Логика. Непосредственное дедуктивное умозаключение: преобразование по логическому квадрату. Отношения субконтрарности и подчинения (самое важное)

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Логика. Непосредственное дедуктивное умозаключение: преобразование по логическому квадрату. Отношения субконтрарности и подчинения (самое важное)

Lecture notes, cheat sheets

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41. НЕПОСРЕДСТВЕННОЕ ДЕДУКТИВНОЕ УМОЗАКЛЮЧЕНИЕ: ПРЕОБРАЗОВАНИЕ ПО ЛОГИЧЕСКОМУ КВАДРАТУ. ОТНОШЕНИЯ СУБКОНТРАРНОСТИ И ПОДЧИНЕНИЯ

Relation of partial compatibility (subcontrast): I-O. Из ложности одного суждения следует истинность другого, но из истинности одного из них может следовать как истинность, так и ложность другого суждения. Истинными могут быть оба суждения. Напр., из ложного суждения "Некоторые врачи не имеют медицинского образования" следует истинное суждение "Некоторые врачи имеют медицинское образование", из истинного суждения "Некоторые свидетели допрошены" следует суждение "Некоторые свидетели не допрошены", которое может быть как истинным, так и ложным.

Таким образом, субконтрарные суждения не могут быть вместе ложными; по крайней мере одно из них истинно:

⌉I → O; ⌉0→I; I → (О ∨ ⌉О); O → (I ∨ ⌉1).

Subordination relationship (A-I, E-O). Из истинности подчиняющего суждения следует истинность подчиненного суждения, но не наоборот: из истинности подчиненного суждения истинность подчиняющего суждения не следует, оно может быть истинным, но может быть ложным. Напр., из истинности подчиняющего суждения А "Все врачи имеют медицинское образование" следует истинность подчиненного ему суждения I "Некоторые врачи имеют медицинское образование". Из истинного подчиненного суждения "Некоторые свидетели допрошены" нельзя с необходимостью утверждать об истинности подчиняющего суждения "Все свидетели допрошены":

A → I; E → O; I → (A ∨ 1 A); O → (E ∨ 1E).

Из ложности подчиненного суждения следует ложность подчиняющего суждения, но не наоборот: из ложности подчиняющего суждения ложность подчиненного с необходимостью не следует; оно может быть истинным, но может быть и ложным. Напр., из ложности подчиненного суждения (О) "Некоторые народы не имеют права на самоопределение" следует ложность подчиняющего суждения (Е) "Ни один народ не имеет права на самоопределение". Если ложным является подчиняющее суждение (А) "Все свидетели допрошены", то подчиненное ему суждение (I) "Некоторые свидетели допрошены" может быть истинным, но может быть ложным (возможно, что ни один свидетель не допрошен).

В логическом квадрате слово "некоторые" употребляется в значении "по крайней мере, некоторые".

⌉I →⌉ A; ⌉O → ⌉E; ⌉A → (I ∨ ⌉I); ⌉E→ (O ∨ ⌉0).

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Dogs look like their owners 17.08.2004

Observant people have been talking about this for a long time, but a scientific assessment of the degree of similarity between dogs and their owners has been carried out for the first time.

Psychologists from the University of California at San Diego (USA) went to a park where local dog owners walk with their pets and photographed 45 dogs (25 purebreds and 20 mutts) and their owners. They were filmed separately and against different backgrounds. Then the obtained photographs were shown to 28 students and asked to arrange the pictures in pairs "dog - owner".

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