I can't think of a better place among SO siblings to pose such a question. Originally I wanted to ask "Is python a pure OO language?" but considering troubles and some sort of discomfort people experience while trying to define the term I decided to start with obtaining a clear definition for the term itself.

It would be rather fair to start with correspondence by Dr. Alan Kay, who has coined the term (note the inspiration in biological analogy to cells or other living objects).

There are following ways to approach the task:

• Give a comparative analysis by listing programming languages that exhibits certain properties unique and sufficient to define the term (although Smalltalk and Java are passing examples but IMO this way seems neither really complete or nor fruitful)
• Give a formal definition (or close to it, e.g. in more academic or mathematical style).
• Give a philosophical definition that would totally rely on semantical context of concrete language or a priori programming experience (there must be some chance of successful explanation by the community).

My current version: "If a certain programing (formal) language that can (grammatically) differentiate between operations and operands as well as infer about the type of each operand whether this type is an object (in sense of OOP) or not then we call such a language an OO-language as long as there is at least one type in this language which is an object. Finally, if all types of the language are also objects we define such language to be pure OO-language."

Would appreciate any possible improvement of it. As you can see I just made the definition dependent on the term "object" (often fully referenced as class of objects).