Dear Matthew, Christopher, and Doug, (01)
Following are the points I was trying to make: (02)
1. The criterion of adequacy for all theories of science and all
informal views is that they must "preserve the phenomena" 
i.e., they must be consistent with observation statements that
avoid theoryladen terminology as far as possible. (03)
2. Different theories and views may make further assumptions about
theoretical or hypothetical entities that only indirectly map
to observable phenomena. Their statements about such entities
may be inconsistent with one another. (04)
3. But any adequate theories, formal or informal, must be consistent
at the level of simple observation statements. (05)
4. Therefore, multiple adequate theories, which may be inconsistent
in their detailed axioms and methods of reasoning, can successfully
share data at the level of observation statements. (06)
5. For any theories that can successfully share observational data,
it must be possible to state a general and underspecified theory
whose terminology and axioms can be related to each of those
specialized theories. (07)
6. Theories that are sufficiently similar may have a common
generalization that includes some assumptions about theoretical
entities that are not directly observable. They can share data
about those nonobservable entities. (08)
JFS>> For example, the relation (red p) says that a pattern of redness
>> is observed at point p. Similarly, (frog p) merely says that
>> a pattern of frogness is observed at point p. It does not make
>> any assumption about the existence of entities of type frog. (09)
MW> The problem now is that this could just as easily be about 3
> different egg/tadpole/frog as about one. It might just be that
> I nickname all frogs as "Kermit". (010)
That is true. A pure observation language must avoid assumptions
about the identity of individuals. Similarity is observable, but
identity is *always* an inference. Just ask any trained magician,
who would be happy to show you innumerable examples where your
assumptions about identity are false. (011)
MW> What I am looking for is not something that can be interpreted
> this widely, but where if indeed the objects referred to are the
> same frog, when I add 3D or 4D axioms to the situation (or some
> other schemes axioms) then I get something where the mapping
> between the 3D and 4D interpretation would be the expected one
> for them to mean the same thing. (012)
What I have demonstrated is a theory that corresponds to point #5
on the above list. What you are asking for is a theory that goes
beyond #5 to a theory that includes assumptions about identity. (013)
CS> I'm afraid I have great difficulty in giving any sense to
> "a pattern of redness" or "a pattern of frogness" without any
> notion of individual (or entity, for that matter, which you
> also claimed to have dispensed with in your example of a very
> simple ontology). (014)
One way to think about a pure observation language is to imagine
that you're dreaming or looking at a movie screen. The patterns
you "see" might be pure illusions that have no connection to
any physical objects. The "sense" that you're asking for would
have to be added by making assumptions about what generates
those patterns. (015)
Doug F's suggestion of adding a variable e that links each
of the observations is one way to extend that theory. But
as Matthew noted, some of Doug's further suggestions may be
inconsistent with a 4D ontology. (016)
A specialization of my original theory with something like
the variable e for entity could be useful. Then additional
axioms and definitions could relate e to a 4D or 3D view. (017)
I agree that we should look for a theory that is somewhat
more specialized than the very simple one I stated, but
with some assumptions about something behind those
observations. The variable e is a beginning. (018)
John (019)
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