The Mechanics of Reason

Aristotle fathered the syllogism, or at least was first to investigate it rigorously. He defined it as a formal argument in which the conclusion follows logically from the premises. There are four common statements of this type:

All S (for subject)is P (for predicate)
No S (for subject)is P
Some S (for subject)is P
Some S (for subject)is not P

Thus, Aristotle might say “All men are mortal” or “No men are immortal” as his subject. Adding an M (middle term), “Aristotle is a man,” as a minor premise, he could logically go on and conclude “Aristotle, being a man, is thus mortal.” Of course the syllogism unwisely used, as it often is, can lead to some ridiculously silly answers. “All tables have four legs. Two men have four legs. Thus, two men equal a table.”

Despite the weaknesses of the syllogism, nevertheless it led eventually to the science of symbolic logic. The pathway was circuitous, even devious at times, but slowly the idea of putting thought down as letters or numbers to be logically manipulated to reach proper conclusions gained force and credence. While the Greeks did not have the final say, they did have words for the subject as they did for nearly everything else.

Let us leave the subject of pure logic for a moment and talk of another kind of computing machine, that of the mechanical doer of work. In the Iliad, Homer has Hephaestus, the god of natural fire and metalworking, construct twenty three-wheeled chariots which propel themselves to and fro bringing back messages and instructions from the councils of the gods. These early automatons boasted pure gold wheels, and handles of “curious cunning.”

Man has apparently been a lazy cuss from the start and began straightway to dream of mechanical servants to do his chores. In an age of magic and fear of the supernatural his dreams were fraught with such machines that turned into evil monsters. The Hebrew “golem” was made in the shape of man, but without a soul, and often got out of hand. Literature has perpetuated the idea of machines running amok, as the broom in “The Sorcerer’s Apprentice,” but there have been benevolent machines too. Tik-Tok, a latter-day windup man in The Road to Oz, could think and talk and do many other things men could do. He was not alive, of course, but he had the saving grace of always doing just what he “was wound up to do.”

Having touched on the subject of mechanical men, let us now return to mechanical logic. Since the Greeks, many men have traveled the road of reason, but some stand out more brightly, more colorfully, than others. Such a standout was the Spanish monk Ramón Lull. Lull was born in 1232. A court page, he rose in influence, married young, and had two children, but did not settle down to married domesticity. A wildly reckless romantic, he was given to such stunts as galloping his horse into church in pursuit of some lady who caught his eye. One such escapade led to a remorseful re-examination of himself, and dramatic conversion to Christianity.

He began to write books in conventional praise of Christ, but early in his writings a preoccupation with numbers appears. His Book of Contemplation, for example, actually contains five books for the five wounds of the Saviour, and forty subdivisions for the days He spent in the wilderness. There are 365 chapters for daily reading, plus one for reading only in leap years! Each chapter has ten paragraphs, symbolizing the ten commandments, and three parts to each chapter. These multiplied give thirty, for the pieces of silver. Beside religious and mystical connotations, geometric terms are also used, and one interesting device is the symbolizing of words and even phrases by letters. This ties in neatly with syllogism. A sample follows: