Context

Sections 11 and 12 are devoted to the examination of two types of probability: that of chance and that of causes. Both of these types are recognized as legitimate by philosophers. In the present Section, the author will consider four forms of probability that are deemed to be unphilosophical and illegitimate by the philosophers.

Background

In Book IV, Chapter XX of Locke’s Essay, there is a discussion of wrong assent that is contrary to probability Locke cites as the sources of error: 1) external circumstances that preclude proper reasoning, 2) lack of skill in reasoning, 3) neglect of the use of reasoning skills, 4) wrong measures of probability, stemming from passions, authority, etc. None of these falls under that author’s heading of unphilosophical probability.

The Treatise

1. The probability of chances (Section 11) and the probability of causes (Section 12) are both receiv’d by philosophers, and allow’d to be reasonable foundations of belief and opinion. The system of the author allows other forms of probability to be deriv’d from the same principles as those of chance and causes, but these forms have not been sanctioned by the philosophers as reasonable bases for belief. [Perhaps with tongue in cheek,] the author refers to these forms of probability as unphilosophical, despite the fact that they share a common origin with philosophical probabilities. In this opening paragraph, the author immediately describes the first sort of unphilosophical probability. The degree of belief that we have (i.e., the force and vivacity that elevate an idea to the status of a belief) is dependent on the transfer to the idea of the force and vivacity of another perception (an impression or an idea). Any lessening of the transfer of force may reduce the probability of a belief. There are two ways in which the force and vivacity of an idea may diminish over time: either the transition to the idea becomes less easy, or the original impression whose force is transferred becomes weakened. The first kind of diminution may be the result of a lesser resemblance or a weaker causal connection. The second kind can result from the fading luster of the original impression as it is less and less remembered over time. [Strictly, what is reduced is the force of the present idea of the past impression. See Section 8, paragraph 16 for a discussion of the vivacity of ideas of memory.] The problem for the philosopher is that time will weaken the force of an argument, which itself should remain constant. So the philosophers think that the difference in the degree of conviction is not solid and legitimate. The author maintains that whatever the philosophers think, the fact is that the diminution greatly influences the understanding and secretly changes the authority of the same argument, according to the different times, in which it is propos’d to us. This is a consequence of the author’s system, according to which the belief depends on the force and vivacity of the idea of which it is an instance. [See Section 7 for a full account of this system.]

2. A second difference in the degree of belief never fails to take place, tho’ disclaim’d by the philosophers. Whereas the first difference is that the vivacity of an idea decays with time, the second is that a more vivid impression has a greater effect on both the understanding and the passions than one that is faint, or that is in some measure obliterated. [As noted in the last paragraph, the difference can be attributed either to the original impression or the transmission of its force.] A stronger impression produces a stronger conviction than does a weaker one. And a more recent impression has more force because it activates that custom that is responsible for the transition, which thereby takes place more easily. Thus, a drunkard who has recently seen his comrade die from drinking will, for a time, dread having the same thing happen to himself. But over time, the facility of transmission of the idea of his friend to himself diminishes, and his former security returns, and the danger seems less certain and real.

3. The third way in which the loss of vivacity influences degree of belief is when we make inferences. The author had distinguished in Section 11 between the force of proofs and probabilities. The former are causal arguments that are attended with no doubt or uncertainty, while the latter admit of some uncertainty. But this difference in certainty can disappear in the case of arguments of sufficient length. What would be proofs if each step were considered individually turn out to be probabilities because in the process of connecting a number of steps of the argument, there is a loss of force. ’Tis Certain, that when an inference is drawn immediately from an object, without any intermediate cause or effect, the conviction is much stronger, and the perswasion much more lively, than when the imagination is carry’d thro’ a long chain of connected arguments, however infallible the connexion of each link may be esteem’d. The reason is that the first step is always an impression [or, equivalently, an idea of memory], and the force of this impression must diminish as the inference proceeds away from it. In fact, the diminution of vivacity may be so strong that it reduces the degree of belief more than would counter-examples (contrary experiments). Moreover, the resulting conviction might be so weak that a much-shorter probable argument would produce a stronger conviction. Rarely does a long argument produce any conviction, and to do so requires a very strong and firm imagination to preserve the evidence to the end, where it passes thro’ so many stages [where ‘evidence’ here refers to conviction].

4. The author now considers an apparent counter-example to his description of the effects of reasoning about long chains of causes. Common sense would have it that we have proofs of historical facts in the distant past, such as that Julius Caesar existed. However, there is a very long chain of testimony leading from the eye-witnesses to one’s reading about Caesar’s existence in a history book. It appears that according to the author’s system, the length of the chain should continually diminish the evidence, until eventually that of all ancient history must now be lost; or at least, will be lost in time. So we are left with a dilemma: either, contrary to common sense, historical evidence will eventually decay to nothing, or, if common sense is right, belief is some other than the vivacity of an idea.

5. Before responding to this objection, the author considers a related kind of reasoning in which there is real loss of conviction. This is reasoning in which a step is a probability rather than a proof. The problem is that each new probability weakens the initial probability, so that with enough steps in the argument it becomes so weak that there can be no conviction. If all historical reasoning were of this sort, then there would eventually be no conviction about past events, and in fact, this kind of decay has been cited against the historical claims of the Christian religion. [The reference is to John Craig, Rules of Historical Evidence, 1699.] In fact, all historical claims would fall prey to this kind of objection, but the author maintains that the method just described [interpolating probabilities into proofs] is not how the evidence of historical events is actually obtained. He does grant that in general, chains of probability would extinguish conviction if long enough. But he notes that there is a crucial exception, which will be covered in Part IV, Section 1. [The exception concerns the case of the probability of the correctness of probable reasoning, the assessment of which generates a regress that would extinguish conviction if left unchecked, but does not because the imagination becomes too strained to pursue any more than a few iterations of reasoning about our reasoning.]

6. Now the author offers a solution to the objection, under the assumption that historical evidence is based on proof rather than probability. Although the links connecting the impressions of the eye-witness to the event and the reader of the history are innumerable, they are of the same kind. That is, the transmission of evidence is through printers and copyists, and the evidence amounts to proof if they are accurate in what they copy and print. Each step in the chain is of the same sort, and, After we know one, we know all of them; and after we have made one, we can have no scruple as to the rest. The sameness in kind of the links makes the transition from one to another very easy, with little or no force lost. This easy transition is, moreover, the one thing that preserves the historical evidence. If the links were of different sorts, the transition would not be so easy, and the process of diminution would be in play. In fact, a very long chain of evidence with links of the same sort is more convincing than a much shorter one with different kinds of links.

7. The author turns now to a fourth and final kind of unphilosophical probability, which differs significantly from the first three kinds. Probability may be the result of the operation of general rules [or applications of generalizations]. If these rules are formed rashly, they result in prejudice. An example is the rule that an Irishman cannot be witty in conversation. The interesting thing about prejudice is that it is not overcome when we are actually presented with counter-examples to it, as, in the case just mentioned, when one has an agreeable conversation with an Irishman. So strong is the prejudice that in spite of sense and reason the witty Irishman may still be thought to be without wit. Human nature is very subject to errors of this kind; and perhaps this nation [England] as much as any other.

8. The author now asks why we form general rules that have such a hold on us that they influence our judgment even contrary to present observation and experience. He answers by appealing to the general principles upon which all causal reasoning is based, and specifically that of experience and habit (or custom). In causal reasoning, custom operates with its full force, when objects are presented, that are exactly the same as those to which we have become accustom’d. But custom may also operate when the objects are merely similar, and even though its force diminishes with dissimilarity, it yet remains. An example given is someone who likes pears and peaches but will settle for melons in their absence. This kind of custom was used in the preceding Section to account for analogical reasoning. The force of the custom depends on the degree of resemblance.

9. This explanation, while sufficient for analogical reasoning, does not by itself suffice to explain the force of general rules. The author elaborates on a further feature of comparison of objects, beyond their similarity and dissimilarity. In almost all kinds of causes there is a complication of circumstances, of which some are essential, and others superfluous; some are absolutely requisite to the production of the effect, and others are only conjoin’d by accident. If the accidental circumstances are many and striking, it can be they which influence the imagination to the point that we use them to judge objects to be of a kind even without the essential characteristics that of that kind. This can lead to belief, i.e., a conception that is superior to the mere fictions of the fancy. Custom, then, gives us a bias, even though that bias can be overturned upon reflection.

10. This account is supported by an example of a man who is suspended from a high tower in an iron cage. He realizes that he is perfectly safe in that cage, yet he cannot forbear trembling. He has an image of falling and dying, and though the cases where this would occur (say, if he jumped from the height) do not apply presently, they nonetheless move his imagination because of their great force. This also excites a passion [fear], which further inflames his imagination, which in turn augments his passion, etc. There is a relation of mutual support between the imagination and the passion, which causes the whole to have a very great influence on the man.

11. The example just given illustrates the conflict between the custom that leads to bias by its focus on accidental features of things and the custom that leads to reasonable conclusions by nothing but their essential features. No more examples of this kind are needed, because the topic of unphilosophical probability itself provides an example. Given that both kinds of conviction are based on custom, it might be thought that there could be no opposition between imagination and judgment, respectively. But the influence of general rules explains how the opposition is possible. There are in fact two kinds of general rules. Those which properly regulate our belief and lead to sound judgment are treated in Section 15, following. These rules allow us to distinguish between accidental and essential circumstances and hence serve as a guard against the bias resulting from frequent experience of the accidental ones. When we find that an effect is produced without a given circumstance, we reason that it is not included in the effective part of the cause. Still, we cannot eliminate entirely the influence of repeated exposure to accidental circumstances, so the opposition of these two principles produces a contrariety in our thoughts, and causes us to ascribe the one inference to our judgment, and the other to our imagination. The first inference is based on a general rule that is more effective and constant, and the second is based on one that is more capricious and uncertain.

12. The result reveals that general rules may oppose each other, in a certain way. The first type of general rule is what typically guides the vulgar. Suppose that a general rule for a person describes a causal relationship between things of kind A and things of kind B. We find an object that resembles A in some respects, but not in the most material and most efficacious circumstances. Notwithstanding this difference, the force of the general rule holds sway, and the imagination naturally carries us to a lively conception of the usual effect. The second kind of general rule, typical of the wise man, is reflective and can be applied to the just-described use of the first type of rule. When we review the act of becoming convinced by way of the general rule and compare it with the more general and authentic operations of the understanding, we reject it as being of an irregular nature, and destructive of all the most establish’d principles of reasoning. So the second kind of general rule negates the first kind. This does not always happen, and one or the other use of general rules may take place in the same person, depending on his disposition at the time. This gives comfort to the skeptic, who points out that there is a contradiction in our reason, such that good reasoning is destroyed by bad, only to be rescued again by the very reasoning that has been destroyed. So there is an irony here. On the one hand, the use of general rules is unphilosophical, and on the other, it is only by using general rules that we can correct the unphilosophical use of rules.

13. Just as general rules may push the imagination in opposition to judgment, it also happens that when good judgment and general rules are combined, they produce ideas with greater force than could be produced by either alone. In this and the next three paragraphs, the author illustrates this claim with an example. He maintains that the force of an open insult is greater than that of a satirical innuendo. Suppose that I understand that in both cases the person insulting or satirizing me does so out of contempt for me, so that the judgment about me is the same in both cases. Why does his doing so in an open way, say through a direct insult, affect me more than when it is done slyly? This difference is to be attributed to the influence of general rules.

14. The first point to note is that in both cases, the contempt is understood only through the use of signs, not by direct examination of the ideas in the mind of the contemptuous person. The difference between the signs in the two cases is that with open insult, there are general rules that can be used to interpret the behavior of the insulter. But when subtle methods are used, there are only more singular and uncommon signs. So the generality of the rules of communication make the difference, in that it makes the transition from the impression of what is heard to the idea of its significance easier. This is reflected in the language we use to describe open insult as taking off the mask and innuendo as veiling one’s sentiments. It is easier to see something when it is brought into the open. We can compare the difference between the two resulting ideas to the difference between an impression and an idea [in terms of the relative force and vivacity of the first idea versus the second]. This explains to some extent the differences in the effects on the passions. But there is another factor. Veiling the insult shows a certain consideration for the person insulted, which makes the insult less disagreeable than if it is made without being masked. But why does the subtle insult show more consideration? The reason must be that it is more feeble. So, the effect of an action that does not follow a general rule is weaker, which is what the author is claiming.

15. A further feature of the example is also to be explained by the influence of general rules. At times, the open insult is in fact less displeasing than delicate satire. The reason is that when it is clear that one is being insulted, one has good reason to blame and condemn the person who did the insulting. But if the insult is masked, it is not obvious that there is such a reason. The general rule that is violated by the insulter is one of good breeding. When this rule is violated, one recognizes the crudeness and ill-breeding of the insulter and is not so much affected by the insult. So there is a kid of reversal: It becomes less disagreeable, merely because originally it is more so. And initially it was more disagreeable because it followed rules of conversation that are palpable and undeniable.

16. An analogous phenomenon is the way we overlook obvious violations in the point of honour when they are committed discreetly. There is the same idea of what has taken place but a difference of the manner of presentation of the idea, which accounts for the difference in its influence on us.

17. The explanation for this phenomenon is the same as in the other cases. When the violation is open, there is a single sign that indicates the behavior, such that it is easily subsumed under the relevant general rule. When the violation is discreet, there are many conflicting signs, so that the general rule is not easily brought into play. But ’tis certain true, that any reasoning is always the more convincing, the more single and united it is to the eye, and the less exercise it gives to the imagination to collect all its parts, and run from them to the correlative idea, which forms the conclusion. The work that it takes to puzzle out the behavior detracts from the force that the idea has on the imagination. This phenomenon of the effect of mental labor on the vivacity of our ideas will be discussed at length in Part IV, Section 1.

18. The author now quotes two observations by Cardinal de Retz: that there are may things in which the world wishes to be deceiv’d and that it more easily excuses a person in acting than in talking contrary to the decorum of his profession and character. The explanation is that when someone says what he should not, his fault is more obvious than when he does something that he should not. In the latter case, there are often other explanations of his behavior which make him seem not to be culpable. [Thus, we can apply the general rule in the case of saying something wrong, but not, in many cases at least, in the case of doing something wrong.]

19. At this point, the author has concluded his argument and will summarize his general results. First, all opinion that falls short of knowledge is deriv’d entirely from the force and vivacity of the perception, and that these qualities constitute in the mind, what we call BELIEF of the existence of any object. Memory gives the most vivid perceptions, and hence is most trusted. Cause and effect produce less, but still great, vivacity, when there is perfect constancy in what is observed. There are also lesser degrees of vivacity in various situations, all yielding an inferior degree of evidence:

• The number of instances observed is insufficient to produce a strong habit,
• The instances are contrary to one another,
• The resemblance between the instances is not exact,
• The present impression on which an inference is based is faint and obscure,
• The previous experience of regularity is somewhat obliterated from memory,
• Cause and effect are connected by a long chain of objects,
• The inference is derived from general rules but does not yet conform to them.

20. The system the author has presented gets its authority from the following facts:

• Each of its parts are founded on undoubted arguments,
• The parts agree with one another,
• Each part is needed to explain the other.

The Enquiry

The subject of unphilosophical probability, and specifically that based on general rules, is not discussed in the Enquiry.

[ Previous Section | Next Section | Treatise Contents | Text of the Treatise ]