What Does It Mean To Be Secular?

Septimius Severus Secular Games

In the briefest possible sense, I think we can agree that secular means non-religious. Someone who is secular, whatever else he or she may be, is not religious.

In a recent post on The Secular Life, Dr. Phil Zuckerman drew upon the social sciences to unpack what being non-religious means in this context:

So to be secular means that 1) a person does not believe in supernatural beings, entities, or realms, 2) a person does not engage in religious behaviors, and 3) a person does not identify as religious and is not a member of a religious community.
In expanding upon #1, Dr. Zuckerman notes that being secular "is to maintain a naturalistic worldview in which belief in anything is always proportioned to the evidence available." I like this because it gives us a sense of what a secular person does believe. With so many religious believers telling us that we don't believe anything, this strikes me as important.

Later in the same post, Dr. Zuckerman almost seems to contradict #2 of this definition by writing:

Of course, many secular people -- despite their lack of religious beliefs -- do engage in at least some religious rituals.
If being secular entails not engaging in religious behaviors, I'm not sure it makes sense to suggest that many secular people participate in religious rituals. Then again, I suspect that his point is that secular individuals do not participate in religious rituals for religious reasons. If this is accurate, I'd suggest modifying #2 of the definition to read "2) a person does not engage in religious behaviors for religious reasons..." This would cover the secular person who attends church (i.e., a religious behavior) to appease a family member or for other non-religious reasons.

What do you think? Does this brief definition adequately capture what it means to be secular?