Logical implication.txt

he material conditional (also known as material implication, material consequence, or simply implication, implies, or conditional) is a logical connective (or a binary operator) that is often symbolized by a forward arrow "→". The material conditional is used to form statements of the form 𝑝 → 𝑞 (termed a conditional statement) which is read as "if 𝑝 then 𝑞" or "𝑝 only if 𝑞". Unlike the English construction "if...then...", the material conditional statement 𝑝 → 𝑞 does not specify a causal relationship between 𝑝 and 𝑞. It is merely to be understood to mean "if 𝑝 is true, then 𝑞 is also true" such that the statement 𝑝 → 𝑞 is false only when 𝑝 is true and 𝑞 is false.[1]  The material conditional only states that 𝑞 is true when 𝑝 is true, and makes no claim that 𝑝 causes 𝑞.