positive value, which is really the converse by negation of your
positive observation, a1 is b1; b2 (which is _just_ not-b1) is a2
(which is _just_ not-a1). Thus the two may be represented as the same
judgment in positive and negative forms, which confirm one another.
“Yellow is a compound of red and green”--in Experiment, “if, and as far
as you take away the red or the green you destroy the yellow.” That
describes an experiment with the colour-box. I have inverted the order
in the conversions in compliance with the rule of common Logic, that
Predicate is wider than Subject; but in accurate matter it is a false
rule, and very inconvenient. The common rule means that a man who is
drowned is dead, but a man who is dead need not have been drowned; but
of course if he has the signs of death by drowning then he has been
drowned.
_Classification and Generalisation_
(_g_) _Classification_ is a consequence of all systematic theory; it
is not a separate method of science. It is merely the arrangement
of positive contents negatively related. No doubt where we have a
kind of family relations between individuals classification is more
prominent, and in the theory of continuous matter or operation, where
individualities are not remarkable--_e.g._ in geometry--it is less
prominent. But both are always there--classification and theory.
Classification which expresses no theory is worthless, except that
intended for convenient reference, such as alphabetical classification.
Under classification I may say a word on generalisation. {160} The
common idea of inference from many cases, because they are many, to
all cases of the same kind, is quite without justification. The only
genuine and fundamental law of generalisation is “Once true always
true.” But this might fail to suffice for our practical purposes,
because it might save its truth by abstraction. Let us take the
example, “Water is made of oxygen and hydrogen.” If that is true once,
it is always true _in the same sense_. If you find some fluid of a
different composition which you are inclined to call water, then you
must identify or distinguish the two, and this is a mere question of
classification. _Practically_, however, we could not get on unless our
knowledge had some degree of _exhaustiveness_, _i.e._ unless we knew
roughly that most of _what we take for water_ will have the alleged
properties. But no Induction or analysis, however accurate, can assure
us against confusion and error, viz. assure us that everything we take
to be water will be made of oxygen and hydrogen, nor that water will
always be found on the earth. I call this accurate analysis, which
_may_ be made in a single instance only, and is the only perfectly
scientific generalisation, generalisation by mere determination. Its
classification is hypothetical, _i.e._ in it the individuals are merely
possible individuals.
But this passes into another kind of generalisation, which may be
called generalisation by concrete system, as when we attach scientific
analysis to some extensive individual reality, _e.g._ to the solar
system or the race of man. Then our judgments have a place in the
real world, and our classification is categorical classification. The
generalisation in this case does not follow from the judgment being
extended {161} over a great plurality of possible similar subjects, but
from the subject to which it applies having as an organised totality
a large place in the world; _e.g._ “The human race alone gives moral
interest to the history of bur planet.” These judgments come by making
explicit the reality which underlies such hypothetical judgments as
“all men are capable of morality.” It means that we actually venture to
assign a place in the universe to the system we are speaking of. Then,
though it is an individual, and unique, its name has a meaning, and is
not a mere proper name. The solar system is good instance. Judgments
about it or parts of it are universal but not purely hypothetical,
and as our knowledge of this kind increases it becomes even a little
exhaustive.
_Generalisation by mere likeness or analogy_, on the other hand, is
precarious. It is what popular theory has in its mind in speaking of
Induction, viz. a conclusion from a truth to judgments concerning all
similar cases, _e.g._ from “Water is made of Oxygen and Hydrogen” to
“All liquids which we choose to take for water are made of Oxygen and
Hydrogen.” No scientific method can possibly give us this result. In as
far as it has value it depends upon our guessing rightly by analogy.
It may be replied, “that the signs of recognition are set down in
the law or truth.” Well, if they are certain, generalisation by mere
determination is enough; if they are doubtful, no induction can warrant
your judgment of them in particular cases. Practically, of course, we
get them right pretty often, although wrong very often.
_Hypothesis_
(_h_) Hypothesis is merely supposition; it consists in suggesting a
fact as if it were real, when it is the only way of {162} completing
given facts into a consistent system. If the hypothesis is proved that
is a demonstration. It has been said that “Facts are only familiar
theories.” If a bell rings in the house, I say unhesitatingly, “Some
one rang that bell.” Once in ten years it may be rung, not by a person,
but by some mechanical accident, in which case the “some one” is a
hypothesis, but one always treats it as a fact. The only proof of a
hypothesis is its being the only one that will fit the facts, _i.e._
make our system of reality relatively self-consistent. We believe many
things we can never verify by perception, _e.g._ the existence of the
centre of the earth, or that you have an idea in your minds; and if we
go to ultimate analysis, perception itself involves hypothesis, and
_a fortiori_ all experiment involves hypothesis. Every experimental
interference with nature involves some supposition as to a possible
connection which it is intended to confirm or disprove.
_Deduction_
2. Classification and hypothesis bring us into Deduction, which is not
really a separate kind of inference from Induction, but is a name given
to science when it becomes systematic, so that it goes from the whole
to the parts, and not from the parts to the whole. In Induction you are
finding out the system piecemeal, in Deduction you already have the
clue; but the system, and the system only, is the ground of inference
in both. Induction is tentative because we do not know the system
completely. Their relation may be fairly represented by the relation
of the first figure of the Syllogism to the second and third. The
difference is merely that in deduction we are sure of having knowledge
which covers the whole system. If a man observed, “The difference
{163} between the dark blood in the veins and the bright blood in the
arteries calls for explanation,” that is the beginning of Induction. If
a man states the circulation of the blood as an explanation, that is
Deduction. Really Induction is only a popular name for such Inference
as deals with numbers of instances. Mill’s experimental methods do
not depend upon number of instances, but only upon content; they
presuppose the instances already broken up into conditions A, B, C, and
consequents a, b, c.
I must distinguish subsumption and construction as two forms of
deduction. Only the former _properly_ employs Syllogism in the first
figure.
_Subsumption_
(_a_) Subsumption is argument by subject and attribute; _i.e._ when
we do not know the system so as to construct the detail,--_e.g._ a
man’s character,--and can only state _in_ what individual system the
details occur. Then we _really want_ the major premise to lay down the
properties of the system, and all deduction _can_ therefore be employed
with a major premise, _e.g._ a mathematical argument might ultimately
take the form, “_space is such that_ two parallels cannot meet.”
_Construction_
But (_b_) when the nature of the subject is very obvious, and
the combinations in it very definite, then the major premise is
superfluous, and adds nothing to the elements of the combination.
“A to right of B, B to right of C.
∴ A to right of C.”
This is clear, but it is not formal; as a syllogism it has four terms.
It is simply a construction in a series of which the nature is obvious.
And if you insert a major premise it would be, “What is to the right
of anything is to the right {164} of that which the former is to the
right of,” and that is simply the nature of the series implied in the
inference stated in an abstract form. “Inference is a construction
followed by an intuition.” [1] The construction, I think, however,
must be a stage of the intuition. I am therefore inclined to suggest
that a factor of general insight into principle is neglected in this
definition, from which much may undoubtedly be learned.
[1] Bradley, _Principles of Logic_, p. 235.
_Causation_
3. I have said very little about causation. The fact is, that in
Logic the cause necessarily fades away into the reason, that is, the
explanation. If we follow Mill’s account, we see how this takes place.
I will put the stages very briefly.
_Cause_
(_a_) We start, no doubt, by thinking of a cause as a real event in
time, the priority of which is the condition of another event, the
effect. Pull the trigger--cause--and the gun goes off--effect.
_Complete conditions_
(_b_) The moment we look closer at it, we see that this will not
do, and we begin to say with Mill, that the cause is the antecedent
which includes _all_ the conditions of the effect. The plurality of
alternative causes breaks down, through the conditions defining the
effect. Pull the trigger?--yes, but the cartridge must be in its place,
the striker must be straight, the cap must be in order, the powder must
be dry and chemically fit, and so on, and so on, till it becomes pretty
clear that the cause is a system of circumstances which include the
effect.
_Law_
(_c_) But then our troubles are not ended. Only the essential and
invariable conditions enter into the cause, if the {165} cause is
invariable. This begins to cut away the particular circumstances of
the case. You need not use the trigger, nor even the cap; you may
ignite powder in many ways. You may have many kinds of explosives. All
that is essential is to have an explosion of a certain force and not
too great rapidity. Then you will get this paradox. What is merely
essential to the effect, is always something less than any combination
of real “things” which will produce the effect, because every real
thing has many properties irrelevant to this particular effect. So,
_if the cause means something real_, as a material object is real, it
cannot be invariable and essential. If it is not something real, and
is essential, it fines down into a reason or law--the antecedent in a
hypothetical judgment.
_Ground, or real system with known laws_
(_d_) We can only escape this by identifying both cause and reason
with the complete ground; that is, the nature of a system of reality
within which the cause and effect both lie. But even then, though the
ground is _real_, it is not antecedent in time. We see, indeed, that
the conditions of an effect must be continuous through the effect. If
the process were taken as cut in two at any point, its connection would
be destroyed. If _a_ cause and _b_ effect were really detached events,
what difference could it make if, instead of _a_, _c_ preceded _b_?
_Postulate of Knowledge_
4. The postulate of Knowledge, then, is very badly stated as
Uniformity of Nature. That was due to the vulgar notion of Inductive
“generalisation.” It must be stated in two parts: first, “Once true
always true;” and secondly, “Our truth is enough for us,” that is, it
covers enough of the universe for our practical and theoretical needs.
The {166} two parts may be put together by saying, “The universe is a
rational system,” taking rational to mean not only of such a nature
that it can be known by intelligence, but further of such a nature that
it can be known and handled by our intelligence.
_Conclusion_
5. These lectures have been unavoidably descriptive rather than
thorough, and yet, as I warned you, descriptive of properties which
are in a sense not at all new, but quite familiar, and even trite. You
will not feel, at first, that the full interest which I claimed for
the science of knowledge, really attaches to these dry relations of
abstract thought. You will get no permanent good unless you carry the
study forward for yourselves, and use these ideas as a clue to find
your bearings in the great world of knowledge.
And I would give you one hint about this. _I_ do not suggest that you
should neglect philosophy but yet you should remember that philosophy
can tell you no new facts, and can make no discoveries. All that it
can tell you is the significant connection of what you already know.
And if you know little or nothing, philosophy has little or nothing to
tell you. Plato says, “The synoptical man, the man who has a conspectus
of knowledge, is the philosopher; and the man who is not synoptical,
who cannot see two subjects in their relation, is no philosopher.”
By all means read good logical books; but also and more especially
read good and thorough systematic books on science, or history, or
politics, or fine art--I do not mean on all of these subjects, but on
some, wherever your interest leads you. You cannot learn the nature of
inference, of systematic necessity, of the construction of reality,
by reading logic exclusively; you must {167} feel it and possess it
by working in the world of concrete knowledge. I give one example in
passing. If you study social questions, test for yourselves the value
of statistics--_i.e._ sets of enumerative judgments. Consider what the
causal analysis of any problem demands; remember that all enumeration
implies a ground or whole, on which its value depends; and contrast
the exhaustive examination of an instance thoroughly known, with the
enumeration of thousands of cases lumped under a general predicate.
Determine always to know the truth; welcome all information and all
suggestion, but remember that truth is always systematic, and that
every judgment, when you scrutinise it, demands a fuller and fuller
connection with the structure of life. It is not cleverness or learning
that makes the philosopher; it is a certain spirit; openness of mind,
thoroughness of work, and hatred of superficiality. Each of us,
whatever his opportunities, can become in a true sense, if he has the
real philosophic spirit, in Plato’s magnificent words, “The spectator
of all time and of all existence.”
THE END
End of Project Gutenberg's The Essentials of Logic, by Bernard Bosanquet