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Hi Carlos,
Good questions. I will do my best to help. I think the clearest way
to handle it is to insert explanations into the body of your
text:
Carlos L. posted:
RR wrote: "An essential part of any language resides in
its
implication structure. This comprises a system of entailments, which generally are expressed in the terse form P [entails] Q. The main property of such implications, or entailments, is that they propagate "truth" hereditarily across them; thus if P is assumed to be "true" (whatever truth may be, here), then Q must be true also." This is the standard modus operandi of theoretical
science, as a matter of fact. "If P is true, then that means Q must be true." In
mathematics (which is another language, with its own implication structure,
different from English) it's written as an arrow ( P
---> Q ). Another way to look at it is; "Q depends on the truth of P,
therefore in order for Q to be true, P must be true."
An example might be: "If we have a clear sky tonight, we'll be able
to see the Perseid meteor shower" (which is still continuing, by the way). So, P
= "clear sky tonight" and Q = "see the Perseid meteor shower". If P is not true,
then Q will not be true, either: if the sky is not clear, we will not
be able to see the stars.
This goes in the other direction, too. If someone says; "I was
watching the shooting stars last night-- it was AMAZING!" You know that the sky
had to be clear.
C.L:
RR wrote: "It is often supposed that such
inferential entailments are part of the syntax of the language and do not themselves depend on any external referents or meanings; only the truth values arise semantically. Of course, such truth values may simply be posited, but in either case, they come from outside the syntax itself." The fact that we can give examples of this kind of entailment
structure (If P, then Q) in both English and in mathematics actually
constitutes a proof of both the statement above, and also an example of a
modeling relation.
As a proof that the truth values come outside the syntax,
itself: entailment is the basis of all causality. That's something
that is true outside of all human languages. In a sense, entailment is P
and causality is Q. The fact that entailment patterns hold, regardless of the
venue is the only reason we can "do science" at all, because this
fact is what allows us to make models that actually can predict the future
behavior of the system being modeled.
CL wrote: Then he proposes something called 'modeling relation'.
In this 'modeling relation', he says, there is 'encoding' and 'decoding' between what he calls (at least, in the book 'Life Itself') as 'natural system' and 'formal system'. Rosen says that a 'natural system' has a set of 'causal entailments' and a 'formal system' has a set of 'inferential entailments'. Right. So, assuming that the system we want to model is a natural
system, the entailment structure of the system is called "causal entailment" and
the entailment structure of the model is called "inferential entailment". So, in
our "If P, then Q" scenario... that can be a model if the entailments are
accurately transferred from the natural system we want to model. Let's take
another system and try to model it:
Let's say we want to model the causality of frost forming on our
car, as it sits outside in the driveway in mid-October in New York. In autumn,
around here, the overnight temperatures are low enough to cause a heavy dew
to form on all surfaces outdoors. If the temperatures go below freezing, the dew
crystallizes on all those surfaces. It looks really pretty, actually! But it's a
real pain if you have to drive somewhere early in the morning: You have to
scrape it off all your car windows or else you can't see to drive. So, to form
our model, using this mathematical language: P = "temperatures below freezing"
and Q = "frost on car windows".
We've just encoded the entailment, from the natural system into our
model, by our choices of what aspects of the model represent which aspects of
the actual system. Then, to test it, we have to decode: Our
model predicts several things. It predicts that frost will not be able
to form unless the temperatures go below freezing, and it predicts that the
freezing temperatures must precede the formation of frost. They are not
simultaneous, in other words. So, from our model, we can predict that
if there is frost forming on the car, the temperatures must already be below
freezing. Do you see? Making predictions about the real system's
behavior, based on our model's entailment structure, and
then conducting a series of experiments to see whether our predictions
hold true, we are "decoding"-- following the lines of entailment in our
model to create predictions and then applying those predicted entailments
back to our actual system. If the predictions prove to be accurate, then
our model "commutes".
The first problem I have is with the definition of 'encoding' and 'decoding'. Rosen defines in the book Life Itself encoding and decoding as the 'translation' between 'formalisms'. That's only one particular kind of modeling relation. He begins
with the relation between a natural system and a model of it. Then he goes on to
say that we can make models of models, too. Any model is a type of "formalism".
So, if we have a model and we want to create another model: another way of
studying the entailment structure that the first model possesses... then we
must go through the process of encoding that entailment structure from the first
model into the second model, and also the process of decoding by making
predictions, using the new model's entailments to predict what the original
model's entailments would predict. An example of this would be to take a
statistical model and create a graph from it. The graph is only an accurate
representation if the information from the statistical model is converted
accurately, from one form into the other form. All the entailment relations
contained in the statistical model must be transferred over. That's
encoding. See?
CL wrote: Also, is not very clear to me what qualifies as a
'natural system', since Rosen defines them as systems "in the ambience or external world". Natural systems, in his parlance, are "actual, real
systems" as opposed to models or simulations. They can be systems made by humans
(like a house) or systems which spontaneously self-organize (like a hurricane).
But he takes pains to point out that this is a very subjective
activity: he says that science always is a subjective activity.
Objectivity is a myth, at least the way we define it in science. Worse; the more
we try to achieve it, the less likely we are to actually succeed. In any case,
his use of the word "natural" in this sense refers to "real".
CL wrote: I can't
understand Rosen's point very well, so I'd pleased to know in what exact sense" the entailment structure of the language itself can change by virtue of what the language is about" and if Rosen effectively is asserting this. The point he is trying to make is that language doesn't exist in a
vacuum: it interacts with that which it refers to-- and furthermore; that
which it refers to has an impact on the language as well. This kind of
interactivity relation between a system and its environment is exactly what
drives evolution, for example. Languages evolve and organisms evolve. They do so
in concert with environmental impacts and they impact the environment, in turn,
as well. It never is a one-way thing. So the entailment relations, once again,
commute: He was using language as a model of this aspect of biological system
entailment relations.
Are the logical constants of the
formal language of a formal logic a candidate for "entailment structure"? I would say yes, if by "logical constants" you are talking about
the rules of the formal language. For example, in mathematics a plus
sign is the opposite of a minus sign, in operational terms (not talking about
positive and negative numbers, here). Addition (the plus sign) is the
operation for the process of putting things together and
subtraction (the minus sign), conversely, is separating things
out. This logic is set and always holds true within the language, so a plus
sign isn't sometimes about addition and sometimes about division, say. It's
always the same operational process. The internal rules specifying how the
system works-- that's entailment structure.
But most internal rules have referents to external "things". Even
simple systems, like a car, carry semantic entailment information that isn't
syntactical. For instance, cars have tires. They don't have pontoons or skis,
they don't have a hull, like a boat-- they have tires. Tires refer to roads and
gravity, among other things. Similarly, complex systems also have a great deal
of semantic information about their environment encoded into them and they
interact with their environments in ways that can radically change the
environment in turn. Plants changed the composition of Earth's
atmosphere-- because of the entailment structure of their physiology and
metabolism. Beavers have webbed feet and a rudder-like tail, yet they're
land mammals. Beavers are a really good example of systems which change their
environment purely by following their internal entailment
structure.
Well, it's getting late and I'm not sure if I'm still being lucid,
so I better quit now and pick it up again tomorrow. I hope this has helped at
least a bit?
Cheers,
Judith
BioTheory: An E-Journal of General Science in the Rosennean Complexity
Paradigm http://www.rosen-enterprises.com/RobertRosen/BioTheoryLaunch.htm
Website address: http://www.rosen-enterprises.com/ |