This class includes whatever errors of generalisation are not mere blunders, but arise from some wrong general conception of the inductive process. Only a few kinds can be noted. 1. Under this Fallacy come generalisations which cannot be established by experience, e.g. inferences from the order in the Solar System to other and unknown parts of the universe; and also, except when a particular effect would contradict either the laws of number and extension, or the universal law of causality, all inferences from the fact that we have never known of a particular effect to its impossibility. 2. Those generalisations also are fallacious which resolve, either, as in early Greece, all things into one element, or, as often in modern times, impressions on the senses, differing in quality, and not merely in degree, into the same; e.g. heat, light, and (through vibrations) sensation, into motion; mental, into nervous states; and vital phenomena, into mechanical or chemical processes. In these theories, one fact has its laws applied to another. It may possibly be a condition of that other; but even then the mode in which the new fact is actually produced would have to be explained by its own law, and not by that of the condition. 3. Again, generalisations got by Simple Enumeration, fall under this Fallacy. That sort of Induction 'precariÒ concludit,' says Bacon, 'et periculo exponitur ab instanti contradictoriÂ, ... ex his tantummodÒ quÆ prÆsto sunt pronuncians.' The ancients used it; and in questions relating to man and society, it is still employed by practical men. By it men arrived at the various examples of the formula, Whatsoever has never been (e.g. a State without artificial distinctions of rank; negroes as civilised as the white race) will never be; which, being inductions without elimination, could at most form the ground only of the lowest empirical laws. Higher empirical laws can be got, when a phenomenon presents (as no negation can) a series of regular gradations, since something may then be inferred from the observed as to the unobservable terms of the series. Such is the law of man's necessary progression, in contradiction to the above formula. But even this better generalisation is similarly, though not as grossly, fallacious as the preceding, when, though not itself a cause, but only a summary expression for the general result of all the causes, it is accepted as the law of human changes, past and even future. So, empirical generalisations, from present to past time, and from the character of one nation to that of another, are similarly fallacious when employed as causal laws. 4. This Fallacy occurs, not only when an empirical is confounded with a causal law, but when causation is inferred improperly. The mistake sometimes lies in inferring À posteriori that one fact must be the cause of another (e.g. the National Debt, or some special institution, of England's prosperity), because of their casual conjunction; at other times, in assuming À priori that one of several coexisting agents is the sole cause, and then deducing the effects from it exclusively. The latter is properly False Theory. It has been exemplified in medicine by the tracing of all diseases by one school, to viscidity of the blood, by another, to the presence of some acid or alkali, and, in politics, by the assumption that some special form of government or society is absolutely good. 5. In False Analogies (which fall under this Fallacy) there is no pretence of a conclusive induction. The argument from Analogy is the inferring, in the absence of evidence either way, that an object resembles a second object in one point, because it is seen to resemble it in another point, which either is not known to be connected with the first by causation (as, that the planets must be inhabited because they obey the same astronomical laws with the earth, which is), or which is known to be, not, indeed, its cause or its effect, but either one of a set of conditions, which together are its cause, or an occasional effect of its cause. Now, persons (usually from poverty, not from luxuriance, of imagination) often overrate the weight of true analogies; but the fallacy specially consists in inferring resemblance in one point from resemblance in another, when the evidence is not only not in favour of, but even positively against the connection of the two by way of causation. It is so in the argument in favour of absolutism, on the ground of its resemblance to paternal government in the one point of irresponsibility, as though the assumed benefits of paternal rule flowed from this quality. Similarly fallacious are the inferences, through analogies, from the liability to decay of bodies natural to that of bodies politic; from the supposed need of a primum mobile in nature to that of an irresponsible power in a state; and from the effects of a decrease of a country's corn to the effects of a decrease of its gold (the utility of which, but not of corn, depends on its value, and its value on its scarcity). Such, also, were the Pythagorean inferences that there is a music of the spheres, because the intervals between the planets have the same proportion as the divisions of the monochord; and, again, that the movements of the stars as being divine must be regular, because so are those even of orderly men. So, Aristotle and other ancients supposed perfection to obtain in all natural facts, because it appeared to exist in some; and so, the Stoics tried to prove the equality of all crimes by reference to various similes and metaphors (as, that the man held half an inch below the surface will be drowned as certainly as the man at the bottom of the sea; and that want of skill is shown as much in steering a straw-laden boat as a treasure galleon on to the rocks). But, in fact, the connection by causation between the known and the inferred resemblance, which is assumed by these metaphors, is the very thing which they are brought to prove. The real use of such cases of analogy as metaphors is that they serve, not as an argument, but as an assertion that one exists. Though they cannot prove, they sometimes suggest the proof, and point to a case in which the same grounds for a conclusion have been found adequate. Such are d'Alembert's classification of successful politicians as either eagles or serpents; and the statement, as an argument for education, that, in waste land weeds will spring up; and such is not Bacon's inference from the levity of floating straw to the worthlessness of the extant scientific works of the ancients.

The great source of fallacious generalisation is bad classification, by which things with no, or no important, common properties, are grouped together. Worst is it, when a word which commonly signifies some definite fact is applied to other facts only slightly similar. Bacon (who has himself thus erred in his enquiries into heat) specifies, as examples of this, the various applications (got, by unscientific abstraction, from the original sense) of the word 'wet,' to flame, air, dust, and glass, as well as to water. The application by Plato, Aristotle, and other ancients, of the terms Generation, Corruption, and ????s?? [Greek: kinÊsis] to many heterogeneous phenomena, with a mixture of the ideas belonging to them severally, caused many perplexities, which may be noticed under Fallacies of Confusion.