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150 Are the Androids Dreaming Yet?

I could say, “All gorillas eat leaves.” “All leaves are green.” Therefore I can infer all gorillas eat some green things. This is a valid inference. It is not correct to say, gorillas eat only green things.

There are 256 ways you can arrange four Aristotle statements with four relationships but only 19 valid deductive conclusions can be drawn. The kitten puzzle at the start of the chapter is an example of such a logical puzzle. Can you reach the right conclusion?

TRY SOLVING THE KITTEN PUZZLE WITHOUT READING ON

Aristotle’s syllogisms are only a start. There are many other types of logic. In antiquity, the Stoics developed a different brand of logic based on the idea of larger and smaller. Stoic logic allows us to answer questions of relative size. If a Mini is smaller than an Audi, and an Audi is smaller than a Rolls Royce, then a Mini is smaller than a Rolls Royce. The Stoics pursued their branch of logic until around 180AD when study of this sort died out. It’s not quite clear why. Perhaps the rise of religious power and the onset of the Dark Ages curtailed intellectual inquiry. Even after the Enlightenment began around 1650 it took some time for the discipline of logic to re-emerge. If you want to learn more about syllogistic logic and how to solve Lewis Carroll’s puzzle you should read his book The Game of Logic. The definitive book on the logic of language, in my opinion, is Logic by Wilfrid Hodges.

Logic for Computers

Western civilization mostly survived on syllogisms and stoic logic for nearly two thousand years before George Boole devised his theory of binary logic in 1847. Boole developed an elegant mathematical system for representing logical statements that allowed simple arithmetical operations to answer logical questions. We now call this system Boolean logic and he gave us the modern convention of using one for true, and zero for false. Computers use his principles all the time. For example, if it is true my bank account shows less than zero, then make it true that someone will send me a letter warning me I am overdrawn. The best way to get your head around Boolean logic is to solve the ancient puzzle of the Two Guards. The puzzle featured in the 1986 movie, The Labyrinth,

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