concepts of "state"

[Howard Pattee <***>]

There are many ideas here, but I have not been following my own
suggestion and Tim's wishes that we focus on what Rosen actually wrote.
So here is a new thread about Rosen's concept of state.

Rosen's discussion of "state" is fundamental for his whole
argument. In the LI Chapter, "Entailment Without States", Rosen
uses "state" in the narrow classical Newtonian dynamics sense
of a set of observable values at an instant of time that define the
system being modeled. These encoded values act as initial conditions on
the formal differential (with respect to time) equations of motion. As he
correctly points out, this time-dependent concept of state is clearly
inadequate for memory and anticipatory models that have no coherent
temporal dynamics. 

Consequently, Rosen had to dispense with Newtonian states; but instead of
eliminating all concepts of state I think what he actually does, or
should have done, is to generalize the concept of state. I think it is
more accurate to say that Rosen has abstracted away only physical time as
the state transition parameter, but he retains the conceptual equivalents
of states and state transitions in his formal morphisms. (Note: As I see
it, this generalization would strengthen, not weaken, Rosen's
argument.)

The more general meaning of "state" now used in physics and
systems science refers to all (and only) the information or specification
that is necessary to define a morphism, function, or mapping from one
abstract configuration to another. This requires specification of members
from a domain set and their images in the range set. An individual member
of the set is equivalent to a "state" of the domain that is
being mapped to its image "state."  The only concept that
is actually abstracted away is the Newtonian interpretation of the
morphism as occurring in real time. Clearly, Rosen uses this more general
concept of state in his many mappings. 

I think this is what he implies in the second sentence in LI p.109:
"Our systems are assigned no states, no environments, and there
is no recursion. Nevertheless, all these are recaptured, as we shall
see, by very special instances of the relational formalisms." Also,
on LI p. 134 Rosen says: "In the relational picture, on the other
hand, the situation is quite different [from the Newtonian picture]. As I
have developed it so far, there is no time parameter, no states, no state
transition sequences. There are only components (mappings), and the
organizations, the abstract block diagrams that can be built from
them." I am saying that these mappings amount to generalized state
(set) transitions.

Why is adopting this general view of states important? Can one really
think of a model without this more general concept of "state",
along with the concepts of "transition", and
"relation"? It would be as difficult as speaking without nouns,
verbs, and prepositions. These concepts are all inherent in natural
language grammar because they reflect basic epistemic structures. Nouns
are state-like. They refer to whatever things we are talking about. Verbs
are transition-like. Verbs describe what happens to (or what we do with)
the things we are talking about. Prepositions, like "to" and
"about", express the relations between things.  (By the
way, since Aristotle's causes are not precisely definable, as an analogy
can we think of material cause as noun-like or state-like, efficient
cause as verb-like or effecting change, and formal cause as
preposition-like or relational?) 

Mathematics makes this natural grammar precise by defining sets (members
are nouns), operations (are verbs), and relations (prepositions) as pure
syntax without reference to interpretations (encodings) or causality
(entailments). Mathematics began with counting things (e.g., Lakoff and
Nunez, Where Mathematics Comes From, Basic Books, NY, 2000). The
first measurement was counting (encoding) things, but mathematicians
learned to "count" without referring to things. As Rosen points
out, logicians found that such syntactic purity can lead to sterility and
paradoxes. However, it is just because mathematics cleanly separates
syntax (inferential entailments) and semantics (via encodings) that a
more precise modeling relation is possible, one that avoids many of the
ambiguities of natural language. 

I repeat: As I see it, by using this generalization of state and
state-transition as time-independent morphisms, and then clearly
distinguishing them from Newtonian temporal states, Rosen's argument
would be intuitively more persuasive and more defensible. Does anyone see
my point?

Howard