Overview

truth-function


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A truth function of a number of propositions or sentences is a function of them that has a definite truth value, dependent only on the truth values of the constituents. Thus (p & q) is a combination whose truthvalue is true when p is true and q is true, and false otherwise. ¬p is a truth function of p, false when p is true and true when p is false. The way in which the value of the whole is determined by the combinations of values of constituents is presented in a truth table.The propositional calculus is the standard treatment of truth-functional combinations. Its constants, &, ∨, ¬, → and ↔, are all truth-functors, i.e. expressions standing for truth functions.

p

q

p & q

p ∨ q

p→q

p↔q

T

T

T

T

T

T

T

F

F

T

F

F

F

T

F

T

T

F

F

F

F

F

T

T

Subjects: Philosophy.


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