When we discussed this at great length a dozen years ago, th= e arguments mustered -- which I can't reconstruct from memory -- led to= the clear conclusion that {ro} (given its undisputed properties) means &qu= ot;however many there are", i.e. a cardinal number whose value can be = zero, but this did not mean that there should not be another word meaning a= n existential import universal quantifier.

So there are two or three different and separate arguments h= ere, all confounding each other:
1. What does ro mean, and does it have EI? (A question settled a dozen year= s ago.)
2. Should there be a non-EI universal quantifier?
3. Should there be an EI universal quantifier? This is the question John se= ems to be addressing.

4. In any bpfk revision of the CLL specification, which mean= ing should be paired with the phonological form /ro/?

On 9 Nov 2014 00:46, "John Cowan" <= cowan@mercury.ccil.org> wr= ote:

Ozymandias Hayn= es scripsit:

> The way that "All unicorns are white." is represented in pre= dicate logic is
> with the formula $$ \forall x : [ U(x) \rightarrow W(x) ] $$.

This is precisely the point that pc (and following him, I) disputed.
This first-order predicate logic (FOPL) translation is *not* semantically identical to the natural-language (NL) claim (which the Aristotelian
formulation follows), precisely because the FOPL version does not have
existential import (EI), whereas the NL version does.=C2=A0 If you ask some= one
"Do all unicorns fly?"=C2=A0 they do not normally reply "Yes= "; they either say
"No" or reject the question metalinguistically.

Pc and I hold that there is good reason to provide Lojban expressions
of both the FOPL and the NL versions of the claim, since they are
semantically distinct.=C2=A0 This can be easily done by saying that "r= o da"
without a following "poi" (unrestricted quantification) takes the= FOPL
interpretation, whereas "ro da poi broda" (restricted quantificat= ion)
takes the NL interpretation.=C2=A0 This does not in any way restrict FOPL,<= br> since FOPL has *only* unrestricted variables, not restricted ones.=C2=A0 So= it
would be easy to say that "ro" has EI in restricted quantificatio= ns,
and lacks EI in unrestricted ones.

Pc's further insight, however, is that it is essentially harmless to extend "ro" to have EI in all cases.=C2=A0 Given the sentence, &q= uot;ro da zo'u
ganai da broda gi da brode", it is obvious that this does not entail "da broda", since it is under negation, and negated claims can ne= ver
have EI.=C2=A0 However, it is safe to replace "ro da" with "= so'u da", *except*
in the case of an entirely empty universe.=C2=A0 If we are willing to give<= br> up the desire to make vacuous universal claims about empty universes,
we have no trouble taking "ro" to always have EI.

When I first heard this argument, I didn't accept it either.=C2=A0 It t= ook pc
about an hour of intensive two-way conversation to convince me that this view is both self-consistent and consistent with FOPL-as-we-know-it (apart<= br> from empty universes), so I don't expect you to swallow it as a result = of
a brief email.=C2=A0 Nevertheless, however counterintuitive to people who k= now
FOPL, it is I believe sound, and has desirable properties for ordinary
NL statements, while in no way inhibiting properly formulated FOPL Lojban.<= br>
--
John Cowan=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 http://www.ccil.org/~cowan=C2=A0 =C2=A0 =C2= =A0 =C2=A0 cowan@ccil.org
My confusion is rapidly waxing

> between the dollar signs is LaTeX markup; if you can't read it you= can plug
> it into an online renderer. \forall is the universal quantifier, x is = the
> bound variable, \rightarrow is implication, and U and W are functions<= br> > corresponding to 'x is a unicorn' and 'x is white' res= p.).=C2=A0 As John says,
> one way to translate this into Lojban is "ro da zo'u ganai da= pavyseljirna
> gi da blabi".=C2=A0 This is irrelevant to la mukti's construc= tion, however.=C2=A0 He
> did not use that Lojban sentence in his example, he used one that'= s
> formally equivalent to da with poi.=C2=A0 The negation theorem is stat= ed in its
> full generality in the CLL and not only on sentences of the form above= .
>=C2=A0 Indeed, using that implication form as a definition of "ro = da poi X" is
> precisely what is needed to fit with the negation theorem and with
> predicate logic, and those are precisely the semantics that I am advoc= ating.
>
> It=E2=80=99s easy to see that these sentences are consistent with the = negation
> theorem.=C2=A0 Recall that a logical implication is a function of stat= ements;
> it's truth value depends only on the truth value of the statements= it acts
> on.=C2=A0 An IF (...) THEN (...) statement is defined to be false when= the first
> argument, called the antecedent, is true and the second argument, call= ed
> the consequent, is false.=C2=A0 All other pairs of arguments result in= true.
>
> Under our assumption that nothing satisfies pavyseljirna, "ro da = zo'u ganai
> da pavyseljirna gi da blabi" is true because for every value of d= a, the
> antecedent is false.=C2=A0 Therefore "naku ro da zo'u ganai d= a pavyseljirna gi
> da blabi" is false.=C2=A0 According to the negation theorem "= ;su'o da naku zo'u
> ganai da pavyseljirna gi da blabi" must also be false.=C2=A0 This= says that
> there must an object which falsifies the implication, and as I said in= the
> last paragraph this can only happen when the antecedent is true and th= e
> consequent false.=C2=A0 The antecedent claims that x is a unicorn, so = a true
> antecedent would contradict our assumption about unicorns.=C2=A0 Of co= urse the
> particular functions we chose, unicorns and white, are not important; = all
> statements of this form are consistent with the negation theorem.
>
> So if we wanted to keep the importing semantics, how would negation ha= ve to
> work?=C2=A0 We first rewrite "ro da poi P" in the importing = sense as a formula
> in predicate logic to manipulate it symbolically, then translate it ba= ck
> into Lojban.=C2=A0 This still uses the implication, but includes the a= dditional
> restriction that something must satisfy P.=C2=A0 We therefore represen= t "naku ro
> da poi P zo=E2=80=99u Q" as $$ \neg \forall x \exists y : P(y) \l= and [P(x)
> \rightarrow Q(x)]) $$.=C2=A0 Applying the theorem to the formula, we g= et $$
> \exists x \forall y : \neg (P(y) \land [P(x) \rightarrow Q(x)]) $$ whi= ch is
> equivalent by another elementary theorem to $$ \exists x \forall y : \= neg
> P(y) \lor \neg (P(x) \rightarrow Q(x)) $$ which can be translated back= into
> Lojban as =E2=80=9Cro da su=E2=80=99o de zo=E2=80=99u de P inajanai ga= nai da P gi da Q=E2=80=9D.=C2=A0 Notice in
> particular that there are now two sumti involved.=C2=A0 This is becaus= e in the
> importing sense there are really two different claims being made and e= ach
> use their own variable.=C2=A0 I played with this for about half an hou= r tonight
> and couldn=E2=80=99t find an equivalent form that resulted in more ele= gant Lojban;
> perhaps an importing advocate can do better.
>
> That=E2=80=99s one of four cases; three others are treated similarly, = and then
> negation dragging across unrestricted da operates according to the nor= mal
> rules.=C2=A0 Imagine trying to move naku around in an ordinary sentenc= e under
> these rules!
>
> I don=E2=80=99t know what pc said to John but it is simply not true th= at the
> Aristotelian sense of =E2=80=9CAll P are Q=E2=80=9D is compatible with= predicate logic.=C2=A0 On
> page 54 of Hilbert and Ackermann=E2=80=99s classic _Principles of Math= ematical
> Logic_ appears the following:
>
> =E2=80=9CAccording to Aristotle the sentence =E2=80=98All A is B=E2=80= =99 is valid only when there
> are objects which are A.=C2=A0 Our deviation from Aristotle in this re= spect is
> justified by the mathematical applications of logic, in which the
> Aristotelian interpretation would not be useful.=E2=80=9D
>
> Its possible that there is some confusion over an elementary theorem w= hich
> states $$ \forall x : P(x) $$ implies $$ \exists x : P(x) $$.=C2=A0 If= we look
> closely at that we see that, in John=E2=80=99s words, the quantificati= on there
> corresponds to Lojban=E2=80=99s unrestricted logical variables; restri= cted logical
> variables must first be rewritten as pure formulae, as I did above, be= fore
> applying the theorem.
>
> mi=E2=80=99e az
>
>
> On Sunday, October 19, 2014 10:08:14 AM UTC-7, John Cowan wrote:
> >
> > Alex Burka scripsit:
> >
> > > Ok, so just to clarify what you were correcting, with import= ing {ro}
> > > you would say {ro broda cu brode} and {ro da poi broda cu br= ode} are
> > > the same thing and require {su'o da broda}, while {ro da= ganai broda
> > > gi brode} is different and just requires a non-empty univers= e?
> >
> > Right.=C2=A0 The difference is between restricted and unrestricte= d
> > quantification.
> >
> > --
> > John Cowan=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 http://www.ccil.org/~cowan=C2=A0 = =C2=A0 =C2=A0 =C2=A0 co...@ccil.org > > <javascript:>
> > Lope de Vega: "It wonders me I can speak at all.=C2=A0 Some = caitiff rogue
> > did rudely yerk me on the knob, wherefrom my wits yet wander.&quo= t;
> > An Englishman: "Ay, belike a filchman to the nab'll leav= e you
> > crank for a spell." --Harry Turtledove, Ruled Britannia
> >

--
John Cowan=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 http://www.ccil.org/~cowan=C2=A0 =C2=A0 =C2= =A0 =C2=A0 cowan@ccil.org
If you have ever wondered if you are in hell, it has been said, then
you are on a well-traveled road of spiritual inquiry.=C2=A0 If you are
absolutely sure you are in hell, however, then you must be on the Cross
Bronx Expressway.=C2=A0 --Alan Feuer, New York Times, 2002-09-20

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