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Date: Sat, 29 May 2021 22:15:01 -0400
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Subject: Re: [lojban] {zo'e}
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Just a couple tentative thoughts on this old thread.

On Sun, Nov 22, 2020 at 5:07 PM Ilmen <ilmen.pokebip@gmail.com> wrote:

> Hello everybody,
>
> I would like to ask you clarifications on the meaning of the cmavo
> {zo'e}, which is defined in the CLL at
> https://lojban.github.io/cll/7/7/index.html
> <https://lojban.github.io/cll/7/7/index.html> as meaning =E2=80=9Cthe obv=
ious
> value=E2=80=9D, =E2=80=9Cwhatever I want it to mean but haven=E2=80=99t b=
othered to figure out,
> or figure out how to express=E2=80=9D.
>
> Let's consider the following three example sentences:
>
> =E2=80=A2 [A] {mi tirna zo'e}
> =E2=80=A2 [B] {mi tirna su'o da}
> =E2=80=A2 [C] {(da'o) mi tirna ko'a} (usage of a constant {ko'a} which ha=
sn't
> been assigned a value explicitly earlier)
>
> How does [A] semantically differ from [B] and [C]? (I suspect that the
> two latters ultimately mean the same thing.)
>

I think you're right about [B] and [C] as full sentences -- with the {da'o}
in front, there seems to be no possible world in which one is true (or
false) and not the other.  And if two propositions have the same truth
value in all possible worlds, then they must have the same
truth-conditions, and therefore the same meaning.  I believe this logical
equivalence is reflected in a standard rewriting/transformation rule called
existential instantiation (a.k.a existential elimination) which allows you
to replace an existential quantifier and its variable with a constant under
certain conditions.  And there is a rewriting rule that goes in the
opposite direction called existential generalization (a.k.a. existential
introduction).

https://en.wikipedia.org/wiki/Existential_instantiation
https://en.wikipedia.org/wiki/Existential_generalization

So it's not surprising that this is a confusing issue.  In a lot of cases,
whether you choose an existential quantifier or a constant does not matter
much.

However, assuming that {ko'a} is unquantified and presupposed, then I do
not believe [B] and [C] are freely interchangeable in practice as *nested*
propositions.  For example, under negation:

=E2=80=A2 [B1] {naku mi tirna su'o da}
I don't hear anything.

=E2=80=A2 [C1] {(da'o) naku mi tirna ko'a}
I don't hear [whatever it is I don't hear].

It seems to me that the {naku} causes a pragmatic difference to surface --
[B1] is a universal claim based on the dual nature of {su'o} under de
Morgan's laws, while [C1] invites the listener to try to pick out a salient
value.  And although perhaps {ko'a} could in principle mean something like
"the whole domain of discourse", that would not be very cooperative, given
that {su'o da} is available.

When forming questions it seems a similar difference surfaces:

=E2=80=A2 [B2] {xu do tirna su'o da}
Do you hear anything (at all)?

=E2=80=A2 [C2] {(da'o) xu mi tirna ko'a}
Do you hear it?

We shouldn't be too surprised to discover these differences; {su'o} seems
to be about plugging in totally arbitrary values, or it could be conceived
as a way to generate an iterated logical-disjunction of (a possibly
infinite number of) propositions, in the same way that summation with
capital sigma is iterates over addition); {ko'a} is much more like an
anaphor for a certain semantic value, whether we know what it is exactly or
not -- whatever it is though, it's not quite arbitrary.

I think there are three possibilities for defining {zo'e}:
1. {zo'e} means {da'o ko'a}, at least at first glance.
2. {zo'e} means {su'o da}.
3. {zo'e} means either depending on context.

It's not hard to find examples that pull us both directions, given usual
contexts:

D {mi na djuno [zo'e]}
pulls us toward {da'o ko'a} (option 1).

E. {mi na mlatu [zo'e]}
pulls us toward {su'o da} (option 2).

The xorlo-izing BPFK definition of {lo} makes options 2 and 3 problematic,
and so ultimately, it seems to me like the choice should be option 1.  The
problem, however, is that it would probably necessitate debloatification
and/or polymorphism for many existing predicates (entailing a change to
official definitions), to avoid undesirable "na mlatu" sentences.  Or
maybe, teach people to say {mi mlatu no da} instead of {mi na mlatu}.   Or
maybe just tolerate some rather odd pragmatics.  (BTW the community is the
boss; I am just giving an opinion.)


How [A] should be represented in logical notation?
>

In the simplest cases, {zo'e} could be represented by an unbound symbol,
say the letter theta, subscripted with sequential integers for each
appearance.  The rule of interpretation would be that theta-symbols pick
out whatever works. Some people would say there is a hidden existential
quantifier in there, but I say no, it's a constant-like symbol with a
presupposed value determined by context.

Another device increasingly used in formal semantics is the choice
operator, borrowed from Hilbert, represented by curly lowercase epsilon,
which I'll skip describing for now.


> {zo'e} cannot be a constant as it changes its referent(s) on each
> occurrence.
>

Yes, ultimately, {da'o ko'a} probably isn't adequate; {zo'e} has to be some
kind of function that changes meaning depending on context and even takes
arguments; that's sensitive to quantifiers (allowing it to take multiple
values with {ro}, as Martin Bays pointed out once on the list); and yet
also impervious to the scope of {naku}.   Maybe something like Skolem
functions, as Guskant suggested, though how exactly to formalize this for a
logical notational rewriting for Lojban (or for any other loglang) remains
to be seen (I can't remember how Martin did it).  Maybe something like:

ro remna cu prami zo'e
[=E2=88=80x remna(x)] prami(x, zohe(x))

Where {zohe} here is not a predicate but a contextually determined function
from entities to entities.

mi'e .maik.
mu'o

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<div dir=3D"ltr"><div>Just a couple tentative thoughts on this old thread. =
<br></div><br><div><div dir=3D"ltr" class=3D"gmail_attr">On Sun, Nov 22, 20=
20 at 5:07 PM Ilmen &lt;<a href=3D"mailto:ilmen.pokebip@gmail.com">ilmen.po=
kebip@gmail.com</a>&gt; wrote:<br></div><blockquote class=3D"gmail_quote" s=
tyle=3D"margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);pad=
ding-left:1ex">Hello everybody,<br>
<br>
I would like to ask you clarifications on the meaning of the cmavo <br>
{zo&#39;e}, which is defined in the CLL at <br>
<a href=3D"https://lojban.github.io/cll/7/7/index.html" rel=3D"noreferrer" =
target=3D"_blank">https://lojban.github.io/cll/7/7/index.html</a> <br>
&lt;<a href=3D"https://lojban.github.io/cll/7/7/index.html" rel=3D"noreferr=
er" target=3D"_blank">https://lojban.github.io/cll/7/7/index.html</a>&gt; a=
s meaning =E2=80=9Cthe obvious <br>
value=E2=80=9D, =E2=80=9Cwhatever I want it to mean but haven=E2=80=99t bot=
hered to figure out, <br>
or figure out how to express=E2=80=9D.<br>
<br>
Let&#39;s consider the following three example sentences:<br>
<br>
=E2=80=A2 [A] {mi tirna zo&#39;e}<br>
=E2=80=A2 [B] {mi tirna su&#39;o da}<br>
=E2=80=A2 [C] {(da&#39;o) mi tirna ko&#39;a} (usage of a constant {ko&#39;a=
} which hasn&#39;t <br>
been assigned a value explicitly earlier)<br>
<br>
How does [A] semantically differ from [B] and [C]? (I suspect that the <br>
two latters ultimately mean the same thing.)<br></blockquote><div><br></div=
><div>I think you&#39;re right about [B] and [C] as full sentences -- with =
the {da&#39;o} in front, there seems to be no possible world in which one i=
s true (or false) and not the other.=C2=A0 And if two propositions have the=
 same truth value in all possible worlds, then they must have the same trut=
h-conditions, and therefore the same meaning.=C2=A0 I believe this logical =
equivalence is reflected in a standard rewriting/transformation rule called=
 existential instantiation (a.k.a existential elimination) which allows you=
 to replace an existential quantifier and its variable with a constant unde=
r certain conditions.=C2=A0 And there is a rewriting rule that goes in the =
opposite direction called existential generalization (a.k.a. existential in=
troduction).</div><div><br></div><div><a href=3D"https://en.wikipedia.org/w=
iki/Existential_instantiation">https://en.wikipedia.org/wiki/Existential_in=
stantiation</a></div><div><a href=3D"https://en.wikipedia.org/wiki/Existent=
ial_generalization">https://en.wikipedia.org/wiki/Existential_generalizatio=
n</a></div><div><br></div><div>So it&#39;s not surprising that this is a co=
nfusing issue.=C2=A0 In a lot of cases, whether you choose an existential q=
uantifier or a constant does not matter much.<br></div><div><br></div><div>=
However, assuming that {ko&#39;a} is unquantified and presupposed, then I d=
o not believe [B] and [C] are freely interchangeable in practice as *nested=
* propositions.=C2=A0 For example, under negation:</div></div><div><br></di=
v><div>
=E2=80=A2 [B1] {naku mi tirna su&#39;o da}</div><div>I don&#39;t hear anyth=
ing.<br></div><div><br></div><div>
=E2=80=A2 [C1] {(da&#39;o) naku mi tirna ko&#39;a}</div><div class=3D"gmail=
_quote"><div>I don&#39;t hear [whatever it is I don&#39;t hear].<br></div><=
div><br></div><div>It seems to me that the {naku} causes a pragmatic differ=
ence to surface -- [B1] is a universal claim based on the dual nature of {s=
u&#39;o} under de Morgan&#39;s laws, while [C1] invites the listener to try=
 to pick out a salient value.=C2=A0 And although perhaps {ko&#39;a} could i=
n principle mean something like &quot;the whole domain of discourse&quot;, =
that would not be very cooperative, given that {su&#39;o da} is available.<=
br></div><div><br></div><div>When forming questions it seems a similar diff=
erence surfaces:<br></div><div><br></div><div>
<div>
=E2=80=A2 [B2] {xu do tirna su&#39;o da}</div><div>Do you hear anything (at=
 all)?<br></div><div><br>
=E2=80=A2 [C2] {(da&#39;o) xu mi tirna ko&#39;a}</div><div class=3D"gmail_q=
uote"><div>Do you hear it?</div><div><br></div><div>We shouldn&#39;t be too=
 surprised to discover these differences; {su&#39;o} seems to be about plug=
ging in totally arbitrary values, or it could be conceived as a way to gene=
rate an iterated logical-disjunction of (a possibly infinite number of) pro=
positions, in the same way that summation with capital sigma is iterates ov=
er addition); {ko&#39;a} is much more like an anaphor for a certain semanti=
c value, whether we know what it is exactly or not -- whatever it is though=
, it&#39;s not quite arbitrary.<br></div><div><br></div><div>I think there =
are three possibilities for
 defining {zo&#39;e}:</div><div>1.=20
 {zo&#39;e} means
 {da&#39;o ko&#39;a}, at least at first glance.</div><div>2. {zo&#39;e} mea=
ns {su&#39;o da}.


</div><div>
<div>3. {zo&#39;e} means either depending on context.<br></div>

</div><div><br></div><div>It&#39;s not hard to find examples that pull us b=
oth directions, given usual contexts:</div><div><br></div><div>D {mi na dju=
no [zo&#39;e]} <br></div><div>pulls us toward=20
{da&#39;o ko&#39;a} (option 1).</div><div><br></div><div>E. {mi na mlatu [z=
o&#39;e]} <br></div><div>pulls us toward {su&#39;o da} (option 2).</div><di=
v><br></div><div>The xorlo-izing BPFK definition of {lo} makes options 2 an=
d 3 problematic, and so ultimately, it seems to me like the choice should b=
e option 1.=C2=A0 The problem, however, is that it would probably necessita=
te debloatification and/or polymorphism for many existing predicates (entai=
ling a change to official definitions), to avoid undesirable &quot;na mlatu=
&quot; sentences.=C2=A0 Or maybe, teach people to say {mi mlatu no da} inst=
ead of {mi na mlatu}.=C2=A0=C2=A0 Or maybe just tolerate some rather odd pr=
agmatics.=C2=A0 (BTW the community is the boss; I am just giving an opinion=
.)<br></div><div><br></div><div><br></div><div></div></div>

</div><div></div><blockquote class=3D"gmail_quote" style=3D"margin:0px 0px =
0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">
How [A] should be represented in logical notation?<br></blockquote><div><br=
></div><div>In the simplest cases, {zo&#39;e} could be represented by an un=
bound symbol, say the letter theta, subscripted with sequential integers fo=
r each appearance.=C2=A0 The rule of interpretation would be that theta-sym=
bols pick out whatever works. Some people would say there is a hidden exist=
ential quantifier in there, but I say no, it&#39;s a constant-like symbol w=
ith a presupposed value determined by context.=C2=A0 <br></div><div><br></d=
iv><div>Another device increasingly used in formal semantics is the choice =
operator, borrowed from Hilbert, represented by curly lowercase epsilon, wh=
ich I&#39;ll skip describing for now. <br></div><div></div><div><br></div><=
div>=C2=A0</div><blockquote class=3D"gmail_quote" style=3D"margin:0px 0px 0=
px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">
{zo&#39;e} cannot be a constant as it changes its referent(s) on each <br>
occurrence.<br></blockquote><div><br></div><div>Yes, ultimately, {da&#39;o =
ko&#39;a} probably isn&#39;t adequate; {zo&#39;e} has to be some kind of fu=
nction that changes meaning depending on context and even takes arguments; =
that&#39;s sensitive to quantifiers (allowing it to take multiple values wi=
th {ro}, as Martin Bays pointed out once on the list); and yet also impervi=
ous to the scope of {naku}.=C2=A0=C2=A0 Maybe something like Skolem functio=
ns, as Guskant suggested, though how exactly to formalize this for a logica=
l notational rewriting for Lojban (or for any other loglang) remains to be =
seen (I can&#39;t remember how Martin did it).=C2=A0 Maybe something like:<=
br></div><div><br></div><div>ro remna cu prami zo&#39;e<br></div><div>[=E2=
=88=80x remna(x)] prami(x, zohe(x))</div><div><br></div><div>Where=20
{zohe} here is not a predicate but a contextually determined function from =
entities to entities.</div><div><br></div><div>mi&#39;e .maik.<br></div><di=
v>mu&#39;o<br></div><div><br></div></div></div>

<p></p>

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