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Date: Sat, 27 Sep 2014 21:07:55 -0400
From: Martin Bays <mbays@sdf.org>
To: lojban@googlegroups.com
Subject: Re: [lojban] Re: tersmu 0.2
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* Saturday, 2014-09-27 at 17:11 -0700 - Romaji #### <nxt101@gmail.com>:
> On Saturday, September 27, 2014 8:03:28 PM UTC-4, TR NS wrote:
> > On Saturday, September 27, 2014 3:59:15 PM UTC-4, Martin Bays wrote:
> >> Yes. Here's a simpler example:=20
> >>
> >> ro da poi verba cu prami lo mamta be da=20
> >>
> >> FA x1:(verba(_)). mamta(f0(x1),x1)=20
> >> FA x1:(verba(_)). prami(x1,f0(x1))=20
> >>
> >> ro da poi ke'a verba ku'o zo'u li ma'o fyno mo'e da lo'o mamta da=20
> >> .i ro da poi ke'a verba ku'o zo'u da prami li ma'o fyno mo'e da lo'o=
=20
> >>
> >>
> >> Here, we interpret {lo mamta be da} as a function from children to the=
ir=20
> >> mothers; the first proposition expresses this, and the second is then=
=20
> >> the main statement.=20
> >
> > Sorry if I am being daft, but what is `f0`?=20
>
> Some kinda  subfunction?

Well, this is one of those cases where I've opted to transform
lojban expressions with unclear semantics to corresponding expressions
in the logic with equally unclear semantics. So a null answer would be:
it's whatever it has to be to make this an accurate translation of the
lojban.

But roughly, the intention is that since the externally bound variable
means {lo mamta be da} can't refer to a constant, as xorlo would usually
have a description sumti doing, it refers instead to the next best thing
- something constant with respect to everything but {da}. Since in this
context the domain over which {da} is quantified is the individuals
which verba, we should think therefore that for each da which verbas,
{lo mamta be da} refers to something which mamtas da (or some things
which mamta da). Then f0 is the function with value at a verba
that/those corresponding mamta.

The inclarity for me comes in when we ask how freely that function is
meant to be able to be chosen. Does it have to be something I "have in
mind or would have in mind if I thought about it"? Does it have to be
something I could describe? Are we assuming such a function always
actually exists in some sense (which ends up meaning we're assuming an
axiom of choice)?

But probably it's fine not to have official answers to these questions.
As far as formal semantics is concerned, we can sidestep them in the
same way we do for constant {lo} expressions: we consider the function
f0 just to be part of the structure we're evaluating the expression with
respect to.

Martin

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