Re hierarchy typing, natural & artifical intelligence - sci.logic

Message from discussion Re hierarchy typing, natural & artifical intelligence

Vesa Monisto

More options Jun 29 1996, 3:00 am

Newsgroups: sci.logic, comp.ai, comp.ai.philosophy

From: Vesa Monisto <ve...@sturman.pp.fi>

Date: 1996/06/29

Subject: Re: Re hierarchy typing, natural & artifical intelligence

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>Marvin Minsky wrote:
>>How about this as a serious question for what we might call metatheory of
>>philosophy.
>> How can so many people who understand recursive proof
>> theory not see how to construct sequences of metalanguages.

>>Surely this has something to do with the late John Myhill's theory of
>>creative sets.

> At the risk of thread drift, I would like to focus on the
>notion of "sequences of metalanguages" because it relates to something
>else I've been thinking about.

>Bob_Kowsky wrote:
> The place to start is Whitehead & Russell's Theory of Types. This
>is an external constraint that is imposed in set theory and logic to avoid
>a class of paradoxes. Perhaps the most paradox is "the set of all sets
>that do not include themselves," which is not well-defined because its own
>membership in itself is ambiguous.

Yes. It is not only ambiguous but a 'category error' (a projection). If we
are implementing 'sets' as *tools*, then the error is obvious: you cannot put
a packet (a container) to itself (to be it's own containment). There is
a BIT: you can use the notion 'set' implicitly (= without implementation)
or explicitly (by implementing it). ('Different paradigms', < Kuhn)

> Whitehead and Russell imposed a hierarchy of types: sets (the
>lowest), classes (contains sets) and so forth. A set cannot be a member
>of a set, but can be a member of a class, etc. The theory of types
>"worked" like a good fudge in avoiding the problems posed, but it created
>new problems that (AFAIK) have not been resolved.

Yes. Classes are mental implementations of sets. There are the same problems
with classes, as with sets, if you are using classes as carelessly as you used
sets before classification. All the problems are easily solved by the
'typification' which restricts the mixing (mixing of types is an error).
Without types (= in a Flatland of 'objects') the errors are lurking everywhere.
You must either 'restrict' your thinking to a Flatland of extants (= UI)
or use types as containers (= as tools not to be taken as 'actual facts').
("Quarks" < "Three quarks for muster mark!" (= "Don't take the pointers too
seriously!"))

(By the way, Galilei solved easily the paradox of Zenon by using a parameter
called "time". Why not use a parameter called information or 'deepness' or ...)

The technic is implemented to modern programming languages quite consciously
but, what irritates me, there are not (= I've not found) any books making the
obvious *explicit* even philosophically. (I hope someone could correct me!)

> In general, I speculate that any organized collection of
>mathematical objects requires a hierarchy of internal references in the
>nature of a theory of types. Hence "meta" and "sequences." These terms
>seem to me to imply such a hierarchy. And such a hierarchy is global:
>the constraints imposed apply uniformly to the entire collection of
>mathematical objects.

Yes. You put it nicely (*internal* references)! As Minsky suggested, it is
easy to practice with recursions. But (basic!) math is not making *explicit*
the differentiation to types; that were against the spirit of math. Even
Cartesius explicated coordinates, mathematicians do not make explicit their
*internal* creative procedures. When the solution is iterated (by all sorts
of loopings top-down+bottom-up) it is given explicitly as a logical UI
(= User Interface/Use-Intelligence). - Generality? - Occam's KISS!

> Folks using the brains they were born with do not require global
>hierarchies. We get along ok without theories of types too. Cretans
>notwithstanding. In fact, global hierarchies often play us false. (We
>posit the existence and consistency of "higher levels" without any
>assurance of validity.

Yes! KISS! No need for types in a normal speech. It does not mean the
types were not used *implicitly*. AI is to make 'implicit intelligence'
*explicit* (to conceale it to programs). 'Typologies' are needed only when
something is systematized for routinal (automated) use. Folks use tools,
all sorts of containers (words) quite intuitively/intelligently (and
fragmentally) 'in situ et in statu nascendi' - and mix all up to doses.

"The stones must be avoided when shooting the rapids" but if you must
shoot the same rapids every morning, there is some need for rock'n rolling.
The 'economics of rationality' (Minsky pointed lately) is a very important
question! It is a bit complex ... should we avoid (simplify by packeting)
or open, ex-plain and put the 'problem' in a usable and *working* black-box?
The structure (architecture, *workings*) makes the emergent 'ex-tants'.
Logic is not enough. There are skills needed to use logic (UI-icons) and
creativity needed to make 'black-boxes'. - Double trouble ...!? - IDLE!

> I looked at these issue many years ago (when my skills in logic
>were sharper) but found no satisfaction. Curious if anyone else has
>something to say.

Well, a happy man! (You have still curiosity! - THAT makes good for LIFE.)

(Please, try to translate my Finglish freely to English to make any sense!)

V.M.

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