Wow, here is a question that is hotly debated in gatherings everywhere!
Initiation is a formal commitment to the Craft and the Gods. Different groups have different initiations; but it seems to me that the important part in all of them is that formal commitment, a dedication of your life and yourself to the Lord and Lady, and an opening of your far memories if you have traveled this path before.
In my own case, my initiation was absolutely necessary. It changed me in many ways, instantly. Part of that was because I hadn't had the training I probably should have had. I knew a lot of stuff, but I couldn't even ground and center. My life felt like I was clinging to the bed of a moving truck with my fingernails, with my body streaming out flat behind. At a specific point in the initation, I felt as if I was picked up, and put in the cab of the truck. Nothing was ever that badly out of whack again.
Most of my students have also felt profound change when they were initiatied; but not all of them have. Those that haven't seem to have undergone the change some little while before the formal initiation.
We have a saying, "The Gods initiate. We just officiate."
In my opinion, which is just mine, whether you need a formal initiation depends on the tradition you are interested in. To be a Gardnarian, for instance, you need an initiation. And not just any initiation; it has to be done by a Gardnarian High Priestess, with a Gardnarian High Priest in attendance, in a Gardnarian Circle. And after you are finished, you won't be able to tell anyone about it unless they are in a Gardnarian Circle too.
In the Livingtree Tradition, which I seem to have started, calling yourself a Witch implies that you have been through an initiation ceremony. If you haven't been, then you call yourself a Pagan.
But if you decide to call yourself a Witch, I'm certainly not going to tell you you aren't one, no matter what sort of ceremony you have or have not had. That is between you and the Gods, and basically none of my business. However, if you do call yourself a Witch, I am likely to assume a basic level of training and ability. If you lack these, I might expect you to do something you can't really be expected to do. I'm terribly sorry about that; but just as calling yourself a Christian Minister carries certain implications, so does calling yourself a Witch.
As for self-initiation, I think it's more fun in a group, but not necessarily more valid. In fact, in our tradition, you are expected to write your own initiation ceremony (after all, only you know what you really need to hear to trigger the memories of all the other times you did this.) We add stuff, of course, and some of what we add we don't warn you about before hand, but it's all relatively minor stuff. Once again, this is only my opinion. Wiccans are a very opinionated bunch, by and large, and we can debate this one for hours and hours.
But I say, when it all comes down to it, if you are solitary (and this question is hardly likely to come up otherwise) follow your own instincts in this, as in everything else. Ask around, listen to the Goddess' voice, listen to your own voice within, and then do what you think is right for you. And after you have done it, don't let anyone give you any grief. After all, who initiated the very first person to take this path? I would say, the Goddess. And She can initiate you, too.
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