[Illustration]
(2) Cesare.
No D is C.
All A is C.
.'. No A is D.
(3) Camestres.
All E is D.
No A is D.
.'. No A is E.
§ 826. A chain argument may be composed consisting of conjunctive instead of simple propositions. This is subject to the same laws as the simple sorites, to which it is immediately reducible.
Progressive. Regressive.
If A is B, C is D. If E is F, G is H.
If C is D, E is F. If C is D, E is F.
If E is F, G is H. If A is B, C is D.
.'. If A is B, G is H. .'. If A is B, G is H.
CHAPTER XXX.
Of Fallacies.
§ 827. After examining the conditions on which correct thoughts depend, it is expedient to classify some of the most familiar forms of error. It is by the treatment of the Fallacies that logic chiefly vindicates its claim to be considered a practical rather than a speculative science. To explain and give a name to fallacies is like setting up so many sign-posts on the various turns which it is possible to take off the road of truth.
§ 828. By a fallacy is meant a piece of reasoning which appears to establish a conclusion without really doing so. The term applies both to the legitimate deduction of a conclusion from false premisses and to the illegitimate deduction of a conclusion from any premisses. There are errors incidental to conception and judgement, which might well be brought under the name; but the fallacies with which we shall concern ourselves are confined to errors connected with inference.
§ 829. When any inference leads to a false conclusion, the error may have arisen either in the thought itself or in the signs by which the thought is conveyed. The main sources of fallacy then are confined to two—