Definition:Conditional/Notational Variants/Sign of Illation

Definition

The sign of illation $-\!\!\!<$ is a notation invented by Charles Sanders Peirce to denote the conditional operator.

Peirce derives $-\!\!\!<$ as a variant of the sign $\le$ for less than or equal to, so as to denote that:

$A \mathop {-\!\!\!<} B$

represents the situation such that whenever a particular statement $A$ is true, then so is statement $B$.

It is rarely (if ever) seen nowadays except as a historical curiosity.

The word illation derives from the Latin illātiō, whose meaning is logical inference, deduction or conclusion.

The $\LaTeX$ code for $A \mathop {-\!\!\!<} B$ is A \mathop {-\!\!\!<} B .

1885: Charles Sanders Peirce: On the Algebra of Logic: A Contribution to the Philosophy of Notation (Amer. J. Math. Vol. 7: pp. 180 – 202) www.jstor.org/stable/2369451