Registered: Feb 2004
Posts: 551

SPIE. Note 1

I would like to introduce some of the basic concepts of the
pragmatic model of inquiry into the discussion of scientific
method and to explore how these concepts might apply to the
use of simple programs in explaining objective phenomena.

The word "inquiry" is used to cover what most people mean
by "scientific method", with all due concession to those
who think that "method" is not the right word for what
goes on in science, but it also covers the analogous
structures of everyday reasoning, no doubt going
back to the dawn of intelligent life.

Figure 1 illustrates several different types of reasoning
that we use in applying theoretical models to "real world"
phenomena. I am using the word "system" here to refer to
the real world thing that we typically imagine to "carry
the action" or to embody the phenomena that we observe.

The texts attached to the sides of the triangle exemplify
the different offices of propositions that come into play,
and I have assigned them their traditional titles of Fact,
Rule, and Case.

o-------------------------------------------------o
| ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` o ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` |\` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` | \ ` ` Rule: ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` | `\` ` All systems of type M ` |
| Fact: ` ` ` ` ` | ` \ ` exhibit the pattern P.` |
| These systems ` | ` `\` ` ` ` ` ` ` ` ` ` ` ` ` |
| exhibit the ` ` | ` ` o ` ` ` ` ` ` ` ` ` ` ` ` |
| pattern P.` ` ` | ` `/` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` | ` / ` Case: ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` | `/` ` These systems ` ` ` ` ` |
| ` ` ` ` ` ` ` ` | / ` ` are of type M.` ` ` ` ` |
| ` ` ` ` ` ` ` ` |/` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` o ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
o-------------------------------------------------o
Figure 1. Components and Patterns of Inference

Reading the Figure three different ways, we can extract
the patterns of reasoning that are classically referred
to as "deductive", "inductive", and "abductive" inference.

In the Deductive pattern, we are given the two statements
of the Figure that are identified as the Case and the Rule,
and we deduce with certainty that the statement in the Fact
position must be true.

In the Inductive pattern, we are given the two statements
of the Figure that are identified as the Fact and the Case,
and we induce that the statement in the Rule position might
be true, not of course with any certainty of being right,
but with a risk of error that is controlled by the ratio
of the sample set "these" to the universal set "all".

In the Abductive pattern, we are given the two statements
of the Figure that are identified as the Fact and the Rule,
and we abduce that the statement in the Case position might
be true, again with no certainty of having guessed right,
and here with a risk of error that cannot under ordinary
circumstances be estimated or controlled in advance.

The pattern of abductive inference is what we follow when
we seek to "explain" some real world phenomenon in terms
of some class of theoretical models, whatever they may be.
There is more to science than looking at a cloud of data
and saying that it looks "very like a whale" or whatever,
but that is not a bad metaphor to convey how inquiry begins.

In the case of simple program models, a typical example
of a "middle term" M would be a statement that specifies
a particular ECA rule, with or without initial conditions.

Jon Awbrey

CC: Inquiry, Principia Cybernetica, SemioCom Lists

Last edited by Jon Awbrey on 08-07-2004 at 02:30 AM

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SPIE. Note 2

Having in mind the sorts of patterns that we see generated by
cellular automata and other simple programs, let's assume that
we understand what it means for a real world system to exhibit
a pattern P, and let's assume that we understand what it means
for a mathematical system of type M, for example, a particular
program starting from given initial conditions, to exhibit the
pattern P. But what does it mean when we state the Case that
a real world system is of type M? It may seem at first that
there is a category confusion here, violating a distinction
between real world systems and mathematical models. On the
other hand, it appears that we make these types of judgments
all the time, to some purpose in explaining real world facts,
and so I have confidence that it must be possible to sort out
what is going on here.

There are a couple possibilities that we can explore:

• There may be some order of analogical reasoning
  that is called on to make the connection between
  the application domain or object system and the
  mathematical model.
  
  
• I used the common phrase "real world system" to indicate the
  application domain or object system, the source of phenomena
  in view, but the pragmatic model of inquiry does not depend
  on any sort of absolute ontological distinction between the
  objective real world and the world of mathematical models.
  There is a practical distinction, but this is relative to
  the application in view, a matter of roles in a modeling
  relation between two domains of experience and not of
  necessity an absolute distinction between essences.
  

Last edited by Jon Awbrey on 08-07-2004 at 08:36 PM

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SPIE. Note 3

The abductive formation of an explanatory hypothesis,
for instance, "these systems are of type M", forms the
first inferential step in the pragmatic model of inquiry.
It remains to test the explanatory worth of the hypothesis,
and this is assumed to require a step of deductive reasoning,
that generates further logical consequences of the hypothesis,
followed by a step of inductive reasoning, where the degree of
of fit between the properties of the real world system and the
properties predicated on the hypothetical model is assessed,
leading us to accept or reject the hypothesis.

The continuation of our inquiry example from the first abductive step
through a typical form of deductive step is illustrated in Figure 3.

o-----------------------------------------------------------o
| ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` P ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` Q ` ` |
| ` ` `o` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `o` ` ` |
| ` ` ` \ * ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` * / ` ` ` |
| ` ` ` `\` * ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` * `/` ` ` ` |
| ` ` ` ` \ ` * ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` * ` / ` ` ` ` |
| ` ` ` ` `\` ` * ` ` ` ` ` ` ` ` ` ` ` ` ` * ` `/` ` ` ` ` |
| ` ` ` ` ` \ ` ` * ` ` ` ` ` ` ` ` ` ` ` * ` ` / ` ` ` ` ` |
| ` ` ` ` ` `\` `R u l e` ` ` ` ` ` `R u l e` `/` ` ` ` ` ` |
| ` ` ` ` ` ` \ ` ` ` * ` ` ` ` ` ` ` * ` ` ` / ` ` ` ` ` ` |
| ` ` ` ` ` ` `\` ` ` ` * ` ` ` ` ` * ` ` ` `/` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` \ ` ` ` ` * ` ` ` * ` ` ` ` / ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` `\` ` ` ` ` * M * ` ` ` ` `/` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` `F a c t` ` ` ` o ` ` ` `F a c t` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` `\` ` ` ` ` * ` ` ` ` `/` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` \ ` ` ` ` * ` ` ` ` / ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` `\` ` ` ` * ` ` ` `/` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` \ ` ` ` * ` ` ` / ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` `\` `C a s e` `/` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` \ ` ` * ` ` / ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` `\` ` * ` `/` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` ` \ ` * ` / ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` ` `\` * `/` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` ` ` \ * / ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` ` ` `\*/` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` ` ` ` o ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` ` ` ` S ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| P `=` systems exhibiting property P ` ` ` ` ` ` ` ` ` ` ` |
| Q `=` systems exhibiting property Q ` ` ` ` ` ` ` ` ` ` ` |
| M `=` systems of the type M ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| S `=` systems in the current sample ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
o-----------------------------------------------------------o
Figure 3. Abductive and Deductive Steps of Inquiry

The abductive step already taken is shown in the left hand triangle:

Fact. These systems exhibit the property P.
Rule. All systems of type M exhibit the property P.
----------------------------------------------------
Case. These systems are of type M.

Last edited by Jon Awbrey on 08-07-2004 at 08:00 PM

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SPIE. Note 4

Inquiry is a complex subject, and a lifetime of inquiry into it
seems barely enough to scratch the surface, so this is very much
an active exploration for me. I have been laying out what I call
"the pragmatic model of inquiry" -- let's hope that nobody reads
any connotation of uniqueness into my use of the article "the" --
but most of the concepts that I've outlined up to this point go
all the way back to Aristotle, with a lot of handy terminology
being added in the Middle Ages. As a result, these ideas form
the common core of what the pragmatic model shares with the
classical model, and thus with most other models of inquiry,
no matter what diversities of conceptual compartments may
be used by the various schools to organize the subject.

The abductive and deductive steps of the inquiry process seem
relatively straightforward and easy to understand, once again
being common to most other models of inquiry, at least, after
the vagaries of terminology are dispelled, but the next step,
tagged in the pragmatic model as the "inductive step", is one
that I do not understand very well at present, nor even with
complete confidence why it might deserve the name "induction".

C.S. Peirce, who is mainly responsible for hammering the pragmatic
model of inquiry into its current shape, expressed from the first
a preference for Aristotle's account of induction, but starting
from that material he worked such a subtle metamorphosis on it
that his readers cannot agree whether the change was radical
or continuous. My guess is that it was more gradual than
otherwise, but the proof of that sort of claim usually
depends on the luck of finding the missing links.

All of that makes it a good idea to slow down at this point
and to pick our way more carefully through the question of
what inductive reasoning might mean in the context of the
pragmatic model of inquiry, with especial reference to
the use of simple programs in explaining phenomena.

Before I forget, I probably ought to explain my twofold interest
in the connections between inquiry processes and simple programs.

First, computational programs, the effective descriptions (codes)
of effective procedures (computations), are evidently capable of
performing the offices that explanatory hypotheses need to serve
within the ordinary course of inquiry into real world phenomena.

Second, if we seek to support inquiry through computational means,
we have to inquire into what parts of the inquiry process can be
supported by effective procedures, and, if there are significant
portions of inquiry that can be supported by programs, what are
the computational properties of these programs, for instance,
what are the simplest programs that can do the required work?

To sum it up, how do systematic agents
that are capable of inquiry come to be?
What are the simplest parts from which
they effectively reassemble themselves?

Jon Awbrey

CC: Inquiry, NKS, Principia Cybernetica, SemioCom Lists

Last edited by Jon Awbrey on 08-09-2004 at 07:54 PM

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SPIE. Note 5

Something has been troubling me about some of the things that
I've written so far on this thread, and I need to go back and
make my next try at correcting them.

We had this bare bones picture of the first two steps of inquiry,
to which I have added some extra labels just to be clear about
the epistemic status of the various propositions involved:

o-----------------------------------------------------------o
| ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` P ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` Q ` ` |
| ` ` `o` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `o` ` ` |
| ` ` ` \ * ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` * / ` ` ` |
| ` ` ` `\` * ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` * `/` ` ` ` |
| ` ` ` ` \ ` * ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` * ` / ` ` ` ` |
| ` ` ` ` `\` ` * ` ` ` ` ` ` ` ` ` ` ` ` ` * ` `/` ` ` ` ` |
| ` ` ` ` ` \ ` ` * ` ` ` ` ` ` ` ` ` ` ` * ` ` / ` ` ` ` ` |
| ` ` ` ` ` `\` ` Rule` ` ` ` ` ` ` ` `Rule ` `/` ` ` ` ` ` |
| ` ` ` ` ` ` \ ` ` ` * ` ` ` ` ` ` ` * ` ` ` / ` ` ` ` ` ` |
| ` ` ` ` ` ` `\` ` ` ` * ` ` ` ` ` * ` ` ` `/` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` \ ` ` ` ` * ` ` ` * ` ` ` ` / ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` `\` ` ` ` ` * M * ` ` ` ` `/` ` ` ` ` ` ` ` |
| ` ` ` Observed` \ ` ` ` ` ` o ` ` ` ` ` / Projected ` ` ` |
| ` ` ` ` Fact` ` `\` ` ` ` ` * ` ` ` ` `/` ` Fact` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` \ ` ` ` ` * ` ` ` ` / ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` `\` ` ` ` * ` ` ` `/` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` \ Hypothetical` / ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` `\` ` Case` ` `/` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` \ ` ` * ` ` / ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` `\` ` * ` `/` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` ` \ ` * ` / ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` ` `\` * `/` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` ` ` \ * / ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` ` ` `\*/` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` ` ` ` o ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` ` ` ` S ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| P `=` systems exhibiting property P ` ` ` ` ` ` ` ` ` ` ` |
| Q `=` systems exhibiting property Q ` ` ` ` ` ` ` ` ` ` ` |
| M `=` systems of the type M ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| S `=` systems in the current sample ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
o-----------------------------------------------------------o
Figure 5. Abductive and Deductive Steps of Inquiry

As far as I can see, this is still a good picture for the way that
inquiry begins in general, but I made a mistake in trying to force
our simple program models, or any type of simulation models, into
the place of the middle term that is marked by "M" in the Figure.
This would amount to saying that the type of simulation systems
that we are invoking to explain the observed properties of our
sample of object systems, what we loosely call the "real world
systems", have no properties that are not possessed by this
sample of object systems. But there is no reason to think
that the simulation systems, taken as concrete realities
in their own right, will not have a host of independent
properties that are not possessed by the object systems.
And, lest it go without saying, vice versa.

As a matter of fact, the systems in our sample of object systems,
as a concrete sample from a larger class that we may have in mind,
are likely to have many properties in common with each other that
do not generalize to the larger class. What this symptomizes is
the fact that a sample and a simulation both have the character
that they serve as "signs" in relation to the intended "object".

But let us focus on the simulation relations for now,
leaving the matter of sampling relations to one side.

As I see it now, the actual relationship between the object system
and the simulation system is not the subordination of a subject to
a predicate, but the relationship of analogy between a subject and
a similar subject.

Another way of saying this is that only some properties
of the explanatory models are useful in the explanation.

The next time that you see this Figure, I will probably
change the "M" to a "T", to remind us that it indicates
a theoretical predicate, a predicate that is shared by
the object system and the simulation system both, or
else that it marks the place of a type of system
that includes both ends of the analogical arrow
or the paradigmatic morphism between the two.

Due consideration of these issues will require us to examine
the logical features of analogical reasoning, involving the
concepts of analogue models, icons, morphisms, simulations,
and so on.

Jon Awbrey

CC: Inquiry, NKS, Principia Cybernetica, SemioCom Lists

Last edited by Jon Awbrey on 08-19-2004 at 03:18 PM

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