LOGIC TOOK A LONG TIME TO REFINE

We don't want you to think all of these theories of logic happened overnight. Logic and reasoning have evolved over thousands of years. The ideas are still the same, but the methods have been documented and examined. Scientists are now able to take the ideas they have developed and apply them to new computer systems. You may have heard of Artificial Intelligence and fuzzy logic. Computers that use those methods of analysis are doing amazing things.

Back in the beginning, there was a guy in ancient Greece who started writing down a lot of these ideas. His name was Aristotle. He didn't invent this way of thinking; people had been using logic forever. Aristotle was just the first guy to start writing down the ideas and rules of what makes something a logical process.

SYLLOGISTIC REASONING

Aristotle described something called syllogistic reasoning. A syllogism is an argument. Arguments are statements used when you describe things with logic. There are four different types of syllogistic arguments.

(1) All A's are B's (universal affirmative)
(2) No A's are B's (universal negative)
(3) Some A's are B's (particular affirmative)
(4) Some A's are not B's (particular negative)

If you look at these statements, they all start with the basic idea that A (a thing) exists. You can't make any of those four statements if A does not exist or is not true.

As logic has evolved, modern logic has changed the first statement to say, "If something is A, then it is also B." It can get a bit confusing. For many scientists, logic is a completely separate branch of science and philosophy. Don't worry if you don't get it from our quick overview. Try this example.

(1) All cats are animals (universal affirmative)
(2) No cats are plants (universal negative)
(3) Some animals are cats (particular affirmative)
(4) Some animals are not cats (particular negative)

Each of these arguments (statements) is true and they all are examples of the four different types of syllogistic arguments.

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