ALTERNATIVE (from Latin alter— one of two)—in the colloquial sense: a situation that demands a choice between two possibilities; in logic: a proposition composed of two or more members joined by the alternative functor, where this functor joins these propositions either in view of their logical value (the extensional alternative) or in view of their content (the intensional alternative which serves to express lack of knowledge of hesitation when a decision must be made for one of several possibilities).
In formal logic the extensional alternative is analyzed, and several types of alternatives are distinguished:
—the common alternative (inclusive)—this represents a state of affairs where at least one among the states of affairs asserted by the particular members of the alternative occurs, namely when the state of affairs complement each other but do not exclude each other (the proposition is true when at least one member of the proposition is true).; the disjunctive copula “or” in natural language corresponds to this functor [Translator’s note: the English term “or” is not as precise here as Polish];
—the negative alternative (disjunction, Scheffer’s disjunction)—this represents a state of affairs where at least one of the states of affairs do not occur: the states of affairs affirmed by the members of the proposition exclude each other but do not complement each other (a disjunctive proposition is true when at least one of its members is false); the expression “it is not true that at the same time … and …” corresponds to the functor of disjunction;
—the exclusive alternative—this affirms a state of affairs where precisely one of the states of affairs represented by its members occurs, namely, that these states of affairs are mutually exclusive and complementary (an alternative proposition is true when the logical value of one of its members is different from the value of the other member); in natural language the disjunction “either…or&hellip” corresponds to the exclusive alternative functor.
K. Ajdukiewicz, Zarys logiki [Outline of logic], Wwa 1953, 19607; L. Borkowski, Wprowadzenie do logiki i teorii mnogości [Introduction to logic and set theory], Lb 1991.