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Date: Mon, 21 Oct 2024 11:47:23 -0700 (PDT)
From: Corbin Simpson <mostawesomedude@gmail.com>
To: lojban <lojban@googlegroups.com>
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References: <5341e420-cb13-4f0e-a66a-1cfe3d2caf43n@googlegroups.com>
 <ZwyzgIKpVkurbNLS@stodi.digitalkingdom.org>
Subject: Re: [lojban] RBDS and GDS are false
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Great to hear! I've updated the wiki with these examples and a couple links=
=20
to Wikipedia and nLab:=20
https://mw-live.lojban.org/papri/ralju_brivla_deep_structure Thanks!

di'ai

On Sunday, October 13, 2024 at 11:00:41=E2=80=AFPM UTC-7 robinle...@gmail.c=
om wrote:

> 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.
>
> On Sun, Oct 13, 2024 at 10:47:31AM -0700, Corbin Simpson wrote:
> > coi
> >=20
> > RBDS and GDS are two hypotheses about semantic space and (baseline)=20
> gismu.=20
> > They claim (1) that a universal covering of semantics exists as a space=
=20
> > independent of syntax, and (2) that the set of "main verbs" (RBDS) or=
=20
> > (baseline) gismu (GDS) generates a vector space which covers the=20
> semantic=20
> > space from (1).
> >=20
> > Note first that we can do rank arithmetic here, suggesting that the=20
> > universal semantics is finite-dimensional as a vector space. This=20
> already=20
> > makes it highly suspicious, given that the category of models for a=20
> theory=20
> > is usually not so well-behaved.
> >=20
> > Now, the short version: {xlane}, the fourth temporal tense, is not=20
> > baseline; yet, we have too much evidence for Special & General=20
> Relativity=20
> > to ignore it. Whoops!
> >=20
> > The long version, unrelated: Lojban is not good at algebra or equations=
.=20
> > Mathematics is all about giving multiple names to individual objects,=
=20
> but=20
> > Lojban struggles to even show that {dugri} and {tenfa} are related, let=
=20
> > alone that they are equivalent selbri. This leads to a first big gap in=
=20
> > semantics where we cannot express algebraic theories or Lawvere=20
> theories;=20
> > we can add valsi for monoids, groups, rings, etc. but have no sense of=
=20
> how=20
> > they are individual instances of a more general construction.
> >=20
> > We can't internalize categories or similarly universal big objects=20
> > directly. The problem is that we have no way to talk about inaccessible=
=20
> > cardinals, which means that Tarski's axiom would genuinely extend our=
=20
> > set-theoretic semantics beyond {cmima}. This is a pretty common=20
> phenomenon=20
> > in type theory but we are unprepared for it. Indeed, Lojban doesn't kno=
w=20
> > what an h-level is; it thinks all types are sets, and the bicategory of=
=20
> > relations Rel is a model for Lojban, so we can't actually insist=20
> otherwise.
> >=20
> > A surprising amount of 19th- and 20th-century science is missing. The=
=20
> worst=20
> > offender is probably entropy, which outside Lojban is a=20
> cross-disciplinary=20
> > concept connecting epistemic observations to states of systems, and=20
> inside=20
> > Lojban is entirely absent.
> >=20
> > Okay, there's three examples. What's actually going on here? Well,=20
> RBDS/GDS=20
> > start from the assumption that the semantic space exists. Whoops! That'=
s=20
> > almost entirely backwards from how languages should be defined. A=20
> language=20
> > definitionally, from its deductive logic, has a naturally-associated=20
> > category of models for that language. Each model is a semantics. There=
=20
> is=20
> > no one single universal standard semantics; or, rather, logicians say=
=20
> that=20
> > the syntax itself is the universal semantics: anything which provably=
=20
> > exists in Lojban's syntax will also exist in every semantics.
> >=20
> > di'ai
> >=20
> > Hope this helps,
> > ~ C.
> >=20
> > --=20
> > You received this message because you are subscribed to the Google=20
> Groups "lojban" group.
> > To unsubscribe from this group and stop receiving emails from it, send=
=20
> an email to lojban+un...@googlegroups.com.
> > To view this discussion on the web visit=20
> https://groups.google.com/d/msgid/lojban/5341e420-cb13-4f0e-a66a-1cfe3d2c=
af43n%40googlegroups.com
> .
>
>

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<div>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!<br /><br />di'ai<br /></div><br /><div class=3D"gmai=
l_quote"><div dir=3D"auto" class=3D"gmail_attr">On Sunday, October 13, 2024=
 at 11:00:41=E2=80=AFPM UTC-7 robinle...@gmail.com wrote:<br/></div><blockq=
uote class=3D"gmail_quote" style=3D"margin: 0 0 0 0.8ex; border-left: 1px s=
olid rgb(204, 204, 204); padding-left: 1ex;">I&#39;m not sure I followed al=
l of this, but it&#39;s worth noting that
<br>people have been asserting &quot;the gismu don&#39;t cover semantic spa=
ce
<br>evenly or completely&quot; for uh at least twenty years.  Like, that=
9;s
<br>not a point of contention.
<br>
<br>On Sun, Oct 13, 2024 at 10:47:31AM -0700, Corbin Simpson wrote:
<br>&gt; coi
<br>&gt;=20
<br>&gt; RBDS and GDS are two hypotheses about semantic space and (baseline=
) gismu.=20
<br>&gt; They claim (1) that a universal covering of semantics exists as a =
space=20
<br>&gt; independent of syntax, and (2) that the set of &quot;main verbs&qu=
ot; (RBDS) or=20
<br>&gt; (baseline) gismu (GDS) generates a vector space which covers the s=
emantic=20
<br>&gt; space from (1).
<br>&gt;=20
<br>&gt; Note first that we can do rank arithmetic here, suggesting that th=
e=20
<br>&gt; universal semantics is finite-dimensional as a vector space. This =
already=20
<br>&gt; makes it highly suspicious, given that the category of models for =
a theory=20
<br>&gt; is usually not so well-behaved.
<br>&gt;=20
<br>&gt; Now, the short version: {xlane}, the fourth temporal tense, is not=
=20
<br>&gt; baseline; yet, we have too much evidence for Special &amp; General=
 Relativity=20
<br>&gt; to ignore it. Whoops!
<br>&gt;=20
<br>&gt; The long version, unrelated: Lojban is not good at algebra or equa=
tions.=20
<br>&gt; Mathematics is all about giving multiple names to individual objec=
ts, but=20
<br>&gt; Lojban struggles to even show that {dugri} and {tenfa} are related=
, let=20
<br>&gt; alone that they are equivalent selbri. This leads to a first big g=
ap in=20
<br>&gt; semantics where we cannot express algebraic theories or Lawvere th=
eories;=20
<br>&gt; we can add valsi for monoids, groups, rings, etc. but have no sens=
e of how=20
<br>&gt; they are individual instances of a more general construction.
<br>&gt;=20
<br>&gt; We can&#39;t internalize categories or similarly universal big obj=
ects=20
<br>&gt; directly. The problem is that we have no way to talk about inacces=
sible=20
<br>&gt; cardinals, which means that Tarski&#39;s axiom would genuinely ext=
end our=20
<br>&gt; set-theoretic semantics beyond {cmima}. This is a pretty common ph=
enomenon=20
<br>&gt; in type theory but we are unprepared for it. Indeed, Lojban doesn&=
#39;t know=20
<br>&gt; what an h-level is; it thinks all types are sets, and the bicatego=
ry of=20
<br>&gt; relations Rel is a model for Lojban, so we can&#39;t actually insi=
st otherwise.
<br>&gt;=20
<br>&gt; A surprising amount of 19th- and 20th-century science is missing. =
The worst=20
<br>&gt; offender is probably entropy, which outside Lojban is a cross-disc=
iplinary=20
<br>&gt; concept connecting epistemic observations to states of systems, an=
d inside=20
<br>&gt; Lojban is entirely absent.
<br>&gt;=20
<br>&gt; Okay, there&#39;s three examples. What&#39;s actually going on her=
e? Well, RBDS/GDS=20
<br>&gt; start from the assumption that the semantic space exists. Whoops! =
That&#39;s=20
<br>&gt; almost entirely backwards from how languages should be defined. A =
language=20
<br>&gt; definitionally, from its deductive logic, has a naturally-associat=
ed=20
<br>&gt; category of models for that language. Each model is a semantics. T=
here is=20
<br>&gt; no one single universal standard semantics; or, rather, logicians =
say that=20
<br>&gt; the syntax itself is the universal semantics: anything which prova=
bly=20
<br>&gt; exists in Lojban&#39;s syntax will also exist in every semantics.
<br>&gt;=20
<br>&gt; di&#39;ai
<br>&gt;=20
<br>&gt; Hope this helps,
<br>&gt; ~ C.
<br>&gt;=20
<br>&gt; --=20
<br>&gt; You received this message because you are subscribed to the Google=
 Groups &quot;lojban&quot; group.
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send an email to <a href data-email-masked rel=3D"nofollow">lojban+un...@go=
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.google.com/d/msgid/lojban/5341e420-cb13-4f0e-a66a-1cfe3d2caf43n%40googlegr=
oups.com" target=3D"_blank" rel=3D"nofollow" data-saferedirecturl=3D"https:=
//www.google.com/url?hl=3Den&amp;q=3Dhttps://groups.google.com/d/msgid/lojb=
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tps://groups.google.com/d/msgid/lojban/5341e420-cb13-4f0e-a66a-1cfe3d2caf43=
n%40googlegroups.com</a>.
<br>
<br></blockquote></div>

<p></p>

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