Consider this list of philosophies:
Rationalism,
Empiricism,
Analytic philosophy,
Existentialism,
Phenomenology,
German Idealism,
Socialism,
Anarcho-Socialism,
State-Communism,
Libertarianism,
Moral Realism,
Solipsism.
Next, consider this list of philosophies:
Platonism,
Kantianism,
Hegelianism,
The philosophy of Nietzsche,
The philosophy of Sartre,
Aristotelianism,
The philosophy of Wittgenstein,
Marxism,
The philosophy of John Locke.
Each of these things are what ordinary people would call a "philosophy." But these are not one thing, these are two types of things, the first set of which, from the first list, is what I call a systematic philosophy, and the second set of which, from the second list set forth above, I would call an individual's philosophy. A systematic philosophy is a philosophical system comprised of a set of philosophical views, while an individual's philosophy is the philosophy of one individual philosopher. Note, however, that each systematic philosophy is formed by importing a set of ideas and views from a set of individual's philosophies, or else one individual's philosophy could form its own entire one systematic philosophy. For example, the philosophy of John Locke contributed views to Empiricism, and Marxism contributed views to socialism. Multiple individual's philosophies can contribute to the same systematic philosophy. For example, the philosophy of Nietzsche and the philosophy of Sartre both contributed to Existentialism. One systematic philosophy can also have multiple systematic philosophies which are variations or sub-parts of it as a whole. For example, Anarcho-Socialism and State-Communism are both coherent systematic philosophies in their own right, but each is also a sub-part of the broader systematic philosophy of Socialism.
Now, the question is: What is Objectivism? Is it a systemic philosophy? Or is it an individual's philosophy?
Within the Objectivist movement, there is a great debate and conflict between the open-system and closed-system Objectivists. Closed-system people believe that Objectivism is limited to the philosophy created by Ayn Rand, and it ended with her death. Open-system people believe that Objectivism can be added to and expanded by other people and is not only limited to Ayn Rand's ideas.
I have come to believe that the conflict arises from linguistic imprecision, that the closed-system people understand Objectivism to be an individual's philosophy, merely another name for Randianism, the philosophy of Ayn Rand, while the open-system people believe that Objectivism is a systematic philosophy, a set of philosophical views united around the theme of a common worldview in philosophy, and therefore obviously it could be added to by anyone, although at its time of original creation, 100% of the ideas in systematic Objectivism came from having been imported from the individual's philosophy of Ayn Rand, Randianism.
The two sides in the debate do not understand each other and cannot understand what the other side is saying, because they are using two different definitions of the same word, "philosophy," so it is impossible for the two sides to communicate, and neither side understands what the other side means. If Objectivism is an individual's philosophy, then it is the philosophy of Ayn Rand, and obviously the closed-system side is correct. If Objectivism is a systematic philosophy, then it is defined by a set of philosophical views, and anyone who holds those views while adding ideas could add to it, and then obviously the open-system side is correct. The two sides mean different things and so can't see eye to eye to resolve their dispute.
I propose to solve this confusion by creating a new word, "Randianism," to describe Ayn Rand's individual's philosophy, which is defined as the philosophy of Ayn Rand, while keeping "Objectivism" as the name for the systematic philosophy, the philosophical system defined by that certain set of views about objectivity, reality, reason, rational selfishness in ethics, free-market capitalism and the moral defense of capitalism in economics, individual rights in politics, etc. At its inception, Objectivism was formed 100% from Randianism, but the two are analytically distinct, based on the understanding which I have provided.
Some critics might say that, as I have defined it, only an individual's philosophy is a "real" philosophy, and what I call a systematic philosophy is merely a historical category, or a worldview, or a philosophical view, or set of views. But that is not, in fact, how ordinary people use the term "philosophy." Each of those systematic philosophies is, in fact, a philosophy.