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The following is a refinement of the 2nd ExSol. I am neutral
about whether it is proposed only for AL or also for SL to
be considered by the BF. But regarding BF and SL, at least
as far as gadri are concerned, I have come to the conclusion
that all *I* am able to do is evaluate concrete schemes for
remedying the mess that is current SL. So in a sense my
contribution to the BF regarding gadri is this scheme plus
evaluation of any other schemes that anybody else proposes.
If somebody wants to propose a more fundamentalist scheme,
one way to go about it would be to show how everything below
would be rendered.
*****
Version 3.
1. No new cmavo are required. (But see 4.)
2. lo'e & le'e aren't really part of the system, and can serve
as Nicolaic Prototypes.
3. Either lV is gadrow for Kind and lVi is gadrow for Jbomass, or
vice versa. It's hard to say which is more compatible with SL,
but lVi for Kind and lV for Jbomass is more compatible with the
bits of SL that are not a mess. In exx below I will use lo for
Jbomass and loi for Kind (in a reversal from 2nd Ex Sol), but
this assignment is not part of the proposal, which is neutral
between the two alternative assignments.
4. SL lV'i is ambiguous between extensionally and intensionally
defined sets -- or if it SL lV'i ambiguously means the one then
there is no gadri for the other. Extensionally defined sets
pattern with Jbomass and Intensionally defined sets with Kind,
so one solution (which I prefer) would be to make lo'i/le'i/la'i
extensional and add loi'i/lei'i/lai'i for intensional, while another
solution would be to use a LAhE that takes a collective as
argument and yields a set corresponding to it. In that case,
if lu'i were that LAhE, then extensional sets would be
{lu'i lo/le/la} and intensional sets would be {lu'i loi/lei/lai},
while {lo'i/le'i/la'i} would be by intent ambiguous between
extensional and intensional. (NB It cannot be assumed that
{lu'i} would be the requisite LAhE; it may be that a new LAhE
is required.)
5. There is no implicit outer PA on any gadri. IOW, the default
outer PA is always mo'ezi'o. (Cf. 19.)
6. The default inner PA is mo'ezo'e, which here includes tu'o
(= mo'ezi'o). That is, inner PA is glorked from context if it
is not explicitly specified.
7. Inner tu'o encodes uncountability.
{lo tu'o broda} = the substance-mass of all broda.
{loi tu'o broda} = the substance-mass of all broda-kind = Mr Broda-stuff.
8. {lo pa broda} = a single broda
{lo re broda} = a collective consisting of two broda
{lo ro broda} = the collective consisting of every broda
{le re broda} = a certain collective (described as) consisting of two
broda
{le broda} would normally be glorked as {le pa broda} or {le tu'o
broda}. (In contexts where collectives make some sense, it would
be glorked as {le su'o broda}, and in contexts where only collectives
make sense, it would of course be glorked as {lo za'u}.)
{lo broda} would normally be glorked as {lo tu'o broda} or either {lo
su'o broda} or {lo za'u broda} (because {lo pa broda} can be said as
{pa broda} = {pa lo pa broda} -- see 13 & 17).
9. {loi pa broda} = Mr Single Broda.
{loi re broda} = Mr Pair of Broda.
{loi ro broda} = Mr Collective of All Broda.
{lei re broda} = a certain Kind embodying what is described as
the property of being a pair of broda.
{loi broda} would normally be glorked as {loi pa broda} or {loi
tu'o broda}.
10. {lo pimu broda} = a collective consisting of one in every two
broda.
{le pimu broda} = a certain collective consisting of one in every two
broda.
11. {loi pimu broda} = Mr One in Every Two Broda.
{lei pimu broda} = a certain Kind embodying what is described as
the property of being a collective consisting of one in every two
broda.
12. To talk about "half a broda", it will be necessary to use
{si'e} (or {pimumei}).
13. {PA lo broda} = PA members of the collective expressed by
{lo broda}.
{PA loi broda} = PA Kinds of the Kind expressed by {loi broda}.
14. {pimu lo PA} (PA other than tu'o) = one in every two members
of the collective expressed by {lo broda}.
{pimu loi PA} = one in every two kinds of the Kind expressed by {loi
broda}.
15. {pimu lo tu'o} = one in every two arbitrarily-delimited but
equal bits of the mass of all broda.
{pimu loi tu'o} = one in every two kinds of Mr Broda-stuff.
{loi pimu lo tu'o} = Mr One in Every Two Arbitrarily-Delimited but
Equal Bits of Broda-stuff.
16. {piro lo} and {piso'e lo} imply inner tu'o, because if
inner PA was not tu'o then outer ro and so'e could be used.
17. {PA broda} = {PA lo broda}, which in most contexts would
be glorked as {PA lo ro broda}. The same goes for {piPA broda}.
Because inner PA is mo'ezo'e and so does not specify whether
broda is construed countably, {PA broda} = {PA lo broda} =
{PA da poi broda}.
18. The element of meaning encoded by inner PA is part of the
meaning encoded by the cmene following la and lai. E.g. {nik}
may name a single thing xor a manysome xor some stuff.
19. Although in syntax there is no implicit quantifier before
{lo}, other than mo'ezi'o, in the underlying meaning there is
existential quantification -- "There is a collective" --
except when inner PA is tu'o or ro. Hence bare lo is sensitive
to scope.
--And.