INDUCTION, in logic, that method of reasoning which establishes general laws or specific predictions of future, present or past facts on the basis of individual experiences. It is the type of argument by which, let us say, the law of universal gravitation is demon strated on the basis of observations as to the mutual attraction of certain given bodies, or by which an insurance 'company is able to determine a safe price for future policies on the basis of past statistical tables, or by which the geologist may describe the history of a certain drainage system through his knowledge of the present status of the system and of the modi fications taking place in the drainage systems of the present time. Induction differs from deduc tion not only in that it starts from particular facts rather than general laws, but also in that the propositions derived by an induction (not covering every single case of the law it sets out to establish) never even appear to have that apodictic certainty which we naturally attribute to the results of correct deduction from indis putable premises. An induced conclusion is only probably true; furthermore, if it is at all precise in its terms, it is in general only ap proximately true. The probable correctness of the successive digits of a decimal fraction ob tained by inductive reasoning falls off with amazing rapidity. A number, the first nine digits of which are all but absolutely certain, may well have a highly probable 10th digit, a likely 1 1th and an absolutely worthless 12th.
Induction, then, is the probable and approxi mate demonstration of laws or predictions on the basis of concrete experiences. It is not what it has been considered by Hume and the other 18th century British empiricists: the for mation of general ideas — i.e., universals — from mere particulars. In the first place, a universal is not a universal law, nor is a fact a particular. But furthermore, we do not form the notion of red by looking at this red thing and that, and abstracting from them their common quality, nor by associating with the image of one red thing all our past experiences of red objects.
There are an endless number of attributes pos sessed by a group of and even exclu sively possessed by this group. Redness can only be one of these. When we see the group we recognize redness either as the color quality they possess in common or as their simplest common attribute, or because redness is the property that most attracts our attention. In all these cases we must have a concomitant or ante cedent consciousness of a universal — of color, simplicity or redness itself. The process de scribed by the British empiricists simply does not exist, and every formation of a general notion from experience involves an existing awareness of general notions. That is, not withstanding the contrary opinion of the nomi nalists, the general notions of qualities and rela tions which enter into the presentment of in ductive laws are not mere mosaics of particular sense data. In a like manner, the inductive laws themselves are not mere mosaics of partic ular facts. A very common expression among inductive logicians, due to J. S. Mill, is °the uniformity of nature> We are justified in pro ceeding from this fact and that fact and the other fact to the general law subsuming them all because nature is uniform. This principle of the uniformity of nature has two very dif ferent meanings. It may be little more than a tautology or it may be the cardinal law of natural science — or all science, for the matter of that. If the uniformity of nature means simply what it says, it means merely that two occurrences can never agree in all but one aspect and disagree in that one. Now, as even an approximately complete inventory of the aspects of an occurrence is never at our dis posal, and since moreover the temporal and spatial position of an occurrence must be con sidered in enumerating its aspects, this law tells us, for all practical purposes, absolutely noth ing. Nature might be perfectly uniform, even though the jumping of a flea should determine the motions of the planets; the establishment of astronomical laws, however, would be a some what difficult pursuit.