From jjllambias@hotmail.com Wed Mar 13 11:45:55 2002 Return-Path: X-Sender: jjllambias@hotmail.com X-Apparently-To: lojban@yahoogroups.com Received: (EGP: unknown); 13 Mar 2002 19:45:55 -0000 Received: (qmail 47675 invoked from network); 13 Mar 2002 19:45:53 -0000 Received: from unknown (216.115.97.167) by m12.grp.snv.yahoo.com with QMQP; 13 Mar 2002 19:45:53 -0000 Received: from unknown (HELO hotmail.com) (216.33.240.132) by mta1.grp.snv.yahoo.com with SMTP; 13 Mar 2002 19:45:53 -0000 Received: from mail pickup service by hotmail.com with Microsoft SMTPSVC; Wed, 13 Mar 2002 11:45:53 -0800 Received: from 200.49.74.2 by lw8fd.law8.hotmail.msn.com with HTTP; Wed, 13 Mar 2002 19:45:53 GMT To: lojban@yahoogroups.com Bcc: Subject: Re: [lojban] More about quantifiers Date: Wed, 13 Mar 2002 19:45:53 Mime-Version: 1.0 Content-Type: text/plain; format=flowed Message-ID: X-OriginalArrivalTime: 13 Mar 2002 19:45:53.0891 (UTC) FILETIME=[AFBEE330:01C1CAC7] From: "Jorge Llambias" X-Originating-IP: [200.49.74.2] X-Yahoo-Group-Post: member; u=6071566 X-Yahoo-Profile: jjllambias2000 la pycyn cusku di'e >If you check other pages, you will find that Helman is not dealing with >restricted quantification as such but using the notation as a stage in the >process of translating English into symbols in ordinatry first-order logic. On the contrary, he specifically defines restricted universal quantification and unrestricted universal quantification, and then gives the following "principle of equivalence": (Ax: Sx) Px =||= Ax (Sx -> Px). (where should be inverted). What's more, in the chapter about existential quantification he also has the equivalence between the restricted and unrestricted forms: (Ex: Sx) Px =||= Ex (Sx & Px) and also the principle of obversion: ¬ (Ax: Sx) Px =||= (Ex: Sx) ~Px which works only if the restricted universal is A-. >Once the block attached to the quantifier is correctly filled in, the whole >can then be correctly moved into the formula in the usual way. But the >"restricted quantifier" (as the regular use of "thing" suggests) is just a >passing phase of translation, not a part of the logic. I'm sorry, I don't understand the difference. I would put the above formulas in Lojban as saying that {ro da poi broda cu brode} is {roda zo'u ganai da broda gi da brode} and that {su'o da poi broda cu brode} is {su'o da zo'u ge da broda gi da brode}. >Alas, I fear that agreeing about As and Is will not yet help us to >agree about {ro} and {su'o} even in ultimate forms ({ro} does always imply >{su'o} and you can work it out, but that is unconvincing somehow to some). Saying "you can work it out" is unconvincing. Maybe if you actually did work it out it would be more convincing, but since in the end it is just a matter of definitions... mu'o mi'e xorxes _________________________________________________________________ MSN Photos is the easiest way to share and print your photos: http://photos.msn.com/support/worldwide.aspx