The study of logic as a subject dates back to the times of Greek philosopher Aristotle (384-322 b.c. ). While Francis Bacon (1561-1626), Gottfried Leibniz (1646-1716) and René Descartes (1596-1650) all made valuable contributions in the development of logical thinking during the Renaissance, it was not until the mid-nineteenth century that true breakthroughs occurred. Two mathematicians, George Boole (1815-1864) and Augustus De Morgan (1806-1871), independently proposed forms of algebra representing logical expressions. In 1854 Boole published The Laws of Thought, which expressed logic in algebraic form. Boolean algebra, as his discovery is called, has only two values, 0 and 1. These values are the basis of the binary numbering system used in machine language. By the nineteenth century, various logic devices were constructed which incorporated Boolean algebra to mimic logic. In 1864 William Stanley Jevons (1835-1882), an economist and logician, published Pure Logic: or the Logic of Quality Apart...