Yes, but to be a new implementation shouldn't I be able to install it without already needing Common Lisp?

For instance, I can install SBCL without already having another Common Lisp implementation right?

If you want to compile it, you need a Common Lisp implementation. SBCL, CLISP, and Clozure CL can usually do it, though SBCL is the most reliable and well-tested.

There are binary versions available for download, too. They've been precompiled with an existing CL compiler.

> Yes, but to be a new implementation shouldn't I be able to install it without already needing Common Lisp?

No? E.g. Clang is a C++ implementation that you can't install without an existing C++ compiler.

Right, this is what I was missing in my thought process. Thanks.

It's exactly like building a C compiler if it is written in C. You just happen to have gcc around and the problem is just "invisible" in that case.

Most likely you are right that you can install without already needing Common Lisp for your particular platform, but that is not always the case. http://www.sbcl.org/porting.html

You bootstrap it w/ a binary build, generally