§ 820. A sorites may be either Regular or Irregular.
§ 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 versâ. 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.