Randall, (01)
I completely agree with that point: (02)
> We fundamentally cannot write programs that are anything other
> than encodings of formal systems! (03)
A formal logic is one whose semantics is defined by the semantics
of its atomic symbols and by the form or syntax that combines
those symbols into larger statements. (04)
In that sense, natural languages are not formal because (a) the
semantics of the individual words are not fully specified, and
(b) even if the semantics of the words were known, the semantics
of a complete sentence is not fully determined by the way those
words are combined. (05)
On the other hand, it is possible to store natural language text
(such as our email notes) on a digital computer. But the act of
storing a sentence on a digital computer cannot, by itself, make
an informal statement formal. (06)
> I think it's quite curious that we're talking about anything
> that is _not_ formal. (07)
If we perform some formal operation on some English sentence,
does that cause the informal sentence to become formal? (08)
I would say no. There is no formal operation that we can perform
on that sentence that can completely determine its meaning. If
it was in any way vague or ambiguous, the formal operations cannot
precisely determine its truth value. If they somehow assign a truth
value to that sentence, we cannot be absolutely certain that it is
correct. (09)
> If you cannot formalize it, you cannot compute it! (010)
That is certainly true. What we compute are formal operations
on informal data. But the formal operation does not in any way
cause any informal statement to become formal. (011)
When we're talking about the WWW, we find billions of web pages
filled with informal NL sentences. If we use analogies to find
patterns in those sentences that relate in one way or another
to a natural language question, what we compute are some measures
of semantic distance between that question and one or more
answers that were found on some web pages. (012)
The semantic distance measures are derived from the sentences
by some formal algorithm. But since the sentences are not
formally defined, all we can know is that the semantic distance
measure is some reasonable estimation of how closely the sentences
are related. (013)
You hear, read, write, and speak informal statements all day long.
If they're informal when then go into the computer, any act of
munging them around by formal operations inside the computer isn't
going to make them formal when they come out. (014)
That's life. C'est la vie. Tant pis. (015)
John (016)
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