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 'tis 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 'tis 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.
'Tis 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. 'Tis
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, 'tis 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.
'Twould 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 'tis
frequently found, that one observation is contrary to another, and that
causes and effects follow not in the same order, of which we have 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 'tis 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
hinderance 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 artisan 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 phenomena; though I
am persuaded 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.
'Tis 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 'tis 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; 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 'twould 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 'tis 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 discovered by experience, which
presents us with a view of contrary events, 'tis plain that, when we
transfer the past to the future, the known to the unknown, every past
experiment has the same weight, and that 'tis only a superior number
of them, which can throw the balance 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 phenomena, wherever any cause consists of a
number of parts, and the effect increases or diminishes, according
to the variation of that number, the effect, 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 increases or diminishes by the increase 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, increases or diminishes according to the number of chances
or past experiments, 'tis 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, 'tis 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 transferred to any future
event. As to the manner of their _opposition_,'tis evident that, as the
contrary views are incompatible with each other, and 'tis 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 persuaded 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 degree of
evidence.
_First_,'tis obvious that, in reasonings of this kind, 'tis not the
object presented to us, which, considered in itself, affords us any
reason to draw a conclusion concerning any other object or event. For
as this latter object is supposed uncertain, and as the uncertainty is
derived from a concealed contrariety of causes in the former, were any
of the causes placed in the known qualities of that object, they would
no longer be concealed, nor would our conclusion be uncertain.
But, _secondly_,'tis equally obvious in this species of reasoning, that
if the transference of the past to the future were founded merely on
a conclusion of the understanding, it could never occasion any belief
or assurance. When we transfer contrary experiments to the future,
we can only repeat these contrary experiments with their particular
proportions; which could not produce assurance in any single event upon
which we reason, unless the fancy melted together all those images
that concur, and extracted from them one single idea or image, which
is intense and lively in proportion to the number of experiments from
which it is derived, and their superiority above their antagonists.
Our past experience presents no determinate object; and as our belief,
however faint, fixes itself on a determinate object, 'tis evident that
the belief arises not merely from the transference of past to future,
but from some operation of the _fancy_ conjoined with it. This may lead
us to conceive the manner in which that faculty enters into all our
reasonings.
I shall conclude this subject with two reflections which may deserve
our attention. The _first_ may be explained after this manner: When
the mind forms a reasoning concerning any matter of fact, which is
only probable, it casts its eye backward upon past experience, and,
transferring it to the future, is presented with so many contrary
views of its object, of which those that are of the same kind uniting
together and running into one act of the mind, serve to fortify and
enliven it. But suppose that this multitude of views or glimpses of an
object proceeds not from experience, but from a voluntary act of the
imagination; this effect does not follow, or, at least, follows not in
the same degree. For though custom and education produce belief by
such a repetition as is not derived from experience, yet this requires
a long tract of time, along with a very frequent and _undesigned_
repetition. In general we may pronounce, that a person, who would
_voluntarily_ repeat any idea in his mind, though supported by one
past experience, would be no more inclined to believe the existence of
its object, than if he had contented himself with one survey of it.
Beside the effect of design, each act of the mind, being separate and
independent, has a separate influence, and joins not its force with
that of its fellows. Not being united by any common object producing
them, they have no relation to each other; and consequently make no
transition or union of forces. This phenomenon we shall understand
better afterwards.
My _second_ reflection is founded on those large probabilities which
the mind can judge of, and the minute differences it can observe
betwixt them. When the chances or experiments on one side amount to ten
thousand, and on the other to ten thousand and one, the judgment gives
the preference to the latter upon account of that superiority; though
'tis plainly impossible for the mind to run over every particular view,
and distinguish the superior vivacity of the image arising from the
superior number, where the difference is so inconsiderable. We have a
parallel instance in the affections. 'Tis evident, according to the
principles above mentioned, that when an object produces any passion in
us, which varies according to the different quantity of the object; I
say, 'tis evident, that the passion, properly speaking, is not a simple
emotion, but a compounded one, of a great number of weaker passions,
derived from a view of each part of the object; for otherwise 'twere
impossible the passion should increase by the increase of these parts.
Thus, a man who desires a thousand pounds has, in reality, a thousand
or more desires which, uniting together, seem to make only one passion;
though the composition evidently betrays itself upon every alteration
of the object, by the preference he gives to the larger number, if
superior only by an unit. Yet nothing can be more certain, than that
so small a difference would not be discernible in the passions, nor
could render them distinguishable from each other. The difference,
therefore, of our conduct in preferring the greater number depends not
upon our passions, but upon custom and _general rules_. We have found
in a multitude of instances that the augmenting the numbers of any sum
augments the passion, where the numbers are precise and the difference
sensible. The mind can perceive, from its immediate feeling, that three
guineas produce a greater passion than two; and _this_ it transfers
to larger numbers, because of the resemblance; and by a general rule
assigns to a thousand guineas a stronger passion than to nine hundred
and ninety-nine. These general rules we shall explain presently.
But beside these two species of probability, which are derived
from an _imperfect_ experience and from _contrary_ causes, there
is a third arising from _analogy_, which differs from them in some
material circumstances. According to the hypothesis above explained,
all kinds of reasoning from causes or effects are founded on two
particulars, viz. the constant conjunction of any two objects in all
past experience, and the resemblance of a present object to any one
of them. The effect of these two particulars is, that the present
object invigorates and enlivens the imagination; and the resemblance,
along with the constant union, conveys this force and vivacity to
the related idea; which we are therefore said to believe or assent
to. If you weaken either the union or resemblance, you weaken the
principle of transition, and of consequence that belief which arises
from it. The vivacity of the first impression cannot be fully conveyed
to the related idea, either where the conjunction of their objects
is not constant, or where the present impression does not perfectly
resemble any of those whose union we are accustomed to observe. In
those probabilities of chance and causes above explained, 'tis the
constancy of the union which is diminished; and in the probability
derived from analogy, 'tis the resemblance only which is affected.
Without some degree of resemblance, as well as union, 'tis impossible
there can be any reasoning. But as this resemblance admits of many
different degrees, the reasoning becomes proportionably more or less
firm and certain. An experiment loses of its force, when transferred to
instances which are not exactly resembling; though 'tis evident it may
still retain as much as may be the foundation of probability, as long
as there is any resemblance remaining.