Jerry and Auke,
In the Worlds article, my primary goal was to convince readers
that a definition of modality in terms of laws and facts is
more fruitful than a definition in terms of possible worlds.
The final paragraph of that article summarizes what I was trying
to show. (See below.) What Peirce himself said about modality
and his Gamma graphs is fragmentary, and I don't claim to know
what he would have said in answer to your questions.
JLRC
Can you provide the names of the four subdivisions of the universe
of actualities?
Since Peirce didn't attach any names to those subdivisions, I won't
attempt to do so. Don Roberts reproduced Peirce's diagram on p. 94
of his book on existential graphs. But he doesn't name them either.
But by analogy with the labels Peirce assigned to the subdivisions
of possibilities and necessities, I would guess that the 3rd and 4th
subdivisions of actualities would represent something actual with
respect to an observer or to some other person. Peirce may have had
some ideas in mind, but hadn't made a final decision.
AvB
I would say...
Maybe. But these are issues for which we could benefit from
more easily accessible resources -- such as well organized
and cross referenced transcriptions of all of Peirce's MSS.
It would also be useful to have all of the MSS cross linked
to everything that any and all Peirce scholars have written
about any or all the MSS.
John
____________________________________________________________________
From the final paragraph of http://jfsowa.com/pubs/worlds.pdf
The combination of semiotics with Dunn's semantics of laws and facts
provides a theoretical foundation for modality and intentionality that
captures more of the intended interpretation than a undefinable relation
R over an undefined set W. An important promise of this combination is
the ability to support multimodal reasoning as a kind of metalevel
reasoning about the source of the laws and facts. Instead of complex
axioms for each mode with even more complex interactions between modes,
it enables the laws to be partitioned in a hierarchy that represents
grades of necessity or levels of entrenchment: logical, physical,
economic, legal, social, cultural, or personal (Sowa 2003). Exploring
the full implications of Peirce's semiotics is far beyond the scope of
this article, but the outline presented here suggests a wealth of
resources waiting to be developed.
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