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list of impossibilities, and inserted in the accredited catalogue of scientific truths. It used to be vulgar and ridiculous to admit them; now the vulgarity and absurdity consist in denying their existence.

Mesmeric phenomena, on the other hand, are an example of improbabilities that have not yet passed muster.

“When I was in Paris,” says Rogers, (the poet,) in his “Table-Talk," "I went to Alexis, and desired him to describe my house in St. James Place. On my word, he astonished me! He described most exactly the peculiarities of the staircase; said that not far from the window in the drawing-room there was a picture of a man in armor, (the painting by Giorgone, and so on. Colonel Gurwood, shortly before his death, assured me that he was reminded by Alexis of some circumstances that had happened to him in Spain, and which he could not conceive how any human being except himself should know. Still, I cannot believe in clairvoyance,-because the thing is impossible."'*

Not because the opportunities for observation were too few, and the experiments needed repetition: that would have been a valid objection. Not because the evidence was imperfect and lacked confirmation : Rogers’s difficulty was a more radical one. No evidence would suffice. Fish cannot have wings: the thing is impossible.t

* Let us deal fairly by Science, and give her the credit of this quotation. I found it in the (London) Medical Times and Gazette, No. 444, new series ; and the italics are not mine, but those of the medical editor.

| Rogers evidently had never read La Place's celebrated work on Probabilities, or else he did not agree with its doctrine. Witness this passage :“It is exceedingly unphilosophical to deny magnetic phenomena merely because they are inexplicable in the present state of our knowledge."Calcul des Probabilités, p. 348.

It is remarkable enough that in a matter like this, usually deemed to savor of imagination, the mathematician should reprove the incredulity of the poet.



An example of graver character and more influential effect is to be found in a lecture, delivered in 1854, at the Royal Institution, before Prince Albert and a select audience, by England's first electrician. Rogers's flyingfish was clairvoyance; Faraday's is table-moving.

But if great men fall into one extreme, let us not, for that reason, be betrayed into another. Let us bear in mind that, antecedent to sufficient proof adduced to establish them, the circulation of the blood, the fall of meteorites, the phenomena of clairvoyance, the reality of table-moving,-all are, or were, improbabilities.

But there are few propositions to which the common sense of mankind, indorsing the most accredited scientific authority,* assents more readily, or with greater justice, than this : that in proportion as an event or phenomenon is in its nature improbable is greater weight of evidence required to produce a rational belief in its reality.

The converse of this proposition, it is true, has been plausibly argued, sometimes where one would least expect to find an apology for credulity;t but men have been so frequently deceivers, and so much more frequently themselves deceived, that, when their testimony is adduced to prove something of a marvelous and unexampled nature, every dictate of experience warns us against its reception, except after severest scrutiny, or the concurrence, when that can be had, of many disinterested witnesses, testifying independently of each other.

The argument, however, in regard to the weight of evidence which may be procured through such concurrence of testimony to one and the same fact, has, in my

*“Plus un fait est extraordinaire, plus il a besoin d'être appuyé de fortes preuves. Car ceux qui l'attestent pouvant ou tromper, ou avoir été trompés, ees deux causes sont d'autant plus probables que la réalité du fait l'est moins en elle-même.”—LA PLACE: Théorie analytique des Probabilités, Introd. p. 12.

† As in the French Encyclopedia, article Certitude."

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judgment, sometimes been pushed beyond what it will bear. Where human testimony enters as an element into the calculation, its disturbing agency may be such as to weaken, almost to the point of overthrowing, the force of all strictly mathematical demonstration. Thus, in substance, has the argument been put.*

. Let us suppose two persons, A. and B., of such a character for veracity and clear-sightedness that the chances are that they will speak the truth, and will avoid being deceived, in nine cases out of ten. And let us suppose that these two persons, absolutely unknown to and unoonnected with each other, are about to testify in regard to any fact. What are the chances that, if their testimony shall agree, the fact has happened?

Evidently, a hundred to one. For if their testimony agree and the fact has not happened, there must be a concurrent lie or self-deception. But, as, in the first place, the chances are ten to one against A. lying or being deceived, and then, in the contingency that he should be, the chances are again ten to one against B. failing to relate the truth, it is evident that the chances against the double event are ten times ten (or one hundred) to one.

Pursuing the same calculation, we find that, in the event of three such witnesses concurring, the chances are a thousand to one against the falsehood of their testimony; if four such concur, ten thousand to one; and so

So that it requires but a small number of such witnesses to establish a degree of probability which, in practice, is scarcely short of certainty itself.


* The reader may consult La Place's "Théorie analytique des Probabilités,” where all the calculations connected with this argument are given in detail; or, if unprepared for the difficulties of Calculus, he will find the matter set out in more condensed and popular form, by Babbage, in his Ninth Bridgewater Treatise,” 2d ed., pp. 124 to 131; and in Note E of Appendix to the same work.



And, following out this principle, it will be found that, if we can but procure witnesses of such a character that it is more probable that their testimony is true than that it is false, we can always assign a sufficient number of such to establish the occurrence of any event or the reality of any phenomenon, no matter how improbable or marvelous such event or phenomenon, in itself considered, may be.

If the postulates be granted, these conclusions clearly follow; and they have been employed by Dr. Chalmers* and others, in treating of miracles, to illustrate the great accumulation of probability which arises from the concurrence of independent witnesses.

The difficulty lies in the postulates. It seems, at first, a very easy matter to find witnesses of such moderate veracity and intelligence that we are justified in declaring it to be more probable that their testimony shall be true than that it shall be false.

As to willful falsehood, the matter is beyond doubt. Let cynicism portray the world as it will, there is far more of truth than of falsehood in it. But as to freedom from self-deception, that is a condition much more difficult to obtain. It depends to a great extent upon the nature of the event witnessed or the phenomenon observed.

An extreme case may assure us of this. If two independent witnesses of good character depose to having seen a market-woman count out six dozen eggs from a basket which was evidently of capacity sufficient to contain them, we deem the fact sufficiently proved. But if two thousand witnesses of equally good character testify that they saw Signor Blitz or Robert-Houdin take that number of eggs out of an ordinary-sized hat, they fail to convince us that the hat really contained

* Evidences of Christian Revelation," vol. i. p. 129.



them. We conclude that they were deceived by sleight of hand.

Here, therefore, the postulates must be rejected. And, without speaking of mathematical impossibilities, in regard to which, of course, no imaginable number of concurrent witnesses avail in proof, the character of tho event or phenomenon testified to must ever count for much; and, whatever theorists may say, it will always greatly influence our opinion, not perhaps of the honesty, but of the freedom from delusion, of the testifiers. So that, in a case where proof of some marvel is in question, the assumed condition, namely, that we shall find witnesses whom we believe more likely to speak the truth than to lie or be deceived, may not be capable of fulfillment.

And the difficulty of procuring such may, under certain circumstances, greatly increase. There are mental as well as physical epidemics, and during their prevalence men's minds may be so morbidly excited, and their imaginations so exalted, that entire masses may become incapacitated to serve as dispassionate witnesses.

There is another consideration, noticed by Hume in his chapter on Miracles, which should not be overlooked. “Though we readily reject,” says he, “any fact which is unusual and incredible in an ordinary degree, yet, in advancing further, the mind observes not always the same rule.” We sometimes accept, he thinks, a statement made to us, for the very reason which should cause us to reject it; on account of its ultra-marvelous character The reason is shrewdly assigned :-“The passion of surprise and wonder arising from miracles, being an agreeable emotion, gives a sensible tendency toward the belief of those events from which it is derived." In a word, we should be on

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* Hume': Essays, vol. ii. p. 125.

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