The Probability of Causes

There are 3 Origins of Chances: Experience, Contrariety, Analogy

My explanation of the probability of chances is only for explaining the probability of causes.

Philosophers say that what the vulgar call ‘chance’ is just a secret and concealed cause. Therefore, we must examine the probability of causes. There are several kinds of the probabilities of causes, all derived from the same origin: the association of ideas to a present impression.

The habit produces the association and arises from the frequent conjunction of objects.

The habit must:

• arrive at its perfection by degrees, and
• acquire new force from each instance that we experience.

The first instance has little or no force.

The second makes some force added to it.

The third becomes still more sensible.

Our judgment arrives at a full assurance by these slow steps.

But before it attains this perfection, it passes through several inferior degrees.

In all of them, it is only a presumption or probability.

Therefore, the gradation from probabilities to proofs is insensible in many cases.

The difference between these kinds of evidence is more easily perceived in the remote differences than in those near and contiguous.

Imperfect Experience as a Kind of Probability and an Origin of Chance

1. Our first experience of anything happens before any proof can exist.

However, no mature person refers to his first experiences of anything all the time. Learned people most commonly have attained only an imperfect experience of many events. But their minds have developed observations on the connection of causes and effects. It gives their minds a new force to its reasonings which allows it to build an argument on one single experience when duly prepared and examined. What we have found once to follow from any object, we conclude will always follow from it. If this maxim is not always certain, it is not because we lack a sufficient number of experiences. It is because we frequently meet contrary experiences. These experiences lead us to the second species of probability, where there is a contrariety in our experience and observation. The Contrariety of Causes as a Kind of Probability and an Origin of Chance 2. The second kind of probability is the one where we reason with knowledge and reflection from a contrariety of past experiments.

Our lives would be very happy if: the same experiences were always conjoined together, and we had nothing to fear but the mistakes of our own judgment, without thinking about nature’s uncertainty. This uncertainty causes our reasoning to consider the contrariety of events because: one observation is frequently contrary to another, and causes and effects do not follow in the same order as we had experienced. Our first question on this contrariety, is the nature and causes of contrariety. The vulgar take things as they first appear.

They attribute the uncertainty of outcomes to an uncertainty in the causes. This uncertainty in the causes makes those outcomes often fail of their usual influence, even if there is no obstacle in their operation. But philosophers do the opposite and instead observe every part of nature.

They see so many principles hidden by minuteness or remoteness. They find that it is possible for the contrariety of outcomes to not come from any contingency in the cause, but from the secret operation of contrary causes. This possibility is converted into certainty by further observation. Upon an exact scrutiny, they see that a contrariety of effects always betrays a contrariety of causes. They see that this contrariety comes from their mutual hindrance and opposition. A peasant sees the stopping of a clock.

The only reason that he can give is to say that there is something wrong. But a craftsman knows that the clock’s spring always acts on the clock’s gears. He perceives that the spring had failed perhaps by dust which stopped the whole movement. From the observation of parallel experiences, philosophers form a maxim that: the connection between all causes and effects is equally necessary, and its seeming uncertainty in some experiences comes from the secret opposition of contrary causes. Philosophers and simple people differ in their explanation of the contrariety of events. But their inferences from it are always: of the same kind, and founded on the same principles. A contrariety of past events might make us hesitate by producing an imperfect transition from the present impression to the related idea.

When the conjunction of any two objects is frequent but not constant, the mind is deteremined to pass from one object to the other. But when the union is uninterrupted and all the instances that we have experienced are uniform and of a piece, this transition becomes habitual. In our life, we find that a constant perseverance in our actions and reasonings creates a strong tendency to continue, even if there are inferior habits proportional to the inferior uniformity of our conduct. This principle sometimes takes place to produce those inferences we draw from contrary phenomena. But ths principle does not commonly influence the mind in this species of reasoning. When we only follow the mind’s habitual determination, we make the transition instantly without any reflection. This habit does not depend on any deliberation. It operates immediately without allowing any time for reflection. But we have few instances of this method in our probable reasonings. We have even fewer than in those derived from the uninterrupted conjunction of objects. In this method of reasoning, we knowingly take into consideration the contrariety of past events. We compare the different sides of the contrariety. We carefully weigh the experiments we have on each side. We may conclude that our reasonings of this kind do not arise directly from the habit. It arises instead in an oblique way which we must now explain. When an object is attended with contrary effects, we:

judge of them only by our past experience, and always consider its subsequent effects as possible. Past experience regulates our judgment on the possibility and probability of these effects.

We always esteem the effect which has been the most common, as the most likely. Two things are to be considered: the reasons which determine us to make the past a standard for the future, and how we extract a single judgment from a contrariety of past events. The supposition that the future resembles the past, is not founded on arguments. It is derived entirely from habit. Habit makes us expect the same train of objects, which we have been accustomed to, for the future. This habit or determination to transfer the past to the future is full and perfect. Consequently, the first impulse of the imagination in this species of reasoning is endowed with the same qualities. When we consider past experiments and find them of a contrary nature, this determination, though full and perfect in itself, presents us with no steady object. It offers us a number of disagreeing images in a certain order and proportion. The first impulse, therefore: is broken into pieces, and diffuses itself over all those images which has an equal share of that force and vivacity derived from the impulse. Any of these past events may again happen.

We judge that, when they do happen, they will be mixed in the same proportion as in the past. If our intention, therefore, is to consider the proportions of contrary events in many instances, the images presented by our past experience must: remain in their first form, and preserve their first proportions. Suppose through time, I find that only 19 ships return out of 20 that go to sea. I see at present 20 ships that leave the port. I transfer my past experience to the future. I expect 19 of these ships as returning safely with one perishing. We frequently run over past events to create a judgment on a 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 we refer the outcome of that event to the imagination. A superior number are supposed to concur on one side. These agreeing images: unite together, and render the idea more strong and lively than: a mere fiction of the imagination, and any idea supported by fewer experiments. Each new experiment is a new stroke of the pencil. Each stroke bestows an additional vivacity on the colours without multiplying or enlarging the figure. This operation of the mind has been explained in the section on the probability of chance. Every past experiment is a kind of chance. We are uncertain whether the object will exist conformable to one experiment or another. For this reason, everything that has been said on the one subject is applicable to both. Thus on the whole, contrary experiments produce an imperfect belief by: weakening the habit, or dividing and afterwards joining that perfect habit. That habit makes us conclude that instances we have no experience of, must resemble the instances which we have experience of. I propose three subtle considerations to justify the second kind of probability.

Just reasoning should retain its force, however subtle, in the same way as matter preserves its solidity: in the air, fire, and animal spirits, and in the grosser and more sensible forms. No probability is so great as not to allow of a contrary possibility because otherwise it would cease to be a probability and become a certainty. That most extensive probability of causes depends on a contrariety of experiments. An experiment in the past proves at least a possibility for the future. The component parts of this possibility and probability are of the same nature, and differ in number only, but not in kind. All single chances are entirely equal. The only circumstance which can give any contingent event a superiority over another is a superior number of chances. The uncertainty of causes is discovered by experience, which presents us with a view of contrary events. When we transfer the past to the future and the known to the unknown, every past experiment has the same weight. Only a superior number of experiments can throw the balance on any side. The possibility, therefore, which enters into every reasoning of this kind, is composed of parts. These parts are of the same nature: among themselves, and with those that compose the opposite probability. We establish a certain maxim, that in all moral and natural phenomena, wherever any cause consists of a number parts and the effect changes according to change in that number, the effects are 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 changes by the change 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 the absence of a proportional part of the effect. This connection or constant conjunction sufficiently proves the one part to be the cause of the other. Our belief of any event changes according to the number of chances or past experiments. Our belief is a compounded effect. Each part of the effect arises from a proportional number of chances or experiments. Let us:

join these three observations, and see what conclusion we can draw from them. There is an opposite possibility to every probability.

This possibility is composed of parts. These parts have the same nature as the probability. Consequently, they have the same influence on the mind and understanding. The belief, which attends the probability, is a compounded effect. It is formed by the concurrence of the several effects which proceed from each part of the probability. Since each part of the probability contributes to producing the belief, each part of the possibility must have the same influence on the opposite side, the nature of these parts being the same. The contrary belief, attending the possibility, implies a view of a certain object, as the probability does an opposite view. In this, both these degrees of belief are alike. Only by producing a stronger and more lively view of its object can the superior number of similar parts in the one can: exert its influence, and prevail above the inferior in the other. Each part presents a particular view.

All these views unite together to produce one general view. This view is fuller and more distinct by the greater number of causes or principles it is derived from. The component parts of the probability and possibility are alike in their nature. They must produce like effects. The likeness of their effects is that each of them presents a view of a particular object. These parts are alike in their nature. But they are very different in their amount. This difference must appear in the effect and in the similarity. The view they present in both cases: is full and entire, and comprehends the object in all its parts, it is impossible that in this particular there can be any difference There is only a superior vivacity in the probability, arising from the concurrence of a superior number of views distinguishing these effects. Here is almost the same argument in a different light.

All our reasonings on the probability of causes are founded on the transferring of past to future. The transferring of any past experiment to the future is enough to give us a view of the object whether: that experiment is single or combined with others of the same kind, and it is entire or is opposed by others of a contrary kind. Suppose it acquires both these qualities of combination and opposition. It does not lose its former power of presenting a view of the object. It only concurs with, and opposes other experiments, that have a like influence. A question may arise on the manner of the concurrence and opposition.

Concurrence is based on two hypotheses: The view of the object, created by the transference of each past experiment preserves itself entirely and only multiplies the number of views. This hypothesis is erroneous from experience. Experience tells us that the belief attending any reasoning, consists in one conclusion, not in many similar ones. Having many conclusions would only distract the mind. Our finite capacity cannot comprehend too many conclusions. The view of the object runs into the other similar and correspondent views, and gives them a superior force and vivacity. This is how past experiments concur when they are transferred to any future event. The contrary views are incompatible with each other. It is impossible that the object can at once exist conformable to both of them. Thus, their influence becomes mutually destructive. The mind is determined to the superior only with that force remaining after subtracting the inferior force. To the general readers, this reasoning is abstruse.

They are not accustomed to such profound reflections on the intellectual faculties of the mind. They will reject as chimerical whatever does not strike with the: common received notions, and easiest and most obvious principles of philosophy. Some pains are required to enter into these arguments. Perhaps very little pains are necessary to perceive the imperfection of: every vulgar hypothesis on this subject, and the little light, which philosophy can afford us in such sublime and such curious speculations. Let men be fully persuaded of these two principles:

There is nothing in any object, considered in itself, which can afford us a reason for drawing a conclusion beyond it Even after the observation of the frequent or constant conjunction of objects, we have no reason to draw any inference on any object beyond those of which we have had experience. These will throw men so loose from all common systems, that they will more easily receive any extraordinary system.

These principles are sufficiently convincing, even with regard to our most certain reasonings from causation. With regard to these conjectural or probable reasonings, they acquire further a new degree of evidence. It is not the object presented to us which makes us draw a conclusion on any other object, because this latter object is supposed as uncertain. The uncertainty is derived from a concealed contrariety of causes in the first presented object. If any of the causes were placed in the known qualities of that object: the causes would no longer be concealed, or our conclusion would no longer be uncertain. But it is equally obvious that if the transference of the past to the future were founded merely on a conclusion of the understanding, it could never bring any belief or assurance. When we transfer contrary experiments to the future, we can only repeat these contrary experiments with their particular proportions. Those proportions could not produce assurance in any single event, unless the fancy: melted together all those images that concur extracted from them a 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. Our belief, however faint, fixes itself on a determinate object. 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 with two reflections:

When the mind forms a reasoning on any matter of fact which is only probable, it views its past experience and transfers it to the future. The mind is presented with so many contrary views of its object. The views of the same kind unite and run into one act of the mind, to fortify and inliven it. But if this multitude of views comes from voluntary imagination and not experience, this effect does not follow. If it follows, it does not follow in the same degree. Custom and education produce belief by a repetition not derived from experience. Yet this requires a long time and a very frequent and undesigned repetition. In general, a person who voluntarily repeats any idea in his mind, supported only by one past experience, would not be more inclined to believe the object’s existence, than if he was contented with just one survey of it. Each act of the mind is separate and independent. It has a separate influence. It does not join its force with the force of its fellows. Each act is not united by any common object. They have no relation to each other. Consequently they make no transition or union of forces. We shall understand this phenomenon better afterwards. My second reflection is founded on: those large probabilities which the mind can judge of, and the minute differences it can observe between them. When the chances or experiments amount to 10,000 on one side and 10,001 on the other, the judgment prefers the latter because of that superiority.

Though it is plainly impossible for the mind to: run over every particular view, and distinguish the superior vivacity of 10,001, when its difference from 10,000 is so small. We have a parallel instance in the affections. According to the above-mentioned principles, when an object produces any passion in us which varies with the different quantities of the object, the passion is not a simple emotion. It instead is a compounded emotion made up of many weaker passions derived from a view of the object’s parts. Otherwise it would be impossible for the passion to increase by the increase of these parts. Thus a man, who desires £1,000, in reality has 1,000 or more desires which seem to make only one united passion. This union betrays itself on every change of the quantity, by his preference for the larger number, even by just 1. So small a difference would not be discernible in the passions. It could not render them distinguishable from each other. Therefore, the difference of our conduct in preferring the greater number, does not depend on our passions. It depends on custom and general rules. The adding of numbers adds to the passion if the numbers are precise and the difference is sensible. From its immediate feeling, the mind can perceive that three guinea coins produce a greater passion than two guinea coins. It transfers this to larger numbers, because of the resemblance. By a general rule, the mind assigns a stronger passion to 1,000 guineas than to 999 guineas. We shall explain these general rules. Those two kinds of probability are derived from:

an imperfect experience, and contrary causes. 3. Analogy as a Kind of Probability and Origin of Chance There is a third kind of probability arising from analogy.

This differs from the two in some material circumstances. According to the above hypothesis, all kinds of reasoning from causes or effects are founded on: the constant conjunction of any two objects in all past experience, and the resemblance of a present object to any one of them. These two invigorate the present object and enlivens the imagination. The resemblance, along with the constant union, conveys this force and vivacity to the related idea that we believe. If you weaken the union or resemblance, you weaken: the transition, and consequently, the belief arising from it. The vivacity of the first impression cannot be fully conveyed to the related idea: if the conjunction of their objects is not constant, or if the present impression does not perfectly resemble any of those, whose union we are used to. In those probabilities of chance and causes above-explained, the constancy of the union is reduced.

In the probability derived from analogy, only the resemblance is affected. Without some degree of resemblance and union, there can be no reasoning. But this resemblance admits of many different degrees. The reasoning becomes proportionally firm and certain. An experiment loses its force when transferred to instances which are not exactly resembling. Though it may still retain as much as may be the foundation of probability, as long as there is any resemblance remaining.