Chapter 47
-- 821. In the regular form the terms which connect each proposition in the series with its predecessor, that is to say, the middle terms, maintain a fixed relative position; so that, if the middle term be subject in one, it will always be predicate in the other, and vice versa. In the irregular form this symmetrical arrangement is violated.
-- 822. The syllogisms which compose a regular sorites, whether progressive or regressive, will always be in the first figure.
In the irregular sorites the syllogisms may fall into different figures.
-- 823. For the regular sorites the following rules may be laid down.
(1) Only one premiss can be particular, namely, the first, if the sorites be progressive, the last, if it be regressive.
(2) Only one premiss can be negative, namely, the last, if the sorites be progressive, the first, if it be regressive.
-- 824. _Proof of the Rules for the Regular Sorites_.
(1) In the progressive sorites the proposition which stands first is the only one which appears as a minor premiss in the expanded form. Each of the others is used in its turn as a major. If any proposition, therefore, but the first were particular, there would be a particular major, which involves undistributed middle, if the minor be affirmative, as it must be in the first figure.
In the regressive sorites, if any proposition except the last were particular, we should have a particular conclusion in the syllogism in which it occurred as a premiss, and so a particular major in the next syllogism, which again is inadmissible, as involving undistributed middle.
(2) In the progressive sorites, if any premiss before the last were negative, we should have a negative conclusion in the syllogism in which it occurs. This would necessitate a negative minor in the next syllogism, which is inadmissible in the first figure, as involving illicit process of the major.
In the regressive sorites the proposition which stands first is the only one which appears as a major premiss in the expanded form.
Each of the others is used in its turn as a minor. If any premiss, therefore, but the first were negative, we should have a negative minor in the first figure, which involves illicit process of the major.
-- 825. The rules above given do not apply to the irregular sorites, except so far as that only one premiss
(1) Barbara.
All B is A.
All C is B.
All C is A.
All B is A.
All C is B.
Some C is D.
All D is E.'. Some A is E
[Ill.u.s.tration]
(2) Disamis.
Some C is D.
All C is A.
Some A is D.
(3) Darii.
All D is E Some A is D.
Some A is E.
(1) Barbara.
All B is C.
All A is B.
All A is C.
All A is B.
All B is C.
No D is C.
All E is D.
.'. No A is E.
[Ill.u.s.tration]
(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 x.x.x.
_Of Fallacies_.
-- 827. After examining the conditions on which correct thoughts depend, it is expedient to cla.s.sify 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--
(1) thought,
(2) language.
-- 830. This is the basis of Aristotle's division of fallacies, which has not yet been superseded. Fallacies, according to him, are either in the language or outside of it. Outside of language there is no source of error but thought. For things themselves do not deceive us, but error arises owing to a misinterpretation of things by the mind. Thought, however, may err either in its form or in its matter. The former is the case where there is some violation of the laws of thought; the latter whenever thought disagrees with its object. Hence we arrive at the important distinction between Formal and Material fallacies, both of which, however, fall under the same negative head of fallacies other than those of language.
| In the language | (in the signs of thought) | Fallacy -| |--In the Form.
|--Outside the language -| | (in the thought itself) | | |--in the Matter.
-- 831. There are then three heads to which fallacies may be referred-namely, Formal Fallacies, Fallacies of Language, which are commonly known as Fallacies of Ambiguity, and, lastly, Material Fallacies.