Grammar of Assent
Compare with this avowal the language of Butler, when discussing the proof of Revelation. “Probable proofs,” he says, “by being added, not only increase the evidence, but multiply it. The truth of our religion, like the truth of common matters, is to be judged by the whole evidence taken together ... in like manner as, if in any common case numerous events acknowledged were to be alleged in proof of any other event disputed, the truth of the disputed event would be proved, not only if any one of the acknowledged ones did of itself clearly imply it, but though no one of them singly did so, if the whole of the acknowledged events taken together could not in reason be supposed to have happened, unless the disputed one were true.” Here, as in Astronomy, is the same absence of demonstration of the thesis, the same cumulating and converging indications of it, the same indirectness in the proof, as being per impossibile, the same recognition nevertheless that the conclusion is not only probable, but true. One other characteristic of the argumentative process is given, which is unnecessary in a subject-matter so clear and simple as astronomical science, viz. the moral state of the parties inquiring or disputing. They must be “as much in earnest about religion, as about their temporal affairs, capable of being convinced, on real evidence, that there is a God who governs the world, and feel themselves to be of a moral nature and accountable creatures.”
This being the state of the case, the question arises, whether, granting that the personality (so to speak) of the parties reasoning is an important element in proving propositions in concrete matter, any account can be given of the ratiocinative method in such proofs, over and above that analysis into syllogism which is possible in each of its steps in detail. I think there can; though I fear, lest to some minds it may appear far-fetched or fanciful; however, I will hazard this imputation. I consider, then, that the principle of concrete reasoning is parallel to the method of proof which is the foundation of modern mathematical science, as contained in the celebrated lemma with which Newton opens his “Principia.” We know that a regular polygon, inscribed in a circle, its sides being continually diminished, tends to become that circle, as its limit; but it vanishes before it has coincided with the circle, so that its tendency to be the circle, though ever nearer fulfilment, never in fact gets beyond a tendency. In like manner, the conclusion in a real or concrete question is foreseen and predicted rather than actually attained; foreseen in the number and direction of accumulated premisses, which all converge to it, and approach it, as the result of their combination, more nearly than any assignable difference, yet do not touch it logically, (though only not touching it,) on account of the nature of its subject-matter, and the delicate and implicit character of at least part of the reasonings on which it depends. It is by the strength, variety, or multiplicity of premisses, which are only probable, not by invincible syllogisms,—by objections overcome, by adverse theories neutralized, by difficulties gradually clearing up, by exceptions proving the rule, by unlooked-for correlations found with received truths, by suspense and delay in the process issuing in triumphant reactions,—by all these ways, and many others, the practised and experienced mind is able to make a sure divination that a conclusion is inevitable, of which his lines of reasoning do not actually put him in possession. This is what is meant by a proposition being “as good as proved,” a conclusion as undeniable “as if it were proved,” and by the reasons for it “amounting to a proof,” for a proof is the limit of converging probabilities.
It may be added, that, whereas the logical form of this argument, is, as I have already observed, indirect, viz. that “the conclusion cannot be otherwise,” and Butler says that an event is proved, if its antecedents “could not in reason be supposed to have happened unless it were true,” and law-books tell us that the principle of circumstantial evidence is the reductio ad absurdum, so Newton is forced to the same mode of proof for the establishment of his lemma, about prime and ultimate ratios. “If you deny that they become ultimately equal,” he says, “let them be ultimately unequal;” and the consequence follows, “which is against the supposition.”
Such being the character of the mental process in concrete reasoning, I should wish to adduce some good instances of it in illustration, instances in which the person reasoning confesses that he is reasoning on this very process, as I have been stating it; but these are difficult to find, from the very circumstance that the process from first to last is carried on as much without words as with them. However, I will set down three such.
1. First, an instance in physics. Wood, treating of the laws of motion, thus describes the line of reasoning by which the mind is certified of them. “They are not indeed self-evident, nor do they admit of accurate proof by experiment, on account of the effects of friction and the air’s resistance, which cannot entirely be removed. They are, however, constantly and invariably suggested to our senses, and they agree with experiment, as far as experiment can go; and the more accurately the experiments are made, and the greater care we take to remove all those impediments which tend to render the conclusions erroneous, the more nearly do the experiments coincide with these laws.
“Their truth is also established upon a different ground: from these general principles innumerable particular conclusions have been deducted; sometimes the deductions are simple and immediate, sometimes they are made by tedious and intricate operations; yet they are all, without exception, consistent with each other and with experiment. It follows thereby, that the principles upon which the calculations are founded are true.”
The reasoning of this passage (in which the uniformity of the laws of nature is assumed) seems to me a good illustration of what must be considered the principle or form of an induction. The conclusion, which is its scope, is, by its own confession, not proved; but it ought to be proved, or is as good as proved, and a man would be irrational who did not take it to be virtually proved; first, because the imperfections in the proof arise out of its subject-matter and the nature of the case, so that it is proved interpretativè; and next, because in the same degree in which these faults in the subject-matter are overcome here or there, are the involved imperfections here or there of the proof remedied; and further, because, when the conclusion is assumed as an hypothesis, it throws light upon a multitude of collateral facts, accounting for them, and uniting them together in one whole. Consistency is not always the guarantee of truth; but there may be a consistency in a theory so variously tried and exemplified as to lead to belief in it, as reasonably as a witness in a court of law may, after a severe cross-examination, satisfy and assure judge, jury, and the whole court, of his simple veracity.
2. And from the courts of law shall my second illustration be taken.
A learned writer says, “In criminal prosecutions, the circumstantial evidence should be such, as to produce nearly the same degree of certainty as that which arises from direct testimony, and to exclude a rational probability of innocence.” By degrees of certainty he seems to mean, together with many other writers, degrees of proof, or approximations towards proof, and not certitude, as a state of mind; and he says that no one should be pronounced guilty on evidence which is not equivalent in weight to direct testimony. So far is clear; but what is meant by the expression “rational probability”? for there can be no probability but what is rational. I consider that the “exclusion of a rational probability” means “the exclusion of any argument in the man’s favour which has a rational claim to be called probable,” or rather, “the rational exclusion of any supposition that he is innocent;” and “rational” is used in contradistinction to argumentative, and means “resting on implicit reasons,” such as we feel, indeed, but which for some cause or other, because they are too subtle or too circuitous, we cannot put into words so as to satisfy logic. If this is a correct account of his meaning, he says that the evidence against a criminal, in order to be decisive of his guilt, to the satisfaction of our conscience, must bear with it, along with the palpable arguments for that guilt, such a reasonableness, or body of implicit reasons for it in addition, as may exclude any probability, really such, that he is not guilty,—that is, it must be an evidence free from anything obscure, suspicious, unnatural, or defective, such as (in the judgment of a prudent man) to hinder that summation or coalescence of the evidence into a proof, which I have compared to the running into a limit, in the case of mathematical ratios. Just as an algebraical series may be of a nature never to terminate or admit of valuation, as being the equivalent of an irrational quantity or surd, so there may be some grave imperfections in a body of reasons, explicit or implicit, which is directed to a proof, sufficient to interfere with its successful issue or resolution, and to balk us with an irrational, that is, an indeterminate, conclusion.
So much as to the principle of conclusions made upon evidence in criminal cases; now let us turn to an instance of its application in a particular instance. Some years ago there was a murder committed, which unusually agitated the popular mind, and the evidence against the culprit was necessarily circumstantial. At the trial the Judge, in addressing the Jury, instructed them on the kind of evidence necessary for a verdict of guilty. Of course he could not mean to say that they must convict a man, of whose guilt they were not certain, especially in a case in which two foreign countries, Germany and the American States, were attentively looking on. If the Jury had any doubt, that is, reasonable doubt, about the man’s guilt, of course they would give him the benefit of that doubt. Nor could the certitude, which would be necessary for an adverse verdict, be merely that which is sometimes called a “practical certitude,” that is, a certitude indeed, but a certitude that it was a “duty,” “expedient,” “safe,” to bring in a verdict of guilty. Of course the Judge spoke of what is called a “speculative certitude,” that is, a certitude of the fact that the man was guilty; the only question being, what evidence was sufficient for the proof, for the certitude of that fact. This is what the Judge meant; and these are among the remarks which, with this drift, he made upon the occasion:—
After observing that by circumstantial evidence he meant a case in which “the facts do not directly prove the actual crime, but lead to the conclusion that the prisoner committed that crime,” he went on to disclaim the suggestion, made by counsel in the case, that the Jury could not pronounce a verdict of guilty, unless they were as much satisfied that the prisoner did the deed as if they had seen him commit it. “That is not the certainty,” he said, “which is required of you to discharge your duty to the prisoner, whose safety is in your hands.” Then he stated what was the “degree of certainty,” that is, of certainty or perfection of proof, which was necessary to the question, “involving as it did the life of the prisoner at the bar,”—it was such as that “with which,” he said, “you decide upon and conclude your own most important transactions in life. Take the facts which are proved before you, separate those you believe from those which you do not believe, and all the conclusions that naturally and almost necessarily result from those facts, you may confide in as much as in the facts themselves. The case on the part of the prosecution is the story of the murder, told by the different witnesses, who unfold the circumstances one after another, according to their occurrence, together with the gradual discovery of some apparent connexion between the property that was lost, and the possession of it by the prisoner.”