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The square of opposition, under this Boolean set of assumptions, is often called the modern Square of opposition. In the modern square of opposition, A and O claims are contradictories, as are E and I, but all other forms of opposition cease to hold; there are no contraries, subcontraries, subalternations, and superalternations. Thus, from a ...
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]
The logical hexagon extends the square of opposition to six statements. In philosophical logic, the logical hexagon (also called the hexagon of opposition) is a conceptual model of the relationships between the truth values of six statements. It is an extension of Aristotle's square of opposition.
Classical logic is a 19th and 20th-century innovation. The name does not refer to classical antiquity, which used the term logic of Aristotle. Classical logic was the reconciliation of Aristotle's logic, which dominated most of the last 2000 years, with the propositional Stoic logic. The two were sometimes seen as irreconcilable.
In classical logic, particularly in propositional and first-order logic, a proposition is a contradiction if and only if. Since for contradictory φ {\displaystyle \varphi } it is true that ⊢ φ → ψ {\displaystyle \vdash \varphi \rightarrow \psi } for all ψ {\displaystyle \psi } (because ⊥ ⊢ ψ {\displaystyle \bot \vdash \psi } ), one ...
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 ...
The hypothetical viewpoint, being the weaker view, has the effect of removing some of the relations present in the traditional square of opposition. Arguments consisting of three categorical propositions — two as premises and one as conclusion — are known as categorical syllogisms and were of paramount importance from the times of ancient ...
In the system of Aristotelian logic, the triangle of opposition is a diagram [which?] representing the different ways in which each of the three propositions of the system is logically related ('opposed') to each of the others. The system is also useful in the analysis of syllogistic logic, serving to identify the allowed logical conversions ...