The joy of happenstance

Intentions

We have been to the mountains after Christmas and before the new year. The girls were skiing - I was going to take the chill to chill, meditate, read, and stop smoking.

I find it good to manage my intentions before so the crossover from the intense thinking I’ve been doing to chill is smooth as it can be. I’d started to think it’d be good to formulate the Maths of Buddhism as I see it.

When meditating I get a nice sense of oneness and with meta meditation it seems like the natural state of the universe is one of a positive energy. I’ve been deep (for me) in formalism so I thought it’d be good for me to nurture that concept as a good bridge to letting it all be.

It didn’t go that way - Sophie was ill so I took on almost all of the organising and driving and then she hurt her knee so we spent the time together whilst the kids were skiing.

I got some good meditation on the first day, before she was hurt, and started to get the physical benefits though so that was perfect.

Anyway, we had an awesome time together, we all love the mountains and have pencilled in a return to them in Feb - I’m thinking of taking lessons as well.

Coming back I’m letting my paper be more and more, taking the time to do nothing, and also watching some edge interests on YouTube.

Following interests

Including a lecture by Irving Finkel on the Arc before Noah. This was excellent - he’d translated text that, with impressive engineering/mathematical precision, described how to build an arc! Well worth a watch.

Next up was the Lex Friedman interview with Joel David Hamkins. As with some of his interviews there’s so much information to process. After 2 days I’m still only half way through and trying to backfill on the notes I’ve already made 🫠😆

I’m particularly taken by two points:

  1. Viewing Godel’s work as a response to Hilbert’s formalism means Godel’s work has so much more meaning to me.

  2. Joel’s definition of Structuralism is like a foghorn to me. I needed to learn more about that - it’s something that I relate to. I need to be careful the appeal is not a siren song or a rabbit hole… This blog post will help with letting it be.

I’ve been chatting with Claude about these two elements. I’ve given it my blog to cross reference and categorise my writing. I’ve got a post on the 5 aggregates of Buddhism and Claude picked up on that.

Final Summary from Claude

Historical Arc:

  • Frege/Russell (logicism): Math reducible to logic → blocked by paradoxes and incompleteness
  • Hilbert (formalism): Prove formal systems consistent → Gödel showed impossible
  • Gödel’s theorems ended both programs as originally conceived

Your Position:

  • Methodologically formalist: Rigorous formal specification (your dual-state architecture, TLA+ interest)
  • Ontologically structuralist: What matters is relational structure, not substrate
  • Non-dualist: No “out there” vs “in here”—dissolves ante rem / in re debate entirely

Implication: You don’t hold structuralism as a view about mathematical objects. You reject the framing that asks what objects “really are” independent of relations. Structure is fundamental; the question of what underlies it is malformed.

This is consistent with ontic structural realism and Buddhist dependent origination. It’s also practically expressed in your agent work—the agent function defines a relational structure, implementations are isomorphic realizations, and asking what the “real” agent is beyond that structure doesn’t compute.

Further reading (based on chatting about what I’m interested in)

Primary sources (readable):

  • Gödel’s 1931 paper — Van Heijenoort’s “From Frege to Gödel” has it with commentary
  • Russell’s “Introduction to Mathematical Philosophy” — accessible, covers logicism
  • Hilbert’s “On the Infinite” (1925) — his clearest statement of formalism

Philosophy of mathematics:

  • Benacerraf’s “What Numbers Could Not Be” (1965) — the paper that launched modern structuralism
  • Shapiro’s “Philosophy of Mathematics: Structure and Ontology” — systematic defense of ante rem structuralism (useful even if you reject the framing)

Category theory:

  • Lawvere & Schanuel’s “Conceptual Mathematics” — accessible entry point
  • Awodey’s “Category Theory” — more rigorous, still readable

Connecting to your non-dualist view:

  • Ladyman & Ross’s “Every Thing Must Go” — ontic structural realism in philosophy of science
  • Priest’s work on Nagarjuna and paraconsistent logic — bridges Buddhist philosophy and formal systems

For your agent work specifically:

  • Abramsky’s papers on game semantics — category-theoretic view of computation as interaction

my conclusion

Happenstance… I’ve ended up being recommended this paper, by Priest, on Buddhist Logic.

ABSTRACT: In early Buddhist logic, it was standard to assume that for any state of affairs there were four possibilities: that it held, that it did not, both, or neither. This is the catuskoti (or tetralemma). Classical logicians have had a hard time making sense of this, but it makes perfectly good sense in the semantics of various paraconsistent logics, such as First Degree Entailment. Matters are more complicated for later Buddhist thinkers, such as Nagarjuna, who appear to suggest that none of these options, or more than one, may hold. The point of this paper is to examine the matter, including the formal logical machinery that may be appropriate.

I love it, like I said earlier, when in a good meditation state there is a sense that everything is nothing and nothing is everything. To read the catuakoti/telralemma covers every options and then that Nagarjuna suggests that none or more than one hold is brilliant - as a reminder I think this is pretty (in)complete by first order logic: “that it held, that it did not, both, or neither”

It really ties in with my belief in the “observer” - not in the easily misunderstood Quantum Physics definition of observer, rather as a name for experience - is critical to any logic we consider.

I find the most peaceful way of looking at it is that some elements of life are Computational Irreducible, however I think that we can get a better understanding than “we’ll have to wait and see”.

So, I didn’t get to think about the Maths of Buddhism whilst meditating but the universe presented a direct link in the paper above 😊 and a mate shared this: The Blind Spot by Adam Frank, Marcelo Gleiser, Evan Thompson which I’ll listen to after HHGTG!

Being Human