Definition:Conditional/Antecedent
Definition
In a conditional $p \implies q$, the statement $p$ is the antecedent.
Also known as
The terms:
- premise
- assumption
- hypothesis
can often be found in the literature as a word for this concept, but on $\mathsf{Pr} \infty \mathsf{fWiki}$ we reserve the use of premise, assumption and hypothesis for elements of the structure of logical arguments.
The term antecedent clause can sometimes be seen, particularly when the conditional it is part of consists of a statement in natural language.
The archaic terms implicans and protasis can sometimes be found.
Also defined as
Let $P = a \circ b$ be an expression.
The term $a$ is known as the antecedent of $P$.
Also see
Linguistic Note
The word antecedent is usually found in classical mathematical literature, notably Euclid's The Elements.
The word comes from the Greek, and literally means leading term.
It is pronounced an-tee-see-dent.
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
- 1964: Donald Kalish and Richard Montague: Logic: Techniques of Formal Reasoning ... (previous) ... (next): $\text{I}$: 'NOT' and 'IF': $\S 1$
- 1965: E.J. Lemmon: Beginning Logic ... (previous) ... (next): Chapter $1$: The Propositional Calculus $1$: $2$ Conditionals and Negation
- 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
- 1980: D.J. O'Connor and Betty Powell: Elementary Logic ... (previous) ... (next): $\S \text{I}: 3$: Logical Constants $(2)$
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): antecedent
- 1993: M. Ben-Ari: Mathematical Logic for Computer Science ... (previous) ... (next): Chapter $2$: Propositional Calculus: $\S 2.1$: Boolean operators
- 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
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): conditional
- 2012: M. Ben-Ari: Mathematical Logic for Computer Science (3rd ed.) ... (previous) ... (next): $\S 2.2.3$
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): conditional