In this book two ethical systems are described in the language of mathematics. Ordinarily mathematics is thought to be a science of quantity. Indeed, manipulation of quantities constitutes much of mathematics. Elementary applied mathematics deals with reckoning and measurement, where concrete quantities are objects of attention, such as counting sheep or weighing corno But the operations on these quantities are performed with the help of symbols, from which concrete referents have been 'abstracted out': 3 + 5 = 8 regardless of whether the symbols stand for numbers of sheep or tons of corno...