Of probable Reasoning.
The field of demonstration, as has been observed, is necessary truth; the field of probable reasoning is contingent truth, not what necessarily must be at all times, but what is, or was, or shall be.
No contingent truth is capable of strict demonstration; but necessary truths may sometimes have probable evidence.
Dr Wallis discovered many important mathematical truths, by that kind of induction which draws a general conclusion from particular premises. This is not strict demonstration, but, in some cases, gives as full conviction as demonstration itself; and a man may be certain, that a truth is demonstrable before it ever has been demonstrated. In other cases, a mathematical proposition may have such probable evidence from induction or analogy, as encourages the Mathematician to investigate its demonstration. But still the reasoning proper to mathematical and other necessary truths, is demonstration; and that which is proper to contingent truths, is probable reasoning.
These two kinds of reasoning differ in other respects. In demonstrative reasoning, one argument is as good as a thousand. One demonstration may be more elegant than another; it may be more easily comprehended, or it may be more subservient to some purpose beyond the present. On any of these accounts it may deserve a preference: But then it is sufficient by itself; it needs no aid from another; it can receive none. To add more demonstrations of the fame conclusion, would be a kind of tautology in reasoning; because one demonstration, clearly comprehended, gives all the evidence we are capable of receiving.
The strength of probable reasoning, for the most part, depends not upon any one argument, but upon many, which unite their force, and lead to the fame conclusion. Any one of them by itself would be insufficient to convince; but the whole taken together may have a force that is irresistible, so that to desire more evidence would be absurd. Would any man seek new arguments to prove that there were such persons as King Charles the First, or Oliver Cromwell?
Such evidence may be compared to a rope made up of many slender filaments twisted together. The rope has strength more than sufficient to bear the stress laid upon it, though no one of the filaments of which it w composed would be sufficient for that purpose.
It is a common observation, that it is unreasonable to require demonstration for things which do not admit of it. It is no less unreasonable to require reasoning of any kind for things which are known without reasoning. All reasoning must be grounded upon truths which are known without reasoning. In every branch of real knowledge there must be first principles whose truth is known intuitively, without reasoning, either probable or demonstrative. They are not grounded on reasoning, but all reasoning is grounded on them. It has been shown, that there are first principles of necessary truths, and first principles of contingent truths. Demonstrative reasoning is grounded upon the former, and probable reasoning upon the latter.
That we may not be embarrassed by the ambiguity of words, it is proper to observe, that there is a popular meaning of probable evidence, which ought not to be confounded with the philosophical meaning, above explained.
In common language, probable evidence is considered as an inferior degree of evidence, and is opposed to certainty: So that what is certain is more than probable, and what is only probable is not certain. Philosophers consider probable evidence, not as a degree, but as a species of evidence which is opposed, not to certainty, but to another species of evidence called demonstration.
Demonstrative evidence has no degrees; but probable evidence, taken in the philosophical sense, has all degrees, from the very least, to the greatest which we call certainty.
That there is such a city as Rome, I am as certain as of any proposition in Euclid ; but the evidence is not demonstrative, but of that kind which Philosophers call probable. Yet, in common language, it would found oddly to fay, it is probable there is such a city as Rome, because it would imply some degree of doubt or uncertainty.
Taking probable evidence, therefore, in the philosophical sense, as it is opposed to demonstrative, it may have any degrees of evidence, from the least to the greatest.
I think, in most cafes, we measure the degrees of evidence by the effect they have upon a found understanding, when comprehended clearly and without prejudice. Every degree of evidence perceived by the mind, produces a proportioned degree of assent or belief. The judgment may be in perfect suspense between two contradictory opinions, when there is no evidence for either, or equal evidence for both. The least preponderancy on one side inclines the judgment in proportion. Belief is mixed with doubt, more or less, until we come to the highest degree of evidence, when all doubt vanishes, and the belief is firm and immoveable. This degree of evidence, the highest the human faculties can attain, we call certainty.
Chap. in. but js itself of different kinds. The chief of these, I shall mention., without pretending to make a complete enumeration.
The first kind is that of human testimony, upon which the greatest part of human knowledge is built.
The faith of history depends upon it, as well as the judgment of solemn tribunals, with regard to mens acquired rights, and with regard to their guilt or innocence when they are charged with, crimes. A great part of the business of the Judge, of Counsel at the bar, of the Historian, the Critic, and the Antiquarian, is to canvass and weigh this kind of evidence ; and no man can act with common prudence in the ordinary occurrences of life, who has not some competent judgment of it.
The belief we give to testimony in many cases is not solely grounded upon the veracity of the testifier. In a single testimony, we consider the motives.a man might have to falsify. If there be no appearance of any such motive, much more if there be motives on the other side, his testimony has weight independent of his moral character. If the/ testimony be circumstantial, we consider how far the circumstances agree together, and with things that are known. It is so very difficult to fabricate a story, which cannot be detected by a judicious examination of the circumstances, that it acquires evidence, by being able to bear such a trial. There is an art in detecting false evidence in judicial proceedings, well known to able judges and barristers; so that I believe few false witnesses leave the bar without suspicion of their guilt..
When there is an agreement of many witnesses, in a great variety of circumstances, without the possibility of a previous con^ cert, the evidence may be equal to that of demonstration*
A second kind of probable evidence, is the authority of those who are good judges of the point in question. The supreme court of judicature of the British nation, is often determined by the opinion of lawyers in a point of law, of physicians in a point of medicine, and of other artists, in what relates to their several professions. And, in the common affairs of life, we frequently rely upon the judgment of others, in points of, which we are not proper judges ourselves.
A third kind of probable evidence, is that by which we recognise the identity of things, and persons of our acquaintance: That two swords, two horses, or two persons, may be so perfectly alike, as not to be distinguishable by those to whom they are best known, cannot be shown to be impossible. But we learn either from nature, or from experience, that it never happens; or so, very rarely, that a person or thing, well known to us, is immediately recognised without any doubt, when we perceive the marks or signs by which we were in use to distinguish it from all other individuals of the kind..
This evidence we rely upon in the most important affairs of life; and, by this evidence, the identity, both of things and of persons, is determined in courts of judicature.
A fourth kind of probable evidence, is that which we have of mens future actions and conduct, from the general principles of action in man, or from our knowledge of the individuals..
Notwithstanding the folly and vice that is to be found among men, there is a certain degree of prudence and probity which we rely upon in every man that is not insane. If it were not so, no man would be safe in the company of another, and there could be no society among mankind. If men were, as much disposed to • hurt as to do good, to lie as to speak truth, they could not live together; they would keep at as great distance from one another as possible, and the race would soon perish.
We expect that men will take some care of themselves, of their family, friends, and reputation: That they will not injure others without some temptation: That they will have some gratitude for good offices, and some resentment of injuries.
Such maxims with regard to human conduct are the foundation of all political reasoning, and of common prudence in the conduct of life. Hardly can a man form any project in public or in private life, which does not depend upon the conduct of other men, as well as his own, and which does not go upon the supposition that men will act such a part in such circumstances. This evidence may be probable in a very high degree, but can never be demonstrative. The best concerted project may fail, and wife counsels may be frustrated, because some individual acted a part which it would have been against all reason to expect.
Another kind of probable evidence, the counterpart of the last, is that by which we collect mens characters and designs from their actions, speech, and other external signs.
We fee not mens hearts, nor the principles by which they are actuated ; but there are external signs of their principles and dispositions, which, though not certain, may sometimes be more trusted than their professions; and it is from external signs that we must draw all the knowledge we can attain of “men’s characters.
The next kind of probable evidence I mention, is that which Mathematicians call the probability of chances.
We attribute some events to chance, because we know only the remote cause which must produce some one event of a number; but know not the more immediate cause which determines a particular event of that number in preference to the others.
I think all the chances about which we reason in mathematics CHAP. Hi. are of this kind. Thus, in throwing a just die upon a table, we fay it is an equal chance which of the six sides shall be turned up; because neither the person who throws, nor the bystanders know the precise measure of force and direction necessary to turn up any one side rather than another. There are here therefore six events, one of which must happen; and as all are supposed to have equal probability, the probability of any one side being turned up, the ace, for instance, is as one to the remaining number five.
The probability of turning up two aces with two dice is as one to thirty-five; because here there are thirty-six events, each of which has equal probability.
Upon such principles as these, the doctrine of chances has furnished a field of demonstrative reasoning of great extent, although the events about which this reasoning is employed be not necessary, but contingent, and be not certain, but probable.
This may seem to contradict a principle before advanced, that contingent truths are not capable of demonstration; but it does not: For, in the mathematical reasonings about chance, the conclusion demonstrated, is not, that such an event shall happen, but that the probability of its happening bears such a ratio to the probability of its failing; and this conclusion is necessary upon the suppositions on which it is grounded.
The last kind of probable evidence I shall mention, is that by which the known laws of Nature have been discovered, and the effects which have been produced by them in former ages, or which may be expected in time to come.
The laws of Nature are the rules by which the Supreme Being governs the world. We deduce them only from facts that fall within our own observation, or are properly attested by those who have observed them.
The knowledge of some of the laws of Nature is necessary to all men in the conduct of life. These are soon discovered even by savages. They know that fire burns, that water drowns, that bodies gravitate towards the earth. They know that day and night, summer and winter, regularly succeed each other. As far back as their experience and information reach, they know that these have happened regularly; and, upon this ground, they are led, by the constitution of human nature, to expect that they will happen in time to come, in like circumstances.
The knowledge which the Philosopher attains of the laws of Nature differs from that of the vulgar, not in the first principles on which it is grounded, but in its extent and accuracy. He collects with care the phenomena that lead to the fame conclusion, and compares them with those that seem to contradict or to limit’ it. He observes the circumstances on which every phenomenon depends, and distinguishes them carefully from those that are accidentally conjoined with it. He puts natural bodies in various situations, and applies them to one another in various ways, oh purpose to observe the effect; and thus acquires from his fenses a more extensive knowledge of the course of Nature in a short time, than could be collected by casual observation in many ages.
But what is the result of his laborious researches? It is, that, as far as he has been able to observe, such things have always happened in such circumstances, and such bodies have always been found to have such properties. These are matters of fact, attested by fense, memory and testimony, just as the few facts which the vulgar know are attested to them.
And what conclusions does the Philosopher draw from the facts he has collected? They are, that like events have happened in former times in like circumstances, and will happen in time to come; and these conclusions are built on the very fame ground on which the simple rustic concludes that the fun will rife to-morrow.
Facts reduced to general rules, and the consequences of those general rules, are all that we really know of the material world. And the evidence that such general rules have no exceptions, as well as the evidence that they will be the fame in time to come as they have been in time past, can never be demonstrative. It is only that species of evidence which Philosophers call probable. General rules may have exceptions or limitations which no man ever had occasion to observe. The laws of Nature may be changed by him who established them. But we are led by our constitution to rely upon their continuance with as little doubt as if it was demonstrable.
I pretend not to have made a complete enumeration of all the kinds of probable evidence; but those I have mentioned are sufficient to show, that the far greatest part, and the most interesting part of our knowledge, must rest upon evidence of this kind; and that many things are certain for which we have only that kind of evidence which Philosophers call probable.