No, there are analogous theorems about structures other than graphs. But there are not analogous theorems about all structures.
In order to use Ramsey theory to dispute the physicists' claim that "most universes are lifeless" (which is backed up by a technical, though not indefeasible argument), one would have to make a technical argument that
I don't imagine this can be done in an interesting way.
On your second point - my definition of interestingness is any distinguishing feature. Anything at all that can be used to tell universes apart. If you think I am talking about life or something like it, you have not understood my argument. It claims that life is an arbitrary feature to focus on to begin with. I don't know which scientists have made the 'lifeless universes' argument and how, but my argument has nothing to do with that.
On your first point - If we accept Tegmark's identification of universes-in-general with mathematical objects, the questio...
I had posted a while back on my proposed dissolution of the Fine Tuning argument. My main argument was as follows:
I've been pondering how to process that response, and if the argument is salvageable, ever since. Do we really have to explain anthropics and the multiverse to diffuse the FTA?
Today I came across a great article with an elegant description of Ramsey's Theorem:
As I understand it, positing few 'interesting' vs. the vast majority of 'uninteresting' universes is in direct contradiction with Ramsey's theorem. I put this to the more mathematically educated among this community for feedback. Beyond pushing forward this particular internal dialog of mine, it should have more general application in the fine tuning debate, should someone choose to use it there.