Hypothetical and disjunctive syllogism

Japanese: 仮言選言三段論法 - かげんせんげんさんだんろんぽう
Hypothetical and disjunctive syllogism

… (5) “Only one of p and q is true” “not q ” ⇒ “ p ” is called the “negative affirmative formula” of a disjunctive syllogism, and “Only one of p and q is true” “ p ” ⇒ “not q ” is called the “affirmative negation formula” of the same disjunctive syllogism. (6) In addition to the above, there is a type of reasoning called a hypothetical disjunctive syllogism, and “If p , then r , and if q , then r ” “Only one of p and q is true” ⇒ “ r ” is one example. When reconsidering syllogisms from the standpoint of modern logic, first, each proposition that constitutes a categorical syllogism (3) is usually interpreted as a formula of predicate logic as follows: …

*Some of the terminology explanations that refer to "hypothetical-disjunctive syllogism" are listed below.

Source | Heibonsha World Encyclopedia 2nd Edition | Information

Japanese:

… (5)〈“pqのどちらか一方だけ成立する”,“qでない”⇒“p”〉は〈選言三段論法〉の〈否定肯定式〉,〈“pqのどちらか一方だけ成立する”,“p”⇒“qでない”〉は同論法の〈肯定否定式〉と呼ばれる。 (6)このほかに,〈仮言選言三段論法〉と呼ばれる推論の型があり,〈“pならばr,かつ,qならばrである”,“pqのどちらか一方だけ成立する”⇒“r”〉はその一例である。 現代論理学の立場から三段論法をとらえなおすとき,まず,定言的三段論法(3)を構成する各命題は述語論理の式として通常つぎのように解釈される。…

※「仮言選言三段論法」について言及している用語解説の一部を掲載しています。

出典|株式会社平凡社世界大百科事典 第2版について | 情報

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