Inductive inference might attain to certainty if our knowledge of the agents existing throughout the universe were complete, and if we were at the same time certain that the same Power which created the universe would allow it to proceed without arbitrary change. There is always a possibility of causes being in existence without our knowledge, and these may at any moment produce an unexpected effect. Even when by the theory of probabilities we succeed in forming some notion of the comparative confidence with which we should receive inductive results, it yet appears to me that we must make an assumption. Events come out like balls from the vast ballot-box of nature, and close observation will enable us to form some notion, as we shall see in the next chapter, of the contents of that ballot-box. But we must still assume that, between the time of an observation and that to which our inferences relate, no change in the ballot-box has been made. CHAPTER XII. THE INDUCTIVE OR INVERSE APPLICATION OF THE THEORY OF PROBABILITY. We have hitherto considered the theory of probability only in its simple deductive employment, in which it enables us to determine from given conditions the probable character of events happening under those conditions. But as deductive reasoning when inversely applied constitutes the process of induction, so the calculation of probabilities may be inversely applied; from the known character of certain events we may argue backwards to the probability of a certain law or condition governing those events. Having satisfactorily accomplished this work, we may indeed calculate forwards to the probable character of future events happening under the same conditions; but this part of the process is a direct use of deductive reasoning (p. 226). Now it is highly instructive to find that whether the theory of probability be deductively or inductively applied, the calculation is always performed according to the principles and rules of deduction. The probability that an event has a particular condition entirely depends upon the probability that if the condition existed the event would follow. If we take up a pack of common playing cards, and observe that they are arranged in perfect numerical order, we conclude beyond all reasonable doubt that they have been thus intentionally arranged by some person acquainted with the usual order of sequence. This conclusion is quite irresistible, and rightly so; for there are but two suppositions which we can make as to the reason of the cards being in that particular order:-- 1. They may have been intentionally arranged by some one who would probably prefer the numerical order. 2. They may have fallen into that order by chance, that is, by some series of conditions which, being unknown to us, cannot be known to lead by preference to the particular order in question.