Extension (predicate logic)

Imagine that you are playing with building blocks, and you have blocks with different colors and shapes. You can put these blocks together in different ways to create something new.

In a similar way, a sentence in logic is made up of different parts which we call predicates. These predicates describe things, like the color or shape of a block.

Now, when we say extension of a predicate, all that means is the group of things that the predicate applies to. So if we have a predicate "is red" the extension of that predicate would be all the things that are red, like a red block or a red car.

Basically, the extension is the set of objects that qualify to be part of the group described by that predicate. It helps us to understand what things we are talking about with our predicate.