Re: The notion of semantics in Rosen's writings

[Tim Gwinn <***>]

Carlos,

> What are 'entailment structures' and
> how they're transferred?

TG: 'Entailment structures' refer to the organization of entailments in a
system. In a formal system, entailments are the inferential relations; in a
natural system, entailments are the causal relations in a system. The
entailment structures are *mapped* across the modeling relation.

> Even more, Rosen in the
> mentioned essay in my previous post says:
>
> "The crucial ingredients are the arrows 2 and 4, which
> I call encoding and decoding, respectively. (I have
> discussed the anomalous features of these arrows in
> more
> detail in Life Itself, section 3H.) They do not fit
> entirely inside either the object system or the model;
> they do not represent entailments, nor are they
> themselves entailed. They manifest what Einstein (with
> Infeld; 1938:33) once called ?free creations of the
> human mind,? on which he believed science depends.
> They introduce an obvious further semantic element
> into the model, over and above what semantic (e.g.,
> nonformalizable)
> features may already be present in the model."
>
> Does he believe that the act of measurement is a "free
> creation of the human mind" and "introduce an obvious
> further semantic element into the model, over and
> above what semantic (e.g., nonformalizable) features
> may already be present in the model"? Suppose I want
> to calculate the translational kinetic energy of a
> body, using the simple formula Et = 1/2m*v^2. Is Rosen
> suggesting the measurement instrument I use in order
> to determine the mass of a body introduce "an obvious
> further semantic element"?


TG: No, no. Again, encodings and decodings are the *mappings*. What he is
saying is that choosing how a physical observable will *map* to a formal
model (and thus also, the inverse mapping back to the natural system), is
our free choice. We do not have omniscient knowledge which tells us that
there is a "right" mapping and a "right" model in science, nor are the
specific nature of the mappings mandated by the natural system. We must
instead observe the natural system, decide for ourselves what to measure and
how we shall represent those measurements in formal terms; as well as decide
what kind of model to build which will incorporate those mappings from the
measurements. These decisions are "free creations of the mind".

If you are familiar with category theory, you may find it useful to think of
the encoding/decoding in the modelling relation as analogous to functors
mapping between two categories, and entailment structures as analogous to a
collection of morphisms within each category.


> Tim Gwinn wrote:
>
> >TG:  A natural system is simply a collection of
> observables from the
> >World outside of us. A 'car' or a 'cat' or a 'proton'
> is a natural system,
> >comprised of the observables we have chosen to
> consider as belonging to
> >that system. Again, the books AS and FM go into much
> more detail.
>
> A computer running a simulation is not a natural
> system?

TG: A physical computer? Of course it is would be a natural system. Where
did I say it wasn't?

> If the definition is "very subjective", a rock
> perfectly could be a 'natural system'.

TG: Yes, absolutely.

> What are the
> 'causal entailments' of a rock?


TG: This depends on how you define the system. If you define the system as a
single, solid, inelastic entity, then there are very few observables to this
system, and it has little or no causal entailment structures. If you define
the rock to include its sub-atomic interactions, its thermal properties,
etc., then there is alot of causal interactions going on within the system.
*How* you define the system is subjective in this sense. The point is that
there is no absolute "right" way to define a given system.


> Tim Gwinn wrote:
>
> >TG: 'Entailment structure' refers to relationships
> between entities,
> >not to
> >entities themselves. Can you give an example of what
> you mean?
>
> I'm using the traditional definition of logical
> constant or operators or connectives like not, or,
> and, implication, biconditional (replace by the
> correspondent signs).


TG: Ah, logical *connectives*. Ok, now I see. Your original question was:
"Are the logical constants [connectives]of the formal language of a formal
logic a candidate for "entailment structure"?"  Yes, logical "implication"
is in fact just another name for "inferential entailment" (See LI p. 46).

Regards,
Tim