binxo, the "logic" of Lojban, and terminology (very long)

[lojbab (Bob LeChevalier)]

The following, if long, may be worthwhile even for new people.  I am
attempting to explain some of the logical aspects of Lojban, as well as
clarify some terms that are frequently misused.  My apologies if this
comes out a little dense though.

jimc finally made one thing clear in his latest discussion of binxo
that I didn;t see he was saying before.

>Returning to the head of the discussion, my major objection to the
>(sumti) binxo (sumti) form is that for good reason we discourage (sumti)
>du (sumti) when a predicate form is possible, e.g.
>
>        la banthas. mlatu               la banthas. du lo mlatu
>        Bantha      cats (preferred)    Bantha      is  a cat (deprecated)

If I read what jimc is not quite saying here, he is relating the meaning
of binxo in contrast to "du" as opposed to the contrast with "cenba" and
"galfi" that was our motivation for "binxo".

In short, he sees our "binxo" sentence as a type of identity sentence,
and not as a predication.

If so, he may have a point in that "become" is seen as the future tense
of "to be" in English; however, I am yet not convinced that a change is
needed, other than the one already done:  to take the discussion of "du"
out from the start of the textbook to prevent people from concentrating
on same from the beginning.  Because "binxo" is NOT an identity sentence.

Similar arguments have been raised on "gasnu", however, and its meaning
has been drastically changed/clarified to distinguish it from the
English "do".  We may need to make similar changes to the definition of
"binxo" - for clarity.

The following sticks my logically inexpert neck out, in an attempt to
clarify what I see as the meanings of some of these words, and why
jimc's problem disappears.  I may be off-base, and will therefore be
quite prepared to back off from any point - this is NOT any formal LLG
prescription of the language (unless I'm right) though it summarizes a
lot of intentions.  If there are no logical flaws, I think it is a safe
claim that learning Loglan/Lojban has had a significant effect onmy
thinking, since I would never have gotten this right after nearly
flunking college logic class.  On the other hand, even if I may be a
little off base, I am reasonably sure that I have my terminology
straight, and this may reduce confusion about things jimc and others
have been writing.

"du" IS an identity 'predicate', and its morphology alone flags it as
different from other predicate words.  It claims that the two sumti on
either side are alternate and equivalent designations for the same thing.
Translate it best as the mathematical "=" sign.

(Nora adds that she sees "du", other than in a mathematical context, as
having a somewhat metalinguistic effect.  It equates two labels for the
same thing.  No other words in Lojban, other than the relativizers
"po'u" and "no'u", and the assigners "goi" and "cei", have this
metalinguistic effect.)

In:
> la banthas. du  lo   mlatu                    (1)
> Bantha      =   a    cat (deprecated)

(Bob correcting=> some cat(s)),

we have a legal/grammatical but probably false statement.  "lo mlatu" is
a description that can apply to a cat, or the members of any collection
of cats, in the universe of discourse (possibly including the
non-domesticated species).  I doubt that there exists anyone that would
apply the name "la banthas." to all of these cats.  If the name had been
the Latin name for the cat family, well, maybe ...

"lo" might be referring to a specific cat or set of cats, but it might not.
We can't say, because there is no logically quantified variable.

Let us look at a similar sentence:

  la banthas. du da poi [ke'a] mlatu         (2)

  la banthas. du da        poi       [ke'a]  mlatu
  Bantha      =  something such-that it="da" is-a-cat

(ke'a is the usually omitted-as-understood relative pro-sumti, in this case
 referring back to "da")

I say that this does not mean the same thing as (1) in that "da" is an
existential variable, logically quantified as "some (at least one) x".
In prenex form, (2) is:

da poi [ke'a] mlatu zo'u la banthas. du da         (2a)

da                  poi       [ke'a] mlatu    zo'u      la banthas. du da
There exists some x such-that it="x" is-a-cat such-that Bantha      =  x
(inverted E)

and this statement is probably true, since I presume jimc did not coin
the name at random but actually knows a cat with that name.

There is a 'predication' (as opposed to 'identity') "predicate word"
that is near-equivalent to "du", and that is "mintu" - "x1 is identical
to x2" ("du" while etymologically tied to "dunli" is not really related
due to place structure differences).  There have been some probably
legitimate but inconclusive debates about whether "du" and "mintu" are
the same predicate.  (Nora thinks not.  She feels that "mintu" can be used
more broadly, as in "this plate is the same as that one", when the two are
interchangeable for the intended function.  "du" would not be correct in
translating such a statement, since presumably "this plate" and "that one"
refer to different objects.)

la banthas. mintu da poi [ke'a] mlatu                 (3)

la banthas. mintu           da        poi       [ke'a]  mlatu
Bantha      is-identical-to something such-that it="da" is-a-cat


da poi [ke'a] mlatu zo'u la banthas. mintu da         (3a)

da                  poi       [ke'a] mlatu    zo'u
There exists some x such-that it="x" is-a-cat such-that
(inverted E)
              la banthas. mintu            da
              Bantha      is-identical-to  x

I think that means approximately the same thing as (2), but we have now
expressed a predication rather than an identity.  In symbolic logic, we
might write this as a predicate:

        Ex | M(Bantha, x)

I believe that predicate logic does not write identity sentences as
predicates.  Lojban's predicate grammar requires even an identity
sentence to be phrased as a predication, and as such is a mirror image
of natural languages.

One difference I can see that (may be) true about a predication and not
an identity is tense.  Lojban is tense-optional, but it does have the
concept.

I think it is meaningful to put a tense on "mintu", but not on "du".  (Lojban's
grammar allows both, but I would have trouble interpreting:

?        la djan. ba   du                   le  speni  be la salis. (4)
?        John     will mathematically-equal the spouse of Sally.
                       =

as having any meaning at all, while the following is at least meaningful
to me:

         la djan. ba   mintu           le  speni  be la salis.      (5)
         John     will be-identical-to the spouse of Sally

Assuming the sentence:

         la djan. speni            la salis.                        (6)
         John     is-the-spouse-of Sally.

will some day be true, I would class (5) as true.  Indeed, both may be true
now, since "mintu" says nothing about change.

"binxo" does.  "le pu'u mintu" (the process of [x1] being identical to
[x2]) is a strange concept, hard to think about.  "le pu'u binxo" (the
process of [x1] becoming [x2]) is not.

jimc's claims  the following 3 sentences are equivalent to "binxo":
>        x1 changes                                     (7a)
>        x1 doesn't (pred) before                       (7b)
>        x1 does (pred) afterward                       (7c)

Well, I'm not sure I agree.  Certainly (7a) is involved in "binxo", but
(7b) and (7c) are more like steps on the way to deducing (7a) - we
identify change by relationships that come into being and others that
cease.  We have thus moved from linguistics to epistemology.  So jimc's
"semantic universal" isn't.

I'll qualify this by saying that (7c) presumably is at least momentarily
true at the end of the "binxo" process, though I've known some marriages
that failed to last very long.  But what can we make of:

         la djan. binxo   la. djan.                 (8)
         John     becomes John

This violates (7b), but might be true in Lojban, by analogy with:

le djacu                                             cu binxo le  djacu    (9)
The water (after freezing into ice and then melting) becomes  the water (again).


Turning now to jimc's:
>                   loi  bisli cu likbi'o (likti binxo)          (10)
>                   Some ice      melts   (liquid become)

(I prefer                Ice      melts.
or expanding to

 Some of the mass of all ice      melts.

but this is a side point.)

jimc has recognized that there is an obvious interpretation to "likbi'o"
(from "liquid-becomes") that allowed him to make this lujvo compound.

This word is DIFFERENT from "binxo".  All jimc's and mine and your
desire to deduce its meaning analytically will fail to some extent, when
we start playing at the level of semantics that we are in this
discussion.  Human language just doesn't work that analytically at the
semantic level, and we do not have the goal in Lojban of making a
semantically analytical language.  Perhaps Loglan-sub-n+1 will.

There is no argument in the place structure of "likbi'o" containing a
description of the final state of the process.  It is the metaphorical
aspect of the source tanru that tells us that there is some liquid in
the process, and based on binxo being roughly a "change with result", we
know that the liquid is probably either the thing that changes or the
result.  In the case of "binxo" we the speakers of the language may make
it a convention that "...bi'o" is "becomes lo ..." but we are debating
that type of convention now and until the 5-year baseline ends since
that is NOT part of what I see LLG's charter for the pre-baseline
prescription.

(Of course this one may be sufficiently stable-and-general that we may
note it in the dictionary as a >descriptive< guideline based on prior
usage before the baseline.)

I think the x1 place of binxo is a description of some prior state that
changes into x2, without necessarily any external agent involved.

I think the x1 place of likbi'o is a description of some prior state
that changes into a liquid, without necessarily an external agent
involved.

What you put in that x1 place should not change the meaning of the
predicate word "binxo" or "likbi'o" (I should note that pc does not even
claim this latter - he says that pragmatics overrides logic in
interpreting the semantics of natural language use.)

>In other words, every bridi (with arguments even if not specified by
>words) expresses an event, but only some of them express predications,
>called "claims" by some, "calling it to the listener's attention" by
>others.  Specifically, jufra (main-level sentences) and clauses linked
>with "noi" always call attention.

No.  Every bridi is a predication, with the possible exception of one
with predicate (selbri) "du".  A predication (bridi) is a specification
of a relationship between 1 or more arguments (sumti) which has a truth
value:  it is true if the relationship holds under the conditions of the
sentence and false if it does not, (and is possibly indeterminate).

Main-level bridi-sentences (jufra) usually make claims on the basis of
that truth value.  Some jufra-bridi may not make claims if modified by
certain discursives and attitudinals (these can change whether a claim
is being made, but do not change the truth value of the bridi), or when
embedded in a logical structure.  In a disjunction (XOR) between two
sentences, it is not the case that both sentences are claimed as true.

A description is a part of a sentence, most commonly a sumti, marked
with "le", "lo", "loi", or other "descriptors" in selma'o LE and LA, or
a vocative marked with COI or DOI vocative markers.  By omitting the x1
sumti of a predication, it describes that sumti as something that can
fill that place so as to make the descriptive predication true in the
case of the "lo" series or agreeably identifiable in the case of most
other descriptors and vocatives.  "le", for example, makes no claim
about the descripted thing, while "lo" does (we say "lo" is
'veridical'.)

bridi in relative clauses are 'veridical' as well.  The clause as a
whole makes claims about the relative pronoun that is referenced in the
clause, that it is part of the indicated relation(s).  This MIGHT be
modified if certain attitudinals are present, but there is no usage
history or analysis of what such sentences might mean (in other words,
I'm not going out very far on this limb).

Events, properties, amounts, in the form of NU abstraction clauses, are
just that - abstractions.  Something concrete is not its abstract and
the abstract is not its concretion(s).  This is why I object to jimc's
"... binxo lenu ...".  You can evaluate the truth value of the bridi
within an abstraction; we even have an abstraction cmavo for this: "jei".
But the abstraction itself is a different predicate (a selbri), with its
own sumti (usually only an x1):

x1 is the event/property/truth value/amount/etc. of the predication
(x1a abstraction-selbri x2a ...)

Lojban has no defined semantics of "attention-calling", although there
is a pattern, reflected in the observative construct, that particular
attention is focussed on the beginning of the sentence, with lesser
focus on the end of the sentence, and on any deviations from the
speaker's normal word order.

The following is an exchange between John Cowan (jc) and jimc (unmarked):
>jc> ...
>jc> Therefore your "x1 changes so that event x2 is true" should be rewritten as
>jc> "x1 changes so that property x2 (a one-place predicate) is true of it".
>
>I pretty close to agree.  How about "x1 changes so bridi-tail x2 becomes
>true (was false and is later true) when x1 is replicated as its first
>argument after conversion"?

You've introduced the previously undefined term "bridi-tail".  By your
usage, regarding it as something that is missing an x1 that can be
filled in (whether by replication or whatever), you want the word
"description" as I defined above.  The only propoer way to incorporate a
description into a sumti is with a descriptor, as described above.  An
abstraction operator would turn that description (now merely a bridi
with an elliptically unspecified x1) into something else, only
abstractly related to the original, and the abstraction itself becomes
a selbri, possibly a description, which with a descriptor can become
a sumti.

"bridi-tail" is a non-terminal figment of the grammar, consisting of the
selbri and any and all sumti that come afterwards.  The grammar says
nothing about which sumti is x1 or how many sumti are found either
before or after the selbri, so a bridi-tail may or may not be missing
any sumti, or it may be missing more than one.  A bridi-tail has no
semantics - it doesn't mean anything (unless you decide that it is
a complete expression, in which case it is an observative).

The following, with my mild reformatting, and insertion of "cu" was from
John Cowan, quoted by jimc, with the translation marked as un-correct
("*") by me.

>jc>    lemi ratcu cu binxo           le  du'u                morsi
>jc>   *my   rat      changes-so-that the predication-of (it)-is-dead (is true)
>jc>
>jc> where the x1 place of "morsi" is elliptically the rat.
>jc> Of course, this is not official LLG doctrine.  :-)

A correct translation, for those looking on for the first time, is,
        my   rat      becomes         the predication that ...is-dead


Regardless of the actual translation, the bridi implied by the English
is a relation between:

lemi ratcu         a rat
le du'u morsi      a predication about a dead thing

Rats do not "become" predications, so that if this place structure were
adopted, "become" would be a truly inappropriate keyword.  I daresay
that no natural language includes many sentences relating rats and
predications.  One (to show the INTENDED usage of "du'u") might be:

lemi ratcu cu jinvi le du'u morsi

lemi ratcu cu jinvi       le  du'u                          morsi
My   rat      opines-that the predication (...(unspecified) is-dead) is true

_________
Hope this is neither clear-as-mud nor tinder-for-flaming.  I would like
comments, especially on what is unclear, since this is my first attempt
to cover logical aspects in writing, and I WILL have to talk about these
aspects in the textbook.

lojbab