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Because the definition would be circular.

Does a field of study have to be defined in order for the concepts in it to be defined? I don’t see why.

Can’t you define concepts x,y,z, and then define the field of study as being “about x,y,z and the things related to them”?

I’m guessing you mean something different by “defining a field of study” (different from my default/initial interpretation of the phrase I mean), but I’m not sure what else you mean by it.

You can do that, but that's surely not the best way to do it, unless the concepts don't have anything to do with each other aside from being part of that field of study.

If it lets me avoid a circular definition, I’m willing to tolerate a bit of ugliness in my definitions (at least, provided that it can be shown to be equivalent (under assumptions of some results that can also be proven under the awkward form) to a nicer framing).

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