What is an antecedent in formal logic?

In formal logic, an antecedent is the first half or if-clause of a hypothetical proposition, which is connected to a consequent via a logical connective. For example, in the statement that if P then Q, P is the antecedent. In some contexts, it is also referred to as the protasis.

What we know

• An antecedent is the first half of a hypothetical proposition, appearing whenever the if-clause precedes the then-clause. [1, 2]
• In some contexts, the antecedent is also known as the protasis. [1, 2]
• In the implication where phi implies psi, phi is called the antecedent and psi is called the consequent. [2]
• Denying the antecedent is a formal fallacy that assumes the negation of the antecedent implies the negation of the consequent. [4]

Where to go next

• compared withWhat is a consequent in logic?
• how it workedHow does modus ponens work?
• what followedWhat is the fallacy of denying the antecedent?
• the bigger pictureWhat are hypothetical propositions?
• whoWho first described modus ponens in antiquity?
• an unexpected connectionHow does Theophrastus connect to modern propositional logic?The historical origins of evaluating the antecedent and rules like modus ponens stretch back to antiquity through thinkers like Theophrastus.

Sources

• [1]antecedent (Wikidata Q260460) · CC0 1.0
• [2]Antecedent (logic) · CC BY-SA 4.0
• [3]Antecedent · CC BY-SA 4.0
• [4]Denying the antecedent · CC BY-SA 4.0
• [5]Modus ponens · CC BY-SA 4.0

Your path

1. What was Pythagoreanism in ancient philosophy?
2. /What is an antecedent in formal logic?