I realize that the ODM document is the result of a lot of
very hard work, but what I find depressing about all such
efforts is that they get lost in syntactic detail. (01)
Syntax is certainly important for readability and usability,
but the purpose of Common Logic is to eliminate syntax from
consideration when analyzing the options for interchange of
semantics from one notation to another. (02)
All of the languages in the ODM report can be translated to
Common Logic. When that is done, all syntactic issues are
eliminated, and it is possible to examine exactly which
aspects of logic each source language can or cannot support. (03)
People often complain that logic is hard to understand, but
logic is actually an extremely simple subset of the language
people use every day. Just the following words in normal
English syntax provides the full power of Common Logic: (04)
and, or, not, if-then, some, every, equals (05)
If you throw arithmetic and sets into the ontology, you get
everything that is present in any of those languages listed
in the ODM document. (06)
Names are certainly important, but any naming scheme ever
invented can be adopted and used in English or logic. (07)
That's all there is to first-order logic. You can add the word
"that" in order to support metalanguage for using logic to talk
about any other language, including logic itself. And you can
add some modal words -- may, can, must, shall -- if you want
to use modal logic (which can be defined in terms of FOL plus
the word "that" for metalanguage). (08)
The complexity results from the option of using and reusing
those basic words in all possible combinations. But the
foundation is extremely simple. (09)
John Sowa (010)
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