ONT Re: Inquiry Into Models
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Sung, & All,
I apologize for my earlier brevity -- now how often do I get to say that!? --
but I was earnestly being called to dinner and had to rush off post haste.
Also, it seems I must try to reconstruct your diagrams in a fixed-width
character font. (During my early days in discussion groups, I tried to
use HTML-mail, but got so traumatized by people complaining about the
extra Kbytes and so on that I abandoned its use altogether for email.)
Sungchul Ji wrote (SJ):
SJ: Dear Howard, I have been enjoying and learning a lot from your passionate
dialogue with Jon these several weeks, and I hope you will continue.
SJ: For now, I have a question for you. What is the essential difference, if any,
between the Hertz's and Rosen's theories of modeling? If they are different
in some essential ways, what was the influence, if any, of Hertz's theory
on Rosen's?
SJ: To facilitate discussions, I have tried to reproduce Rosen's "modeling relation"
[Figure 3H.2 in his book, 'Life Itself', Columbia University Press, 1991, p. 60]
as follows:
| 4
| -------->
| /\ / \ /\
| 1 ^ N F ^ 3
| \/ \ / \/
| <--------
| 2
|
| Figure 1. Rosen's Theory of Modeling
|
| N stands for a natural system, and F for a formal system.
| The numbers indicate the following:
|
| 1 = causal entailment, which I presume is synonymous with causality,
| 2 = encoding,
| 3 = inference or inferential entailment,
| 4 = decoding.
JS: On 8/4/01, you [Howard] tried to represent
Hertz's theory of modeling with a scheme
that had three columns and three rows:
| EO o----W-F----o ISP
| | | |
| | | |
| NL o----S-T----o LMM
| | | |
| | | |
| NC o----S-A----o LNC
|
| Figure 2. Howard's Representation of the Hertzian Theory of Modeling.
| The following abbreviations are used:
|
| EO = External Objects;
| NL = Natural Laws;
| NC = necessary Natural Consequents;
| W-F = We Form for our selves;
| S-T = Such That;
| S-A = are the Same As the;
| ISP = Images, Symbols, Pictures;
| LMM = Logical, Mathematical Model;
| LNC = Logically Necessary Consequents of the model.
(I may have missed some diagonal lines from Howard's original scheme.)
One difference between Figures 1 and 2, I noticed, is that Howard regards
Natural Laws as a part of the the left column, whereas Rosen regards the
whole scheme in Figure 1 as an embodiment of Natural Laws. Let me quote
him [Rosen 1991: 58]:
| A modeling relation between causal entailment in a natural system and
| syntactic entailment in formal one provides a concrete embodiment of
| the concept of Natural Laws. It is worth spending a moment discussing
| natural Law, for it provides the explicit underpinning on which all of
| science rests.
|
| Natural Law makes two separate assertions about the self and its ambiance:
|
| 1. The succession of events or phenomena that we perceive
| in the ambiance is not entirely arbitrary or whimsical;
| there are relations (e.g., causal relations) manifest
| in the world of phenomena.
|
| 2. The relations between phenomena that we have just posited are,
| at least in part, capable of being perceived and grasped by
| the human mind, i.e., by the cognitive self.
|
| Science depends in equal parts on these two separate prongs of Natural Law.
| The first, which says something about the ambiance, asserts that it is in some
| sense orderly enough to manifest relations or laws. Clearly, if this is not so,
| there can be no science, also no natural language, and most likely, no sanity either.
| So it is, for most of us at any rate, not too great an exercise of faith to believe this.
|
| The second part of Natural Law ways something about ourselves. It asserts that
| the orderliness of the ambiance is (to some unspecified extent) discernible to,
| and even more, is articulable by, the self. It asserts then that the posited
| orderliness in the ambiance can be matched by, or put into correspondence with,
| some equivalent orderliness within the self.
|
| In other words, the first part of Natural Law is what permits science to exist in the abstract.
| The second part of Natural Law is what allows scientists to exist. Clearly, concrete science
| requires both. ...
JS: In short, according to Rosen's theory of modeling,
it is Natural Law itself that dictates not only the
causal entailment in N and the inferential entailment
in F but also the two-way correspondence between N and F.
In an interesting contrast, Figure 2 depicts a situation
where an impression is given that Natural Laws operate
mainly in the realm of external objects.
JA: Sorry to break in -- I am still behind in my homework on Rosen, so I promise that
I will quickly retire to the peanut gallery with respect to that side of the issue --
but there is a generic component of this question that I have worried about since
I first woke up one fine or fuzzy day in one of my old phil or phys or psy classes
and started to think seriously about causality, and since I have already tried to
air my worries about this several times in this forum already, I feel entitled to
keep on pestering folks about it until I arrive at a measure of satisfaction.
JA: Let me express it, this time around, in the form of a very old question:
|
| Does not the effect imply its causes?
|
JS: My naive answer would be:
JS: If Y is the effect of X, then one can say that X causes Y,
according to the common usages of terms, 'effect' and 'cause'
in English language.
JS: Apparently there are many theories about "cause",
"causation", or "causality", including regularity
(or nomological) analysis, counterfactual analysis,
manipulation analysis, and the probabilistic analysis.
Probably all of these and more apply to the meaning
of "causal entailment" that Rosen's modeling diagram
refers to, but the regularity theory of causation may
cover most of what Rosen meant by causality.
Let me try it again, as I see that my haste
may have caused me to speak too colloquially.
First, let me smooth out the unnecessary kink
of that rhetorically leading form of question,
and try to ask it a bit more straightforwardly:
|
| Does the effect imply its causes?
|
Next, let me try to explain how I intend these terms.
Suppose that the event C is a "cause" of the event E.
Vice versa the event E is an "effect" of the event C.
Perhaps I should remark that I do not yet have a definition of causation.
In this respect, it could only be my quest to find a suitable definition,
or else to know the reason why.
I do know that people commonly speak of this as a "natural relation",
that is to say, I reckon, a relation that is in the nature of things.
By "imply" I mean to imply the logical relation of "implication" between propositions
that is the one most commonly meant by those of us who still trust mathematical logic,
if only a little bit, and typically symbolized in the form "A => B" for "A implies B".
Now here is where I was being a little too loose in my speech,
for events and propositions are certainly not the same things,
even if there is a well-known analogy between the two domains
that has slipped into automatic habit since the days of Boole.
But maybe I can try to rephrase my question better this way:
Let Prop(A) be the proposition that event A has happened.
And suppose that all of the appurtenant circumstances are
appropriate for it to be true that event C causes event E.
Then let me essay to ask my question this way:
Using your common sense understanding or your
own favorite definition of "cause and effect",
would you call the following a true statement?
1. Prop(E) => Prop(C).
Paraphrasing:
1. If it is true that the effect has happened
then it is true that the cause has happened.
Would you say that Proposition 1 is true, or
would you say that Proposition 1 is false?
Jon Awbrey
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