Re: [lojban] Second-order quantification has uses

[Jacob Thomas Errington <jake@mail.jerrington.me>]

coi

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

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

  .i ro da se ckaji x1 .o x2

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

  .i ro bu'a zo'u x1 .o x2 bu'a

?

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

  .i x1 x2 x3 ... broda === x1 x2 x3 ... me'au lo ka ce'u ce'u ce'u ... 
broda

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

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

.i mi'e la tsani mu'o

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