Definition:Conditional/Formal Implication

Definition

Formal implication is a usage of an implication in which it is necessary for there to be a formal connection between the antecedent and the consequent in order for the implication to have any semantic meaning.

Also known as

Some sources refer to formal implication as causal implication.

Also see

• Rule of Material Implication, which defines a mode of usage of a conditional statement which allows for there to be no direct physical or linguistic connection between the antecedent and the consequent.

Sources

• 1946: Alfred Tarski: Introduction to Logic and to the Methodology of Deductive Sciences (2nd ed.) ... (previous) ... (next): $\S \text{II}.8$: Implication or Conditional Sentence
• 1959: A.H. Basson and D.J. O'Connor: Introduction to Symbolic Logic (3rd ed.) ... (previous) ... (next): $\S 2.3$: Basic Truth-Tables of the Propositional Calculus
• 1988: Alan G. Hamilton: Logic for Mathematicians (2nd ed.) ... (previous) ... (next): $\S 1$: Informal statement calculus: $\S 1.2$: Truth functions and truth tables: Conditional