Free logic facts for kids

A free logic is a special kind of logic that is more flexible than regular (classical) logic. It's called "free" because it doesn't automatically assume that everything you talk about actually exists. This means you can use terms or names that don't refer to any real object, like "Pegasus" or "Unicorn".

Sometimes, free logic also allows for situations where there's nothing at all in the "world" or "domain" being discussed. A free logic that allows for an empty world is called an inclusive logic.

What Makes Free Logic Different?

In classical logic, which is the most common type, there are some rules that always assume something exists. For example, a basic rule says: "If something is true for everything, then it must be true for at least one thing." This sounds logical, right?

But what if you're talking about something that doesn't exist? Imagine you say, "Every unicorn has a horn." In classical logic, this statement might lead you to believe that at least one unicorn exists, because the rule says "if true for everything, then true for something."

The Problem with Non-Existent Things

Classical logic has trouble with names or terms that don't point to anything real. For instance, if you say "Pegasus is a winged horse," classical logic might struggle because Pegasus isn't a real animal. It assumes that if you use a name, that thing must exist.

Here's an example:

• If you say, "Everything identical with Pegasus is Pegasus," classical logic might make you think that something identical with Pegasus actually exists. This happens because classical logic doesn't have a way to handle names that don't refer to anything real.

How Free Logic Solves This

Free logic changes some of the basic rules of classical logic to fix this problem. It adds a special check to see if something actually exists before making conclusions about it.

For example, instead of just saying "If something is true for everything, then it must be true for at least one thing", free logic adds a condition. It says: "If something is true for everything, then if a specific thing exists, then it's true for that specific thing."

This means that if you're talking about Pegasus, free logic would first ask, "Does Pegasus exist?" If the answer is no, then it won't make assumptions about Pegasus existing just because you used its name.

This special "existence check" is often shown using a symbol like "E!". So, "E!t" would mean "t exists."

Several logicians have developed different ways to set up free logic, including Theodore Hailperin (in 1957), Jaakko Hintikka (in 1959), Karel Lambert (in 1967), and Richard L. Mendelsohn (in 1989).

See also

In Spanish: Lógica libre para niños

• Logical cube
• Logical hexagon
• Octagon of Prophecies
• Square of opposition
• Triangle of opposition
• Table of logic symbols