Obversion | EPFL Graph Search

Are you an EPFL student looking for a semester project?

Work with us on data science and visualisation projects, and deploy your project as an app on top of GraphSearch.

In traditional logic, obversion is a "type of immediate inference in which from a given proposition another proposition is inferred whose subject is the same as the original subject, whose predicate is the contradictory of the original predicate, and whose quality is affirmative if the original proposition's quality was negative and vice versa". The quality of the inferred categorical proposition is changed but the truth value is the same to the original proposition. The immediately inferred proposition is termed the "obverse" of the original proposition, and is a valid form of inference for all types (A, E, I, O) of categorical propositions. In a universal affirmative and a universal negative proposition the subject term and the predicate term are both replaced by their negated counterparts: The universal affirmative ("A" proposition) is obverted to a universal negative ("E" proposition). "All S are P" and "No S are non-P" "All cats are animals" and "No cats are non-animals" The universal negative ("E" proposition) is obverted to a universal affirmative ("A" proposition). "No S are P" and "All S are non-P" "No cats are friendly" and "All cats are non-friendly" In the particular affirmative the quantity of the subject term remains unchanged, but the predicate term of the inferred proposition negates the complement of the predicate term of the original proposition. The particular affirmative ("I" proposition) is obverted to a particular negative ("O" proposition). "Some S are P" and "Some S are not non-P" "Some animals are friendly creatures" and "Some animals are not unfriendly creatures." In the obversion of a particular negative to a particular affirmative the quantity of the subject also remains unchanged, and the predicate term is changed from simple negation to a term of the complementary class. The particular negative ("O") proposition is obverted to a particular affirmative ("I" proposition). "Some S are not P" and "Some S are non-P" "Some animals are not friendly creatures" and "Some animals are unfriendly creatures.

About this result

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related concepts (4)

Categorical proposition

In logic, a categorical proposition, or categorical statement, is a proposition that asserts or denies that all or some of the members of one category (the subject term) are included in another (the predicate term). The study of arguments using categorical statements (i.e., syllogisms) forms an important branch of deductive reasoning that began with the Ancient Greeks. The Ancient Greeks such as Aristotle identified four primary distinct types of categorical proposition and gave them standard forms (now often called A, E, I, and O).

Square of opposition

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. However, Aristotle did not draw any diagram; this was done several centuries later by Apuleius and Boethius.

Converse (logic)

In logic and mathematics, the converse of a categorical or implicational statement is the result of reversing its two constituent statements. For the implication P → Q, the converse is Q → P. For the categorical proposition All S are P, the converse is All P are S. Either way, the truth of the converse is generally independent from that of the original statement. Let S be a statement of the form P implies Q (P → Q). Then the converse of S is the statement Q implies P (Q → P).