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The considerations now stated, may help us to conceive in what manner conclusions derived from experience come to be insensibly extended from the individual to the species; partly in consequence of the grass and undistinguishing nature of our first perceptions, and partly in consequence of the magical influence of a common name. They seem also to show, that this natural process of thought, though not always justified by a sound logic, is not without its use in the infancy of human knowledge.
4. Evidence of testimony tacitly recognized as a ground of belief, in our most certain conclusions concerning contingent truths.
In some of the conclusions which have been already under our consideration with respect to contingent truths, a species of evidence is admitted, of which no mention has hitherto been made; I mean the evidence of testimony. In astronomical calculations, for example, how few are the instances in which the data rest on the evidence of our own senses; and yet our confidence in the result is not, on that account, in the smallest degree weakened. On the contrary, what certainty can be more complete than that with which we look forward to an eclipse of the sun or the moon, on the faith of elements and of computations which we have never verified, and for the accuracy of which we have no ground of assurance whatever, but the scientific reputation of the writers from whom we have borrowed. them. An astronomer who should affect any skepticism with respect to an event so predicted, would render himself no less an object of ridicule, than if he were disposed to cavil about the certainty of the sun's rising to-morrow.
Even in pure mathematics, a similar regard to testimony, accompanied with a similar faith in the faculties of others, is by no means uncommon. Who would scruple, in a geometrical investigation, to adopt as a link in the chain, a theorem of Apollonius or of Archimedes, although he might not have leisure at the moment to satisfy himself, by an actual examination of their demonstrations, that they had been guilty of no paralogism, either from accident or design, in the course of their reasonings?
Difference between the logical and the popular meaning of the word probability.-In our anticipations of astronomical phenomena, as well as in those which we form concerning the result of any familiar experiment in physics, philosophers are accustomed to speak of the event as only probable, although our confidence in its happening is not less complete than if it rested on the basis of mathematical demonstration. The word probable, therefore, when thus used, does not imply any deficiency in the proof, but only marks the particular nature of that proof, as con- tradistinguished from another species of evidence. It is opposed, not to what is certain, but to what admits of being demonstrated after the manner of mathematicians. This differs widely from the meaning annexed to the same word in popular discourse: according to which, whatever event is said to be probable, is understood to be expected with some degree of doubt. "As certain as death". -"as certain as the rising of the sun are proverbial modes of expression in all countries; and they are both of them, borrowed from events which, in philosophical language, are only probable or contingent. In like manner, the existence of the city of Pekin, and the reality of Cæsar's assassination, which the philosopher classes with probabilities, because they rest solely upon the evidence of testimony, are universally classed with certainties by the rest of mankind; and in any case but the statement of a logical theory, the application to such truths of the word probable, would be justly regarded as an impropriety of speech. This difference between the technical meaning of the word probability, as employed by logicians, and the notion usually attached to it in the business of life, together with the erroneous theories concerning the nature of demonstration, which I have already endeavored to refute, have led many authors of the highest name, in some of the most important arguments which can employ human reason, to overlook that irresistible evidence which was placed before their eyes, in search of another mode of proof altogether unattainable in moral inquiries, and which, if it could be attained, would not be less liable to the cavils of skeptics.
But although, in philosophical language, the epithet probable be applied to events which are acknowledged to be certain, it is also applied to those events which are called probable by the vulgar. The philosophical meaning of the word, therefore, is more comprehensive than the popular; the former denoting that particular species of evidence of which contingent truths admit; the latter being confined to such degrees of this evidence as fall short of the highest. These different degrees of probability the philosopher considers as a series, beginning with bare possibility, and terminating in that apprehended infallibility with which the phrase moral certainty is synonymous. To this last term of the series, the word probable is, in its ordinary acceptation, plainly inapplicable.
The satisfaction which the astronomer derives from the exact coincidence, in point of time, between his theoretical predictions. concerning the phenomena of the heavens, and the corresponding events when they actually occur, does not imply the smallest doubt, on his part, of the constancy of the laws of nature. It resolves partly into the pleasure of arriving at the knowledge of the same truth or of the same fact by different media; but chiefly into the gratifying assurance which he thus receives, of the correctness of his principles, and of the competency of the human faculties to these sublime investigations. What exquisite delight must La Place have felt, when, by deducing from the theory of gravitation the cause of the acceleration of the moon's mean motion an acceleration which proceeds at the rate of little more than 11" in a century, he accounted, with such mathematical precision, for all the recorded observations of the place from the infancy of astronomical science! It is from the length and abstruseness, however, of the reasoning process, and from the powerful effect produced on the imagination, by a calculus which brings into immediate contrast with the immensity of time such evanescent elements as the fractional parts of a second, that the coincidence between the computation and the event appears in this instance so peculiarly striking. In other respects, our confidence in the future result
rests on the same principle with our expectation that the sun will rise to-morrow at a particular instant; and, accordingly, now that the correctness of the theory has been so wonderfully verified by a comparison with facts, the one event is expected with no less assurance than the other.