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ROL. Note 1 (02)
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JA = Jon Awbrey
JS = John Sowa (04)
Re: http://ontolog.cim3.net/forum/ontolog-forum/2007-08/msg00194.html (05)
Best I can recall, long time passing, this thread started with some
of our more logically inclined people expressing a nagging -- and I
do mean "nagging" -- sense that the invitee Proof had been slighted
in same way by the manner of distributing the sundry layers of cake
at the proposed Wedding of Webs. (06)
Now, I sympathize with that nagging feeling, to the extent
that I can understand what it is all about, but the reason
that I do so is that I conceive Proof as a form of inquiry,
in other words, a way of transforming signs that preserves --
but more to the point clarifies -- their meanings. And so
it is a matter of process once again, not merely a product
of languages interminably fussed over for their own sakes. (07)
So let me try yet another transformation of the
title by way of clarifying the business at hand. (08)
Now, I'm not really calling for anything like a Copernican Revolution
in logic, where we finally get around to realizing that logic revolves
around reality and not the other way round, because I believe that just
such a revolution already occurred a long time ago. It is just that we
seem to have gone through some kind of Reactionary Movement in the last
century that got all our priorities for logical work turned upside dowm. (09)
JA: I am referring to the conception of logic as a
normative science, which is part of what Peirce
meant by defining logic as formal semiotic. (010)
JS: That is an important issue, but it's not what I was talking about. (011)
JS: I was talking about an extremely narrow point.
Consider the following three notations: (012)
JS: 1. The first-order subset of Peirce's Algebra of Logic of 1885. (013)
JS: 2. The first-order subset of Frege's Begriffsschrift of 1879. (014)
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. (015)
JS: My claim was that any statement s1 expressed in notation #1 can be
translated to a statement s2 in notation #2 (and vice-versa) 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). (016)
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. (017)
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. (018)
I think that I follow the business of inter-translatability 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. (019)
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. (020)
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. (021)
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. (022)
Jon Awbrey (023)
CC: Arisbe List, Inquiry List, Ontolog Forum, SemWeb List (024)
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