[Logic by Carveth Read]@TWC D-Link bookLogic CHAPTER V 15/24
Such cases are of very slight logical interest.
It is as exercises in formal thinking that hypotheticals are of most value; inasmuch as many people find them more difficult than categoricals to manipulate. In discussing Conditional Propositions, the conditional sentence of a Hypothetical, or the first alternative of a Disjunctive, is called the Antecedent; the indicative sentence of a Hypothetical, or the second alternative of a Disjunctive, is called the Consequent. Hypotheticals, like Categoricals, have been classed according to Quantity and Quality.
Premising that the quantity of a Hypothetical depends on the quantity of its Antecedent (which determines its limitation), whilst its quality depends on the quality of its consequent (which makes the predication), we may exhibit four forms: A._If A is B, C is D;_ I._Sometimes when A is B, C is D;_ E._If A is B, C is not D;_ O._Sometimes when A is B, C is not D._ But I.and O.are rarely used. As for Disjunctives, it is easy to distinguish the two quantities thus: A._Either A is B, or C is D;_ I._Sometimes either A is B or C is D._ But I.is rarely used.
The distinction of quality, however, cannot be made: there are no true negative forms; for if we write-- _Neither is A B, nor C D,_ there is here no alternative predication, but only an Exponible equivalent to _No A is B, and No C is D_.
And if we write-- _Either A is not B, or C is not D,_ this is affirmative as to the alternation, and is for all methods of treatment equivalent to A. Logicians are divided in opinion as to the interpretation of the conjunction 'either, or'; some holding that it means 'not both,' others that it means 'it may be both.' Grammatical usage, upon which the question is sometimes argued, does not seem to be established in favour of either view.
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