o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o (01)
ROL. Note 2 (02)
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o (03)
JA = Jon Awbrey
JS = John Sowa (04)
Re: Re: http://ontolog.cim3.net/forum/ontologforum/200708/msg00194.html
CC: Arisbe List, Inquiry List, Ontolog Forum, SemWeb List (05)
John, (06)
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. (07)
JS: Consider the following three notations: (08)
JS: 1. The firstorder subset of Peirce's Algebra of Logic of 1885. (09)
JS: 2. The firstorder subset of Frege's Begriffsschrift of 1879. (010)
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. (011)
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. (012)
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. (013)
Here is a diagram of the process: (014)
x_1 : L_1 > x_2 : L_2
 

 

 
V V
y_1 : L_1 < y_2 : L_2 (015)
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. (016)
Breaking here ... (017)
Jon Awbrey (018)
JS: My claim was that any statement s1 expressed in notation #1 can be
translated to a statement s2 in notation #2 (and viceversa) in such
a way that s1 and s2 have exactly the same truth values in all possible
models (in Tarski's sense) or states of affairs (in Peirce's sense). (019)
JS: Furthermore, s1 can be translated to a statement s31 in notation #3,
and s2 can be translated to a statement s32 in notation #3 in such
a way that s1, s2, s31, and s32 have the same truth values in all
possible models or states of affairs. (020)
JS: That is what I meant by interoperability: any person with any
philosophical views of any kind can, if he or she wishes, map
any statement from #1 to #2, or from #2 to #1, or from #1 to #3,
or from #2 to #3  and back to the original language  in such
a way that the truth values in the source and target languages
are identical. (021)
JA: I think that I follow the business of intertranslatability between two
formal languages, L_1 and L_2, sparing the italics until we are in Rome,
translations that preserve the models, the whatevers that their various
signs are supposed to be about. But I can't help sensing that there is
just something wrong with the conclusions that you jump to in that last
paragraph. (022)
JA: Part of the problem may be that I do not consider Peirce's AOL of 1885
to be the ''ne plus ultra'' of his logic. There are bits and hints of
deep insights and radical innovations in his Logic of Relatives (1870)
that are either missing or not as explicit in his papers of the 1880's.
And there are features of his work on Logical Graphs that reform basic
conceptions of what we mean by logic in the first place. (023)
JA: Your last paragraph echoes once again the wish for an ontologically or
a philosophically neutral language. Whether that is a will o'th' wisp
or not, as I suspect that it is, it does not describe the facts of the
matter in this case. There are definite ontological assumptions  in
particular those affecting the role of "individuals" in the "universe" 
that one takes for granted in the systems that devolve from Frege, but
those same assumptions are quite expressly examined and not assumed in
the intentions that inform Peirce's calculi for his Logic of Relatives. (024)
JA: So if you are claiming merely that you can attach meanings to Peirce's
language in a way that makes it say the same thing as the meanings you
attach to some other thinker's language, then fine, I guess that might
be possible, and the fact that you can interpret them so might even be
a significant property of the languages and their relationship. But I
would not go so far as saying that these languages are saying the same
things, because that equivalence is relative to a pair of choices that
you made in equating them. Your reading would have to be reductive on
one side of the balance in a way that it's not on the other side of it. (025)
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