Probability⁹

46. Though there be no such thing as Chance in the world; our ignorance of the real cause of any event has the same influence on the understanding, and begets a like species of belief or opinion.

46. Although there is no such thing as Chance in the world, our ignorance of an event’s real cause has the same effect on our understanding. It gives rise to a similar kind of belief or opinion.

There is certainly a probability, which arises from a superiority of chances on any side; and according as this superiority encreases, and surpasses the opposite chances, the probability receives a proportionable encrease, and begets still a higher degree of belief or assent to that side, in which we discover the superiority. If a dye were marked with one figure or number of spots on four sides, and with another figure or number of spots on the two remaining sides, it would be more probable, that the former would turn up than the latter; though, if it had a thousand sides marked in the same manner, and only one side different, the probability would be much higher, and our belief or expectation of the event more steady and secure. This process of the thought or reasoning may seem trivial and obvious; but to those who consider it more narrowly, it may, perhaps, afford matter for curious speculation.

Probability certainly arises when the chances favor one side over another. As the advantage over the opposing chances increases, the probability increases proportionately. This produces a higher degree of belief or confidence in the side with the greater chance. Suppose a die had one number of spots on four sides and another number on the remaining two sides. The first number would be more likely to turn up than the second. But suppose the die had a thousand sides marked with the first number and only one with the second. The probability would then be much higher, and our belief or expectation about the outcome more steady and secure. This process of thought or reasoning may seem trivial and obvious. But for those who examine it more closely, it may perhaps provide material for interesting speculation.

It seems evident, that, when the mind looks forward to discover the event, which may result from the throw of such a dye, it considers the turning up of each particular side as alike probable; and this is the very nature of chance, to render all the particular events, comprehended in it, entirely equal. But finding a greater number of sides concur in the one event than in the other, the mind is carried more frequently to that event, and meets it oftener, in revolving the various possibilities or chances, on which the ultimate result depends. This concurrence of several views in one particular event begets immediately, by an inexplicable contrivance of nature, the sentiment of belief, and gives that event the advantage over its antagonist, which is supported by a smaller number of views, and recurs less frequently to the mind. If we allow, that belief is nothing but a firmer and stronger conception of an object than what attends the mere fictions of the imagination, this operation may, perhaps, in some measure, be accounted for. The concurrence of these several views or glimpses imprints the idea more strongly on the imagination; gives it superior force and vigour; renders its influence on the passions and affections more sensible; and in a word, begets that reliance or security, which constitutes the nature of belief and opinion.

It seems clear that when the mind looks ahead to the outcome of a throw of such a die, it considers each side equally likely to turn up. This is the very nature of chance: it makes all the possible outcomes entirely equal. But the mind finds that more sides lead to one outcome than to the other. So, as it considers the various possibilities or chances on which the final result depends, it turns more often to that outcome and encounters it more frequently. When several thoughts converge on one outcome, they immediately produce a feeling of belief, through some inexplicable mechanism of nature. This gives that outcome an advantage over its rival, which is supported by fewer thoughts and comes to mind less often. If we accept that belief is nothing more than a firmer and stronger conception of something than accompanies mere fictions of the imagination, we may perhaps be able to explain this process to some extent. The convergence of these several thoughts or glimpses impresses the idea more strongly on the imagination. It gives the idea greater force and vigor and makes its influence on the passions and feelings more noticeable. In short, it produces the confidence or assurance that makes up the nature of belief and opinion.

47. The case is the same with the probability of causes, as with that of chance. There are some causes, which are entirely uniform and constant in producing a particular effect; and no instance has ever yet been found of any failure or irregularity in their operation. Fire has always burned, and water suffocated every human creature: The production of motion by impulse and gravity is an universal law, which has hitherto admitted of no exception. But there are other causes, which have been found more irregular and uncertain; nor has rhubarb always proved a purge, or opium a soporific to every one, who has taken these medicines. It is true, when any cause fails of producing its usual effect, philosophers ascribe not this to any irregularity in nature; but suppose, that some secret causes, in the particular structure of parts, have prevented the operation. Our reasonings, however, and conclusions concerning the event are the same as if this principle had no place. Being determined by custom to transfer the past to the future, in all our inferences; where the past has been entirely regular and uniform, we expect the event with the greatest assurance, and leave no room for any contrary supposition. But where different effects have been found to follow from causes, which are to appearance exactly similar, all these various effects must occur to the mind in transferring the past to the future, and enter into our consideration, when we determine the probability of the event. Though we give the preference to that which has been found most usual, and believe that this effect will exist, we must not overlook the other effects, but must assign to each of them a particular weight and authority, in proportion as we have found it to be more or less frequent. It is more probable, in almost every country of Europe, that there will be frost sometime in January, than that the weather will continue open throughout that whole month; though this probability varies according to the different climates, and approaches to a certainty in the more northern kingdoms. Here then it seems evident, that, when we transfer the past to the future, in order to determine the effect, which will result from any cause, we transfer all the different events, in the same proportion as they have appeared in the past, and conceive one to have existed a hundred times, for instance, another ten times, and another once. As a great number of views do here concur in one event, they fortify and confirm it to the imagination, beget that sentiment which we call belief, and give its object the preference above the contrary event, which is not supported by an equal number of experiments, and recurs not so frequently to the thought in transferring the past to the future. Let any one try to account for this operation of the mind upon any of the received systems of philosophy, and he will be sensible of the difficulty. For my part, I shall think it sufficient, if the present hints excite the curiosity of philosophers, and make them sensible how defective all common theories are in treating of such curious and such sublime subjects.

47. The same is true of the probability of causes as of the probability of chance. Some causes are entirely uniform and constant in producing a particular effect. No instance has ever been found in which their operation failed or was irregular. Fire has always burned, and water has suffocated every human being. The production of motion by impulse and gravity is a universal law that has so far admitted no exception. But other causes have proved more irregular and uncertain. Rhubarb has not always acted as a purge, nor has opium always induced sleep in everyone who has taken it. It is true that philosophers do not attribute a cause’s failure to produce its usual effect to any irregularity in nature. They suppose instead that hidden causes in the particular structure of parts have prevented it from operating. Even so, our reasoning and conclusions about the outcome are the same as if this principle did not apply. In all our inferences, custom leads us to carry the past forward into the future. When the past has been entirely regular and uniform, we expect the outcome with the greatest assurance. We leave no room for any contrary possibility. But causes that are apparently exactly alike have been found to produce different effects. When we carry the past forward into the future, all these different effects must come to mind. They must enter into our consideration when we determine the probability of the outcome. We favor the effect that has been most common, and we believe that this effect will occur. But we must not overlook the other effects. We must give each its own weight and authority, according to how often we have found it to occur. In almost every European country, frost is more likely at some time in January than mild weather throughout the month. This probability varies with the climate, though, and approaches certainty in the more northern kingdoms. So it seems clear that we carry all the different past events forward into the future. We do this to determine the effect that will result from any cause. We carry the events forward in the same proportions as they appeared in the past. For example, we imagine that one occurred a hundred times, another ten times, and another once. A great number of these instances come together in support of one event. They strengthen and confirm the event in the imagination and produce the feeling we call belief. They lead us to favor that event over a contrary one. The contrary event is not supported by an equal number of observations. It does not recur as often to our thoughts when we carry the past forward into the future. Let anyone try to explain this operation of the mind using any of the accepted systems of philosophy. They will become aware of the difficulty. For my part, I will consider it enough if these suggestions awaken philosophers’ curiosity. I hope they will also make philosophers aware of how inadequate all common theories are when treating such curious and sublime subjects.