Definition:Consequent/Also known as

Definition

Some authors use the term conclusion for consequent, but on $\mathsf{Pr} \infty \mathsf{fWiki}$ we reserve the use of conclusion for an element of the structure of a logical argument.

The term consequent clause can sometimes be seen, particularly when the conditional it is part of consists of a statement in natural language.

The archaic terms implicate and apodosis can sometimes be found.

Linguistic Note

The word consequent is usually found in classical mathematical literature, notably Euclid's The Elements.

The word comes from the Greek, and literally means following term.

Sources

• 1971: Robert H. Kasriel: Undergraduate Topology ... (previous) ... (next): Chapter $1$: Sets, Functions, and Relations: $\S 2$: Some Remarks on the Use of the Connectives and, or, implies
• 1972: A.G. Howson: A Handbook of Terms used in Algebra and Analysis ... (previous) ... (next): $\S 1$: Some mathematical language: Connectives
• 1973: Irving M. Copi: Symbolic Logic (4th ed.) ... (previous) ... (next): $2$ Arguments Containing Compound Statements: $2.2$: Conditional Statements
• 2000: Michael R.A. Huth and Mark D. Ryan: Logic in Computer Science: Modelling and reasoning about systems ... (previous) ... (next): $\S 1.1$: Declarative sentences
• 2000: James R. Munkres: Topology (2nd ed.) ... (previous) ... (next): $1$: Set Theory and Logic: $\S 1$: Fundamental Concepts