coloured crows is a tacit
comment on Mill's illustration. The colour of crows is obviously
considered by modern men of science as implying causal relations.

80. Logic, p. 382 (bk. iii. ch. xxii. section 6).

81. Ibid., p. 381 (bk. iii. ch. xxii. section 4).

82. Logic, p. 470 (bk. iv. ch. vii. section 4). It is curious
that this remains in the last edition, that is, after the first
Darwinian controversies.

83. See Sigwart's Logik (1889), ii. 456, etc.

84. Logic, pp. 370-76 (bk. iii. ch. xx. section 1, 4).

85. Ibid. p. 372 (bk. iii. ch. xxi. section 2).

86. Ibid. p. 373 (bk. iii. ch. xxi. section 3).

87. Logic, p. 382 (bk. iii. ch. xxii. section 5).

88. Ibid. p. 384 (bk. iii. ch. xxii. section 8).

89. As he says in the Examination of Hamilton, ch. xix.

90. Logic. p. 142 (bk. ii. ch. iv. section 4).

91. Some writers, especially G.H. Lewes, have tried to maintain
that the statement of the uniformity of Nature is an 'identical
proposition.' The attempt is unsatisfactory, and certainly does
not seem to have found favour with later writers; but, though I
am unable to discuss the question, I will suggest that it seems
to indicate the ideal result of reasoning. We assume that, if our
knowledge were complete, we could state all the laws of action
and reaction of any element as necessary consequences of its
primitive constitution, as we can deduce all the properties of
number and space from primary principles. Though we can never
attain such a consummation, we can reject any theory which
contradicts it, and, therefore, such doctrines as the 'plurality
of causes,' which come to supposing that an identical process may
be analysed in two inconsistent ways.

92. E.g., by Mr F.H. Bradley in his Principles of Logic (1883),
pp. 329-42. Dr Venn, who is much more favourable to Mill,
discusses them in his Empirical or Inductive Logic (1889), pp.
400-31, shows very clearly how they assume what he calls the
'popular', as distinguished from the 'rigidly scientific', view
of causation. Elsewhere (p. 58) he remarks that the popular might
be called the 'Brown-Herschel-Mill view,' as those writers
popularised the doctrine first clearly set forth by Hume. See
also Sigwart's Logik (1889), ii. 469-500.

93. Logic, p. 284 (bk. iii. ch. ix. section 6).

94. Sigwart's Logik (1889) ii. 461.

95. Herschel's Discourse first appeared in 1830 as the first
volume of Lardner's Cabinet Cyclopaedia. The 'four methods' are
noticed, as Mill states, though with comparative vagueness, in
chap. vi of the Discourse. Jevons prefers the statement to
Mill's. Whewell makes the obvious remark (Philosophy of
Discovery, p. 284) that the four methods resemble some of Bacon's
Praerogative Instantiarum.

96. For Whewell, see the Writing so described as to form a
biography by I. Todhunter (2 vols. 1876). The Life and
Correspondence, by Mrs Stair Douglas, appeared in 1888. Whewell's
chief philosophical works are: History of the Inductive Sciences
(3 vols. 8vo, 1837; section edition, 1840; third edition, 1857);
Philosophy of the Inductive Sciences (2 vols. 1840: second
edition, 1857). This book was afterwards divided into three: --
History of Scientific Ideas, 2 vols. 1858; Novum Organum
Renovatum, 1 vol. 1858; and Philosophy of Discovery, 1 vol. 1860.
Whewell also wrote a pamphlet Of Induction with special reference
to Mr J. Stuart Mill's 'System of Logic'. This is republished as
chap. xxii of his Philosophy of Discovery.

97. Republished in Herschel's Essays (1857), pp. 142-256.

98. Scientific Ideas, i. 88 (note added to this edition).

99. Philosophy of the Inductive Sciences (1847), ii. 311.

100. Philosophy of the Inductive Sciences, i. 80.

101. Whewell's Philosophy of Inductive Sciences, i. 216-21;
Mill's Logic, pp. 160, 265 (bk. ii. ch. v. section 6, and bk.
iii. ch. viii. section 7).

102. Whewell, indeed, says that the 'necessary law' is that a
change of velocity must have a cause; the 'empirical law' tells
us that the time during which it has been moving is not a cause.
-- Philosophy of the Inductive Sciences, ii. 591. I need not go
into this.

103. Logic, p. 151 (bk. ii. ch. v. section 3).

104. Logic, p. 190, etc. (bk. iii. ch. ii. section 3, 4); Ibid.
p. 423 (bk. iv. ch. i. section 4).

105. Logic, p. 207 (bk. iii. ch. iv. section 1).

106. Autobiography, pp. 168, 173.

107. Logic, p. 548 (bk. vi. ch. ii. section 2).

108. Autobiography, p. 108.

109. Logic, p. 557 (bk. vi. ch. iv. section 3).

110. See his view that the difference of character between the
sexes is due to external circumstances, and therefore removable.
-- Logic, p. 566 (bk. vi. ch. v. section 3).

111. Logic, pp. 567, 569 (bk. vi. ch. v. section 4, 5). (Art is
misprinted 'act' in the last edition.)

112. Ibid. p. 185 (bk. iii. ch. i. section 1).

113. Logic. p. 144 (bk. ii. ch. iv. section 5).

114. Ibid. pp. 576, 585 (bk. vi. ch. vii. section 4; bk. iv. ch.
ix. section 2).

115. Ibid, p. 303 (bk. iii. ch. xi. section 3).

116. Autobiography, p. 159.

117. Autobiography, p. 160.

118. Logic, p. 583 (bk. vi. ch. ix. section 1).

119. Ibid. p. 590 (bk. vi. ch. i. section 3).

120. Ibid. p. 584 (bk. vi. ch. ix. section 1).

121. Bk. vi. ch. x.

122. See especially the reviews of Tocqueville, Michelet, and
Guizot in the Dissertations.

123. Dissertations, ii. 121.

124. Lettres inédites de Mill à Comte (1899), p. xxxv. Mill's
letters to Comte upon his view of ethology are significant.