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Subject: Re: [lojban] Second-order quantification has uses
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From: Jacob Thomas Errington <jake@mail.jerrington.me>
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Date: Tue, 12 Jan 2021 15:24:27 GMT
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coi

On 2021-01-08 13:17, Corbin Simpson wrote:
> That is, {x1 du x2} means that x1 and x2 are references which are=20
> equivalent under the operation of looking up their referents; x1 and=20
> x2 refer to the same thing. This definition relies upon {mintu} and=20
> {sinxa}; I would hope that at least {mintu} could instead be defined=20
> in terms of {du}! (la xorxes also goes on to define {mintu} in terms=20
> of {dunli}.) Meanwhile, there's also this definition from la ilmen:
>
> =C2=A0=C2=A0=C2=A0 x1 jo'u x2 simxu lo ka ro da poi selkai ce'u cu selkai=
 ce'u .i=20
> va'i ro da se ckaji x1 .o x2
>
> That is, {x1 du x2} means that the collection/set of {x1, x2} is=20
> self-similar/automorphic when we try to tell x1 and x2 apart by=20
> looking at the properties which characterize them; in other words, all=20
> properties apply to x1 iff they apply to x2. This is what la tsani=20
> refers to by discussing reified {ka} abstractions.

Let's forget the first sentence from Ilmen's definition and look at the=20
second sentence, which he says is a rephrasing of the first.

 =C2=A0 .i ro da se ckaji x1 .o x2

Now we need to squint a little and pretend that this {ro da} is=20
referring only to properties, doesn't this work out to the same thing as

 =C2=A0 .i ro bu'a zo'u x1 .o x2 bu'a

?

Lojban is funny in that you can smuggle selbri around as sumti (as=20
witnessed by the very common {lo ka}) and 'unbox' them with {ckaji} --=20
this unboxing is very flavourless, but there are delicious unboxings=20
like {carmi}, {pluka}, etc. -- and more generally you can unbox any=20
reified selbri with the experimental cmavo {me'au}:

 =C2=A0 .i x1 x2 x3 ... broda =3D=3D=3D x1 x2 x3 ... me'au lo ka ce'u ce'u =
ce'u ...=20
broda

I think a consequence of this is bu'a et al are made obsolete by=20
'first-order' quantification with da et al.

Surely, there must be a reason why things aren't done this way in math=20
as opposed to in Lojban. I'd bet it introduces some kind of paradox(es).

.i mi'e la tsani mu'o

--=20
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