I'm not really sure what you mean by higher level, but I'm still not sure that's the case if one is assuming you mean works that are more introductory in nature.
For example, from the introduction in the first chapter, titled "Consistency", in Wilfred Hodge's Logic:
> Logic can be defined as the study of consistent sets of beliefs; this will be our starting-point. Some people prefer to define logic as the study of valid arguments. Between them and us there is no real disagreement, as section 11 will show. But consistency makes an easier beginning.
> Logic is about consistency – but not about all types of consistency. ...
> The type of consistency which concerns logicians is not loyalty or justice or sincerity; it is compatibility of beliefs. A set of beliefs is consistent if the beliefs are compatible with each other. To give a slightly more precise definition, which will guide us through the rest of this book: a set of beliefs is called consistent if these beliefs could all be true together in some possible situation. The set of beliefs is called inconsistent if there is no possible situation in which all the beliefs are true.
Note that this is identical to the parent comment, and this book is originally from the 1970s.
By higher level, I mean big picture. Not necessarily introductory, but ones that don't employ logical concepts such as "proof", "formal" etc, because you cannot define a field of study using concepts from that field. This example is good, but not sure what are you trying to say by posting it (I didn't say that noone ever wrote anything on what logic is.)
> 6.2.1 Let us start with a look at the original rationale for intuitionism. Consider the sentence ‘Granny had led a sedate life until she decided to start pushing crack on a small tropical island just south of the Equator.’ You can understand this, and indefinitely many other sentences that you have never (I presume) heard before. How is this possible?
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).
