Shortly after posting The End of the World on my blog, someone suggested that I should submit my super-reality paper to the peer-reviewed journal, Axiomathes. No, I hadn’t heard of it either: I had to look it up on Google. The blurb from the publisher, Springer, says: “Axiomathes publishes studies of evolving ideas, perspectives, and methods in science, mathematics, and philosophy”. Yes! Exactly the right fit for my paper!
I was still wary of including the term “super-reality” in the title, though, and so I just sent Springer what I had submitted to the PhilSci archive, including the toned-down title “Levels of reality: emergent properties of a mathematical multiverse”.
In due course, Springer accepted the paper, with the proviso that I complied with the referees’ comments (it is quite normal for referees to comment on articles – for one thing, it proves that they have read them!) What I did not expect was that one of the referees would be unhappy with the title. In particular, s/he pointed out that “levels of reality” is a technical term in “philosophical ontology”. Apparently, it refers to a specific theory discussed by Nicolai Hartmann among many others.
I was fairly sure that Hartmann would not have been referring to the same super-reality that had emerged through the analysis in my website, but my curiosity was piqued, and I looked up the Stanford Encyclopedia of Philosophy (as you do). It said that Hartmann distinguished four main levels of reality: “the inanimate, the biological, the psychological and the spiritual. This last includes all historical realities (history, language, customs, law, art, etc.)”.
So, there it was – a vindication of all my prejudices about philosophy (arising from my not knowing anything about the subject). Anyway, there was clearly no overlap between Hartmann and me, and so I bit the bullet and inserted “super-reality” into the title. So the title now read: “Reality and Super-Reality: Properties of a Mathematical Multiverse”, and, after attending to the referees’ other suggestions, I resubmitted the article, which they were happy with.
I should acknowledge here the University of St Andrews. In the PhilSci article, I had styled myself “Alumnus of the University of St Andrews, Scotland”. That turned out to be a happy decision, because Springer offered me the choice of publishing the paper as Open Access, meaning that anyone can download it without having to pay a fee to the journal. Many journals offer this facility, but the authors have to pay an Article Processing Charge (APC), as it is euphemistically known, to compensate for the publisher’s consequent loss of readership fees. I checked with the University of St Andrews, and, since I had cited them as my affiliation, they were happy to pay the APC for me (thank you, St Andrews!).
“Super-reality” is a loaded term. As I explain in the Reality and super-reality page, I think that the super-reality that emerges from the analysis in that page is probably the same higher level that is implied by Gödel’s enigmatic footnote 48a (see The Mathematical Structure of the Plexus). Why “loaded”? Because, to quote Debbie Russell at the end of Lucy and David and the God Equation, the “…work has obvious religious significance”. Essentially, as Lucy argued, if the mathematical superstructure which is the multiverse can contain universes with self-aware substructures, then surely the multiverse itself can be said to be self-aware? David was doubtful about that conclusion, of course, perhaps because he realised that a self-awareness in a higher reality could be interpreted as a deity.
What is clear is that, if a deity can account for everything in our universe, then such a deity could never be proved within our universe, because of the very same theorem that started it all: Gödel’s incompleteness theorem. But, then again, where is the mystery of a deity whose existence you can prove?
For the record, this is the link to the paper in Axiomathes: https://doi.org/10.1007/s10516-019-09466-7