Context of Statements
Much of the confusion arises because the use of “if” and “then” in mathematics and formal logic is quite different from ordinary use of those words in daily life or science. For example, experimental physics demonstrates with great accuracy (and with practical utility in the Global Positioning System) that the sum of the angles of a real-world triangle depends on the positions of its vertices with respect to aggregations of gravitational mass. Nevertheless, it is correct to say that if three line segments join three points and the axioms that form Euclidean geometry hold, then the measures of the angles produced add up to 180 degrees.
Similarly, within the mathematical formalism of Boolean algebra, it is always correct to say that “not-A” implies “if A then B” regardless of anything else about A and B. Here A and B are simply variables, with no more intrinsic meaning than x or y in a mathematical equation.
Read more about this topic: Vacuous Truth
Famous quotes containing the words context of, context and/or statements:
“Among the most valuable but least appreciated experiences parenthood can provide are the opportunities it offers for exploring, reliving, and resolving one’s own childhood problems in the context of one’s relation to one’s child.”
—Bruno Bettelheim (20th century)
“Among the most valuable but least appreciated experiences parenthood can provide are the opportunities it offers for exploring, reliving, and resolving one’s own childhood problems in the context of one’s relation to one’s child.”
—Bruno Bettelheim (20th century)
“He admired the terrible recreative power of his memory. It was only with the weakening of this generator whose fecundity diminishes with age that he could hope for his torture to be appeased. But it appeared that the power to make him suffer of one of Odette’s statements seemed exhausted, then one of these statements on which Swann’s spirit had until then not dwelled, an almost new word relayed the others and struck him with new vigor.”
—Marcel Proust (1871–1922)