From: Jon Awbrey <jawbrey@att.net>

Date: Thu, 09 Aug 2007 08:56:53 -0400

Message-ID: <46BB0F15.A113EB8C@att.net>

To: Arisbe <arisbe@stderr.org>, Inquiry <inquiry@stderr.org>, Ontolog <ontolog-forum@ontolog.cim3.net>, Semantic Web <semantic-web@w3.org>

Date: Thu, 09 Aug 2007 08:56:53 -0400

Message-ID: <46BB0F15.A113EB8C@att.net>

To: Arisbe <arisbe@stderr.org>, Inquiry <inquiry@stderr.org>, Ontolog <ontolog-forum@ontolog.cim3.net>, Semantic Web <semantic-web@w3.org>

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o ROL. Note 3 o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o JA = Jon Awbrey JS = John Sowa Cf: http://ontolog.cim3.net/forum/ontolog-forum/2007-08/msg00190.html Cf: http://ontolog.cim3.net/forum/ontolog-forum/2007-08/msg00194.html CC: Arisbe List, Inquiry List, Ontolog Forum, SemWeb List John, Continuing from where I left off, with current comments unindented. JA: Let's look again at the concept of "inter-operability" that you outlined last time. I'm a little hesitant about calling it that just yet, and would prefer to call it "inter-translatability" until I know more about it. JS: Consider the following three notations: JS: 1. The first-order subset of Peirce's Algebra of Logic of 1885. JS: 2. The first-order subset of Frege's Begriffsschrift of 1879. JS: 3. Any of the three concrete notations in Annex A, B, or C of the Final Draft International Standard of Common Logic of 2007. JA: I am told by people who apparently understand these things that having not just 2 but 3 distinct languages on the Rosetta Stone was crucial to finding the key, but let me first consider a far simpler example of the ilk that I know from practical endeavors. JA: Something that I spent a goodly portion of the (19)80's doing, and in such primitive computing circumstances that I had to write all of the necessary utilities myself, was to translate an articula x_1 of one language, medium, or type L_1 (written x_1 : L_1) into an articula x_2 of another language, medium, or type L_2 (written x_2 : L_2), perform a computation on x_2 : L_2 that would yield an articula y_2 : L_2, then translate y_2 : L_2 back into the corresponding y_1 : L_1. JA: Here is a diagram of the process: x_1 : L_1 ----------> x_2 : L_2 | | | | | | | | V V y_1 : L_1 <---------- y_2 : L_2 JA: The more solid arrows indicate the actual computations. The more dashing arrow, the road not taken, as it were, suggests the virtual computation, in effect exchanging x_1 : L_1 for y_1 : L_1 or transforming x_1 : L_1 into y_1 : L_1. Why do we do this? Why such a roundabout calculation? Well, it's important to note that the reason for this detour is not just some equivalence between languages but based on the existence of complex factors, namely, that L_1 and L_2 are analogous in an abstract logical or mathematical sense while departing from each other in a pertinent class of concrete pragmatic properties. The computational archetype of this particular gambit is probably the trick known as "logarithms", where we convert what was once considered a "hard" computation, namely, multiplication, into a relatively "easy" task, namely, addition. The trick works because there is a homomorphism log : (X,*) -> (Y,+) on suitably bounded subsets X and Y of the real numbers R that enables us to start with a problem presented in the form a*b and to re-present it in the form log(a) + log(b), and all the computations involved in this long way round used to be in former times appreciably easier to carry out than the corresponding multiplication task. As a general observation, then, the reason that we keep a diversity of languages around is not because they are indifferent in all of their characters but because they provide us with different advantages at different times. Breaking here ... Jon Awbrey o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o inquiry e-lab: http://stderr.org/pipermail/inquiry/ ¢iare: http://www.centiare.com/Directory:Jon_Awbrey getwiki: http://www.getwiki.net/-UserTalk:Jon_Awbrey zhongwen wp: http://zh.wikipedia.org/wiki/User:Jon_Awbrey http://www.altheim.com/ceryle/wiki/Wiki.jsp?page=JonAwbrey wp review: http://wikipediareview.com/index.php?showuser=398 o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~oReceived on Thursday, 9 August 2007 12:57:16 UTC

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