When an event has happened a very great number of times, its happening once again approaches nearly to certainty. If we suppose the sun to have risen one thousand million times, the probability that it will rise again, on the ground of this knowledge merely, is (1,000,000,000 + 1)/(1,000,000,000 + 1 + 1). But then the probability that it will continue to rise for as long a period in the future is only (1,000,000,000 + 1)/(2,000,000,000 + 1), or almost exactly 1/2. The probability that it will continue so rising a thousand times as long is only about 1/1001. The lesson which we may draw from these figures is quite that which we should adopt on other grounds, namely, that experience never affords certain knowledge, and that it is exceedingly improbable that events will always happen as we observe them. Inferences pushed far beyond their data soon lose any considerable probability. De Morgan has said,[170] “No finite experience whatsoever can justify us in saying that the future shall coincide with the past in all time to come, or that there is any probability for such a conclusion.” On the other hand, we gain the assurance that experience sufficiently extended and prolonged will give us the knowledge of future events with an unlimited degree of probability, provided indeed that those events are not subject to arbitrary interference. [170] *Essay on Probabilities*, p. 128. It must be clearly understood that these probabilities are only such as arise from the mere happening of the events, irrespective of any knowledge derived from other sources concerning those events or the general laws of nature. All our knowledge of nature is indeed founded in like manner upon observation, and is therefore only probable. The law of gravitation itself is only probably true. But when a number of different facts, observed under the most diverse circumstances, are found to be harmonized under a supposed law of nature, the probability of the law approximates closely to certainty. Each science rests upon so many observed facts, and derives so much support from analogies or connections with other sciences, that there are comparatively few cases where our judgment of the probability of an event depends entirely upon a few antecedent events, disconnected from the general body of physical science.