From @YaleVM.YCC.YALE.EDU:LOJBAN@CUVMB.BITNET Mon Aug 23 07:45:10 1993 Received: from ELI.CS.YALE.EDU by NEBULA.SYSTEMSZ.CS.YALE.EDU via SMTP; Mon, 23 Aug 1993 12:12:03 -0400 Received: from YALEVM.YCC.YALE.EDU by eli.CS.YALE.EDU via SMTP; Mon, 23 Aug 1993 12:11:57 -0400 Message-Id: <199308231611.AA08341@eli.CS.YALE.EDU> Received: from CUVMB.CC.COLUMBIA.EDU by YaleVM.YCC.Yale.Edu (IBM VM SMTP V2R2) with BSMTP id 6589; Mon, 23 Aug 93 12:10:31 EDT Received: from CUVMB.COLUMBIA.EDU by CUVMB.CC.COLUMBIA.EDU (Mailer R2.07) with BSMTP id 3926; Mon, 23 Aug 93 12:12:13 EDT Date: Mon, 23 Aug 1993 11:45:10 -0400 Reply-To: John Cowan Sender: Lojban list From: John Cowan Subject: Re: TECH: QUERY: quantifier scope & cumki X-To: Lojban List To: Erik Rauch In-Reply-To: <9308231052.AA05179@relay1.UU.NET> from "Colin Fine" at Aug 23, 93 11:41:37 am Status: O X-Status: la kolin. cusku di'e > And asks: > ++++++> > How does one distinguish: > For every x, it is possible that x is .... > It is possible that every x is .... > >++++++++ > > I don't see a problem: > > ro da zo'u cumki fa le nu da broda > > cumki fa le nu ro da zo'u da broda Correct. The rules seem to say that the un-prenexed form cumki fa le nu da broda means the latter, on the assumption that an undeclared logical variable is effectively declared with the smallest possible scope. > Until I noticed your subject I thought you were asking a different > question - not about the predicative 'it is possible' but about > the operators of modal logic - 'it is possible that' and > 'it is necessary that'. Somehow the selbri 'cumki' and > 'nibli' don't seem right for these. Well, they are and they aren't. Loglan, generally speaking, takes a Quinian view of such things. "nibli" is closer to the sentence operator Nec, which in Quine takes a quoted sentence, than to the standard modal operator nec. At least we know that Nec is logically tractable, which is not true of nec -- cf. the well-known paradox: nec 5 < 9 9 = the number of planets nec 5 < the number of planets which is fallacious. Replacing "nec" with "Nec('...')" prevents us from inferring things about the opaque argument, and so such bogosities are Nec ~. :-) -- John Cowan cowan@snark.thyrsus.com ...!uunet!lock60!snark!cowan e'osai ko sarji la lojban.