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In term logic (a branch of philosophical logic), the square of opposition is a diagram representing the relations between the four basic categorical propositions. The origin of the square can be traced back to Aristotle 's tractate On Interpretation and its distinction between two oppositions: contradiction and contrariety .
In syllogistic logic, there are 256 possible ways to construct categorical syllogisms using the A, E, I, and O statement forms in the square of opposition. Of the 256, only 24 are valid forms. Of the 24 valid forms, 15 are unconditionally valid, and 9 are conditionally valid.
Subalternation [1] [2] is an immediate inference which is only made between A (All S are P) and I (Some S are P) categorical propositions and between E (No S are P or originally, No S is P) and O (Some S are not P or originally, Not every S is P) categorical propositions of the traditional square of opposition and the original square of opposition. [3]
Greek investigations resulted in the so-called square of opposition, which codifies the logical relations among the different forms; for example, that an A-statement is contradictory to an O-statement; that is to say, for example, if one believes "All apples are red fruits," one cannot simultaneously believe that "Some apples are not red fruits."
For instance, from the statement "All toads are green", the immediate inference can be made that "no toads are not green" or "no toads are non-green" (Obverse). There are a number of immediate inferences which can validly be made using logical operations, the result of which is a logically equivalent statement form
Square of opposition In the Venn diagrams black areas are empty and red areas are nonempty. The faded arrows and faded red areas apply in traditional logic. Boolean logic is a system of syllogistic logic invented by 19th-century British mathematician George Boole, which attempts to incorporate the "empty set", that is, a class of non-existent entities, such as round squares, without resorting ...
The logical square, also called square of opposition or square of Apuleius has its origin in the four marked sentences to be employed in syllogistic reasoning: Every man is white, the universal affirmative and its negation Not every man is white (or Some men are not white), the particular negative on the one hand, Some men are white, the particular affirmative and its negation No man is white ...
This diagram shows the contradictory relationships between categorical propositions in the square of opposition of Aristotelian logic. In traditional logic, a contradiction occurs when a proposition conflicts either with itself or established fact. It is often used as a tool to detect disingenuous beliefs and bias.