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:
“The hippie is the scion of surplus value. The dropout can only claim sanctity in a society which offers something to be dropped out of—career, ambition, conspicuous consumption. The effects of hippie sanctimony can only be felt in the context of others who plunder his lifestyle for what they find good or profitable, a process known as rip-off by the hippie, who will not see how savagely he has pillaged intricate and demanding civilizations for his own parodic lifestyle.”
—Germaine Greer (b. 1939)
“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)
“In so far as the statements of geometry speak about reality, they are not certain, and in so far as they are certain, they do not speak about reality.”
—Albert Einstein (1879–1955)