- From: Duane Nickull <dnickull@adobe.com>
- Date: Thu, 09 Aug 2007 09:52:07 -0700
- To: "[ontolog-forum]" <ontolog-forum@ontolog.cim3.net>, Arisbe <arisbe@stderr.org>, Inquiry <inquiry@stderr.org>, Semantic Web <semantic-web@w3.org>
I find the title of this thread a bit difficult to grok. "Reality oriented Logic"? As opposed to logic based on non-reality? I am not sure I understand what the alternative is. Can someone please explain? Sorry if I missed the obvious. Duane On 8/9/07 5:56 AM, "Jon Awbrey" <jawbrey@att.net> wrote: > 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~~~~~~~~~o > > > _________________________________________________________________ > Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/ > Subscribe/Config: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/ > Unsubscribe: mailto:ontolog-forum-leave@ontolog.cim3.net > Shared Files: http://ontolog.cim3.net/file/ > Community Wiki: http://ontolog.cim3.net/wiki/ > To Post: mailto:ontolog-forum@ontolog.cim3.net > -- ********************************************************************** "Speaking only for myself" Blog - http://technoracle.blogspot.com Community Music - http://www.mix2r.com My Band - http://www.myspace.com/22ndcentury MAX 2007 - http://technoracle.blogspot.com/2007/07/adobe-max-2007.html **********************************************************************
Received on Thursday, 9 August 2007 16:52:52 UTC