You have a habit of taking everything to the extreme, perhaps a side effect from reading CvC too much?

So, my question is, do we want to define ourselves as a nation in negative terms that declare war on the world,
No where did I or anyone say declare war on the world. In fact, much of the world is with us, and are disappointed in lack of strategy in those we must counter.

I do think that what we are actually bemoaning here is the want of an effective national grand strategy that describes an approach to the world that allows the US to once again be able to "play to win." Our post Cold War strategy has been a "play not to lose" approach to a world full of actors who are all playing to win.
Well said, it would be interesting to see how many counter this and counter that strategies we actually have. We have counternarcotic networks, counter terrorism networks, counter human trafficking networks, counter this networks, counter that networks . . ., the point is we fragment into more and more stove pipes and lack a collective effort that would address all these issues more effectively.

or do we want to define ourselves as a nation in positive terms of peace, but that fully recognize that we will often be dealing with all manner of illegal and violent conflicts in the execution of said strategy?
I can't distinguish between war, conflict, and confrontation. These are terms we tend to throw around carelessly without clear definitions, and they seem to be used to avoid the term war, while to most people they still look like war.

I do not need to call all things war. It is neither accurate nor helpful; and it is not who we are. Americans do not play not to lose well. It grates at our competitive nature. We do not need forever war, but we do need a strategy we can play to win.
This is a fair comment, and it gets back to my original point about DOD as a profession (and the larger national security apparatus) that has failed to develop a relevant lexicon for the 21st Century. If we stick with your definition of war, then the terms war and peace are inadequate and misleading.