The book explores how build a mechanical inferences by making use of arithmetic operations on a string of numbers representing statements. In this way logic is reduced to a branch of the combinatory calculus. It covers the field of traditional logic by showing that any kind of inference can be mechanically reduced to three-variables and two-premise inferences. Meriological inferences can also be easily treated in this way. The book covers the following subjects: structural description of space; three-variable inferences through products, sums, subtractions, and divisions; generalization to n variables; relations; and applications.