I find the title of this thread a bit difficult to grok. "Reality oriented
Logic"? As opposed to logic based on nonreality? I am not sure I
understand what the alternative is. Can someone please explain? Sorry if I
missed the obvious. (01)
Duane (02)
On 8/9/07 5:56 AM, "Jon Awbrey" <jawbrey@xxxxxxx> wrote: (03)
> 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/ontologforum/200708/msg00190.html
> Cf: http://ontolog.cim3.net/forum/ontologforum/200708/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 "interoperability"
> that you outlined last time. I'm a little hesitant
> about calling it that just yet, and would prefer
> to call it "intertranslatability" until I know
> more about it.
>
> JS: Consider the following three notations:
>
> JS: 1. The firstorder subset of Peirce's Algebra of Logic of 1885.
>
> JS: 2. The firstorder 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 represent 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
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>
>
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