Lewis Carroll lectured on mathematics at Oxford University. He wrote several books on logic, illustrated with wonderful problems involving fish, kittens, and gorillas - much less boring than the brown, grass-eating cows of modern textbooks. Kittens and gorillas are not usually in much contact, but I did find one hit on Google, pictured! The words we organize into books, poems and plays are not just a random jumble; they have structure and a logic to them. We group verbs, subjects and objects together to form sentences and, at a larger scale, characters have motivations and relationships: this character loves that character, the valet had the candlestick in the ballroom and could not have stabbed the butler in the kitchen, and so on. We have dictionaries to define words, but to truly understand the information they convey we need to understand the logical rules governing how they can be combined.
A s well as giving us Alice, the Jabberwocky, and the Cheshire Cat,
Everyday conversation is fragmented and repetitive. Fortunately, now and again, we say something definitive. For example, “This gorilla is brown.” The statement links a property, ‘brownness; to a thing, ‘a gorilla. Logical statements are precise but often need to be put in context. IfI were standing in a forest when I made my statement you must guess I mean the nearest gorilla. The word “This implies nearness, but nearness is not well defined. Better to be precise. “The gorilla I am closest to, measured by line of sight distance is the Pantone shade dark brown? However, if I talked like this all day I would not have many friends.
Logical Beginnings
The formal study of logic began in 3848c with the publication ofa treatise called the Organon by the Greek philosopher Aristotle. A student of Plato, Aristotle taught many of the famous leaders of his time, including Alexander The Great. Ancient Greece was not some idyllic think tank. If you annoyed the political establishment you might find yourself having to leave town in a hurry. This happened to Aristotle after Plato’s death, and he spent nearly a decade touring Europe. Eventually, he returned to Athens where he published his study on logic.
In the Organon, Aristotle examined groups of up to four statements, each containing up to four relationships. For example: All kittens eat fish. Some kittens eat fish. No kittens love gorillas. No gorillas eat kittens - luckily. It is possible to put two statements back to back and infer things.
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