lo & da poi

[Gerald Koenig <jlk@NETCOM.COM>]

The discussion about "lo" and "da poi" meaning the same thing goes on and
I want to reformulate some statements I gave last fall saying that "lo"
and "da poi" are not equivalent.

I define that when two terms are syntactically equivalent they can be
substituted for one another in any valid grammatical structure, without
changing the truth value.  Semantic equivalence means two distinct terms
refer to the same thing.

I want to show what happens when "da poi is substituted for "lo" in some
sentences:

(1).   ko'a cu pencu ci {lo} ro gerku
(1'.)  ko'a cu pencu ci {da poi} ro gerku

In (1')  da is defined as something1; it exists.  It is often
symbolized as x. "ci da poi gerku" is, three x's which are dogs:
gerku(x), gerku(x), gerku(x).  This does not assert the existence of
three separate dogs.  To get 3 dogs it is necessary to say; gerku(x),
gerku(y), gerku(z), & x\=y & y\=z & x\=z. That is, this syntactical
view is valid if lojban has more than a superficial connection to
logic.  If lojban is a form of English or algebra then it could as well
mean 3x as in 3x +6y = z, where x,y and z are dogs.

Contrast this incomplete "da poi" version, (1'), with the "lo" version,
(1.):

(1) states that a subset of 3 dogs is selected from a larger set of all
dogs. [Cowan ex. 7.5]. (1) is not syntactically equivalent to (1'). This
is reflected in the machine grammar, which cannot parse (1').  However
the parser will parse:

(1'') ko'a cu pencu ro {da poi cmima lo'i cimei} bo gerku.

So we could say that [ci lo ro] =[ ro da poi cmima lo'i cimei]
syntactically. We can also say that "a subset of 3 dogs selected from
all dogs" is semantically similar to "each x which is a member of a
3-set of dogs"

(2). ko'a pencu ro [lo] ci gerku

The "lo" claims existence in the presence of a universal quantifier
which may not by itself claim existence.  "lo ci" claims that there are
exactly 3 dogs, no more, no less, in the universe of discourse.  I
translate: " she pets exactly 3 dogs."

(2'). ko'a pencu ro [da poi] ci gerku

This claims she pets each something which is 3 dogs- a three dog monster
or maybe a set. This will not parse. So there is no syntactic
equivalence here in the current grammar. The semantics is open to many
interpretations.

(2'') ko'a pencu ro [da poi cmima lo'i cimei] bo gerku

This says that she pets each member of a set of 3 dogs.  There is no
selection from a larger set of all dogs to get this set, it is not
defined as a subset; unlike (1).  This sentence will parse.

Contrasting (2) and (2'') we have to say [lo] = [da poi cmima lo'i
cimei] to get syntactic equivalence.  We certainly cannot simply say
lo=da poi, as in (2').  Semantically too there is a slight difference
between asserting that there are exactly 3 dogs that I touch in the
universe of discourse,(1); and asserting that there exists a 3-set of dogs
and I touch each of the members of the set,(2''). There is a difference
between thinking of individuals and thinking of sets of individuals;
that difference has generated megabytes of debate on this and many
other lists.

lo is a far way from being equivalent to da poi.

To me da poi carries a connotation of "such that" with it. It has an
ontological and existentialist edge to it.

To me lo is a magical little word which means, not as le does, what I
have in mind with all the denyability that carries with it, but rather
it means to me what WE have in mind, what we agree on, what we can
trust as a mutual reality to move forward from to a new position of
understanding. But that is beyond logic, and probably won't ever make
the dictionary, let alone this edition.

djer