Existential claims, prenexes, and variables

Date: Fri Apr 8 19:29:32 2011 -0700 example-imported fixes. diff --git a/todocbook/16.xml b/todocbook/16.xml index 033c043..7044151 100644 --- a/todocbook/16.xml +++ b/todocbook/16.xml @@ -81,28 +81,24 @@ I see the man/men. that there really is a man; the only thing you can conclude is t= hat there is one thing (or more) that I choose to refer to as a man. You ca= nnot even tell which man is meant for sure without asking me (although comm= unication is served if you already know from the context). attitudinalsand logic logicand attitudinals In addition, the use of attitudinals (see=20 ) often reduces or removes the= ability to make deductions about the bridi to which those attitudinals are= applied. From the fact that I hope George will win the election, you can c= onclude nothing about George's actual victory or defeat.

Existential claims, prenexes, and variables Let us consider, to begin with, a sentence that is not in the di= alogue: - =20 - -something sees me<= secondary>example - - FIXME: TAG SPOT <anchor xml:id=3D"c16e2d1"/> + <indexterm type=3D"example"><primary>something sees me</primary><s= econdary>example</secondary></indexterm> Something sees me. There are two plausible Lojban translations of=20 . The simpler one is: <anchor xml:id=3D"c16e2d2"/>

@@ -142,56 +138,56 @@ de, and=20 di (of selma'o KOhA), glossed in the literal translatio= ns as=20 X,=20 Y, and=20 Z respectively. By analogy to the terminology of symbol= ic logic, these cmavo are called=20 variables. Here is an example of a prenex with two variables: <anchor xml:id=3D"c16e2d4"/> + <indexterm type=3D"example"><primary>somebody loves somebody</prim= ary><secondary>example</secondary></indexterm>

da de zo'u da prami de There-is-an-X there-is-a-Y such that X loves Y. Somebody loves somebody.

=20 =20 -somebody loves somebodyexample =20 logical variableseffect of using multiple different somebodycon= trasted with somebody else In=20 , the literal interpretation= of the two variables=20 da and=20 de as=20 there-is-an-X and=20 there-is-a-Y tells us that there are two things which s= tand in the relationship that one loves the other. It might be the case tha= t the supposed two things are really just a single thing that loves itself;= nothing in the Lojban version of=20 rules out that interpretati= on, which is why the colloquial translation does not say=20 Somebody loves somebody else. The things referred to by= different variables may be different or the same. (We use=20 somebody here rather than=20 something for naturalness; lovers and beloveds are usua= lly persons, though the Lojban does not say so.) logical variables= with multiple appearances in bridi It is perfectly all right for the variables to appear more than once i= n the main bridi: <anchor xml:id=3D"c16e2d5"/> + <indexterm type=3D"example"><primary>somebody loves self</primary>= <secondary>example</secondary></indexterm>

da zo'u da prami da =20 There-is-an-X such that X loves X Somebody loves himself/herself.

=20 =20 -somebody loves selfexample =20 da prami decontrasted with da prami da da prami dacontrasted w= ith da prami de What=20 claims is fundamentally dif= ferent from what=20 claims, because=20 da prami da is not structurally the same = as=20 =20 da prami de. However, <anchor xml:id=3D"c16e2d6"/> @@ -200,68 +196,68 @@ <jbo>de zo'u de prami de</jbo> <gloss>There-is-a-Y such that Y loves Y</gloss> </interlinear-gloss> </example> <para> <indexterm type=3D"general-imported"><primary>logical variables= </primary><secondary>effect of global substitution</secondary></indexterm> = means exactly the same thing as=20 <xref linkend=3D"example-random-id-wBYE"/>; it does not matter which v= ariable is used as long as they are used consistently.</para> <para>It is not necessary for a variable to be a sumti of the main bri= di directly:</para> <example role=3D"interlinear-gloss-example" xml:id=3D"example-random-i= d-ArXX"> <title> <anchor xml:id=3D"c16e2d7"/> + <indexterm type=3D"example"><primary>somebody's dog</primary><seco= ndary>example</secondary></indexterm>

da zo'u le da gerku cu viska mi There-is-an-X such-that the of-X dog sees me Somebody's dog sees me

=20 =20 -somebody's dogexample =20 is perfectly correct even though the=20 da is used only in a possessive construction. (Possessi= ves are explained in=20 .) logical variables= when not in main bridi It is v= ery peculiar, however, even if technically grammatical, for the variable no= t to appear in the main bridi at all: <anchor xml:id=3D"c16e2d8"/> + <indexterm type=3D"example"><primary>Ralph</primary><secondary>exa= mple</secondary></indexterm>

da zo'u la ralf. gerku There is something such that Ralph is a dog. =20

=20 =20 -Ralphex= ample =20 has a variable bound in a prenex whose relevance to the claim of the foll= owing bridi is completely unspecified.

Universal claims What happens if we substitute=20 everything for=20 something in=20 ? We get: <anchor xml:id=3D"c16e3d1"/> + <indexterm type=3D"example"><primary>everything sees me</primary><= secondary>example</secondary></indexterm> Everything sees me. universal claims<= /primary>explanation Of course, this exa= mple is false, because there are many things which do not see the speaker. = It is not easy to find simple truthful examples of so-called universal clai= ms (those which are about everything), so bear with us for a while. (Indeed= , some Lojbanists tend to avoid universal claims even in other languages, s= ince they are so rarely true in Lojban.) =20 =20 =20 -everything sees me= example =20 The Lojban translation of=20 is <anchor xml:id=3D"c16e3d2"/>

ro da zo'u da viska mi For-every X : X sees me. @@ -269,28 +265,24 @@

ro da ro everythingexpressing with "ro da" When the variable cmavo=20 da is preceded by=20 ro, the combination means=20 For every X rather than=20 There is an X. Superficially, these English formulation= s look totally unrelated:=20 will bring them withi= n a common viewpoint. For the moment, accept the use of=20 ro da for=20 everything on faith. Here is a universal claim with two variables: - =20 - -everything loves everything<= /primary>example - - FIXME: TAG SPOT <anchor xml:id=3D"c16e3d3"/> + <indexterm type=3D"example"><primary>everything loves everything</= primary><secondary>example</secondary></indexterm>

ro da ro de zo'u da prami de For-every X, for-every Y : X loves Y. Everything loves everything.

Again, X and Y can represent the same thing, so=20 does not mean=20 Everything loves everything else. Furthermore, because = the claim is universal, it is about every thing, not merely every person, s= o we cannot use=20 @@ -299,42 +291,43 @@ universalmixed claim with existential existentialmixed= claim with universal mixed claimdefinition Note that=20 ro appears before both=20 da and=20 de. If=20 ro is omitted before either variable, we get a mixed cl= aim, partly existential like those of=20 =20 , partly universal. <anchor xml:id=3D"c16e3d4"/> + <indexterm type=3D"example"><primary>everything sees something</pr= imary><secondary>example</secondary></indexterm> =20

ro da de zo'u da viska de For-every X, there-is-a-Y : X sees Y. Everything sees something.

<anchor xml:id=3D"c16e3d5"/> + <indexterm type=3D"example"><primary>something sees everything</pr= imary><secondary>example</secondary></indexterm>

da ro de zo'u da viska de There-is-an-X such-that-for-every-Y : X sees Y. Something sees everything.

=20 =20 -something sees everythingexample =20 - everything sees something<= /primary>example logical variableseffect of ord= er in prenex=20 + logical variableseffect of order in prenex=20 and=20 mean completely different t= hings.=20 says that for everything, t= here is something which it sees, not necessarily the same thing seen for ev= ery seer.=20 , on the other hand, says th= at there is a particular thing which can see everything that there is (incl= uding itself). Both of these are fairly silly, but they are different kinds= of silliness. =20 There are various possible translations of universal claims in E= nglish: sometimes we use=20 =20 anybody/anything rather than=20 everybody/everything. Often it makes no difference whic= h of these is used: when it does make a difference, it is a rather subtle o= ne which is explained in=20 . @@ -388,32 +381,29 @@ da poi prenu translates as=20 someone. (The difference between=20 someone and=20 somebody is a matter of English style, with no real cou= nterpart in Lojban.) If=20 is true, then=20 must be true, but not neces= sarily vice versa. universal claims<= /primary>restricting relative clausesuse in res= tricting universal claims Universal claims benefit = even more from the existence of relative clauses. Consider <anchor xml:id=3D"c16e4d3"/> + <indexterm type=3D"example"><primary>everything breathes</primary>= <secondary>example</secondary></indexterm>

ro da zo'u da vasxu For-every X : X breathes Everything breathes

- =20 - -everything breathesexample - - and + and <anchor xml:id=3D"c16e4d4"/>

ro da poi gerku zo'u da vasxu For-every X which is-a-dog : X breathes. Every dog breathes. =20 Each dog breathes. @@ -494,32 +484,33 @@ <anchor xml:id=3D"c16e5d4"/> Every person is bitten by some dog (or other).

If we tried to omit the prenex and move the=20 ro and the relative clauses into the main bridi, we wou= ld get: <anchor xml:id=3D"c16e5d5"/> + <indexterm type=3D"example"><primary>dog bites</primary><secondary= >example</secondary></indexterm> + <indexterm type=3D"example"><primary>Fido</primary><secondary>exam= ple</secondary></indexterm>=20

de poi gerku cu batci ro da poi prenu There-is-a-Y which is-a-dog which-bites every X which is-a-= person Some dog bites everyone.

=20 =20 -dog bitesexample =20 - Fidoe= xample which has the structure of=20 + which has the structure of=20 : it says that there is a do= g (call him Fido) who bites, has bitten, or will bite every person that has= ever existed! We can safely rule out Fido's existence, and say that=20 is false, while agreeing to= =20 . universal claims<= /primary>dangers of using Even so,=20 is most probably false, sin= ce some people never experience dogbite. Examples like 5.3 and 4.4 (might t= here be some dogs which never have breathed, because they died as embryos?)= indicate the danger in Lojban of universal claims even when restricted. In= English we are prone to say that=20 =20 =20 =20 Everyone says or that=20 Everybody does or that=20 @@ -546,32 +537,29 @@ logician's English). This implies that a sentence with = both a universal and an existential variable can't be freely converted with= =20 =20 =20 se; one must be careful to preserve the order of the va= riables. poi= ro poi<= secondary>dropping from multiple appearances on logical variables ro<= secondary>dropping from multiple appearances on logical variables logical varia= bleswith poiin multiple appearan= ces l= ogical variableswith roin multip= le appearances If a variable occurs more than once, = then any=20 ro or=20 poi decorations are moved only to the first occurrence = of the variable when the prenex is dropped. For example, <anchor xml:id=3D"c16e5d7"/> + <indexterm type=3D"example"><primary>weapon against self</primary>= <secondary>example</secondary></indexterm>

di poi prenu zo'u ti xarci di di There-is-a-Z which is-a-person : this-thing is-a-weapon for= -use-against-Z by-Z This is a weapon for someone to use against himself/herse= lf.

- =20 - -weapon against selfexample - - (in which=20 + (in which=20 di is used rather than=20 da just for variety) loses its prenex as follows: <anchor xml:id=3D"c16e5d8"/> ti xarci di poi prenu ku'o di This-thing is-a-weapon-for-use-against some-Z which is-a-pe= rson by-Z. @@ -590,26 +578,26 @@ =20 re prenu means=20 two persons. In fact, unadorned=20 da is also taken to have an implicit number in front of= it, namely=20 su'o, which means=20 at least one. Why is this? Consider=20 again, this time with an ex= plicit=20 su'o: su'o =20 =20 -something sees me<= secondary>example =20 somethingexpressing using "su'o" FIXME: TAG SP= OT <anchor xml:id=3D"c16e6d1"/> + <indexterm type=3D"example"><primary>something sees me</primary><s= econdary>example</secondary></indexterm>

su'o da zo'u da viska mi For-at-least-one X : X sees me. Something sees me.

From this version of=20 , we understand the speaker'= s claim to be that of all the things that there are, at least one of them s= ees him or her. The corresponding universal claim,=20 , says that of all the thing= s that exist, every one of them can see the speaker. @@ -665,21 +653,20 @@ su'ore da viska mi At-least-two Xes see me. respectively, subject to the rules prescribed in=20 . ro prenu =20 =20 -all personsexample =20 restricted variablecompared with indefinite description = indefinite descriptioncompared with restricted variable <= indexterm type=3D"general-imported">indefinite descriptiondefinition Now we can explain the cons= tructions=20 ro prenu for=20 =20 all persons and=20 =20 re prenu for=20 two persons which were casually mentioned at the beginn= ing of this Section. In fact,=20 ro prenu, a so-called=20 =20 @@ -725,31 +712,32 @@

Grouping of quantifiers distribution of q= uantified sumti indefinite sumtimultiple in sentence Let us consider a sentence containing two quantifier expre= ssions neither of which is=20 ro or=20 su'o (remembering that=20 su'o is implicit where no explicit quantifier is given)= : <anchor xml:id=3D"c16e7d1"/> + <indexterm type=3D"example"><primary>dogs bite</primary><secondary= >example</secondary></indexterm> + <indexterm type=3D"example"><primary>three dogs bite two men</prim= ary><secondary>example</secondary></indexterm> =20

ci gerku cu batci re nanmu Three dogs bite two men.

=20 =20 -dogs biteexample =20 - three dogs bite two menexample multiple indefinite sumtimeaning= ind= efinite sumtimeaning when multiple in sentence The question raised by=20 + multiple indefinite su= mtimeaning indefinite sumtimeaning wh= en multiple in sentence The question raised by=20 is, does each of the dogs b= ite the same two men, or is it possible that there are two different men pe= r dog, for six men altogether? If the former interpretation is taken, the n= umber of men involved is fixed at two; but if the latter, then the speaker = has to be taken as saying that there might be any number of men between two= and six inclusive. Let us transform=20 step by step as we did with= =20 : <anchor xml:id=3D"c16e7d2"/>

ci da poi gerku cu batci re de poi nanmu Three Xes which are-dogs bite two Ys which are-men. @@ -821,25 +809,27 @@ [All of] the three dogs bite [all of] the two men.

means that each of the dogs specified bites each of the men spec= ified, for six acts of biting altogether. However, if there is an explicit = quantifier before=20 le other than=20 ro, the problems of this section reappear.

The problem of=20 <quote>any</quote> - Consider the English sentence - anyone who goeswalksexample anyas= a translation problem FIXME: TAG SPOT + Consider the English sentence + anyas a translation problem=20 + <anchor xml:id=3D"c16e8d1"/> + <indexterm type=3D"example"><primary>anyone who goes</primary><sec= ondary>walks</secondary><tertiary>example</tertiary></indexterm>=20 Anyone who goes to the store, walks across the field. Using the facilities already discussed, a plausible translation = might be <anchor xml:id=3D"c16e8d2"/>

ro da poi klama le zarci cu cadzu le foldi @@ -1004,69 +994,59 @@ naku zo'u la djan. klama It is not the case that: John comes. It is false that: John comes.

negation in prene= xeffects of position However,= =20 naku can appear at other points in the pr= enex as well. Compare <anchor xml:id=3D"c16e9d3"/> + <indexterm type=3D"example"><primary>nothing sits</primary><second= ary>example</secondary></indexterm>

naku de zo'u de zutse It is not the case that: for some Y, Y sits. It is false that: for at least one Y, Y sits. It is false that something sits. Nothing sits.

- =20 - -nothing sitsexample - - with + with <anchor xml:id=3D"c16e9d4"/>

su'ode naku zo'u de zutse For at least one Y, it is false that: Y sits. There is something that doesn't sit.

The relative position of negation and quantification terms withi= n a prenex has a drastic effect on meaning. Starting without a negation, we= can have: <anchor xml:id=3D"c16e9d5"/> + <indexterm type=3D"example"><primary>everybody loves something</pr= imary><secondary>example</secondary></indexterm>

roda su'ode zo'u da prami de For every X, there is a Y, such that X loves Y. =20 Everybody loves at least one thing (each, not necessarily= the same thing).

- =20 - -everybody loves somethingexample - - or: - =20 - -something is loved by everyb= odyexample - - FIXME: TAG SPOT + or: <anchor xml:id=3D"c16e9d6"/> + <indexterm type=3D"example"><primary>something is loved by everybo= dy</primary><secondary>example</secondary></indexterm>

su'ode roda zo'u da prami de There is a Y, such that for each X, X loves Y. There is at least one particular thing that is loved by e= verybody.

The simplest form of bridi negation to interpret is one where th= e negation term is at the beginning of the prenex: @@ -1349,28 +1329,24 @@ <para> <indexterm type=3D"general-imported"><primary>prenex manipu= lation</primary><secondary>exporting na from left of prenex</secondary></in= dexterm> <indexterm type=3D"general-imported"><primary>prenex manipulation= </primary><secondary>importing na from selbri</secondary></indexterm> A=20 <valsi>na</valsi> before the selbri is always transformed into a= =20 <oldjbophrase>naku</oldjbophrase> at the left-hand end of the pren= ex, and vice versa.</para> </listitem> </itemizedlist> </section> <section xml:id=3D"section-na-outside-prenex"> <title>Using=20 <oldjbophrase>naku</oldjbophrase> outside a prenex Let us consider the English sentence - =20 - -some do not go to schoolexample - - FIXME: TAG SPOT <anchor xml:id=3D"c16e11d1"/> + <indexterm type=3D"example"><primary>some do not go to school</pri= mary><secondary>example</secondary></indexterm>

Some children do not go to school.

We cannot express this directly with=20 na; the apparently obvious translation <anchor xml:id=3D"c16e11d2"/> @@ -1631,29 +1607,29 @@ <anchor xml:id=3D"c16e12d1"/>

la djan. na klama ga la paris. gi la rom. John [false] goes-to either Paris or Rome.

<anchor xml:id=3D"c16e12d2"/> + <indexterm type=3D"example"><primary>go to Paris or Rome</primary>= <secondary>example</secondary></indexterm>

naku zo'u la djan. klama ga la paris. gi la rom. It-is-false that: John goes-to either Paris or Rome.

=20 =20 -go to Paris or Romeexample =20 DeMorgan's Lawand logically connected sentences logically connected sentencesand DeMorgan's Law negatormovement from br= idi to sumti It is not an acceptable logical manipu= lation to move a negator from the bridi level to one or more sumti. However= ,=20 and related examples are no= t sumti negations, but rather expand to form two logically connected senten= ces. In such a situation, DeMorgan's Law must be applied. For instance,=20 =20 expands to: <anchor xml:id=3D"c16e12d3"/>

@@ -1780,31 +1756,31 @@ =20 =20 bu'a,=20 bu'e and=20 =20 bu'i with F, G, and H respectively. =20 <anchor xml:id=3D"c16e13d1"/> + <indexterm type=3D"example"><primary>some relationship</primary><s= econdary>example</secondary></indexterm>

su'o bu'a zo'u la djim. bu'a la djan. For-at-least-one relationship-F : Jim stands-in-relationshi= p-F to-John. There's some relationship between Jim and John. =20

=20 =20 -some relationship<= secondary>example =20 selbri variables= prenex form as indefinite description Th= e translations of=20 show how unidiomatic selbri= variables are in English; Lojban sentences like=20 =20 need to be totally reworded= in English. Furthermore, when a selbri variable appears in the prenex, it = is necessary to precede it with a quantifier such as=20 su'o; it is ungrammatical to just say=20 bu'a zo'u. This rule is necessary because= only sumti can appear in the prenex, and=20 su'o bu'a is technically a sumti – = in fact, it is an indefinite description like=20 =20 =20 @@ -1836,25 +1812,25 @@ and=20 are almost certainly true= : Jim and John might be brothers, or might live in the same city, or at lea= st have the property of being jointly human.=20 =20 is palpably false, however;= if Jim and John were related by every possible relationship, then they wou= ld have to be both brothers and father-and-son, which is impossible. =20

A few notes on variables quantifieron previously quantified variable A v= ariable may have a quantifier placed in front of it even though it has alre= ady been quantified explicitly or implicitly by a previous appearance, as i= n: - three cats white<= /primary>and two bigexample FIXME: TAG SPOT <anchor xml:id=3D"c16e14d1"/> - + three cats whiteand two bigexample=20 + ci da poi mlatu cu blabi .ije re da cu barda Three Xs which-are cats are white, and two Xs are big. What does=20 mean? The appearance of=20 ci da quantifies=20 da as referring to three things, which are restricted b= y the relative clause to be cats. When=20 re da appears later, it refers to two of = those three things – there is no saying which ones. Further uses of= =20 commit 5cf841c2b194d095e8876ed0d8fe8c7c419a085f Author: Robin Lee Powell Date: Wed Mar 30 02:12:49 2011 -0700 example-imported fixed in c11 diff --git a/todocbook/11.xml b/todocbook/11.xml index 9136533..dac0411 100644 --- a/todocbook/11.xml +++ b/todocbook/11.xml @@ -34,31 +34,29 @@ (Technically,=20 kei is never necessary, because the elidable terminator= =20 vau that closes every bridi can substitute for it; howe= ver,=20 kei is specific to abstractions, and using it is almost= always clearer.) tanruand abstractions abstractionsgrammatical uses The grammatical uses of an abstraction selbri are exac= tly the same as those of a simple brivla. In particular, abstraction selbri= may be used as observatives, as in=20 =20 , or used in tanru: <anchor xml:id=3D"c11e1d3"/> + <indexterm type=3D"example"><primary>want to be a soldier</primary= ><secondary>example</secondary></indexterm>

la djan. cu nu sonci kei djica John is-an-(event-of being-a-soldier) type-of desirer. John wants to be a soldier.

=20 - -want to be a soldierexample - descriptionsand abstractions Abstraction selbri may also= be used in descriptions, preceded by=20 le (or any other member of selma'o LE): <anchor xml:id=3D"c11e1d4"/> la djan. cu djica le nu sonci [kei] John desires the event-of being-a-soldier. @@ -163,36 +161,30 @@ le nu mi vasxu the event-of my breathing is an event which lasts for the whole of my life (under normal c= ircumstances). On the other hand, =20 <anchor xml:id=3D"c11e2d8"/> + <indexterm type=3D"example"><primary>kissing Jane</primary><second= ary>example</secondary></indexterm>

le nu la djan. cinba la djein. the event-of John kissing Jane - =20

=20 - -kissing Janeexample - normal circumstances is relatively brief by comparison (again, under normal cir= cumstances). - =20 - =20 abstractionssumti ellipsis in We can see from= =20 - =20 through=20 that ellipsis of sumti is v= alid in the bridi of abstraction selbri, just as in the main bridi of a sen= tence. Any sumti may be ellipsized if the listener will be able to figure o= ut from context what the proper value of it is, or else to recognize that t= he proper value is unimportant. It is extremely common for=20 =20 nu abstractions in descriptions to have the x1 place el= lipsized: <anchor xml:id=3D"c11e2d9"/>

mi nelci le nu limna @@ -231,32 +223,29 @@ which in this context means My swimming happens often. Event descriptions with=20 le nu are commonly used to fill the=20 under conditions... places, among others, of gismu and = lujvo place structures: <anchor xml:id=3D"c11e2d12"/> + <indexterm type=3D"example"><primary>under conditions</primary><se= condary>example</secondary></indexterm>

la lojban. cu frili mi le nu mi tadni [kei] Lojban is-easy for-me under-conditions-the event-of I study= Lojban is easy for me when I study.

- =20 - -under conditionsexample - - (The=20 + (The=20 when of the English would also be appropriate for a con= struction involving a Lojban tense, but the Lojban sentence says more than = that the studying is concurrent with the ease.) nuplace structure eventsplace structure The place structure of a=20 nu abstraction selbri is simply: x1 is an event of (the bridi)

Types of event abstractions =20 @@ -296,53 +285,47 @@ mu'e achievement ab= stractionsdefinition point-event abstractionsdefinition abstractionsachievement abstractionspoint-event triumph point-event abstractor An eve= nt considered as a point in time is called a=20 point-event, or sometimes an=20 achievement. (This latter word should be divorced, in t= his context, from all connotations of success or triumph.) A point-event ca= n be extended in duration, but it is still a point-event if it is thought o= f as unitary, having no internal structure. The abstractor=20 =20 mu'e means=20 =20 point-event-of: <anchor xml:id=3D"c11e3d1"/> + <indexterm type=3D"example"><primary>killing Jim</primary><seconda= ry>example</secondary></indexterm>

le mu'e la djan. catra la djim. cu zekri - =20 The point-event-of (John kills Jim) is-a-crime. John's killing Jim (considered as a point in time) is a c= rime. - =20

pu'u =20 - -killing Jimexample - abstractionsprocess process abstractionsdefinition<= /indexterm> process abstract= or kil= ling Jim An event considered as extended in time, and= structured with a beginning, a middle containing one or more stages, and a= n end, is called a=20 process. The abstractor=20 pu'u means=20 =20 process-of: <anchor xml:id=3D"c11e3d2"/> + <indexterm type=3D"example"><primary>Roman Empire</primary><second= ary>example</secondary></indexterm>

ca'o le pu'u le latmo balje'a cu porpi kei so'i je'atru cu se= lcatra =20 [continuitive] the process-of( the Latin great-state breaki= ng-up ) many state-rulers were-killed During the fall of the Roman Empire, many Emperors were k= illed.

zu'o =20 - -Roman Empireexample - abstractionsactivity activity abstractionsdefinition activity abstr= actor = Roman Empire An event considered as extended in time = and cyclic or repetitive is called an=20 activity. The abstractor=20 zu'o means=20 =20 activity-of: <anchor xml:id=3D"c11e3d3"/>

@@ -353,33 +336,29 @@

za'i abstractionsstate state abstractionsdefinition state ab= stractor An event considered as something that is eit= her happening or not happening, with sharp boundaries, is called a=20 state. The abstractor=20 za'i means=20 =20 state-of: <anchor xml:id=3D"c11e3d4"/> + <indexterm type=3D"example"><primary>being alive</primary><seconda= ry>example</secondary></indexterm>

le za'i mi jmive cu ckape do - =20 The state-of (I am-alive) is-dangerous-to you. My being alive is dangerous to you. - =20

=20 - -being aliveexample - event typesdescribed The abstractors in=20 through=20 could all have been replace= d by=20 nu, with some loss of precision. Note that Lojban allow= s every sort of event to be viewed in any of these four ways: state eventdescribed the=20 state of running begins when the runner starts and = ends when the runner stops; @@ -470,33 +449,30 @@ nu selbri may correctly be predicated) are only moderat= ely=20 abstract. They are still closely tied to happenings in = space and time. Properties, however, are much more ethereal. What is=20 the property of being blue, or=20 the property of being a go-er? They are what logicians = call=20 intensions. If John has a heart, then=20 =20 the property of having a heart is an abstract object wh= ich, when applied to John, is true. In fact, <anchor xml:id=3D"c11e4d1"/> + <indexterm type=3D"example"><primary>has a heart</primary><seconda= ry>example</secondary></indexterm>

la djan. cu se risna zo'e John has-as-heart something-unspecified. John has a heart. =20

- =20 - -has a heartexample - - has the same truth conditions as + has the same truth conditions as <anchor xml:id=3D"c11e4d2"/>

la djan. cu ckaji le ka se risna [zo'e] [kei] John has-the-property the property-of having-as-heart somet= hing. John has the property of having a heart.

@@ -537,70 +513,64 @@ beachexample sunburnexample It= would be suitable to use=20 and=20 to someone who has returned= from the beach with a sunburn. =20 =20 property abstract= ionsspecifying determining place by sumti ellipsis propert= y abstractionssumti ellipsis in There are several different properties that can be extracted from a bridi= , depending on which place of the bridi is=20 understood as being specified externally. Thus: <anchor xml:id=3D"c11e4d5"/> + <indexterm type=3D"example"><primary>property of loving</primary><= secondary>example</secondary></indexterm>

ka mi prami [zo'e] [kei] a-property-of me loving something-unspecified

- =20 - -property of loving= example - - is quite different from + is quite different from <anchor xml:id=3D"c11e4d6"/>

ka [zo'e] prami mi [kei] a-property-of something-unspecified loving me

In particular, sentences like=20 and=20 are quite different in mean= ing: <anchor xml:id=3D"c11e4d7"/> + <indexterm type=3D"example"><primary>love more</primary><secondary= >example</secondary></indexterm>

la djan. cu zmadu la djordj. le ka mi prami John exceeds George in-the property-of (I love X) I love John more than I love George.

- KOhA selma'o<= /primary> ce= 'u =20 - -love moreexample - - FIXME: TAG SPOT <anchor xml:id=3D"c11e4d8"/> =20 la djan. cu zmadu la djordj. le ka prami mi John exceeds George in the property of (X loves me). John loves me more than George loves me. - property abstract= ionsspecifying determining place with ce'u= The=20 - X used in the glosses of=20 + property abstract= ionsspecifying determining place with ce'u= =20 + KOhA selma'o ce'u =20 + The X used in the glosses of=20 through=20 as a place-holder cannot be= represented only by ellipsis in Lojban, because ellipsis means that there = must be a specific value that can fill the ellipsis, as mentioned in=20 =20 . Instead, the cmavo=20 ce'u of selma'o KOhA is employed when an explicit sumti= is wanted. (The form=20 X will be used in literal translations.) Therefore, an explicit equivalent of=20 , with no ellipsis, is: =20 @@ -620,32 +590,28 @@ la djan. cu zmadu la djordj. le ka ce'u prami mi John exceeds George in-the property-of (X loves me). This convention allows disambiguation of cases like: <anchor xml:id=3D"c11e4d11"/> + <indexterm type=3D"example"><primary>giving the horse</primary><se= condary>example</secondary></indexterm>

le ka [zo'e] dunda le xirma [zo'e] [kei] the property-of giving the horse - =20

- =20 - -giving the horseexample - - into + into <anchor xml:id=3D"c11e4d12"/>

le ka ce'u dunda le xirma [zo'e] [kei] the property-of (X is-a-giver of-the horse to someone-unspe= cified) the property of being a giver of the horse

@@ -781,61 +747,56 @@ jei The=20 blueness of the picture discussed in=20 refers to the measurable amount of= blue pigment (or other source of blueness), not to the degree of truth of = the claim that blueness is present. That abstraction is expressed in Lojban= using=20 jei, which is closely related semantically to=20 ni. In the simplest cases,=20 le jei produces not a number but a truth = value: <anchor xml:id=3D"c11e6d1"/> + <indexterm type=3D"example"><primary>2 + 2</primary><secondary>exa= mple</secondary></indexterm>

le jei li re su'i re du li vo [kei] the truth-value-of the-number 2 + 2 =3D the-number 4 the truth of 2 + 2 being 4

- =20 - -2 + 2ex= ample - - is equivalent to=20 + is equivalent to=20 truth, and <anchor xml:id=3D"c11e6d2"/>

le jei li re su'i re du li mu [kei] the truth-value-of the-number 2 + 2 =3D the-number 5 the truth of 2 + 2 being 5

is equivalent to=20 falsehood. However, not everything in life (or even in Lojban) is simply tr= ue or false. There are shades of gray even in truth value, and=20 jei is Lojban's mechanism for indicating the shade of g= rey intended: <anchor xml:id=3D"c11e6d3"/> + <indexterm type=3D"example"><primary>whether criminal</primary><se= condary>example</secondary></indexterm>

mi ba jdice le jei la djordj. cu zekri gasnu [kei] I [future] decide the truth-value of (George being-a-(crime= doer)). I will decide whether George is a criminal.

=20 - -whether criminalexample - jeipl= ace structure truth-value abstractionsplace structure legal sy= stem=20 does not imply that George = is, or is not, definitely a criminal. Depending on the legal system I am us= ing, I may make some intermediate decision. As a result,=20 =20 jei requires an x2 place analogous to that of=20 ni: jei: x1 is the truth value of (the bridi) under epistemology x2 fuzzy logic and t= ruth-value abstraction abstractionstruth-value and fuzzy log= ic Abstractions using=20 jei are the mechanism for fuzzy logic in Lojban; the=20 @@ -851,28 +812,25 @@ du'u NU predication abstraction =20 abstractionsmental activity abstractionswith knowingbelieving, etc. propositional attitudes There are some selbri which demand an entire predication as a sumti; they= make claims about some predication considered as a whole. Logicians call t= hese the=20 propositional attitudes, and they include (in English) = things like knowing, believing, learning, seeing, hearing, and the like. Co= nsider the English sentence: =20 - =20 - -Frank is a foolexample - - knowe= xample FIXME: TAG SPOT <anchor xml:id=3D"c11e7d1"/> + <indexterm type=3D"example"><primary>Frank is a fool</primary><sec= ondary>example</secondary></indexterm> + <indexterm type=3D"example"><primary>know</primary><secondary>exam= ple</secondary></indexterm>=20 I know that Frank is a fool. =20 How's that in Lojban? Let us try: <anchor xml:id=3D"c11e7d2"/>

@@ -924,37 +882,32 @@ <anchor xml:id=3D"c11e7d5"/>

mi kucli le du'u la frank. cu bebna [kei] I am curious about whether Frank is a fool. =20 =20

- =20 - -Frank is a foolexample - - curiousexample curious and here=20 + curious= and here=20 du'u could probably be replaced by=20 jei without much change in meaning: - FIXME: TAG SPOT <anchor xml:id=3D"c11e7d6"/> + <indexterm type=3D"example"><primary>Frank is a fool</primary><sec= ondary>example</secondary></indexterm> + <indexterm type=3D"example"><primary>curious</primary><secondary>e= xample</secondary></indexterm> =20

mi kucli le jei la frank. cu bebna [kei] I am curious about how true it is that Frank is a fool. - =20 - =20

truth-value abstr= actionsplace structure As a ma= tter of convenience rather than logical necessity,=20 du'u has been given an x2 place, which is a sentence (p= iece of language) expressing the bridi: du'u: x1 is the predication (the bridi), expressed in sentence x2 abstractionsspeakingwriting, etc. se du'u linguistic behavio= r and=20 le se du'u ... is very useful in filling = places of selbri which refer to speaking, writing, or other linguistic beha= vior regarding bridi: =20 @@ -1009,28 +962,25 @@ <anchor xml:id=3D"c11e8d1"/> I know that John went to the store. we can also say things like <anchor xml:id=3D"c11e8d2"/> + <indexterm type=3D"example"><primary>know who</primary><secondary>= example</secondary></indexterm> I know who went to the store. - =20 =20 - -know whoexample - abstractionswith wonderdoubt, etc. = This form is called an=20 indirect question in English because the embedded Engli= sh sentence is a question:=20 =20 Who went to the store? A person who says=20 is claiming to know the ans= wer to this question. Indirect questions can occur with many other English = verbs as well: I can wonder, or doubt, or see, or hear, as well as know who= went to the store. =20 =20 UI selma'o kau<= /primary> To express indirect questions in Lojban, we use a=20 =20 =20 @@ -1176,33 +1126,29 @@ mi nelci le si'o la lojban. cu mulno I enjoy the concept-of Lojban being-complete. su'u abstractionsvague vague abstraction vague abstractor Fin= ally, the abstractor=20 su'u is a vague abstractor, whose meaning must be grasp= ed from context: =20 <anchor xml:id=3D"c11e9d3"/> + <indexterm type=3D"example"><primary>mice</primary><secondary>exam= ple</secondary></indexterm>

ko zgana le su'u le ci smacu cu bajra you [imperative] observe the abstract-nature-of the three m= ice running - =20 See how the three mice run! - =20

=20 - -miceexa= mple - experience abstractionsplace structure All three of thes= e abstractors have an x2 place. An experience requires an experiencer, so t= he place structure of=20 li'i is: =20 li'i: x1 is the experience of (the bridi) as experien= ced by x2 =20 =20 idea abstractions= place structure concept abstractionsp= lace structure Similarly, an idea requires a mind t= o hold it, so the place structure of=20 si'o is: @@ -1231,33 +1177,32 @@ <anchor xml:id=3D"c11e9d5"/>

le su'u mi klama kei be lo fasnu the abstract-nature-of (my going) of-type an event

and there is a book whose title might be rendered in Lojban as:<= /para> =20 - -bicycle raceexample - - Jesus= example intersect <= primary>Jesus FIXME: TAG SPOT <anchor xml:id=3D"c11e9d6"/> + <indexterm type=3D"example"><primary>bicycle race</primary><second= ary>example</secondary></indexterm> + <indexterm type=3D"example"><primary>Jesus</primary><secondary>exa= mple</secondary></indexterm> =20 + <indexterm type=3D"general-imported"><primary>intersect</primary><= /indexterm> + <indexterm type=3D"general-imported"><primary>Jesus</primary></ind= exterm>=20

le su'u la .iecuas. kuctai selcatra kei be lo sa'ordzifa'a ke= nalmatma'e sutyterjvi the abstract-nature-of (Jesus is-an-intersect-shape type-of= -killed-one) of-type a slope-low-direction type-of non-motor-vehicle speed-= competition The Crucifixion of Jesus Considered As A Downhill Bicycle= Race - =20

Note the importance of using=20 kei after=20 su'u when the x2 of=20 su'u (or any other abstractor) is being specified; othe= rwise, the=20 be lo ends up inside the abstraction brid= i. =20

@@ -1295,28 +1240,25 @@ mi troci le nu [mi] gasnu le nu le vorme cu karbi'o I try the event-of (I am-agent-in the event-of (the door op= en-becomes)). which has an abstract description within an abstract description= , quite a complex structure. In English (but not in all other languages), w= e may also say: =20 <anchor xml:id=3D"c11e10d3"/> + <indexterm type=3D"example"><primary>try the door</primary><second= ary>example</secondary></indexterm> I try the door. - =20 LAhE selma'o<= /primary> tu= 'a =20 - -try the doorexample - abstractionssimplification to sumti with tu'a where it i= s understood that what I try is actually not the door itself, but the act o= f opening it. The same simplification can be done in Lojban, but it must be= marked explicitly using a cmavo. The relevant cmavo is=20 tu'a, which belongs to selma'o LAhE. The Lojban equival= ent of=20 is: <anchor xml:id=3D"c11e10d4"/>

mi troci tu'a le vorme I try some-action-to-do-with the door. @@ -1362,32 +1304,29 @@ cafne is an event, and if something that does not seem = to be an event is put there, the Lojbanic listener will attempt to construe= it as one. (Of course, this analysis assumes that=20 djan. is the name of a person, and not th= e name of some event.) JAI selma'o jai= abstr= actionssimplification to sumti with jai abstractionsmaking concrete Logically, a counter= part of some sort is needed to=20 tu'a which transposes an abstract sumti into a concrete= one. This is achieved at the selbri level by the cmavo=20 jai (of selma'o JAI). This cmavo has more than one func= tion, discussed in=20 and=20 ; for the purposes of this chapter, it = operates as a conversion of selbri, similarly to the cmavo of selma'o SE. T= his conversion changes <anchor xml:id=3D"c11e10d7"/> + <indexterm type=3D"example"><primary>cause death</primary><seconda= ry>example</secondary></indexterm>

tu'a mi rinka le nu do morsi something-to-do-with me causes the event-of you are-dead My action causes your death.

- =20 - -cause deathexample - - into + into <anchor xml:id=3D"c11e10d8"/>

mi jai rinka le nu do morsi I am-associated-with causing the event-of your death. I cause your death.

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