{lo} down

[John E Clifford <clifford-j@sbcglobal.net>]

A primary occurrence of a sumti is one not in the
scope of a negation, abstraction, modal or
non-assertive speech act. In general, primary
occurrence sumti can serve as the premise of a
particular generalization: from {[sumti] broda}
to {da broda}.  The usual upshot of this is that
sumti refer to things that exist in the world for
which the sentence is being evaluated.

In xorlo, some primary occurrences of sumti which
do not refer to things existing in the evaluation
world are nonetheless true: certainly {lo
pavyseljirna cu pavyseljirna}, probably {lo
pavyseljirna cu simsa lo xirma}, maybe even {lo
pavyseljirna cu blanu}. 
These are all strictly false in prelo, the
previous interpretation of {lo}.  However, there
are a variety of workarounds.  For xorlo we could
change the domain of descriptions to, say, one in
which every well-formed sumti had a referent and
? insofar as possible given existence constraints
? where that sumti indicated what sort of thing
the referent should be, it was that sort of thing
({lo pavyseljirna co se darxi be mi} would be a
unicorn but not ? in this world -- one hit by me,
since what is hit has to exist in the world of
the hitting).  The quantified variables would
then range over this domain.  Thus, the first
inference would go through, but the second (from
?there is a? to ?there exists a?) would not, in
any case.  There are some inconveniences with
having things this way, but some with not having
it as well. And the inconveniences with having it
are practically less than theory suggests, since
so many interesting predicates require that
significant places be filled by reference to
existents, not just to beings.  

For prelo, the standard workaround has always
been that if we are talking about unicorns then
we are in a world where unicorns exist.  But that
only works sometimes; clearly if someone rushes
in saying ?I just saw a unicorn? and we reply
?Not likely, since they don?t exist? we have not
made the shift.  More satisfying for the certain
cases is the notion that tautologies, like
?unicorns are unicorns? are true even with
vacuous terms: even ?brumpfs are brumpfs? is true
whether or not we have any idea what brumpfs are.
 Strictly speaking this takes advantage of the
fact that anything can be omitted in Lojban (if
?it is clear from the context?) and modals and
the like are particularly apt to fall under this,
so here we have omitted an ?obvious? {ca?e}
(assuming that is the right thing for
definitional claims and closely related items
like tautologies).  The second claim above, that
unicorns are like horses, can similarly be
justified as a hidden {ka?u}.  The third, that
unicorns are blue, is harder, since this goes
against cultural norms (unicorns are typically
white and, at worst, run through horse colors in
the cultural understanding).  But the claim is
also, for those very reasons probably false, even
though it is logically possible that there be
blue unicorns (and on the broad domain view there
certainly are since {lo blanu pavyseljirna} is a
well-formed sumti and nothing prevents its
referent from being blue any more than from being
a unicorn).  
That is, the practical difference between xorlo
and prelo in this area is vanishingly small and
comes down eventually to slightly different
interpretations, differences that will appear
within each of the positions standing alone
(i.e., the difference between the two systems is
no greater than between different instances
within a given system).

Such easy relief does not appear for the other
case of difference.  To say that I want a unicorn
in prelo requires {tu?a}: {mi djica tu?a lo
pavyseljirna}, while xorlo can say just {mi djica
lo pavyseljirna}, what used to be a malglico
solecism. In this case, the fact that there are
no unicorns in the evaluation world is not
crucial; the same problem arises with {mi djica
lo mikce}.  Nor does expanding domains help any
here: even in the widest domain, the move from
{mi djica lo broda} to {da (poi broda) zo?u mi
djica da} does not work in general, for it can be
shown for every broda, fub, even in the extended
domain that {la fub zo?u mi djica fy} is false
even when the original is true -- because I would
have been as satisfied, my desire met, by any
other broda every bit as well as this one.

The problem is, of course, that of intensions. 
For expressing them there are generally two
solutions: intensional places or intensional
expressions.  English does a mix; Lojban aims at
doing the second, though even in unchallenged
areas there are exceptions. For a logical
language to use places would seem to require that
those places be overtly marked to prevent by
formal interdiction the objectionable inferences
(and to allow unmarking where appropriate). 
Merely learning a list (even if guaranteed
exhaustive) does not seem sufficient.  So, for
Lojban, the suggestion that {djica2} is
intensional is at variance with the program, to
be taken up only as a last resort (it also does
not allow marking cases where the inference goes
through).

But there is the other choice, namely to take
expressions in {djica2} as referring to
intensional objects.  One doesn?t want to do this
across the board, since that would again preclude
a marking for the generalizable cases and, more
to the point, some expression pretty much have to
refer to particular, identifiable things (even
though occasionally nonexistent ones) where the
inference usually goes through with only the
existence problem (for which solutions are
available).  That is, most kinds of sumti refer
unambiguously to extensional objects (or
abstracta considered extensionally). In fact, the
severe problems arise only with {lo}, which,
because of its generality, is particularly liable
to the sort of fallacy sketched above.  Thus,
much of the problem presented is solved if {lo
broda} is taken to refer to an intensional
entity, say the broda species or brodahood or
brodaness (what happens in these case differs
somewhat but the overall pattern is pretty much
the same; in what follows we will stick to
brodaness, the property of being a broda). That
is, {mi djica lo broda} describes a relation
between me and brodaness, a relation involving a
tension that would be resolved just in case I
come into some (unspecified, but covered by
having) relation with something that has
brodahood, su?o broda. 

Of course, {lo broda} does not refer to brodahood
only in {djica2}(and other intensional places, as
it were), for that would recreate the problem of
unmarked opaque places, which we are trying to
avoid.  Thus, {lo broda} refers to brodahood in
all places where there is no mark that it does
not (assuming we want to have some such places). 
In particular, since it is brodahood in {djica2}
it must be brodahood in all places of all
predicates (else we would have unmarked places). 
On the other hand, for example, {lo broda} as
part of a more complex description: {Q lo broda}
can be given an extensional reading, if that is
desired (in any case the whole expression is
extensional).

Now ordinarily, we say that {[sumti] brode} is
true just in case the referent(s) (in the
evaluating world) of  [sumti] is/are in the set
of things assigned the predicate {brode}, that
is, have the property brodeness in the evaluating
world.  This will not work for the intended
purpose of {lo broda cu brode} ? to say that
brodas have the property -- however, since
generally brodaness ? the referent of {lo broda}
-- will not have the property brodeness, even if
all the brodas do (or may have it even when all
the brodas lack it).  So, for xorlo to work, we
need a different rule the truth of {lo broda cu
brode}.  Since we want this to sometimes be true
even when there are no brodas, this new rule
cannot appeal directly to ?things which have
brodaness? or the like.  It must rather be
written in terms of the relation between
brodaness and brodeness directly, that there is a
semantic or conceptual overlap.  Now this
overlap, to be effective in the way intended can
come about in either of two ways: by conceptual
inclusion (as in {lo pavyseljirna cu
pavyseljirna} and perhaps {lo pavyseljirna cu
blabi}) or by factual overlap (as in effect
happens in the usual way of doing way of
evaluating truth things that fall under one
property fall also under the other).

Having introduced this intensional definition of
truth for {lo} expressions, we need either to
find a way to apply it to all other sumti
expressions or to recognize that there are two
radically different definitions of truth involved
here, where there was only one with old {lo}.  It
seems clear that we cannot make the intensional
definition work with many sumti expressions ? or
can do so only with the introduction of
considerable ad hoc complexity.  Variable by
their nature do not fall under some concept to be
used.  Neither do names (unless you have ?named
so-and-so? as a concept, which seems to be
straining the notion of ?concept? a bit).  And
{le} expressions are specified exactly by their
referents, not by any concept (unless again ?is
called such-and-such? is a concept and even that
has content only by pointing to the intended
individuals).  So, it seems we must recognize
that we have a more complicated and doubled
conceptual apparatus with xorlo.  Of course, this
makes no practical difference in using the
language, only in theory; so, if it brings about
some simplification in use, it is probably
acceptable.  

As noted earlier, one change that is achieved is
only a theoretical advance: the various things
that can be said about nonexistents work as well
in prelo as in xorlo and, at least in some cases,
the same hidden devices are needed: elided modals
or the like.  As for the intensional cases, we
still need {tu?a} for those desires that are
referred to by other expressions than {lo}s: {mi
djica le mikce} or {mi djica la djinis} or even
{mi djica da} all immediately have ? as they do
in prelo ? the reading equivalent to the fronted
form: {le mikce zo?u mi djica my}, {la djinis
zo?u mi djica dy}, {da zo?u mi djica da}, even
when this is not meant (Jeanie may be only in my
dreams as may be the doctor that I want and I can
obviously want something without there being
something I want).  And, lacking {tu?a} with {lo}
we are deprived of the possibility of quantifying
out that is available for other sumti: I cannot
say directly that the thing I want is something
recognizable even separate from my wants. {mi
djica lo broda} = {lo broda zo?u mi djica by} in
prelo but not in xorlo, since the special reading
of application in terms of property overlap
applies only to {lo} expressions and {by} is not
one, but rather is merely coreferential with one
and so has me wanting a property.  Since, this
problem will arise with every anaphora of a {lo}
expression} we can expand our rule of
interpretation to cover such anaphora as well,
although this requires that we always know what
sort of an expression is being anaphorized
(perhaps, to keep this all formally correct, we
should require different anaphora for {lo}
expressions so we can always tell).  In a similar
way, we need special variables for generalization
of {lo} expressions.  Otherwise the
generalization from {lo pavyseljirna cu
pavyseljirna} would be {da pavyseljirna} which
says there are unicorns as things, not just about
the overlap of properties.  This is all to
complicate the language and either put strain on
the cmavo space or complicate the structure of
pronouns and variables.  Or, of course, we could
ignore these problems and regularly use
expressions that are ambiguous at a fundamental
logical (and ontological) level.

So far, I have seen no concrete suggestions about
how either to deal with these problems or to
circumvent them.  On the whole then, I think it
would make sense to do away with xorlo and return
to prelo.  The one change that this makes at a
practical level (aside from not needing the
duplication of pronouns and variables) is the use
of {tu?a} in all cases except those where the
existence of a particular object is stressed and
this was already a part of Lojban.  And the
theory is greatly simplified, with all sumti
functioning in the same way ? the way we
naturally think they function anyhow.