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Re: [ontolog-forum] Reality Oriented Logic

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>
Message-ID: <C2E09447.5522%dnickull@adobe.com>

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
> 
>  
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Received on Thursday, 9 August 2007 16:52:52 GMT

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