I know a bunch about formal languages (PhD in programming languages), so I did a spot check on the “grammar” described on page 45. It’s described as a “generative grammar”, though instead of words (sequences of symbols) it produces “L_O spacial relationships”. Since he uses these phrases to describe his “grammar”, and they have their standard meaning because he listed their standard definition earlier in the section, he is pretty clearly claiming to be making something akin to a formal grammar.

My spot check is then: is the thing defined here more-or-less a grammar, in the following sense?

  1. There’s a clearly defined thing called a grammar, and there can be more than one of them.
  2. Each grammar can be used to generate something (apparently an L_O) according to clearly defined derivation rules that depend only on the grammar itself.

If you don’t have a thing plus a way to derive stuff from that thing, you don’t have anything resembling a grammar.

My spot check says:

  1. There’s certainly a thing called a grammar. It’s a four-tuple, whose parts closely mimic that of a standard grammar, but using his constructs for all the basic parts.
  2. There’s no definition of how to derive an “L_O spacial relationship” given a grammar. Just some vague references to using “telic recursion”.

I’d categorize this section as “not even wrong”; it isn’t doing anything formal enough to have a mistake in it.

Another fishy aspect of this section is how he makes a point of various things coinciding, and how that’s very different from the standard definitions. But it’s compatible with the standard definitions! E.g. the alphabet of a language is typically a finite set of symbols that have no additional structure, but there’s no reason you couldn’t define a language whose symbols were e.g. grammars over that very language. The definition of a language just says that its symbols form a set. (Perhaps you’d run into issues with making the sets well-ordered, but if so he’s running headlong into the same issues.)

Justin Pombrio, Comment on ‘The Cognitive-Theoretic Model of the Universe: A partial summary and review’, LessWrong, March 29, 2024