The petitio principzi, or " begging of the question." This is when, instead of prov ing a position by some different position, something is assumed that is identical with what is to be proved. The most common form of this fallacy is what is termed reason ing in a circle, where we make two propositions mutually prove each other. The fol lowing would be an example of this mode of reasoning. Suppose we asked why smoke ascends, and any one were to answer, "because it is light;' we then inquire how it is known to be light, and the reply is, "because it ascends." The non canna pro causa. This is a fallacy of insufficient induction, or the inferring a connection of cause and effect where there is only a mere sequence or accompaniment: as when we allege that the prosperity of England is due to its having an aristocracy, or an established church, or any other circumstance that has attached to the country, without ascertaining that there is any real causation between the two facts. Empiri cism in medicine is of this nature; such a one took a certain medicine, and recovered from an illness, therefore the medicine was the cause of the recovery. The post hoe, .ergo propter hoc, is another expression for the same fallacy. which is one of wide range, and whose rectification far transcends the limits of scholastic or formal logic.
The argunzentum ad Ambient is a reference to the circumstances of the party addressed, and means that although a certain reasoning may be good in itself, such party is not entitled to urge it, having perhaps already repudiated the same reasoning in other cases, or acted in a manner inconsistent with the employment of it. (For a full exemplification of fallacies according to the foregoing enumeration, see De Morgan's Formal Logic, Whately's Logic, sir William Hamilton's Lectures on Logic, etc.) The subject of fallacies has received a much more comprehensive treatment in the work on logic by Mr J. S. Mill. who has enlarged the basis of the science itself, by placing induction at the foundation of reasoning, and by recognizing the necessity of laying down rules for the correct performance of that process. See INDUCTION. This -enables him to give a proper place to some of the preceding fallacies, such as the post hoc, ergo propter hoc, which, although occurring in treatises of syllogistic logic, does not violate any rule either of syllogism or of any process included in such treatises. In fact, if we take a complete view of all the cardinal operations that enter into the establish ment of truth by evidence, we ought to enumerate four such operations—Observation, including experiment; definition, or the right use of general terms; induction; and deduction or syllogism. Now, any one of these operations badly performed would necessarily lead to a wrong result, in other words, a fallacy. But in addition to the mistakes arising from the admission of insufficient evidence at any point, there is a class of errors (as well as truths) that arise from our receiving propositions without any evi• dente at all, on the ground that they are self-evident. In every case of reasoning, we must come at last to something that does not need a reason, as, for example, the evidence of our senses, or our actual observation; but we may sometimes admit as self-evident what is really not so, owing, perhaps, to our having a strong sentiment in the matter on hand. It is usual to consider the existence of an external material world, altgether inde pendent of our minds, as certain in itself without requiring any proof or reason for the belief. It is found that we often-commit mistakes in this way, and the mistakes thence arising Mr. Mill illustrates under the title of fallacies of simple inspection, or fallacies a
_priori, which includes the whole of what may be termed natural prejudices. The other members of his classification follow his division of the processes concerned in the inves tigation of truth: they are fallacies of observation, fallacies of generalization, including induction, and fallacies of ratiocination or syllogism. He remarks, moreover, that error does not often take the form of a deliberate infringement of the rules of good observa tion, induction, or deduction, but rather consists in a confused perception of the prem ises involved. In other words, it is the "not conceiving our premises with due clear ness, that is, with due fixity; forming one conception of our evidence when we collect or receive it, and another when we make use of it; or unadvisedly, and iu general uncon sciously, substituting, as We proceed, different premises in the place of those with which we set out, or a different conclusion for that which we undertook to prove. This gives existence to a class of fallacies which may be justly called fallacies of confusion; com prehending, among others, all those which have their source in language, whether aris ing from the vagueness or ambiguity of our terms, or from casual associations with them." It is in this group that Mr. Mill places the petal() principii, the ignoratio elenehi, and ambiguous language generally (Louie, hook v.).
The scholastic fallacies were considered mostly in the light of weaknesses or invol untary errors of the intellect, to be corrected by sound rules or a good method of pro cedure. The syllogistic logician made little count of the natural prejudices, or strong emotions and passions of mind, which forcibly pervert the intellectual views, and render men averse to sound reasoning. This grand omission was first effectively sup plied in the immortal first book of the Novum Organon of Bacon, who, in a vigorous and telling exposition, set forth some of the most powerful prejudices of the natural mind, and their influence in corrupting science and philosophy, as well the every-day judg ments of mankind. Under the name of "idola" he classed four different species of these moral sources of error, against which the mind had to be fortified, not by syllogistic rules, but by a self-denying discipline, and a highly cultivated perception of the true end of science, which was to increase human power in all the arts of life. His first class of idola were idola tribus, or delusions common to the human mind generally, such as errors of the senses, the over-susceptibility of the mind to impressions of sense, the limits of the human faculties, and the interference of prejudices and passions; a very compre hensive class, which even he has failed to do full justice to. The next class are idola speciss, idols of the den or cavern, by which he 'understands the peculiarities and idiosyn crasies of individuals. The third class, idola fori, idols of the market, are intended to include the abuses of language, or the various ways that our conceptions of things are distorted by names. The last class arc the idola theatri, theatrical illusions, under which lie rebukes the great system-builders of antiquity, such as Aristotle, for introducing fanciful and irrelevant considerations into philosophy; and dwells especially on the cor rupting influences of superstition and theology, and also the poetical tendencies of the mind, which are not satisfied with truth unless it can take on in addition a certain warmth or brilliancy of coloring.