## 28 Feb 2009

### Hume, A Treatise of Human Nature, Book 1, Part 3, Sect 12 Of the Probability of Causes §§288-312

by [Search Blog Here. Index-tags are found on the bottom of the left column.]

[The following is summary, up to the end where I reproduce this section in full. My commentary is in brackets. Paragraph headings are my own.]

David Hume

A Treatise of Human Nature

Book I: Of the Understanding

Part III: Of Knowledge and Probability

Section XII: Of the Probability of Causes

§288 Causes Secret and Concealed

Previously we examined how the probability of chances influences our mind. We discovered that we believe more likely outcomes, because there are more common possibilities that recall and combine influence on our mind. The result is that our idea for the more likely outcome is made more vivid in our imagination. This causes us to believe-in it more.

Hume reminds us that we are more interested in causal relations than chance ones. So our previous discussion on chance should now serve our understanding of cause.

There is a reason this might be important. Some argue that really nothing operates by chance. According to this perspective, when people say something happened by chance, that really means they just did not figure out the cause.

Hume will now analyze this sort of probability that has a 'secret and concealed caused.' We call them the 'probabilities of cause.'

§289 Forces Progressing from Probability to a Perfect Pitch of Proof

Recall our Caesar example [in §§193-195.] None of us saw his murder on the senate steps. But some people did see it. Their accounts were passed on to first-generation historians. These accounts continued to be passed down through the generations until arriving at the historians who wrote our school books. So we have an idea of Caesar's murder. And it comes from a direct sense impression. However, there is a chain of causal conveyances mediating between the event and our reception of the idea for it.

More often, the associations are immediate. Every time in the past that someone let-go-of something, it dropped. So when we see someone's hand let slip an egg, we reach out to catch it. First we have the present impression of the egg slipping from the person's hand. Our imaginations instantly associate the slipping egg with the idea of it splattering on the floor.

Now let's imagine that we manage an egg farm. Many workers handle eggs. Frequently we see them be dropped. The image of eggs falling from people's hands has been "burned into our minds" so to speak.

We go home. Our young child has found a fresh egg. He holds it so tight we first worry it will crush. Then mother enters the room with a shiny spoon. Our child loses interest in the egg and now wants to grab the spoon. So we see his grip slip from his egg. Not only do we reach for the egg, we lunge ourselves across the room, and actually catch it. For the image of eggs smashing on floors is so vivid we know it is real even before it happens. And because we have so many times attempted to catch falling eggs, our habits have enhanced our reflexes in these instances.

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. (130c.d emphasis mine)

The first day we managed the egg factory, we saw our first egg slip. We stood frozen, more surprised than ready for action. Then we helped clean it up. Factory production paused. The next time we saw an egg slip from someone's hand, our arms twitched a bit, as a faint image of the spattered egg flashed briefly in our mind. Again we cleaned it and paused production. After each successive slip, the associated image of the egg messing the floor becomes more vibrant in our mind. It takes on a force. We believe it is real. And we are moved to act. After many years of these experiences, we became experts. If someone nearby loses grip on an egg, we have no problem saving it.

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. (130d my emphasis)
Eggs are not the only thing we have seen fall. In fact, every dropped thing falls [so long as it is heavier than air.]

Now imagine that we are an elementary physics teacher. A student dares us: prove that gravity exists. We hold out a book. Then we pause, and let go. It hits the ground. Why do the students laugh? Because by dropping the book, we are doing more than showing one case. We are really suggesting that this is as common and obvious as something could possibly be. We always see things fall. To do it one more time just reminds us of how constant the phenomenon is.

But really it did not begin so obvious. The image of things falling is not so vibrant and forceful in our child's mind. That is why he so easily let the egg slip. He has not developed the tendency to evoke vibrant ideas of things hitting the ground when they are released. The egg-farm manager also was a kid who dropped things. But after many sense-impressions of gravity's effects, he gradually became acutely sensitive to this phenomenon. Soon, one need only let-go of something once to demonstrate gravity. For it evokes in our mind an undeniable vivid idea of it falling to the ground.

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. (130-131 my boldface)

§290 Proof and Repetition

So we have all seen things fall enough to find any one instance to be a demonstration. But, human beings have let-go-of things countless times in the species' past. And we have seen only a very tiny portion of those instances. And there are many more to come, which makes our knowledge even more diminished. Some people even devote their lives to observing the effects of gravity. But even they have very imperfect knowledge.

Consider that to make a logical demonstration, we need absolute certainty. So we need to know that all other possible explanations are self-contradictory. For example, we know that circles are curvilinear. The other possibility is that circles are rectilinear. But this is saying there could be for example a square circle. That is contrary to the definition of the circle. Hence we can say that it is logically demonstrable that circles are curvilinear.

However, we do not have such strong demands for experimental demonstrations. We do not expect scientists to show us every instance of a phenomenon, to prove that there are never any exceptions. Instead, we take every confirming instance to add to the strength of their argument. But the possibility always remains that counter-examples can be discovered to shed doubt on their experimental claims.

Hume will now examine these cases where there are contrary instances. They belong to the second species of probability.

§291 The Contrariety of Events

A more consistent world would be so much easier to comprehend. But as soon as we think we find some rule, someone else presents an anomalous case that the rule cannot explain. We have no choice but to consider the "contrariety of events."

Hume will now examine the causes and nature of this phenomenon.

§292 Vulgar Probability
from the
Secret Opposition of Contrary Causes

We spoke before of how it is common for people to explain things as being the result of chance. Some philosophers would argue that they came to this conclusion really because they failed to determine the real cause. And yet, such "vulgar" people go about their lives without any added difficulties by presuming things happen by chance.

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. (132a)
So we are watching a video of someone holding a pencil. He let's go. But it does not drop. It floats from his hand, gracefully drifting through the air. Clearly we are watching a video of people in outer space. Now imagine that a child who has not yet learned about space happens to see this video. Then he grabs a pen and lets-go to see if it floats. And he keeps trying, each time releasing the pen more gently and carefully. The cause of things falling for him is usually letting-go. The effect is the thing falling. But here the pen floats and does not fall. So in the space video, the effect contradicts the idea that his mind normally evokes when he sees this cause. This leads the child to think that there is some chance that maybe one of the times he releases something, it will float instead of drop. And perhaps he one day becomes an astronaut and experiences this as the normal condition of outer-space.

So in this way, contrary effects caused the child to think there was only a probability of things falling, and not a certainty. The physicist might see things differently. He would not see the floating pen as an effect that is contrary to a commonly known cause. For, he knows that the cause of things dropping on earth is gravity. And there is no gravity in outer-space. So actually, the cause for the pen floating is a cause that is contrary to the cause of the pen dropping on earth. For, a lack of gravity is contrary to a presence of gravity.

Certain philosophers take this to always be the case. So sometimes "vulgar" people attribute contrary evidence to probabilities. But certain philosophers argue that all these cases of contrary effects are really brought-about by contrary causes that we might not yet know.

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. (132bc)
If the clock-artisans cannot at first determine the cause, they do not conclude the problem happens by chance. For they know there is always some explanation for why clocks stop. Philosophers, then, are like meta-artisans. They first note that there are so many cases where there is a hidden cause. Then they inductively infer that in all cases there is a secret cause.

§293 The Secret Cause for Believing in Secret Causes

Hume refutes by turning our attention to mental operations involved in both the philosopher's and the peasant's mind.

Imagine the child watches the space-man video numerous more times. Then he watches another video of someone letting-go-of a pen. But it is not clear whether-or-not the video is taken in space. Before seeing the space video, the child only tended to call to mind things falling when someone released an object. But now, he has two tendencies or habits of association. He has seen many more things fall than float when released. So when watching this new video, the idea of the pen falling is much more vivid in his mind. So he has a stronger tendency to believe the pen will drop, because he has developed a stronger habit of evoking such ideas when having these sense-impressions. Nonetheless, he also has another weaker tendency to call to mind the idea of the pen floating. He has seen fewer of these cases. So the image is less vibrant in his imagination. Hence he believes less in its reality.

But what is interesting here is that both contrary tendencies are present at the same time. [We will later return to this topic when discussing Deleuze's divergent series.]

Now imagine that the physicist also now watches the new video where it is not clear whether or not it was shot in space. When the space-man releases the pen, the physicists will also have two associative tendencies. The philosophers who argue for "secret causes" would say that the child hesitated to have one conclusion, because he thought there was a chance that things can float. The child does not know there are different secret causes. But what about the physicist? Why does he not imagine a single outcome? It is because he knows that there are two possible causes. And he imagines both. For, he has no way of knowing which cause is present in this case. So philosophers who take-up the "secret cause" position would say that the reason the scientist is unsure is because he actually does know there are secret causes at work. And they could be one cause or another. He just does not know which.

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. (133a emphasis mine)

Both the child and the physicist experienced divergent associative tendencies. The child did so, because in the past he had contrary experiences from the same sense-impression of the cause. But so too for the physicist. He also is unsure, because he too has seen contrary effects from the same sense-impression. So Hume's point is that this discussion about secret causes is irrelevant for explaining how we understand cause. Because either way, we learn causes from past experiences.

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. (132c)

§294 Unhesitating Habits

So we sometimes hesitate to make a causal inference on account of incompatible divergent associative tendencies. However, most times we instantly make the transition from a sense impression to evoked idea, and also at the same time believe in it.

As the custom depends not upon any deliberation, it operates immediately, without allowing any time for reflection. (133bc)
So we almost never hesitate when there is consistently an "uninterrupted conjunction of objects."

However in cases of probable reasonings, we often take into account contrary evidence. But habit does not allow for such hesitations. So we obtain this type of reasoning not directly from habit but from an "oblique manner" that Hume will now discuss.

§295 The Probability of Possibility

So let's return again to the floating pen example. We saw that objects with contrary effects lead us to have diverging associative tendencies. We judge that each inference that we could draw is no more than a possibility. But, if one effect was more common in the past, we judge its probability also, and say that it is more likely. So Hume will consider two things:
1) the reasons that lead us to use the past as a standard for what we expect in the future, and
2) our way of obtaining a single judgment about a cause even when we experienced different opposing effects in the past.

§296 The Future is a Habit from the Past

We know that we expect the future to resemble the past. Is this based on any rational argumentation? We seem instead to have just become accustomed to expect the "train of objects" to continue-on in the future just as they have in the past. So this expectation is based on habit and not rational reasoning. It is the basis for the imagination's "inferences" from sense impressions of causes to the idea of their usual effects.

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. (134a)

§297 Scattered Shattered Forces

Yet, we have found that our past experiences are not always consistent. In some cases a cause has one certain result, and in other cases it has another particular effect. Such an experience does not present us with one "steady object," but rather offers us many disagreeing images.

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 deriv'd from the impulse. Any of these past events may again happen; and we judge, that when they do happen, they will be mix'd in the same proportion as in the past. (134bc emphasis mine)

§298 Predicting Peril at Sea:
A New Pencil Stroke Scores Each Idea

To understand Hume's next point, he has us imagine that we watch ships at port. Many times in the past we see a merchant fleet of twenty ships set-sail together to distant lands. And every time twenty ships embark, we discover months later that only nineteen return. So the next time we see twenty set-off, we transfer our past experience to the future. Hence we represent in our minds nineteen of these ships returning, and one perishing at sea.

But suppose a couple times in the past all twenty returned. The next time twenty set out, we will have to consider both possibilities. But in order to do so, each of those past instances will have to be preserved as they originally were, in their "first form." All those images of nineteen ships returning group-together, and all those images of twenty ships returning as well form a group. The number of images with nineteen ships returning is a far greater number.

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. (135a)
We previously detailed this mental operation. So we need not describe it further. Everything we have said regarding the probability of chance may as well apply to these instances where there is a probable cause.

§299 Crisis of Belief

Normally we would expect things to happen as they have in the past. But we see that contrary past experiences either
1) cause us to be altogether uncertain of the outcome, or
2) divide up the possibilities into groups and believe the majority.

§300 A Trial by Fire for Force of Reason

Hume will now further explain this second type of probability where there is contrary past evidence.

These inconsistencies of the past could potentially cause us to be unsure about what is the case. Hume claims that nonetheless our sound reasoning will hold throughout these trials of ambiguity.

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. (135c)

§301 We're Certain that Probabilities are Uncertain

There can only be curvilinear circles; for, there cannot be its alternative, square circles. This is certain. So if something is certain, then nothing can be otherwise. But the earth's rotation may someday slow enough that the sun stopped rising. So it is only probable that the sun will rise tomorrow. Thus if something is probable, then there are different possible outcomes.

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. (135c)

We know that
a) probability results from contrariety in past experiments, and
b) if one experiment has a certain outcome, it is possible that this one outcome may result again in the future from the same cause.

§302 Possibility and Probability are Only Quantitatively Different

Something is probable when there is a predominance of common outcomes, even though some exceptions exist. Something is possible when there is a good chance that any number of different outcomes could happen. So really there is only a quantitative difference between probability and possibility. They both result from the same mental phenomena. But there are a greater quantity of common outcomes when something is probable.

§303 The Gravity of Belief

To grasp the quantitative proportionality between causes and effects, Hume has us consider gravity. We can make something larger by adding more parts to it. And the larger it is, the more gravity the body has. So we come to regard each part as having a quality -- gravity -- that contributes to the whole. So the more parts, the more gravity. And as we remove parts, there is proportionally less gravity. "This connexion or constant conjunction sufficiently proves the one part to be the cause of the other." (136c) In an analogous way, each common past experience adds more "weight" to our whole belief in that outcome.

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. (136d)

§304 Diverging Beliefs

So we know that if something is necessary, then there can be no other possibility. But if something is probable, then there is another possibility that is improbable. We obtain this alternate possibility from experiencing the cause having unexpected effects. Each one of these prior experiences of an anomalous effect is a "part" of that alternate possibility. But, we also obtained our sense for the probable outcome from an overwhelming number of experiences with the same expected outcome. So probability, like possibility, is made up of parts that are of the same nature in either case.

When the expected effect repeats itself, it becomes more vivid in our imaginations. This causes us to believe it more. But likewise, each past experience of the unexpected effect reinforces the vivacity of the idea for the alternate outcome. Hence it too enhances a contrary belief. But there is only a quantitative difference between the belief in the possibility and the belief in the probability. For, they are qualitatively the same and result from the same source and procedure.

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 deriv'd. (137a.b boldface mine)

§305 Numerical Vibrancy in Probability and Possibility

So the component parts of probability and possibility are alike in nature (that is, they are qualitatively the same). So they must produce like effects. And we see that in fact they do. Both probability and possibility presents a view of some particular object. However, we saw that they are quantitatively different.

though these parts be alike in their nature, they are very different in their quantity and number. (137c)
And we noted that this results in probability having superior vivacity, "arising from the concurrence of a superior number of views. (137d)

§306 The Battle for Belief

Hume will give nearly the same argument but from another perspective.

When we consider an effect to be a probable outcome of a present sense-impression, then we are transfering the past into the future.

Now if in the past we only had one such experience of the cause, that still is enough to lead us to infer the effect. But the force of the inference will be stronger if there were more experiences of the same causal connection. For, repeated instances increases the vibrancy of the idea.

Hume makes an important point that will be relevant for Deleuze's Humeanism. So we have the large collection of causal relations that we take as probable, and as well we have the smaller collection of alternate effects that we regard as only possible. Whenever we add more impressions to the smaller possible collection, we make it more vibrant. But that does not subtract from the larger-collection's vibrancy.

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. (138a emphasis mine)
But Hume addresses concerns that arise from this idea.

Consider the predominant causal association. What happens to the grouping when a new instance is added to it? There are two possible answers.

1) the idea inferred as an effect is not changed. Rather, there are just more remembered instances of its connection with a common cause. Or,

2) all the common instances of the causal association "run into each other," giving them "a superior degree of force and vivacity." (138b emphasis mine)

To decide which option is true, Hume first has us consider belief. When there is a greater multitude of common causal pairings, that increases our belief in the inferred effect. But if there were just a higher quantity of common instances, when we perceive the cause, our mind might be scattered among the multitude of common recurrences. This would only burden our mental processes, and cause us to be more hesitant in making the inference. But we know that stronger beliefs make us less hesitant. So the first option -- that the inferred idea remains unchanged -- is not true. Hence the second option must be the case:

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. (138c)
We said before that new contrary minority impressions do not subtract from the majority's vibracy. So in this way it is purely positive. But that does not mean that both 'win.' There is a war. There is a contest of forces: the force of each group's vibrancy clashes with each other. Which ever one is numerically greater, is considered the more probable one. And in the end it wins our beliefs.

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. (138d emphasis mine)

§307 Please Accept Hume's Sublime and Curious Speculations

Hume now sympathizes with us. He acknowledges that we might find it too difficult to grasp such astruse or uncommon ideas.

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. (139a)
So Hume will simply state his basic theses:

1) No object's qualities by itself implies some other object, even if it is causally related.
That there is nothing in any object, consider'd in itself, which can afford us a reason for drawing a conclusion beyond it; and,
2) Even after we discover constant conjunctions between objects, we still cannot conclude there be any causal connnections between objects we have not yet experienced at least once before.

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. (139b)
As soon as we realize these basic principles, we will be in radically new philosophical territory. But these basic notions should be intuitively obvious to us. We know these two principles from a simple examination of our experiences. So if these radical propositions are understandable, then we should also not reject any other of Hume's original claims merely on the basis that they are uncommon to philosophy.

Nonetheless, Hume thinks he needs to provide the following evidence for probabalistic reasonings to make his case fully compelling.

§308 Rationality Spoils Necessity

We awake early. It is still dark. But there is a glimmer of light on the eastern horizon. Our minds instantly conjure the idea of the sun emerging. For dawn draws upon us. There has never been a morning minus dawn.

But if we just use our rational capacities to consider dawn's glimmer, we need not conclude it is necessary to be conjoined with the coming dawn. For we need only think rationally about the physics of bodies in space. We see only one side of the moon at all times. Its outer-side faces away from its center of orbit, which is the earth. Its rotation has slowed to the point that its rotation has "harmonized" with its revolution. Eventually this may happen with earth. Our rotation might slow someday to the point where only one side faces the sun. Then, we need only travel to the part of the earth that just sees the glimmer of sun on the horizon. But never will the sun show us the dawn at that location, because our side of the earth will no longer turn toward the sun. In fact, if we rationally examine the physics of the sun's tidal affect on the earth, we can project that someday this could happen [see the last paragraph of this page

So although every human being who ever lived has experienced a dawn for every day [unless near the poles,] we can rationally presuppose that there might be "concealed contrariety of causes." If we knew all the hidden causes, we could rationally conclude that a cause and effect are necessary. But since we never can know, we can never be rationally certain, even though we fully believe without any doubts that the sun will rise tomorrow. But we have no contrary connection between morning and no-dawn that could cause us to believe something else. So if we went no further than the "inferences" that our minds make through passive association, then we we could make causal inferences based on necessary connections, even if rationally there would be reason to doubt.

§309 The Forces of Inference

Let's consider another matter. Past experiences of causal relations assure us that we may expect the cause to be conjoined with its effect in future instances. This assurance leads to us believing in it.

Now it is possible that we obtain this assurance and belief by reasoning rationally that the effect will ensue or be conjoined with its cause. But, we know that we experience contrary outcomes from the same cause. So what determines which one we believe-in? We noted that the supposed "hidden" causes are often too difficult to discern or deduce. So it cannot be by rational reasoning that we determine which one we believe in. It must instead be the one with the more predominant history of recurrence. But we saw also that even this alone is not enough. Because if it were just the same image that repeated without it being modified, then we would be burdened by recalling all the instances. Instead, it must be that all the common instances are combined into one that is more compelling than the other possibilities. If this is so, then this image becomes more vivid and forceful, which is why we are compelled to believe it.

So we do not infer the future from the past merely by rationally thinking, "If there is a morning glimmer on the eastern horizon, then dawn is upon us. I see faint light rising. Thus dawn is arriving. By Modus Ponens, lines one and two." Rather, we infer it through the degrees of power our imagination endows upon our ideas, based on the quantity of their recurrences. We make the inference because the forces of divergent internal tendencies compete with each other, and one wins. Both tendencies in a Deleuzean sense are virtualities. But only one is actualized. And the power relations between forces decides this.

§310 The Involuntary Union of Fellow Forces:
The Power of Passive Associative Synthesis

Hume will end this section by sharing two reflections on the matter. He begins now with the first.

We have seen that the mind may make inferences from present sense impressions. There is a "reasoning" process in the mind when it infers the future from the past. This is not a rational form of reasoning. It does not happen prior to experience; rather, it happens after or posteriorly to experience. Hence it is a posteriori rather than a priori reasoning. It does so by considering the unities of past common experiences and then resting with the more predominant pattern in the past. This it accomplishes by means of a single "passive synthesis."

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 inliven it. (140b)
Hume now addresses the question of whether we can bring about this associative synthesis by having just one experience, then repeating it over-and-over in the imagination. Hume admits that this can happen when for example some idea "pops into our minds" if you will, frequently over a very long period of our lives. But this is not an intentional evocation of the idea. When we purposefully imagine an idea again-and-again, that will not make it more vibrant. This clarifies the passive nature of this form of associative synthesis.

In general we may pronounce, that a person who wou'd voluntarily repeat any idea in his mind, tho' supported by one past experience, wou'd 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. (140-141, boldface mine)

§311 Quantifying our Passions

Hume now shares his second reflection. He has us consider contrary possibilities. Both have large numbers. But they differ in number by only a little. He has us imagine that we are dealing with one cause. Yet we have ten thousand experiences of one outcome, and ten thousand and one experiences of another outcome. Our minds cannot count them all to determine that one particular outcome is slightly more numerous.

Hume now has us recall how certain associated ideas influence our emotions [see §§264-271 for more on the passions.] We might find the dawn quite pleasant. So when we see its early glimmer, that might evoke a happy feeling. But consider also that for a period of our lives in the past, we worked on a farm. We had to rise before dawn. We worked at a time when we would rather just lie in bed. And as soon as we saw a glimmer of the dawn, that meant the animals would be rising, and we would have to clean up their messes, which involves many foul smells and disgusting sights. But this was just for one summer. Every other dawn was a wonderful moment of beauty and meaning. So tomorrow when we see dawn's glimmer, we will indeed have that good feeling from all the pleasant past experiences. But lurking behind that passion will also be feelings of dread and disgust.

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, deriv'd from a view of each part of the object. (141bc)
Now consider if we were given one coin. That evokes so much passion. But then consider if we obtain three coins. That evokes proportionally more.

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. (141-142)

Thus a man, who desires a thousand pound, 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 unite. (141c)

§312 Degrees of Analogy

We have seen that we often experience contrary effects to the same cause. If there are a majority of common pairings of cause and effect, then we take that as being probable. If there are minorities, they are merely possible. But the difference is quantitative and not qualitative.

Hume now discusses a third type of probablistic reasoning: analogical inference.

We noted that any causal inference results from two factors:
1) the constant conjunction of two objects in our past experience, and
2) the present occurence of one of them.

The effect of these two particulars is, that the present object invigorates and inlivens 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. (142b emphasis mine)
Contrary outcomes can weaken the force of our inferences. This can happen two ways:
a) we experience exceptions to the pattern of outcomes, or
b) the present impression does not perfectly resemble those in the past (hence it is less analogous).

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. (142c)
Now we saw that a disruption in the pattern diminishes the force of causal, probabilistic, and chance-based reasoning. But now imagine we become astronauts who land upon the moon. We see a glimmer of light on the horizon. But it's not yellow. It's purely white. And the horizon is barren gray rock. The stars are much brighter than usual. So we do anticipate the sunrise. But the inference is weakened. Why? Because it is less analogous of an experience. The more resemblence, the greater the analogicaless. Hence the greater the force of inference.

in the probability derived from analogy, it is the resemblance only, which is affected. Without some degree of resemblance, as well as union, it is 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 it is evident it may still retain as much as may be the foundation of probability, as long as there is any resemblance remaining. (142d)

From the original text:

#### 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 degree of evidence.

First, 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 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, it is 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 coued 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 coued 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, it is 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 inliven 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 phaenomenon 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 it is 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. It is 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, it is 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 it were impossible the passion should encrease by the encrease of these parts. Thus a man, who desires a thousand pound, 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 unite. Yet nothing can be more certain, than that so small a difference would not be discernible in the passions, nor coued 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 a-re 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 inlivens 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, it is the constancy of the union, which is diminished; and in the probability derived from analogy, it is the resemblance only, which is affected. Without some degree of resemblance, as well as union, it is 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 it is evident it may still retain as much as may be the foundation of probability, as long as there is any resemblance remaining.

From:

Hume, David. A Treatise of Human Nature. Ed. L.A Selby-Bigge. Oxford: Clarendon Press, 1979.

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