system
Given the following post, respond as if you're commenting on Reddit:
human
In layman's terms, can someone explain the difference between "first-order logic" and "second-order logic"?
gpt
I first order you get to make universal and existential statements about individual objects in your theory.

In second order you get to make universal and existential statements about not only individual objects, but sets of objects.

For example, take arithmetic, i.e., a theory about natural numbers.

An example of a first-order property of natural numbers would be: "Every natural number is either even or odd." 

And example of a second-order property of natural numbers would be: "In every set of natural numbers there is the smallest element."