 This understanding of the conditional has considerable virtues of simplicity, and in that regard the material conditional analysis provides a benchmark for other theories. Probably its main virtue is that it lends itself to a truth-functional treatment (the truth value of a conditional is a function of the truth values of antecedent and consequent). A related one is that it makes the conditional interdefinable with Boolean negation, disjunction, and conjunction. A third, among the driving motivations for Frege, Russell and Whitehead, is that it appears adequate to regiment mathematical proofs involving conditional sentences. Despite that, as granted by Frege himself in the Begriffsschrift, it fails to do justice to some of the ways in which conditionals are ordinarily understood and used in natural language.