Логика. Логические отношения между простыми суждениями (самое важное)

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Логика. Логические отношения между простыми суждениями (самое важное)

Lecture notes, cheat sheets

Directory / Lecture notes, cheat sheets

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29. LOGICAL RELATIONS BETWEEN SIMPLE JUDGMENTS

Relations are established not between any, but only between сравнимыми, т. е. имеющими общий смысл суждениями.

Judgments that have different subjects or predicates are incomparable.. Таковы, напр., два суждения: "Среди космонавтов есть летчики"; "Среди космонавтов есть женщины".

Сравнимыми являются суждения с одинаковыми субъектами и предикатами и различающиеся связкой или квантором. Напр.: "Все американские индейцы живут в резервациях"; "Некоторые американские индейцы не живут в резервациях".

Отношения между простыми суждениями обычно рассматриваются с помощью мнемонической схемы, называемой логическим квадратом. Его вершины символизируют простые категорические суждения - А, Е, I, О; стороны и диагонали - отношения между суждениями.

Among comparable judgments, compatible and incompatible judgments are distinguished.

Compatible propositions are propositions that can be true at the same time.. Различают три вида совместимости: эквивалентность (полная совместимость), частичная совместимость (субконтрарность) и подчинение.

1. Эквивалентными являются такие суждения, которые имеют одинаковые логические характеристики: одинаковые субъекты и предикаты, однотипную - утвердительную или отрицательную - связку, одну и ту же выраженную квантором количественную характеристику.

С помощью логического квадрата отношения между простыми эквивалентными суждениями не иллюстрируются.

2. Частичная совместимость характерна для суждений I и О, которые могут быть одновременно истинными, но не могут быть одновременно ложными. При ложности одного из них другое будет истинным: ⌉1→0,⌉0 → I. Напр., при ложности суждения "Некоторые злаки ядовиты" будет истинным суждение "Некоторые злаки не являются ядовитыми". В то же время при истинности одного из частных суждений другое может быть как истинным, так я ложным: I → (О ∨ ⌉0); O → (I ∨ ⌉I).

3. Subordination takes place between judgments A and I, E and O. Для них характерны следующие две зависимости.

When the general proposition is true, the particular proposition will always be true: А → I, Е → О. Напр., при истинности общего суждения "Всякое правоотношение регулируется нормами права" истинным будет и частное - "Некоторые правоотношения регулируются нормами права". При истинности суждения "Ни один кооператив не относится к государственным организациям" будет истинным и суждение "Некоторые кооперативы не относятся к государственным организациям".

If the particular proposition is false, the general proposition will also be false: ⌉I → ⌉A; ⌉O → ⌉E.

Under subordination, the following dependencies remain undefined: при ложности общего суждения подчиненное частное может быть как истинным, так и ложным: ⌉A → (I ∨⌉I); ⌉Е → (О ∨ ⌉О);

при истинности подчиненного частного общее может быть как истинным, так и ложным: I → (А ∨ ⌉А); O → (E ∨⌉E).

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