Date: Thu, 6 Feb 2014 17:58:19 -0800 (PST)
From: guskant <gusni.kantu@gmail.com>
To: lojban@googlegroups.com
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Subject: Re: [lojban] Individuals and xorlo
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Le vendredi 7 f=C3=A9vrier 2014 06:22:09 UTC+9, xorxes a =C3=A9crit :
>
>
> On Thu, Feb 6, 2014 at 1:34 AM, guskant <gusni...@gmail.com <javascript:>=
>wrote:
>
>>
>> Although it will become out of topic, I have another suggestion related=
=20
>> to the BPFK page of gadri.
>>
>> "Any term without an explicit outer quantifier is a constant" should be=
=20
>> changed to=20
>> "Any term without an explicit outer quantifier can be a constant",
>> because an usual predicate logic has an axiom on a constant c that "F(c)=
=20
>> {inaja} there is at least one (individual) x such that F(x)";
>>
>
> That applies to singular constants, whereas unquantified terms need not b=
e=20
> singular, but the version with plural quantifiers will still be valid.
>


Actually, there is no explicit plural qiantifier in Lojban, though=20
implicitly there are.

Even Thomas McKay does not adopt plural constant. For individual constant=
=20
c, there are two axioms:
- [for all Y: Y {me} c] c {me} Y ;
- F(c) {inaja} there is X such that F(X) .
Even in the plural logic, F(c) implies a quantifier.

If you use the term "constant" as of the version with plural quantifiers,=
=20
you should mention it in the gadri page, and also you should explain how=20
Lojban treats plural quantifiers. Otherwise I don't understand how a=20
constant implies no implicit quantifier.

=20

> =20
>
>> this means that the sentence "any term without an explicit outer=20
>> quantifier is a constant" automatically implicates an outer quantifier=
=20
>> {su'o},
>>
>
> It shouldn't implicate that. "F{c} -> Ex F(x)" does not mean that "F(c)"=
=20
> and "Ex F(x)" have the same meaning, nor that "c" is just a shorthand for=
=20
> "Ex ...x...". Similarly xorlo says that "lo broda" is not just shorthand=
=20
> for "su'o lo broda".
> =20
>


I did not mean that "F(c)" and "Ex F(x)" have the same meaning, nor that=20
"c" is just a shorthand for "Ex ...x...".
When F(c) is said, it says implicitly that "Ex F(x)" is true.


=20

> and it contradicts to xorlo itself that there are no default quantifiers.
>>
>
> Not just no default quantifiers. No implicit hidden quantifiers at all,=
=20
> The point is that "lo broda" is not a quantification of the bridi it=20
> appears in, the way "su'o lo broda" is.
>
>

I agree to that point, and I consider that F(c) implies implicit hidden=20
quantifiers, and conclude that it contradicts xorlo.

=20

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<div dir=3D"ltr"><br><br>Le vendredi 7 f=C3=A9vrier 2014 06:22:09 UTC+9, xo=
rxes a =C3=A9crit&nbsp;:<blockquote class=3D"gmail_quote" style=3D"margin: =
0;margin-left: 0.8ex;border-left: 1px #ccc solid;padding-left: 1ex;"><div d=
ir=3D"ltr"><div><br><div class=3D"gmail_quote">On Thu, Feb 6, 2014 at 1:34 =
AM, guskant <span dir=3D"ltr">&lt;<a href=3D"javascript:" target=3D"_blank"=
 gdf-obfuscated-mailto=3D"_Jfn-OwIgqkJ" onmousedown=3D"this.href=3D'javascr=
ipt:';return true;" onclick=3D"this.href=3D'javascript:';return true;">gusn=
i...@gmail.com</a>&gt;</span> wrote:<br>
<blockquote class=3D"gmail_quote" style=3D"margin:0px 0px 0px 0.8ex;border-=
left-width:1px;border-left-color:rgb(204,204,204);border-left-style:solid;p=
adding-left:1ex"><div dir=3D"ltr"><br><div>Although it will become out of t=
opic, I have another suggestion related to the BPFK page of gadri.</div>
<div><br></div><div>"Any term without an explicit outer quantifier is a con=
stant" should be changed to&nbsp;</div><div>"Any term without an explicit o=
uter quantifier can be a constant",</div><div>because an usual predicate lo=
gic has an axiom on a constant c that "F(c) {inaja} there is at least one (=
individual) x such that F(x)";</div>
</div></blockquote><div><br></div><div>That applies to singular constants, =
whereas unquantified terms need not be singular, but the version with plura=
l quantifiers will still be valid.<br></div></div></div></div></blockquote>=
<div><br></div><div><div><br></div><div>Actually, there is no explicit plur=
al qiantifier in Lojban, though implicitly there are.</div><div><br></div><=
div>Even Thomas McKay does not adopt plural constant. For individual consta=
nt c, there are two axioms:</div><div>- [for all Y: Y {me} c] c {me} Y ;</d=
iv><div>- F(c) {inaja} there is X such that F(X) .</div><div>Even in the pl=
ural logic, F(c) implies a quantifier.</div><div><br></div><div>If you use =
the term "constant" as of the version with plural quantifiers, you should m=
ention it in the gadri page, and also you should explain how Lojban treats =
plural quantifiers. Otherwise I don't understand how a constant implies no =
implicit quantifier.</div></div><div><br></div><div>&nbsp;</div><blockquote=
 class=3D"gmail_quote" style=3D"margin: 0;margin-left: 0.8ex;border-left: 1=
px #ccc solid;padding-left: 1ex;"><div dir=3D"ltr"><div><div class=3D"gmail=
_quote"><div></div><div>&nbsp;</div><blockquote class=3D"gmail_quote" style=
=3D"margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-color:rgb(20=
4,204,204);border-left-style:solid;padding-left:1ex">
<div dir=3D"ltr"><div>this means that the sentence "any term without an exp=
licit outer quantifier is a constant" automatically implicates an outer qua=
ntifier {su'o},</div></div></blockquote><div><br></div><div>
It shouldn't implicate that. "F{c} -&gt; Ex F(x)" does not mean that "F(c)"=
 and "Ex F(x)" have the same meaning, nor that "c" is just a shorthand for =
"Ex ...x...". Similarly xorlo says that "lo broda" is not just shorthand fo=
r "su'o lo broda".<br>
</div><div>&nbsp;</div></div></div></div></blockquote><div><br></div><div><=
br></div><div>I did not mean that "F(c)" and "Ex F(x)" have the same meanin=
g, nor that "c" is just a shorthand for "Ex ...x...".</div><div>When F(c) i=
s said, it says implicitly that "Ex F(x)" is true.</div><div><br></div><div=
><br></div><div>&nbsp;</div><blockquote class=3D"gmail_quote" style=3D"marg=
in: 0;margin-left: 0.8ex;border-left: 1px #ccc solid;padding-left: 1ex;"><d=
iv dir=3D"ltr"><div><div class=3D"gmail_quote"><blockquote class=3D"gmail_q=
uote" style=3D"margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-c=
olor:rgb(204,204,204);border-left-style:solid;padding-left:1ex"><div dir=3D=
"ltr"><div>and it contradicts to xorlo itself that there are no default qua=
ntifiers.</div>
</div></blockquote><div><br></div><div>Not just no default quantifiers. No =
implicit hidden quantifiers at all, The point is that "lo broda" is not a q=
uantification of the bridi it appears in, the way "su'o lo broda" is.</div>
<div><br></div></div></div></div></blockquote><div><br></div><div><br></div=
><div>I agree to that point, and I consider that F(c) implies implicit hidd=
en quantifiers, and conclude that it contradicts xorlo.</div><div><br></div=
><div>&nbsp;</div></div>

<p></p>

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