Sec 11-12: Chances, Causes

SEC. 11: THE PROBABILITY OF CHANCES

• To show the full force and evidence of this system, we must:
  • view its consequences
  • explain from the same principles some other species of reasoning derived from the same origin.

• The following philosophers are obliged to comprehend all our arguments from causes or effects under the general term of probability:
  • Those who have:
    • divided human reason into knowledge and probability
    • defined the reason to be that evidence which arises from the comparison of ideas.
• Everyone is free to use his terms in what sense he pleases.
• However, many arguments from causation:
  • exceed probability
  • may be received as a superior kind of evidence.
• It would be ridiculous to say that it is only probable:
  • that the sun will rise tomorrow, or
  • that all men must die
    • Though we have no assurance of these facts than what experience affords us.
• It might be more convenient to distinguish human reason into three kinds:
  1. From knowledge
  2. From proofs
  3. From probabilities.
  • This is to:
    • preserve the common signification of words
    • mark the several degrees of evidence.
• Knowledge means the assurance arising from the comparison of ideas.
• Proofs mean those arguments:
  • derived from the relation of cause and effect
  • entirely free from doubt and uncertainty.
• Probability means that evidence which is still attended with uncertainty.
  • I shall examine probability.

• Probability is reasoning from conjecture.
• It may be divided into two kinds:
  1. Probability founded on chance
  2. Probability arising from causes.

• The idea of cause and effect is derived from experience.
  • Experience presents us with certain objects constantly conjoined with each other.
    • It produces a habit of surveying them in that relation.
      • We cannot survey them in any other relation, without a sensible violence.
  • On the other hand, chance is not real in itself.
    • It is merely the negation of a cause.
    • Its influence on the mind is contrary to the influence of causation.
    • Chance is essential to the mind.
      • It leaves the imagination perfectly indifferent to consider the existence or non-existence of that object it regards as contingent.
• A cause traces the way to our thought.
  • It forces us to survey such certain objects, in such certain relations.
• Chance can only:
  • destroy this determination of the thought
  • leave the mind in its native situation of indifference; in which it is instantly re-instated on the absence of a cause.

• An entire indifference is essential to chance.
• Therefore, no single chance can possibly be superior to another unless it is composed of a superior number of equal chances.
• For if we affirm that one chance can be superior to another, we must affirm that there is something which:
  • gives it the superiority
  • determines the event rather to that side than the other.
• In other words, we must:
  • allow of a cause
  • destroy the supposition of chance established before.
• A perfect and total indifference is essential to chance.
  • One total indifference can never in itself be superior or inferior to another.
  • This truth is acknowledged by every system that forms calculations on chances.

• Chance and causation are directly contrary.
• • It is remarkable that it is impossible for us to conceive this combination of chances needed to render one hazard superior to another, without supposing:
    • a mixture of causes among the chances
    • a conjunction of necessity in some particulars, with a total indifference in others.
• Where nothing limits the chances, every notion of the fancy is on a footing of equality.
  • There cannot be any circumstance to give one the advantage above another.
  • We cannot calculate the laws of hazard unless we allow that there are some causes to make the dice:
    • fall and preserve their form in their fall
    • lie on some one of their sides.
  • It is easy to arrive at a notion of a superior combination of chances, supposing:
    • these causes to operate
    • all the other causes are indifferent and to be determined by chance.
• A die that has four sides marked with a figure and two sides marked with another figure, affords us an obvious and easy instance of this superiority.
  • The mind is here limited by the causes to such a precise number and quality of the events.
  • At the same time, it is undetermined in its choice of any particular event.

• Chance is merely the negation of a cause.
  • It produces a total indifference in the mind, that one negation of a cause and one total indifference can never be superior or inferior to another.
  • There must always be a mixture of causes among the chances to be the foundation of any reasoning.
• We next consider:
  • what effect a superior combination of chances can have on the mind
  • what manner it influences our judgment and opinion.
• We may repeat all the same arguments we used to examine that belief, which arises from causes.
  • We may prove that a superior number of chances produces our assent not by demonstration nor probability.
• By the comparison of mere ideas, we can never make any discovery which can be of consequence in these affairs.
  • It is impossible to prove with certainty that any event must fall on that side where there is a superior number of chances.
• To suppose any certainty in this case, is to overthrow what we have established about the opposition of chances and their perfect equality and indifference.

• In an opposition of chances, it is impossible to determine on which side the event will fall.
  • Yet we can say that it is more likely and probable that it will be on that side where there is a superior number of chances.
  • What is meant by likelihood and probability here?
• The likelihood and probability of chances is a superior number of equal chances.
  • Consequently, when we say it is likely the event win fall on the superior side, rather than on the inferior side, we only affirm that:
    • where there is a superior number of chances, there is actually a superior side
    • where there is an inferior number of chances, there is an inferior side.
      • These are identical propositions, and of no consequence.
• The question is: how a superior number of equal chances:
  • operates on the mind
  • produces belief or assent?
    • Since by arguments, it is not derived from demonstration nor probability.

• To clear up this difficulty, let us suppose that a person takes a die.
  • Four of its sides are marked with one figure.
  • Two of its sides are marked with another figure.
  • He puts this dye in a box with an intention of throwing it.
  • He must:
    • conclude the one figure to be more probable than the other
    • prefer the figure which is inscribed on the greatest number of sides.
  • He believes that this will lie uppermost, though with hesitation and doubt, proportional to the number of chances, which are contrary.
  • These contrary chances reduce and the superiority increases on the other side, his belief acquires new degrees of stability and assurance.
• This belief arises from an operation of the mind on the simple and limited object before us.
  • Its nature will be the more easily discovered and explained.
• We only have one die to contemplate, to comprehend one of the most curious operations of the understanding.

• This die has three circumstances worthy of our attention.
  1. Certain causes, such as gravity, solidity, a cubical figure, etc. which determine it to:
     • fall
     • preserve its form in its fall
     • turn up one of its sides.
  2. A certain number of sides which are supposed indifferent.
  3. A certain figure inscribed on each side.
• These three particulars form the whole nature of the die
  • These are are the only circumstances regarded by the mind in its forming a judgment on the result of such a throw.
• Therefore, let us carefully consider what must be the influence of these circumstances on the thought and imagination.

1. The mind is determined by custom to pass from any cause to its effect.
   • On the appearance of the one, it is almost impossible for the mind not to form an idea of the other.
   • Their constant conjunction in past instances has produced such a habit in the mind.
     • It always:
       • conjoins them in its thought
       • infers the existence of the one from that of its usual attendant.
   • When it considers the die as no longer supported by the box, it cannot, without violence, regard it as suspended in the air.
     • It naturally:
       • places it on the table
       • views it as turning up one of its sides.
   • This is the effect of the intermingled causes needed to form any calculation concerning chances.

2. It is supposed, that though the die is determined to fall and turn up one of its sides, there is nothing to fix the particular side.
   • This is determined entirely by chance.
   • The very nature and essence of chance is a negation of causes.
   • The leaving the mind in a perfect indifference among those events, which are supposed contingent.
   • When the thought is determined by the causes to consider the die 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 cause is the the throwing of the dye.
   • The effect is the turning up one of the six sides.
   • The imagination passes from the cause to the effect
     • It feels an impossibility of:
       • stopping short in the way
       • forming any other idea.
   • But as all these six sides are incompatible, and the die cannot turn up above one at once, this principle does not direct us to consider all of them at once as lying uppermost.
     • We see this as impossible.
   • It does not direct us with its entire force to any particular side
     • For in that case, this side would be considered as certain and inevitable.
     • Instead, it directs us to the whole six sides as to divide its force equally among them.
   • We conclude 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 die:
  • the causes
  • the number and indifference of the sides
• We have learned how they:
  • give an impulse to the thought
  • 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: the figures inscribed on each side.
• Where several sides have the same figure inscribed on them, they must:
  • concur in their influence on the mind
  • unite on one image or idea of a figure all those divided impulses, that were dispersed over the several sides, on which that figure is inscribed.
• Were the question only what side will be turned up, these are all perfectly equal
  • No one could 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:
• The impulses belonging to all these sides must:
  • re-unite in that one figure
  • 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.
  • Therefore, the impulses of the former are superior to those of the latter.
• But:
  • the events are contrary.
  • it is impossible both these figures can be turned up
• Thus:
  • the impulses likewise become contrary
  • the inferior destroys the superior, as far as its strength goes.
• The vivacity of the idea is always proportional to the degrees of the impulse or tendency to the transition.
  • Belief is the same with the vivacity of the idea, according to the precedent doctrine.

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SEC 12: THE PROBABILITY OF CAUSES

• My explanation of the probability of chances only serves to assist us in explaining the probability of causes.
  • Since philosophers say that what the vulgar call chance is nothing but a secret and concealed cause.
  • Therefore, we must chiefly 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
      • acquire new force from each instance, that falls under our observation.
  • 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 in many cases insensible.
  • The difference between these kinds of evidence is more easily perceived in the remote degrees, than in the near and contiguous.

• The species of probability here explained is the first in order.
  • It naturally takes place before any entire proof can exist.
  • However, no mature person can be acquainted with it any longer.
• People of the most advanced knowledge, most commonly have attained only an imperfect experience of many particular events.
  • This naturally produces only an imperfect habit and transition.
• The mind forms another observation on the connection of causes and effects.
  • It then gives new force to its reasoning from that observation.
  • Through that observation, the mind 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 always follow from it.
  • If this maxim is not always certain, it is not for a lack of a sufficient number of experiments, but because we frequently meet contrary instances.
    • These instances lead us to the second species of probability, where there is a contrariety in our experience and observation.

• It would be very happy if:
  • the same objects were always conjoined together
  • we had nothing to fear but the mistakes of our own judgment, without having any reason to apprehend nature’s uncertainty.
• But since one observation is frequently contrary to another, and that causes and effects do not follow in the same order, of which we have experience, we are obliged to vary our reasoning, on account of this uncertainty.
  • We take into consideration the contrariety of events.
  • The first question concerns the nature and causes of the contrariety.

• The vulgar take things according to their first appearance.
  • They attribute the uncertainty of events to an uncertainty in the causes.
    • This uncertainty makes them often fail of their usual influence.
      • Though they meet with no obstacle nor impediment in their operation.
• In almost every part of nature, there is a vast variety of springs and principles hidden by their minuteness or remoteness.
• Philosophers find that it is possible that 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 further observation, when they remark that on an exact scrutiny, a contrariety of effects always:
    • betrays a contrariety of causes
    • proceeds from their mutual hindrance and opposition.
• A peasant can give no better reason for the stopping of any clock than to say that it does not go right.
  • But an artisan easily perceives that the same force in the spring or pendulum always has the same influence on the wheels, but fails perhaps by dust which stops the whole movement.
• From the observation of several parallel instances, philosophers form a maxim that:
  • the connection between all causes and effects is equally necessary
  • its seeming uncertainty in some instances comes from the secret opposition of contrary causes.

• But however philosophers and the vulgar differ in their explanation of the contrariety of events, their inferences from it are always:
  • of the same kind
  • founded on the same principles.
• A contrariety of past events may give us a hesitating belief for the future in two ways.
  1. By producing an imperfect habit and transition from the present impression to the related idea.
  2. When the conjunction of any two objects is frequent but not entirely constant, the mind is determined to pass from one object to the other.
     • But this is not done with an entire a habit, as when:
       • the union is uninterrupted
       • all the instances we have ever met with are uniform and of a piece.
     • We commonly find that a constant perseverance in any course of life produces a strong inclination and tendency to continue for the future.
       • Even if there are habits of inferior force proportional to our conduct’s inferior steadiness and uniformity.

• This principle sometimes:
  • takes place
  • produces those inferences we draw from contrary phenomena.
• This principle is not the one that most commonly influences the mind in this species of reasoning.
• When we only follow the mind’s habitual determination, we make the transition instantly without any reflection.
• The custom does not depend on any deliberation.
  • It operates immediately without allowing any time for reflection.
• But we have few instances of this method of proceeding in our probable reasonings.
  • We have even fewer than in those derived from the uninterrupted conjunction of objects.
• In the former species of reasoning, we commonly 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
  • always consider the effects, which we have observed to follow from it, 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
  • how we extract a single judgment from a contrariety of past events.

1. 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.

2. 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
     • diffuses itself over all those images which partakes 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
  • preserve their first proportions.
• Suppose by long observation, I have found that only 19 ships return 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 represent to myself 19 of these ships as returning safely with one perishing.
• We frequently run over those several ideas of past events to form a judgment on a single event which appears uncertain.
  • This consideration must:
    • change the first form of our ideas
    • draw together the divided images presented by experience.
      • Since we refer the determination of that particular event to the imagination.
  • Many of these images are supposed to concur.
    • A superior number are supposed to concur on one side.
• These agreeing images:
  • unite together
  • render the idea more strong and lively than:
    • a mere fiction of the imagination
    • 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.

• To justify this second species of probability further, where we reason with knowledge and reflection from a contrariety of past experiments, I propose the following subtle considerations.
• 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 the in the grosser and more sensible forms.

1. 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 most extensive probability of causes depends on a contrariety of experiments.
   • An experiment in the past proves at least a possibility for the future.

2. The component parts of this possibility and probability:
   • are of the same nature
   • 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
    • with those that compose the opposite probability.

3. We may establish it as 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
   • 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
       • 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
  • 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
    • 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
  • 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
    • 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.
  • As to the concurrence, there is only the choice left between these two hypotheses.
    1. The view of the object, created by the transference of each past experiment:
       • preserves itself entirely
       • only multiplies the number of views.
    2. The view of the object:
       1. runs into the other similar and correspondent views
       2. gives them a superior force and vivacity.
• The first 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
      • in many cases, be too numerous to be comprehended distinctly by any finite capacity.
• The only reasonable opinion remains, that these similar views:
  • run into each other
  • unite their forces to produce a stronger and clearer view, than what arises from any one alone.
• 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.

• I know how abstruse this reasoning is to the general readers.
  • 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
    • 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
    • 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 concerning any object beyond those of which we have had experience.
• These will throw men so loose from all common systems, that they will make no difficulty of receiving any extraordinary system.
  • These principles are 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.

1. It is obvious that in reasonings of this kind, it is not the object presented to us, which, considered in itself, affords us any reason to draw a conclusion on any other object or event.
   • Because this latter object is supposed uncertain.
   • The uncertainty is derived from a concealed contrariety of causes in the former.
   • 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.

2. 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
       • 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:
  1. 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.

2. My second reflection is founded on:
   • those large probabilities which the mind can judge of
   • 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
    • 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.
  • 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.
  • The composition betrays itself on every change of the object, by the preference he gives to the larger number, if superior only by a unite.
• 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 guineas produce a greater passion than two guineas.
    • 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.

• These two species of probability are derived from:
  • an imperfect experience
  • contrary causes.
• There is a third species of probability arising from analogy.
  • This third differs from the two in some material circumstances.
• According to the above hypothesis, all kinds of reasoning from causes or effects are founded on two particulars:
  • the constant conjunction of any two objects in all past experience
  • 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.
  • The resemblance, along with the constant union, conveys this force and vivacity to the related idea which we believe.
• If you weaken the union or resemblance, you weaken:
  • the principle of transition
  • consequently, the belief arising from it.
    • The vivacity of the first impression cannot be fully conveyed to the related idea:
      • 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, 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 proportionably 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.

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