Chris, (01)
I apologize for the "cheap shot" about LW's philosopher's disease. (02)
> in place of informed argument, simply a haughty dismissal of "philosophers"
> in their ivory towers by the wise and experienced real-world practitioner.
> It also means that reasoned debate is at an end. (03)
I also apologize for downplaying the importance of the philosophical
logic that deals with some deep paradoxes. Someday that may lead to
important new versions of logic or new ways of using logic. (04)
I should have stated my arguments in the framework I proposed:
Wittgenstein's language games and my suggestions for formalizing
at least a useful subset of them. (05)
The basic idea is that there is no single "natural logic" that underlies
human thought and language. Instead, there is an open-ended number of
ways (LW's games) for using language. I strongly agree with LW that
there is no single ideal logic (or Beweissystem, as he called it). (06)
Some ways are extremely imprecise, because the subject matter itself
cannot be formalized. Other ways can be as precise as any version
of mathematics. For example, two chess players can discuss a game
of chess with exact precision at every step -- because the rules of
chess can be translated to any version of FOL. But when they say
a certain move was "brilliant", that crosses the line to opinions
that cannot be formalized. Brilliant(x) misleadingly looks formal. (07)
I'm currently writing a paper on this topic, but I summarize the ideas
in the final section (Slides 52 to 64) of (08)
http://www.jfsowa.com/talks/dynolang.pdf (09)
I also apologize for not putting numbers on the slides. My usual method
of word processing is to type HTML (with tags) in an ASCII editor and
copy the HTML into OpenOffice (now LibreOffice) to generate PDF files.
I'll try to find the LO help info for numbering slides. (010)
> "Human(Sowa)" (and a corresponding model thereof containing you and the
> property of being human) gets the world exactly right as far as it goes. (011)
Yes, but. I won't even get into issues about the border line between
Homo erectus and Homo sapiens or the ambiguities in proper names.
A single relation Human(Sowa) is not a realistic example. (012)
Just take an arbitrary sentence from any daily newspaper. Let's say
the second sentence of the third paragraph on page 7 of the first
paper you find. If that sentence is simple, then take the next one. (013)
After writing that, I took my own advice and found the following two
sentences from last Sunday's New York Times, page 7, paragraph 3: (014)
"No one wants to choose sides" between the United States and China,
he said. (015)
Indeed, both sides have an interest in channeling their rivalry
into trade more than weaponry, even as China sees itself as
increasingly having the upper hand in the region. (016)
The first sentence is simpler, but it requires a lot of background
knowledge about current events, about "choosing sides", etc. (017)
The second one adds issues about "interest" and "channeling rivalry".
Even worse, how could you formalize the words 'trade' and 'weaponry'
in this context in such a way that rivalry could be "channeled"
into them. And how could you formulate a general theory of language
that could interpret one full page of such language? (018)
JFS
> As engineers say, "All models are wrong, but some are useful." (019)
CM
> It's a stupid slogan. Models are useful (typically) because they
> get the world right to some extent, at some level of granularity.
> If that weren't so, their usefulness would be a complete mystery. (020)
I apologized for dissing philosophers. Please don't diss engineers.
That statement was a warning to engineers, who have a tendency to
believe that models are useful for the reasons you cite. But it is
essential to remind them that no model can be perfect, the correct
level of granularity for a particular problem is far from obvious,
and a tiny error in the model can lead to horrendous disasters. (021)
For examples, I suggest the books by Henry Petroski, who looked down
on engineers when he was a physics major. But he learned better: (022)
http://www.amazon.com/Henry-Petroski/e/B000APOBKA (023)
> [Gödel coding] was just an example of a language the likes of which
> you seemed to be saying didn't exist. (024)
I studied Gödel's paper, and I read a fair amount of the literature
about the Liar Paradox and related issues. As an undergraduate, I
was in awe of such achievements. (025)
> McCarthy's "ist" predicate... is exactly the kind of thing you want
> an account of contexts to be able to express. But "ist" is a semantic
> predicate and it is very easy to generate liar-like paradoxes with it.
> ...
> Do we restrict the language? How do we do so without robbing ourselves
> of the very expressive power we looked to a theory of contexts to provide?
> Do we restrict the logic? How do we do so without robbing ourselves of
> the ability to make the sorts of inferences we need to be able to make? (026)
Following is my approach to answering those questions: (027)
1. I would include the "ist" predicate or something like it in
my knowledge representation language. (028)
2. I would not restrict NLs in any way to prevent people from
getting in trouble. As we know, they get in trouble every day
by saying things they shouldn't. Problems that might result
from misusing 'ist' would be a minor increment by comparison. (029)
3. My solution to the general issue is summarized in my approach to
formalizing LW's language games. I would provide an open-ended
number of logics that could be used for interpreting NLs. If and
when anybody made a breakthrough by inventing a new logic for
representing those issues, I would be delighted to include it. (030)
4. Meanwhile, Tarski's hierarchy of metalanguages is a very powerful
method for handling 99.9...% of the language people use every day.
It makes an important increase beyond the KR languages in use
today, and I would use it until somebody invented something better. (031)
This framework can accommodate an open-ended number of theories of
ontology and logics for representing them. The most challenging
task is to relate any given text (such as the article from the NYT)
to the appropriate theories that could be used to interpret it. (032)
For the logics and reasoning methods in the framework, I would not
exclude anything that anybody found useful for any purpose whatever. (033)
John (034)
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