What is the difference between procedural and object oriented programming?

Object oriented programming makes the assumption that everything can be grouped into objects, and that the object is the ultimate abstraction. Everything is modularized around objects, and operations (methods) on objects.

This is problematic, because not everything is an object. There are operations that have to be performed that are the result of an interaction between objects and the operation isn't specific to any of the objects involved, so the operation itself doesn't belong in any of those abstractions. And if it has no specific data representation itself, then where does it belong? Yes, you can define a class that has just methods and no data, but then your fundamental, axiomatic principle has broken down: you now have something that really isn't an object.