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Date: Sun, 13 Oct 2024 10:47:31 -0700 (PDT)
From: Corbin Simpson <mostawesomedude@gmail.com>
To: lojban <lojban@googlegroups.com>
Message-Id: <5341e420-cb13-4f0e-a66a-1cfe3d2caf43n@googlegroups.com>
Subject: [lojban] RBDS and GDS are false
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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.

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coi<br /><br /><div>RBDS and GDS are two hypotheses about semantic space an=
d (baseline) gismu. They claim (1) that a universal covering of semantics e=
xists 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 th=
e semantic space from (1).</div><div><br /></div><div>Note first that we ca=
n do rank arithmetic here, suggesting that the universal semantics is finit=
e-dimensional as a vector space. This already makes it highly suspicious, g=
iven that the category of models for a theory is usually not so well-behave=
d.</div><div><br /></div><div>Now, the short version: {xlane}, the fourth t=
emporal tense, is not baseline; yet, we have too much evidence for Special =
&amp; General Relativity to ignore it. Whoops!</div><div><br /></div><div>T=
he long version, unrelated: Lojban is not good at algebra or equations. Mat=
hematics is all about giving multiple names to individual objects, but Lojb=
an struggles to even show that {dugri} and {tenfa} are related, let alone t=
hat 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 in=
dividual instances of a more general construction.</div><div><br /></div><d=
iv>We can't internalize categories or similarly universal big objects direc=
tly. The problem is that we have no way to talk about inaccessible cardinal=
s, which means that Tarski's axiom would genuinely extend our set-theoretic=
 semantics beyond {cmima}. This is a pretty common phenomenon in type theor=
y 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.<br /><br />A surp=
rising amount of 19th- and 20th-century science is missing. The worst offen=
der is probably entropy, which outside Lojban is a cross-disciplinary conce=
pt connecting epistemic observations to states of systems, and inside Lojba=
n is entirely absent.<br /><br />Okay, there's three examples. What's actua=
lly going on here? Well, RBDS/GDS start from the assumption that the semant=
ic space exists. Whoops! That's almost entirely backwards from how language=
s should be defined. A language definitionally, from its deductive logic, h=
as a naturally-associated category of models for that language. Each model =
is a semantics. There is no one single universal standard semantics; or, ra=
ther, logicians say that the syntax itself is the universal semantics: anyt=
hing which provably exists in Lojban's syntax will also exist in every sema=
ntics.<br /><br />di'ai<br /><br />Hope this helps,</div><div>~ C.<br /></d=
iv>

<p></p>

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