SUO: Re: General Design
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John,
Given a space X, that is our main domain of interest,
along with a space B = {0, 1} that we use to indicate
distinctions in whatever spaces we choose to build up,
there are only so many things that we can do with them,
only so many constructions that we can make out of them.
For example, an arbitrary distinction that we draw in X
is tantamount to an arbitrary function f : X -> B, and so
the space of all distinctions that might be drawn in X is
information-equivalent to the space (X -> B) = {f : X -> B}.
For another example, a very arbitrary sort of a generalized
quantifier is tantamount to a function q : (X -> B) -> B,
so the space of maximally generalized quantifiers over X
is ((X -> B) -> B). When I said "so many" I did not mean
just a few. Against this pre-established background of
generic or "no-name" constructions, all we have to do
with a candidate concept or term is to decide what
if any type of existing thing it might refer to.
The problem of deciding which of the available distinctions we should
single out with name-brand concepts is the problem of abduction, and
there appear to be strong reasons why no algorithm will rescue us
from the inevitable risks of taking chances on pure hypotheses.
That's not to say that there isn't a form of reasoning that it
would help to formalize to the extent possible, but umpteem
years of cluster, factor, regression, etc.-analytic methods
have probably burned me out personally on trusting people
who confuse the whole problem with deductive or inductive
reasoning. So that would be my first criterion before
I risk getting burned again, namely, the question:
Does this method recognize the 3-phase structure
of inquiry?
Jon Awbrey
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John F. Sowa wrote:
>
> Julian and Jon,
>
> I agree with Julian's three levels, but I would use
> different labels for them:
>
JF> thing
> > philosophical-stuff
> > useful-stuff
>
> The top node could be called the "empty" node since
> it has no axioms and is true of everything. The bottom
> level could be called the "concrete instance" level,
> since the categories apply to instances of things that
> people see, hear, feel, smell, and taste. The middle
> level is the level of generalizations or abstractions
> from the lower levels.
>
> Some labels in the middle may come from philosophical
> discussions, but many of them come from physics (which
> used to be called "natural philosophy"). They are
> extremely useful for stating general principles that
> apply to more than one application. Without them,
> there is no hope of sharing modules between different
> concrete applications.
>
> Jon Awbrey stated it well:
>
> JA> Or maybe axioms are the cart and experiences are the cartload.
> > It can a take a couple hundred or a couple thousand years of
> > experience with a motley crue of crude examples before some
> > people will start to notice that the same darn patterns of
> > thought tend to keep turning up in what appears to be the
> > darndest places, and the useful sorts of axioms only but
> > gradually percolate themselves to the top of the heap.
> > But even this is a retrospective illusion. At the
> > beginning of the story you don't even know what
> > the "examples" are supposed to be examples of.
>
> My major criticism of Cyc, Sumo, and Dolce is that
> the developers started from the top down with some
> preconceived assumptions about what would be
> necessary for every level beneath the top.
>
> I believe that it is important to scour the philosophical
> and scientific literature in order to take an inventory
> of all the best distinctions and generalizations that
> anyone has ever discovered. But rather than organize
> those distinctions according to somebody's best guess,
> I would recommend using an algorithm that would generate
> the organization automatically. And I would iterate and
> reiterate the application of that algorithm with every
> new addition at any level of the hierarchy.
>
> There is a lot more to be said about the algorithms and
> how to use them. But for starters, I would suggest that
> people look at the work on Formal Concept Analysis (FCA)
> for deriving lattices from low-level distinctions. For
> a brief discussion of lattices with an example of FCA,
> see Section 7 of my tutorial on math & logic:
>
> http://www.jfsowa.com/logic/math.htm#Lattice
>
> Note that when you apply FCA or any other method for deriving lattices,
> the algorithms often generate new nodes that don't correspond to any
> names in the original language. When philosophers and scientists
> find such nodes, they coin new words from Greek roots. Those are
> the "philosophical terms" that Julian said were not useful.
> But mathematically, they are important for labeling potential
> generalizations, which may turn out to be very useful for
> applications that no one had ever considered before.
>
> I won't say that FCA is the answer to all our prayers,
> but I will say that it is better than drawing trees or
> lattices by hand.
>
> John Sowa
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