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quality, in each case their most prominent aspect is synthesis.
The first class of constructions are those which are based on
an explicit identity, which so to speak forces the extremes
together.

As compared with these all the rest seem arbitrary. For
we have in none the bond of a given centre, while in some it
is doubtful if any kind of centre exists. The ideal unity is
not anywhere prescribed to us beforehand. In some cases
it looks as if the operation were capricious ; and it is a
question, to which we must hereafter return, how far the con-
clusion can stand either with or without this operation. Since
at present these constructions seem not necessary, like the
first, since their middle term, if they have one, appears our
mere choice, we may distinguish them here as arbitrary syn-
theses.

§ 4. As such (ii) we recognize addition in Arithmetic, and
the geometrical extension of figures. In each, under differ-
ences, we find the same process of free rearrangement. I
obtain a result by composition of elements, and that result is
held true of the elements themselves. The same holds with
Comparison. There I bring the terms together, I unite them
under a certain aspect, and I then see a quality which I pro-
ceed at once to predicate of these, terms. In the process of
Recognition I may seem less at liberty, and still less free in
Dialectic reasoning : but in both cases the main feature is the
construction of a whole — a construction round a centre, which
is not given, into an unity not prescribed by the premises.

§ 5. Our material so far has arranged itself under the head



414 THE PRINCIPLES OF LOGIC. [Bk. IIL Pt. L

of Construction ; and the synthesis seemed in some cases to
be necessary and in others arbitrary. We pass next to the
consideration of that other main type which is the counterpart
of the first.

(B) The essence of analysis consists in the division of a
given totality, and in the predication of either the whole or
part of the discrete result. In the latter case the presence of
Elision is manifest, but even in the former it is to be recog-
nized. When reality first appears as a whole and then as a
number of divided units, something certainly is gained but
something else is eliminated. For the aspect of continuity or
unity is left out ; and thus mere analysis always involves and
must involve some elision.

The first example of this class may be found in Abstrac-
tion. We are burnt, and proceed from this experience to the
result, Fire burns. We have first reality as giving the whole
complex, we have next the elimination of all content, save two
elements in connection, we have thirdly the predication of this
residue ; Fire burning is real. The validity of the process is
open to grave doubt, but it consists in analysis followed by
elision.

Arithmetical subtraction shows the same features. Reality
gives us an integer five. We then divide this into units, and,
removing two of them, get an integer three, which we predi-
cate of reality. And we assume here once more that the
units are not altered by the disruption of their context. This
assumption may be false, but the process is clearly one of
elision.

In Distinction we seem to have a new variety, but we still
may find the same general outline. We are presented with
elements which are taken as one. Altogether, or with refer-
ence to a part of their content, they come before us as a whole,
obscure no doubt but still unbroken. In the result of the
operation this whole has vanished. A and B fall apart and
appear as divided, entirely or in respect of one or more attri-
butes ; and then this result is attributed to the original reality.
We shall once more neglect the suspicion which such an
assumption excites. Confining ourselves to the general
character of the operation employed, we are able again to



Chap. IV.] THE MAIN TYPES OF INFERENCE. 415

verify our type. A totality is divided by a function of
analysis, and ignored in the product by an act of elimination.

§ 6. We have seen so far that all our examples fall under
two heads. Can we advance to the conclusion that inference
consists in two main processes, construction and elision ? Our
way is barred by an unforeseen obstacle ; for we have not yet
dealt with Disjunctive reasoning. And it is impossible to
reduce this wholly to either process or to a mixture of both.
Both indeed are concerned in it, but they do not exhaust it.

If the alternatives are given us with an explicit statement
of their reciprocal exclusion, and of the sequence of each from
the absence of the other, in that case we do not find a new
principle of reasoning. For one of our data removes a pos-
sibility, and that removal does, by virtue of another datum,
assert the remaining possibility as fact. In '' A\s b or c " and
" A is not-^," by combining our premises we bring in not-^,
and so banish c ; and, this affirmation of not-^ being elided,
we can then join b directly to A. Thus where the "or" is
explicit, we have nothing which falls outside our two principles.

But suppose we start with possibilities not given as strict
alternatives. If, for instance, A may be b, and again may be
c, and can be nothing else ; and if we further suppose that A
is not c, what conclusion can we draw ? Can we go to There-
fo7'e A must be b ? We do indeed make this advance, but the
advance is made on the strength of the fresh assumption that
any unopposed possibility is real. And this means a new
principle. For here what we predicate is not the residue of
truth, but the remainder of chance. We attribute to the real,
not something first given and then worked upon by our act,
but an issue from premises which afford nothing positive. We
do not go simply from the mutilation of a whole to the accept-
ance of a part, but we also leap from the possibility of that part
to its unconditional existence. This principle, which we before
had need to mention (Chap. II. § 26), and which will engage
us hereafter, will not fall under the head of either analysis or
synthesis.

§ 7. Disjunctive reasoning may employ all three processes,
but it certainly need not do this. Where alternatives are
explicit, we have seen that it is content with the use of two.



4l6 THE PRINCIPLES OF LOGIC. [Bk. IIL Pt. L

And there is another instance where two are enough. For
where the process is ponendo tollens — where from " A may be b,
and A may be c (though not both), but A is c" we advance on
the«strength of an ideal synthesis to " A excludes b " — we are
not forced to cross from the possible to the actual. We
remain in the latter, and the exclusion of the possible is, as
such, no real quality of A (vid. Book I. Chap. III.).

But in other cases three movements may be seen. The
argument constructs and then eliminates ; and in the end the
residue is predicated with a vital change in its character.
Under this general type, which calls in the third movement,
we may point out several varieties.

In the first of these (§ 6) the possibilities are given, not as
explicit alternatives, and yet as together exhausting the subject ;
and also along with these possibilities may be given the actual
exclusion of one. This is the first variety. In another we
are left to make a complete exhaustion for ourselves ; and
again in another we may have no possibilities given us, and
may even have no statement of exclusion. In this last ex-
treme case we are reduced to operate with mere suggestions.
Thus if on trial b is found possible, and A excludes the sug-
gested c, d, and e, and if in the end we can find nothing else which
we are able to suggest — then we advance to the conclusion, A
must be b. We have conjoined b with A, have eliminated the
rest, and have boldly leapt from " may be " to " must be."
Here the exhaustion was not guaranteed, nor the exclusion
given. Our datum was A ; and it was we ourselves who con-
structed the whole, assumed its completeness, elided one part,
and then sprang to the actuality of our product.

In all these latter varieties of disjunctive reasoning, we
have first synthesis and then elimination, the whole con-
summated thirdly by a transition to fact from mere possibility.

§ 8. In this last section we have already provided for Apa-
gogic inferences (Chap. II. § 29), and have finished our rapid
survey of the principal classes of reasoning. We may now pre-
sent the result in a tabular form, asking the reader to bear in
mind one thing. He must remember that, when a process is
referred to one head, he is not to assume that the other type is
absent. We are to class each operation by its more prominent



Chap. IV.] THE MAIN TYPES OF INFERENCE. 417

feature, and to neglect for the moment our additional step
from the possible to the actual.



A.


Constrtiction.




(i)


Where the whole is madel


(a) necessarily.^




out of the datum |


(/3) arbitrarily.^


(ii;


) Where the whole is made)


(a) necessarily.^




beyond the datum \


(/3) arbitrarily.*


B.


Eliminative analysis.




Where, the whole being given,


1 {a) necessary.^




the elision is


1 (/3) arbitrary.^



We may enumerate the processes here presented. We
have in No. i the three-term inference which we first discussed.
In No. 2 we find addition and comparison. No. 3 gives us
recognition and dialectic movement. With No. 4 we reach
determination (positive or negative) by means of a suggested
possible synthesis. Thence we come in No. 5 to that dis-
junctive reasoning where the possibilities are independent and
one is excluded. Then No. 6 closes the rear with abstraction,
distinction, and arithmetical subtraction.

We may append three remarks. The first of these is that
the Hypothetic judgment may be assigned to No. 3. It may
be said, no doubt, that we are at liberty not to suppose ; but
then on the other hand we also elsewhere are free not to think.
The premise is a datum not given as real ; I treat it logically,
and thus get a result which I conditionally predicate. But
nothing here is my choice, save the resolve to suppose and
then to see what logically comes. But so much choice as this
seems to exist in all reasoning, since everywhere it lies with
ourselves at least to think or not to think.

In the second place addition and subtraction will be
necessary where the quantities are given marked with plus or
miftus. But their result in this case is hypothetical. The
signs do not belong to the nature of the quantities (Chap. II.
§§6 and 10). And the reader must remember that free
spatial rearrangement falls under the heads of 2 and 6.

And the third remark we have to make is this. The
process of suggesting possible predicates, and of then proving
one by excluding the others, may be regarded as a mixture

2 E



41 8 THE PTIINCIPLES OF LOGIC. [Bk. III. Pt. I.

of Nos. 4 and 5 ; but it is not worth while to place it in a class
by itself.

We may end by stating briefly the conclusion of this
Chapter. The middle operation of every inference consists of
analysis or synthesis, or both ; and in certain cases it invokes
besides an additional principle.



( 4i9 )



CHAPTER V.

ANOTHER FEATURE OF INFERENCE.

§ I. We must search into the nature of these general
processes, but there is a question which presses for immediate
answer in the present Chapter. We supposed first of all that
every inference was a construction round an identical centre.
We have since then discovered that reasoning demands a
self-same subject, that appropriates the difference got by the
experiment. But we must return to examine the middle
operation, the experiment itself. We now know that our first
supposition needs correction, since the experiment is not
always a construction through a given "identity. But this
result does not satisfy us. We want to know if our middle
process can ever dispense with all identity. There clearly is
not always an explicit common term ; and when this fails shall
we say that everything has failed 1 Or can we still say, there
is an implicit centre, unavowed but active .? Our instinct leads
us to embrace this latter suggestion.

§ 2. But how shall we support it } There is obviously
some unity in the operation, but it is doubtful if this will give
us what we want. Mere togetherness (so to speak) before the
mind is clearly insufficient ; and we must hence take the mind
itself as a centre, not given but used, and see if on this line we
can make an advance. We may say, " In all relations, where
the terms are able to be separated in idea, the relation may be
considered as an interrelation. The result is an inference, a
putting together of elements which before that inference
existed apart. And since those elements were all related to
one mind, and because of that unity now come together, the
mind may be taken as a common centre of interrelation." Is
this what we want } We must answer in the negative ; for
though I believe it to be true, and a truth whose importance

2 E 2



420 THE PRINCIPLES OF LOGIC. [Bk. III. Pt. I.

can hardly be exaggerated, yet in its abstract form it is simply
irrelevant. It tells us that some relation of some kind exists
between all objects of thought, and that they are all interre-
lated. But then this knowledge must fall outside of any
special inference. Thus A and B are called equal because I
have compared them ; but, before I compared them, I might
have known that some relation must exist between them ; and
this knowledge is therefore not the reason why I now know
that they are equal.

§ 3. From mere interrelation you can make no passage to
a special relation. It does not matter how actively the mind
may work ; you may suppose an intense appreciation of the
fact that we have a common term in the mind ; you may
postulate any degree of attention, or the preferential application
of the intellect to this fact — yet from these general premises
you never will get to the particular conclusion. For the
centre of the operation, if we are to find it at all, must be
found in the unity of that special operation. We can not
settle such a point by abstract reflections, which at the most
serve to raise a vague presumption in our favour. If we
wish to exhibit the identity in our processes, we must be
prepared to show the central point in each particular case.

§ 4. Let us start with what we called Recognition and
Dialectic. The given here is A7, and the mind meets this
with a function 7-8, which extends A to 8. The central point
is here obviously 7 ; and round this point, and by virtue of its
identity, A and 8 are brought together. We must notice how-
ever that 7-S is not given, and further that 7-S may never be
explicit. Our consciousness may pass straight from A7 to h.
It may never suspect the presence of that common middle
term on which everything depends. Hence we might say
that we have subsumed the original datum under a function of
synthesis, which never appears except in its effects : but this
statement would be incorrect, since the process is not a
subsumption at all. It is a construction by means of a hidden
centre.

This seems tolerably clear, and it gives us a principle to
which we must hold. But in its further application the truth
becomes much more difficult to see.



Chap. V.] ANOTHER FEATURE OF INFERENCE. 42 1

§ 5. If we consider the operations of Comparison and
Distinction, we are at first unable to perceive any middle.
The mind, we may say, is the point which compares, and the
centre which separates ; but such a mere generality, however
important, we agreed was not the answer that is wanted.
The question is whether in the process itself we can find a
special interrelation ; and we shall now make this attempt.

Both the processes exhibit a double aspect of unity and
diversity. In Comparison this fact is at once apparent. Irv
"A = B" we have of course the differences of A and B.
These differences are held together in relation, and are
combined on the strength of a common point, since the
quantity of A and B is the same. Thus the relation of each
difference, A and B, to an identical quantity is the very
ground of their interrelation. Take that third term away, and
the connection vanishes ; reproduce it, and the mind requires
nothing else in order once more to construct the relation.

But is it so too with Distinction } Take for instance, " A
is not equal to B," and where is the third term } I answer. It
is there, though we do not perceive it For consider the case
thus ; A and B, it is certain, are still related, since they are
taken as different ; and their difference is not abstract but
specific and definite. It is as quantities that we fail to find
them identical. But, this being grasped, observe what follows.
Just as the general perception of difference implies a mind
which distinguishes, and which serves in some vague character
as the base which supports that general relation — so it is with
every special difference. What is true in general will prove
true in particular. All objects of our thought in the first
place must have so7ne relation because, as our objects, they are
all identical ; and again every distinction of special qualities,
such as sounds or colours, takes place on the basis of a
special community. For instance, the separation of red from
blue must imply the unconscious taking of each as a colour ;
and that felt common quality is the basis upon which the
separation is effected. It is thus too with quantities. A and
B are perceived to be unequal, but inequality presupposes
that both have quantity. In this they are the same^ and it is
because of this point that they can be seen as unequal. Thus



422 THE PRINCIPLES OF LOGIC. [Bk. IIL Pt. 1.

identity in regard to the possession of quantity is here the
third term that was required, and it is relation to this centre
which interrelates the quantitative differences. In short
distinction can never be effected except within an area of
sameness ; and, once outside this area and common meeting-
ground, the relation would vanish.

§ 6. Perception of identity and perception of difference
are two modes of one function or two functions of one process.
The result in both cases depends on a synthesis of diversity
with unity, but with this likeness there goes a striking
contrast. Take first Comparison. Here we start with the
difference, and at the end this difference has been partially
lost, and the identity of the terms has become explicit. It
is otherwise with Distinction. We begin here with a vague
and undiscriminated unity, but in the conclusion the differences
appear, and the identity has passed away from our sight. In
both processes alike the sameness of the terms is the middle
point from which everything hangs ; but that centre is used in
two diverse ways. In the case of Comparison it is the recep-
tive identity which, standing opposite to external differences,
takes them into itself Content with a partial recognition
of its power, satisfied with a declaration made by the
differents that in some point they are the same, the unity
slurs the remainder of diversity, and becomes the mere
relation of similars. But the process of Distinction shows a
contrast to this. The identity here turns against its own
unseen differences, and makes them explicit. It pronounces
the relation which sunders them apart, and is led, by the
emphasis of this its own activity, to forget its own being-
Thus the differents appear as independent varieties, which
subsist and form relations in a passive atmosphere. The
identity which has generated them, which separates and
supports them, is slurred even more than in the former case
diversity was slurred by Comparison. We might say that one
tends to think less of the relatives and more of the relation ;
while the other quite sinks the active ^relation, and keeps its
eye on the terms related.

§ 7. In the ensuing Chapter we shall return to this point
but at present we may try to develope our meaning. / In



Chap. V.] ANOTHER FEATURE OF INFERENCE. 423

Comparison and in Distinction we employ certain functions,
and you might say incorrectly that these processes consist in
subsuming the given under certain activities. What are these
activities ? In a clumsy fashion we may represent them as
follows. In Comparison we apply to the original datum,

X
A and B, a function of synthesis, /\ . Through the

a b
possession by A and B of the qualities a and b, we unite them in
relation to our common point X. The result may be depicted

X

as X\ ; but, since the unity^ is degraded and becomes a

A B
relation, the conclusion which appears is simply A — B.

For Distinction we must bring in another formula. We
may be said to start with a vague totality, in which is latent
an internal diversity ; and we may represent this datum as
X X

/\ . To this unity we apply a function of analysis /\ .
a b A B

Then on the one hand X, now identified with x, becomes less
visible ; while, as this fades away, the other side appears, and
a and b, developed by the application of the function, appear

X

as A and B. The immediate result is /\ , but, since x is

A B
wholly slurred, A and B fall apart as separate facts which
show a distinction.

§ 8. It would be interesting to enter into the finer meta-
physical detail of these processes ; but we can afford no
more than a mere passing remark in protest against an
obstinate prejudice. In answer to the doctrine that sameness
and diversity imply one another, at least when perceived, we
shall be told that Difference is independent, and derives its
origin from the shock of change. And for the apprehension
of this shock, it will be added, no activity is required. Thus
we have no ideal operation at all, and may so dispense
with the illusion of an ideal unity." But this objection, I
must reply, depends upon a complete mistake. It partly
confuses feeling with perception, and partly is wholly



424 THE PRINCIPLES OF LOGIC. [Bk. IIL Pt. I.

wrong about feeling. I will take the second of these points
first.

If a shock is intended to be felt as a shock (and I suppose
it must be so intended), then the feeling must be compound.
There must be some feeling to start with, in collision with
which the inrush of new feeling disturbs the mind. For if the
place were quite empty the new arrival might appear, but
could hardly make a striking sensation. Thus the shock
presupposes another element, and it implies the felt relation
of both. But, if so, once more we have found in this relation
a point of identity, a common sameness not of perception
but of feeling. In other words it will be the continuity of the
feeling which makes us sensible of the change and the shock ;
and this is our first point.

But we have not yet reached the perception of change, and
the failure to see this is the second point of error. Think
what you like about the felt shock, you are yet a long way
from the consciousness of difference, and you can not advance
without calling in an ideal identity. Take a sensation A, and
let it change to a wholly different C. This will give you the
succession of two psychical events, but not the perceived
relation of change, and the question is how this relation can
be given. It can not be given without retention, and retention
is not possible unless what precedes and what follows possess
some point in common. But let AB (for example) be followed
by BC, and the problem is solved. Here the identical B
redintegrates A ; or (if you prefer to say so) the retention of
AB gives us A with a point in common with C ; and, in either

B
case, we have a result which we may write /\ . No change

A C
can be perceived unless by means of an ideal continuity.

§ 9. This ideal identity is a necessary element in the
perception of difference. Without such a centre the extremes
would never be held together, and their relation would never
come before the mind. We may represent as follows the

A .

mode in which this unity operates. In a whole , ,, as it

passes before us, the difference be is not at first noticed.



Chap. V.] ANOTHER FEATURE OF INFERENCE. 425

Hence we do not perceive b and c to be disparate, till we try-
to identify them. But, in going from Kb on to A^, the
self-same A reproduces b, which, thus forced upon us in
identity with ^, is rejected by it ; and then, A retiring from
view, we perceive the difference as B against C.

How then do we become aware of identity } We must
have differences B^ and D^, and we must feel, when we pass
from one to the other, that they are not all different. This
feeling comes from the presence of a^ which is not yet
explicit. It rises to explicitness, through the reproduction of



Online LibraryF. H. (Francis Herbert) BradleyThe principles of logic → online text (page 40 of 50)