[EM] FBC ambiguity & language for EM

Anthony Simmons asimmons at krl.org
Fri Jan 4 18:44:37 PST 2002

>> Subject: [EM] FBC ambiguity & language for EM

The quotes here were from a message that didn't use quote
marks, so when I started trimming it, it quickly became
impossible to recall who said what.  So I'm probably replying
to several people, identity lost.

>> Ok, then "informal" differs from "formal" not in meaning,
>> but only in language of expression. So when you say that
>> something is informal, you're just saying that it isn't in
>> mathematical language.

>> But I don't know if you're right to say that only
>> mathematical language is "formal", because , as many use
>> the word "formal", many people who aren't mathematicians,
>> but who are businessmen, government officials, butlers,
>> etc. speak formally, without using mathematical language.

>> So it seems to me that to say that formal means
>> mathematical would be an incorrect appropriation of the
>> meaning of "formal".

While I would usually consider the definition of "formality"
to be a formality is a circumstance like this, I think this
time a little information on the form of formalism might
inform the forum.

In mathematics, "formal" refers to something specified only
by "form".  (Whence the basic term "well-formed formula" -- a
string of symbols that, rather than being considered valid
because of any meaning it might have,  merely satisfies the
rules for stringing symbols together.)  A formalism is all
syntax and no semantics.  The semantics is an add-on.

An example of a formalism is the basic set theory we are all
familiar with.  While we assign meaning to the symbols, the
meaning is not needed in order for us to go through the
motions of proving theorems and whatever.  All of that can be
done by manipulating the symbols according to the form of the
statements.  In fact, if we replace all of the meanings --
"intersection" with "and", "complement of" with "inverse of",
"empty set" with "false", etc. -- we end up with a completely
different interpretation of the same symbols -- basic
sentential logic.  Engineers are familiar with a similar
example -- the duality principle in electronics.

It seems that in this situation, the problem being examined
is that of creating a formalism for something, monotonicity,
that has a pretty simple meaning, but is hard to
operationalize.  Those discussing it already know, of course,
what monotonicity is, which is why they are able to evaluate
the formalisms.


>> Aside from that, I'm the 1st to admit that mathematical
>> language can sometimes be more precise. But even
>> definitions that use mathematical language as much as
>> possible often have to rely on English in some parts,
>> including the definition of their mathemcatical variable
>> names.

>> That's why I said that using mathematical language can't
>> always get rid of all of English's ambiguity, since
>> English is still needed.

But of course.  The whole point of a formalism is that it's
the form itself that makes it a formalism.  Even if it's not
so extreme as to be a formalism in the mathematical sense, it
can still be somewhat baffling without an accompanying
explanation.  An example might be the Australian
constitution, which says that the Queen is in charge.  In the
U.S. that would mean that the Queen is in charge.  In
Australia, it's a formality.

So formalities often have to be glossed so that everyone can
understand what they mean.  They still offer a tremendous
benefit, however.  Because meaning can be so vague and
elusive, the formalism becomes a standard against which less
formal descriptions can be judged.  Rather like keeping a
cesium clock to set other clocks by, even though one usually
doesn't carry around a cesium clock on a fob.  (Although with
microelectronics, you never know.)

>> Of course that's true if "formal" means "mathematical".
>> But you could speak only of elections, candidates, voters
>> and ballots, in English that would be suitable for a
>> formal meeting, and that would be formal even though it
>> isn't mathematical--according to the most widely-used
>> definition of "formal".

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