PROBABILITY, PROBABILITIES, THEORY OF. A conclusion is said to be known, in two distinct ways ; first, when it is derived from those principles (as we call them) which may be considered as common to all mankind, or which at least no one is found to deny ; secondly, when it results, by a sure process of inference, from premises which are believed to be known. Whether these premises be properly known, that is to say, whether another person assuming to decide on the propriety or impropriety will be satisfied or not, is not a part of i the present inquiry. That knowledge of the first kind exists is un questioned, and most of the results of such knowledge are agreed upon. That knowledge of the second kind exists is also unquestioned, though two men may differ as to whether a given conclusion be part of it or not. The distinction, as elsewhere noticed [Mara EKATICS], is positive, easily apprehended, and useful; it exists moreover, and must exist, whatever may be the system of psychology on which one man or another may explain it.
In the exact sciences, demonstration is always effected in such a wan as to show that nothing contradictory of the proposition demonstrated either is true or eau have been true at any time. Two sides of a triangle are, were, and always will be, greater than the third ; by which we mean that persons with minds constituted as ours are, must have admitted this, must now admit it, and must admit it in all time to come. Those who should deny the proposition must really hold that a whole may be less than its contained part : such is the alternative which geomitrical demonstration offers for acceptance, and we should cease to consider a mind as the proper object of instruction which should prefer the alternative to the proposition. Such truths as these are not the subject of the present article.
The other class of conclusions consists of those which may be false, or which may have been false at one time, or may become so, without the necessity of our supposing an absolute and inconceivable difference of mental constitution between ourselves and the person who may have seen this falsehood, may now see it, or is to see it. Many such conclusions appear to be as certain as if they were absolutely demon strated, until a close and (to those who have not considered the sub ject) a captious test is applied, which shows that this certainty is not what is called mathematical certainty. One of the most certain per
haps of all is this : a ball of iron suspended by a thread will fall to the ground when the thread is cut ; every one is as well persuaded of this truth as of the two sides of a triangle being together greater than the third ; those who have not studied geometry know the former much better than the latter. But let any one assert that he has seen, in a part of Africa unexplored except by himself, a ball of iron sus pended in the air, which, though iron to the sight and touch and iron to every chemical experiment, not only remains in the air without sup port, but, when forced to the ground, rises again of itself to the same height. We should laugh and disbelieve it, but we could not disprove it ; in spite of our laughter and unbelief, no man can know such a thing to be false. Let a number of credible persons solemnly declare that they have seen the same phenomenon, and our unbelief would be shaken: finally, let it be a matter, as it is called, of common notoriety, and let a continual succession of good witnesses passing and repassing con stantly confirm each other in the recital above mentioned, and our positive disbelief would be changed into as positive a belief. But let a new witness declare that the natives use bows and arrows of the common form, in which the straight string of the bow, meaning that part of it which joins the extremities of the bow, is four or five times as long as the curved bow itself; though our disbelief of this first wit ness would not be sensibly stronger than our disbelief of the first witness in the preceding case, yet it must be of this kind, that any succession of respectable witnesses, however numerous, could never add any force to the fact in a mind which can properly appreciate the grounds of the assertion that a straight lino is the shortest distance between two points. A million of witnesses could do no more than one to establish the fact stated, in the mind of a person who knows what geometrical demonstration is; though it is just possible that another, who only learns the connection of the sides of a triangle from experiment, may be capable of being convinced of the second assertion by evidence, as well as of the first.