other. Their constant conjunction in past instances has produced such
a habit in the mind, that it always conjoins them in its thought, and
infers the existence of the one from that of its usual attendant. When
it considers the dye as no longer supported by the box, it can not
without violence regard it as suspended in the air; but naturally places
it on the table, and views it as turning up one of its sides. This
is the effect of the intermingled causes, which are requisite to our
forming any calculation concerning chances.
Secondly, It is supposed, that though the dye be necessarily determined
to fall, and turn up one of its sides, yet there is nothing to fix the
particular side, but that this is determined entirely by chance. The
very nature and essence of chance is a negation of causes, and the
leaving the mind in a perfect indifference among those events, which
are supposed contingent. When therefore the thought is determined by the
causes to consider the dye as falling and turning up one of its sides,
the chances present all these sides as equal, and make us consider every
one of them, one after another, as alike probable and possible. The
imagination passes from the cause, viz. the throwing of the dye, to the
effect, viz. the turning up one of the six sides; and feels a kind of
impossibility both of stopping short in the way, and of forming any
other idea. But as all these six sides are incompatible, and the dye
cannot turn up above one at once, this principle directs us not to
consider all of them at once as lying uppermost; which we look upon
as impossible: Neither does it direct us with its entire force to any
particular side; for in that case this side would be considered as
certain and inevitable; but it directs us to the whole six sides after
such a manner as to divide its force equally among them.
We conclude in
general, that some one of them must result from the throw: We run all
of them over in our minds: The determination of the thought is common to
all; but no more of its force falls to the share of any one, than what
is suitable to its proportion with the rest. It is after this manner the
original impulse, and consequently the vivacity of thought, arising from
the causes, is divided and split in pieces by the intermingled chances.
We have already seen the influence of the two first qualities of the
dye, viz. the causes, and the number and indifference of the sides, and
have learned how they give an impulse to the thought, and divide that
impulse into as many parts as there are unites in the number of sides.
We must now consider the effects of the third particular, viz. the
figures inscribed on each side. It is evident that where several
sides have the same figure inscribe on them, they must concur in their
influence on the mind, and must unite upon one image or idea of a figure
all those divided impulses, that were dispersed over the several sides,
upon which that figure is inscribed. Were the question only what side
will be turned up, these are all perfectly equal, and no one coued ever
have any advantage above another. But as the question is concerning the
figure, and as the same figure is presented by more than one side: it is
evident, that the impulses belonging to all these sides must re-unite
in that one figure, and become stronger and more forcible by the union.
Four sides are supposed in the present case to have the same figure
inscribed on them, and two to have another figure. The impulses of
the former are, therefore, superior to those of the latter. But as the
events are contrary, and it is impossible both these figures can be
turned up; the impulses likewise become contrary, and the inferior
destroys the superior, as far as its strength goes. The vivacity of the
idea is always proportionable to the degrees of the impulse or tendency
to the transition; and belief is the same with the vivacity of the idea,
according to the precedent doctrine.
SECT. XII. OF THE PROBABILITY OF CAUSES.
What I have said concerning the probability of chances can serve to
no other purpose, than to assist us in explaining the probability of
causes; since it is commonly allowed by philosophers, that what the
vulgar call chance is nothing but a secret and concealed cause. That
species of probability, therefore, is what we must chiefly examine.
The probabilities of causes are of several kinds; but are all derived
from the same origin, viz. THE ASSOCIATION OF IDEAS TO A PRESENT
IMPRESSION. As the habit, which produces the association, arises from
the frequent conjunction of objects, it must arrive at its perfection by
degrees, and must acquire new force from each instance, that falls under
our observation. The first instance has little or no force: The second
makes some addition to it: The third becomes still more sensible; and it
is by these slow steps, that our judgment arrives at a full assurance.
But before it attains this pitch of perfection, it passes through
several inferior degrees, and in all of them is only to be esteemed a
presumption or probability. The gradation, therefore, from probabilities
to proofs is in many cases insensible; and the difference betwixt these
kinds of evidence is more easily perceived in the remote degrees, than
in the near and contiguous.
It is worthy of remark on this occasion, that though the species of
probability here explained be the first in order, and naturally takes
place before any entire proof can exist, yet no one, who is arrived at
the age of maturity, can any longer be acquainted with it. It is true,
nothing is more common than for people of the most advanced knowledge
to have attained only an imperfect experience of many particular events;
which naturally produces only an imperfect habit and transition: But
then we must consider, that the mind, having formed another observation
concerning the connexion of causes and effects, gives new force to
its reasoning from that observation; and by means of it can build an
argument on one single experiment, when duly prepared and examined. What
we have found once to follow from any object, we conclude will for ever
follow from it; and if this maxim be not always built upon as certain,
it is not for want of a sufficient number of experiments, but because
we frequently meet with instances to the contrary; which leads us to
the second species of probability, where there is a contrariety in our
experience and observation.
It would be very happy for men in the conduct of their lives and
actions, were the same objects always conjoined together, and, we had
nothing to fear but the mistakes of our own judgment, without having any
reason to apprehend the uncertainty of nature. But as it is frequently
found, that one observation is contrary to another, and that causes and
effects follow not in the same order, of which we have I had experience,
we are obliged to vary our reasoning on, account of this uncertainty,
and take into consideration the contrariety of events.
The first
question, that occurs on this head, is concerning the nature and causes
of the contrariety.
The vulgar, who take things according to their first appearance,
attribute the uncertainty of events to such an uncertainty in the
causes, as makes them often fail of their usual influence, though
they meet with no obstacle nor impediment in their operation. But
philosophers observing, that almost in every part of nature there is
contained a vast variety of springs and principles, which are hid,
by reason of their minuteness or remoteness, find that it is at least
possible the contrariety of events may not proceed from any contingency
in the cause, but from the secret operation of contrary causes. This
possibility is converted into certainty by farther observation, when
they remark, that upon an exact scrutiny, a contrariety of effects
always betrays a contrariety of causes, and proceeds from their mutual
hindrance and opposition. A peasant can give no better reason for the
stopping of any clock or watch than to say, that commonly it does not
go right: But an artizan easily perceives, that the same force in the
spring or pendulum has always the same influence on the wheels; but
fails of its usual effect, perhaps by reason of a grain of dust, which
puts a stop to the whole movement. From the observation of several
parallel instances, philosophers form a maxim, that the connexion
betwixt all causes and effects is equally necessary, and that its
seeming uncertainty in some instances proceeds from the secret
opposition of contrary causes.
But however philosophers and the vulgar may differ in their explication
of the contrariety of events, their inferences from it are always of the
same kind, and founded on the same principles. A contrariety of events
in the past may give us a kind of hesitating belief for the future after
two several ways. First, By producing an imperfect habit and transition
from the present impression to the related idea. When the conjunction of
any two objects is frequent, without being entirely constant, the mind
is determined to pass from one object to the other; but not with
so entire a habit, as when the union is uninterrupted, and all the
instances we have ever met with are uniform and of a piece-.. We find
from common experience, in our actions as well as reasonings, that
a constant perseverance in any course of life produces a strong
inclination and tendency to continue for the future; though there
are habits of inferior degrees of force, proportioned to the inferior
degrees of steadiness and uniformity in our conduct.
There is no doubt but this principle sometimes takes place, and
produces those inferences we draw from contrary phaenomena: though I
am perswaded, that upon examination we shall not find it to be the
principle, that most commonly influences the mind in this species of
reasoning. When we follow only the habitual determination of the mind,
we make the transition without any reflection, and interpose not a
moment's delay betwixt the view of one object and the belief of that,
which is often found to attend it. As the custom depends not upon any
deliberation, it operates immediately, without allowing any time for
reflection. But this method of proceeding we have but few instances
of in our probable reasonings; and even fewer than in those, which are
derived from the uninterrupted conjunction of objects.
In the former
species of reasoning we commonly take knowingly into consideration
the contrariety of past events; we compare the different sides of the
contrariety, and carefully weigh the experiments, which we have on each
side: Whence we may conclude, that our reasonings of this kind arise
not directly from the habit, but in an oblique manner; which we must now
endeavour to explain.
It is evident, that when an object is attended with contrary effects, we
judge of them only by our past experience, and always consider those
as possible, which we have observed to follow from it.
And as past
experience regulates our judgment concerning the possibility of these
effects, so it does that concerning their probability; and that effect,
which has been the most common, we always esteem the most likely. Here
then are two things to be considered, viz. the reasons which determine
us to make the past a standard for the future, and the manner how we
extract a single judgment from a contrariety of past events.
First we may observe, that the supposition, that the future resembles
the past, is not founded on arguments of any kind, but is derived
entirely from habit, by which we are determined to expect for the future
the same train of objects, to which we have been accustomed. This habit
or determination to transfer the past to the future is full and perfect;
and consequently the first impulse of the imagination in this species of
reasoning is endowed with the same qualities.
But, secondly, when in considering past experiments we find them of a
contrary nature, this determination, though full and perfect in itself,
presents us with no steady object, but offers us a number of disagreeing
images in a certain order and proportion. The first impulse, therefore,
is here broke into pieces, and diffuses itself over all those images, of
which each partakes an equal share of that force and vivacity, that is
derived from the impulse. Any of these past events may again happen;
and we judge, that when they do happen, they will be mixed in the same
proportion as in the past.
If our intention, therefore, be to consider the proportions of contrary
events in a great number of instances, the images presented by our past
experience must remain in their FIRST FORM, and preserve their first
proportions. Suppose, for instance, I have found by long observation,
that of twenty ships, which go to sea, only nineteen return. Suppose
I see at present twenty ships that leave the port: I transfer my past
experience to the future, and represent to myself nineteen of these
ships as returning in safety, and one as perishing.
Concerning this
there can be no difficulty. But as we frequently run over those several
ideas of past events, in order to form a judgment concerning one single
event, which appears uncertain; this consideration must change the FIRST
FORM of our ideas, and draw together the divided images presented
by experience; since it is to it we refer the determination of that
particular event, upon which we reason. Many of these images are
supposed to concur, and a superior number to concur on one side. These
agreeing images unite together, and render the idea more strong and
lively, not only than a mere fiction of the imagination, but also than
any idea, which is supported by a lesser number of experiments. Each new
experiment is as a new stroke of the pencil, which bestows an additional
vivacity on the colours without either multiplying or enlarging the
figure. This operation of the mind has been so fully explained in
treating of the probability of chance, that I need not here endeavour to
render it more intelligible. Every past experiment may be considered as
a kind of chance; I it being uncertain to us, whether the object will
exist conformable to one experiment or another. And for this reason
every thing that has been said on the one subject is applicable to both.
Thus upon the whole, contrary experiments produce an imperfect belief,
either by weakening the habit, or by dividing and afterwards joining in
different parts, that perfect habit, which makes us conclude in general,
that instances, of which we have no experience, must necessarily
resemble those of which we have.
To justify still farther this account of the second species of
probability, where we reason with knowledge and reflection from
a contrariety of past experiments, I shall propose the following
considerations, without fearing to give offence by that air of subtilty,
which attends them. Just reasoning ought still, perhaps, to retain
its force, however subtile; in the same manner as matter preserves its
solidity in the air, and fire, and animal spirits, as well as in the
grosser and more sensible forms.
First, We may observe, that there is no probability so great as not to
allow of a contrary possibility; because otherwise it would cease to be
a probability, and would become a certainty. That probability of causes,
which is most extensive, and which we at present examine, depends on a
contrariety of experiments: and it is evident An experiment in the past
proves at least a possibility for the future.
Secondly, The component parts of this possibility and probability are of
the same nature, and differ in number only, but not in kind. It has been
observed, that all single chances are entirely equal, and that the
only circumstance, which can give any event, that is contingent, a
superiority over another is a superior number of chances. In like
manner, as the uncertainty of causes is discovery by experience, which
presents us with a view of contrary events, it is plain, that when we
transfer the past to the future, the known to the unknown, every past
experiment has the same weight, and that it is only a superior number
of them, which can throw the ballance on any side. The possibility,
therefore, which enters into every reasoning of this kind, is composed
of parts, which are of the same nature both among themselves, and with
those, that compose the opposite probability.
Thirdly, We may establish it as a certain maxim, that in all moral as
well as natural phaenomena, wherever any cause consists of a number
of parts, and the effect encreases or diminishes, according to the
variation of that number, the effects properly speaking, is a compounded
one, and arises from the union of the several effects, that proceed from
each part of the cause. Thus, because the gravity of a body encreases or
diminishes by the encrease or diminution of its parts, we conclude that
each part contains this quality and contributes to the gravity of the
whole. The absence or presence of a part of the cause is attended with
that of a proportionable part of the effect. This connexion or constant
conjunction sufficiently proves the one part to be the cause of the
other. As the belief which we have of any event, encreases or diminishes
according to the number of chances or past experiments, it is to be
considered as a compounded effect, of which each part arises from a
proportionable number of chances or experiments.
Let us now join these three observations, and see what conclusion we can
draw from them. To every probability there is an opposite possibility.
This possibility is composed of parts, that are entirely of the same
nature with those of the probability; and consequently have the same
influence on the mind and understanding. The belief, which attends the
probability, is a compounded effect, and is formed by the concurrence
of the several effects, which proceed from each part of the probability.
Since therefore each part of the probability contributes to the
production of the belief, each part of the possibility must have the
same influence on the opposite side; the nature of these parts being
entirely the same. The contrary belief, attending the possibility,
implies a view of a certain object, as well as the probability does
an opposite view. In this particular both these degrees of belief are
alike. The only manner then, in which the superior number of similar
component parts in the one can exert its influence, and prevail above
the inferior in the other, is by producing a stronger and more lively
view of its object. Each part presents a particular view; and all these
views uniting together produce one general view, which is fuller and
more distinct by the greater number of causes or principles, from which
it is derived.
The component parts of the probability and possibility, being alike
in their nature, must produce like effects; and the likeness of their
effects consists in this, that each of them presents a view of a
particular object. But though these parts be alike in their nature, they
are very different in their quantity and number; and this difference
must appear in the effect as well as the similarity. Now as the view
they present is in both cases full and entire, and comprehends the
object in all its parts, it is impossible that in this particular there
can be any difference; nor is there any thing but a superior vivacity
in the probability, arising from the concurrence of a superior number of
views, which can distinguish these effects.
Here is almost the same argument in a different light.
All our
reasonings concerning the probability of causes are founded on the
transferring of past to future. The transferring of any past experiment
to the future is sufficient to give us a view of the object; whether
that experiment be single or combined with others of the same kind;
whether it be entire, or opposed by others of a contrary kind. Suppose,
then, it acquires both these qualities of combination and opposition, it
loses not upon that account its former power of presenting a view of the
object, but only concurs with and opposes other experiments, that have
a like influence. A question, therefore, may arise concerning the manner
both of the concurrence and opposition. As to the concurrence, there is
only the choice left betwixt these two hypotheses.
First, That the view
of the object, occasioned by the transference of each past experiment,
preserves itself entire, and only multiplies the number of views. Or,
SECONDLY, That it runs into the other similar and correspondent views,
and gives them a superior degree of force and vivacity.
But that the
first hypothesis is erroneous, is evident from experience, which
informs us, that the belief, attending any reasoning, consists in
one conclusion, not in a multitude of similar ones, which would only
distract the mind, and in many cases would be too numerous to be
comprehended distinctly by any finite capacity. It remains, therefore,
as the only reasonable opinion, that these similar views run into each
other, and unite their forces; so as to produce a stronger and clearer
view, than what arises from any one alone. This is the manner, in which
past experiments concur, when they are transfered to any future event.
As to the manner of their opposition, it is evident, that as the
contrary views are incompatible with each other, and it is impossible
the object can at once exist conformable to both of them, their
influence becomes mutually destructive, and the mind is determined to
the superior only with that force, which remains, after subtracting the
inferior.
I am sensible how abstruse all this reasoning must appear to the
generality of readers, who not being accustomed to such profound
reflections on the intellectual faculties of the mind, will be apt to
reject as chimerical whatever strikes not in with the common received
notions, and with the easiest and most obvious principles of philosophy.
And no doubt there are some pains required to enter into these
arguments; though perhaps very little are necessary to perceive the
imperfection of every vulgar hypothesis on this subject, and the little
light, which philosophy can yet afford us in such sublime and such
curious speculations. Let men be once fully perswaded of these two
principles, THAT THERE, IS NOTHING IN ANY OBJECT, CONSIDERed IN ITSELF,
WHICH CAN AFFORD US A REASON FOR DRAWING A CONCLUSION
BEYOND it; and,
THAT EVEN AFTER THE OBSERVATION OF THE FREQUENT OR
CONSTANT CONJUNCTION
OF OBJECTS, WE HAVE NO REASON TO DRAW ANY INFERENCE
CONCERNING ANY
OBJECT BEYOND THOSE OF WHICH WE HAVE HAD EXPERIENCE; I say, let men be
once fully convinced of these two principles, and this will throw them
so loose from all common systems, that they will make no difficulty of
receiving any, which may appear the most extraordinary.
These principles
we have found to be sufficiently convincing, even with regard to our
most certain reasonings from causation: But I shall venture to affirm,
that with regard to these conjectural or probable reasonings they still
acquire a new degr