RBDS and GDS are false

[Corbin Simpson]

coi

RBDS and GDS are two hypotheses about semantic space and (baseline) gismu. They claim (1) that a universal covering of semantics exists as a space independent of syntax, and (2) that the set of "main verbs" (RBDS) or (baseline) gismu (GDS) generates a vector space which covers the semantic space from (1).

Note first that we can do rank arithmetic here, suggesting that the universal semantics is finite-dimensional as a vector space. This already makes it highly suspicious, given that the category of models for a theory is usually not so well-behaved.

Now, the short version: {xlane}, the fourth temporal tense, is not baseline; yet, we have too much evidence for Special & General Relativity to ignore it. Whoops!

The long version, unrelated: Lojban is not good at algebra or equations. Mathematics is all about giving multiple names to individual objects, but Lojban struggles to even show that {dugri} and {tenfa} are related, let alone that they are equivalent selbri. This leads to a first big gap in semantics where we cannot express algebraic theories or Lawvere theories; we can add valsi for monoids, groups, rings, etc. but have no sense of how they are individual instances of a more general construction.

We can't internalize categories or similarly universal big objects directly. The problem is that we have no way to talk about inaccessible cardinals, which means that Tarski's axiom would genuinely extend our set-theoretic semantics beyond {cmima}. This is a pretty common phenomenon in type theory but we are unprepared for it. Indeed, Lojban doesn't know what an h-level is; it thinks all types are sets, and the bicategory of relations Rel is a model for Lojban, so we can't actually insist otherwise.

A surprising amount of 19th- and 20th-century science is missing. The worst offender is probably entropy, which outside Lojban is a cross-disciplinary concept connecting epistemic observations to states of systems, and inside Lojban is entirely absent.

Okay, there's three examples. What's actually going on here? Well, RBDS/GDS start from the assumption that the semantic space exists. Whoops! That's almost entirely backwards from how languages should be defined. A language definitionally, from its deductive logic, has a naturally-associated category of models for that language. Each model is a semantics. There is no one single universal standard semantics; or, rather, logicians say that the syntax itself is the universal semantics: anything which provably exists in Lojban's syntax will also exist in every semantics.

di'ai

Hope this helps,

~ C.

[Robin Lee Powell]

I'm not sure I followed all of this, but it's worth noting that
people have been asserting "the gismu don't cover semantic space
evenly or completely" for uh at least twenty years. Like, that's
not a point of contention.

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[Corbin Simpson]

Great to hear! I've updated the wiki with these examples and a couple links to Wikipedia and nLab: https://mw-live.lojban.org/papri/ralju_brivla_deep_structure Thanks!

di'ai