Bill, Chris M, and Ferenc, (01)
Natural languages take advantage of context to reduce the size
and complexity of sentences. The most obvious examples are the
two words 'I' and 'you'. Two people can contradict one another
by making exactly the same statement: (02)
"I can do anything better than you." (03)
Mathematics, logic, and programming languages also take advantage
of context. For example, beginning students in algebra are often
confused by "variables". They think that each letter, such as
x, y, or z, corresponds to a fixed number. Sometimes it helps
to point out that a common name like Bob can refer to different
people in different contexts. (04)
All formal languages have a context-free base grammar. But things
like quantifiers in logic and declarations in programming languages
add context-sensitive constraints. Those constraints are perfectly
logical, but they require a more expressive grammar. The same is
true of natural languages: context free grammars can represent
a lot of the structure, but you need semantics, pragmatics, and
background knowledge for full understanding. (05)
WB> ... the human individuals /creating/ the mechanisms still use
> (and can only use because that's all that's available to them)
> their native linguistic facilities to interpret the ontology
> as documented or explained. (06)
CM> We seem to be in general agreement. (07)
I agree with two qualifications: (08)
1. *Every* feature of *every* version of logic or programming
language is an abstraction from or an abbreviation of some
feature that is common in ordinary languages. (09)
2. Every contextual feature that is necessary to understand any
sentence in any NL can be made explicit in another sentence
in the same language. When those contextual features have
been made explicit, they can be translated to a suitably
expressive version of logic. (010)
The simplest example of point #1 is to note that "2+2=4" is an
abbreviation of "Two plus two is four." All of the operators
of any version of logic are abbreviations for simple words and
phrases in NLs: 'and', 'or', 'not', 'some', 'every', 'necessary',
'possible', 'obligatory', 'permissible', etc. (011)
Each convention, by itself, is no more difficult than recognizing
that the letter 'x' is similar to the name 'Bob'. But I admit
that when you pile up many abbreviations and conventions in the
same statement the result can be overwhelming. (012)
FK> All I am trying to suggest that in the recognition of the law
> of identity emotion, will and reason equally take part - to
> simplify the formula. (013)
I agree. But I would add that any contextual information (fact,
emotion, or purpose) that is needed to interpret any NL sentence
can be expressed in another sentence. It is something like
explaining a joke. It can be done, but when you do it, it's
no longer funny. (014)
John (015)
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