The fallacy of Composition is the converse of this. What is true of several singulars may not be true of all of them taken together. Because each of the witnesses in a law case is liable to error, it does not follow that the concurrent testimony of many is not to be credited. (Jevons.)
Circular or Tautological theorems (Petitio Principii Begging the Question) are a breach of rule 2, section xviii. This fallacy often consists in proposing as a precedent the case, or information drawn from the case and stated in other words. 'To allow every man an unbounded freedom of speech must always be, on the whole, advantageous to the State; for it is highly conducive to the interests of the Community that each individual should enjoy a liberty perfectly unlimited of expressing his sentiments.' (Whately.)
| It is conducive | that each individual should enjoy |
| It is advantageous | to allow |
There may be tautology in a single word—the 'question-begging epithet.' We undertake to prove something, but get no further than the use of metaphors implying the point in dispute. For example, some scientific writers are anxious to promote the belief that animal life is a combination of natural forces—that there is no individual life distinct from cosmic life,—but all their proof consists in calling a man or beast a 'machine,' and calling machines 'creatures.' This might be mistaken for the Substantialist doctrine on the same subject, but the two are radically different. Substantialism asserts that man and nature have similar lives—materialism teaches that they have only one life in common, and that the coarse, mindless life of the cosmos as conceived realistically.
Conclusions may be used as precedents before verification, but it is not lawful to assume a hypothetical precedent on the understanding that it is to be proved in the course of the argument, and then use the conclusion so obtained to prove its own precedent. This is also dialectical tautology, but the circle includes two or more theorems. When naturalists tell us that in the struggle for life the fittest only survive, and when asked how we know which are the fittest they reply that the fittest are known by the fact of their surviving, we have a tautological argument.
| Animals that survive | are the fittest | Fittest animals | survive |
| A particular animal has survived | hence it is the fittest of its species | This animal is the fittest of its species. | which is the reason it has survived |
Survival under competitive conditions is first assumed, and from it is deduced the superiority of the existing type of animal; then this inferential superiority is offered to justify the previously imagined competitive survival. The two hypotheses waltz round each other without making any rational advance.
When a book is quoted to prove its own authenticity we have this fallacy; or when the precedent is as unknown as the conclusion,—'Paradise was in Armenia, therefore Gihon is an Asiatic river.'
The academical syllogism as defined—not always as presented—contains two fallacies, one of which is tautology. 'All Europeans are white; Caius is a European; therefore he is white.' If, as logicians say, the 'all' is absolute and includes Caius even before he is mentioned, then it is clear that the theorem amounts to saying, 'All Europeans are white, and one of them is Caius.' 'Both the twins are fair-haired; Caius is one of the twins; therefore he is fair-haired':—the pretended conclusion is merely a naming of a part of the precedent. The first of these theorems may be interpreted so as to give a valid conclusion. We are informed that an unknown person called Caius is a European; we are not told, and we do not know, what is the colour of his skin; but because all the Europeans we have known have been white, we infer—pending actual knowledge—that Caius is white. Logicians interpret the syllogism otherwise, for they have a notion that reason should give infallible certainty.
After the precedent has been divided into subject and applicate, the former is sometimes used as applicate and so generates a wrong conclusion. This may be called Cross Reasoning or Diagonal Reasoning—the fallacy termed by logicians 'Undistributed Middle.'