Material conditional
Subjunction (Latin subiungere, subordinate ') or conditional (Latin condicio, condition, condition, condition, condition " ) or material implication (Latin materia, that from which something is made of ' and implicare include ') is in the logic called a statement that is " if-then " assembled with the connective of two other statements, for example, the statement " When an electric current flows, then heats up the line ."
Between the subjunction or material implication - or the conditional - as an object-language link that connects two statements to a new statement of the same language level, and the meta-linguistic implication must be carefully distinguished. The metalinguistic implication is a statement of two statements, for example, such a statement: "The statement that it is raining '. Implies the statement' the road is wet ' " The relationship between subjunction (as substantive implication ) and metalinguistic implication is that an implication "The statement that a ' implies the statement B' " can accurately be true if the subjunction "If a, then B " is true.
Classic subjunction
In classical logic only truth-functional statement compounds are used, which means only those in which the truth value of statements linking depends only on the truth value of the partial statements. Already Philo of Megara understand conditional statements as a shortcut panel, the truth-functional subjunction or seq function defined by the following truth table ( "w " stands for " true", "f " stands for " false"):
As a symbol of the connective also the curve ( "horseshoe " ) is in formal languages , a simple arrow, especially in the Anglo-Saxon based on the Peano - Russell notation used occasionally, the arrow with two dashes.
In Polish notation, the capital letter C is used for the material implication, so the statement " If a, then b " as " Cab" would be written.
Gottlob Frege expresses in his Begriffsschrift, the first formalization of the classical predicate logic, the conditional "If A, then B " through out.
The subjunction equivalent. The negation corresponds.
A special feature of subjunction often leads to misunderstandings, the paradoxes of material implication. Thus, for example, the sentence: "If, then, man is immortal" as an overall statement is true because the antecedent " " is incorrect. It does not follow the truth of the following sentence "Man is immortal," because it must be " If A, then B" and the single statement B to distinguish between the overall presentation. If the entire subjunction is true, that does not mean that automatically the single sequence set B is true.
Dialogic subjunction
In the dialogical logic the subjunction is defined by the dialogical rules: