SUO: Re: The lattice of theories + language-games
Folks,
I agree with Robert. But I believe that either he needs to get
a translator or he needs to spend some time learning to write
in English.
John Sowa
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REK> The IFF approach to the "concept lattice of theories" is parametric.
>
> See the discussion of truth concept lattices and 1st-order interpretations
> in the second half of the message
> http://grouper.ieee.org/groups/suo/email/msg05960.html,
> and the example of truth concept lattice morphisms in the message
> http://grouper.ieee.org/groups/suo/email/msg08448.html.
>
> There is no single lattice of theories here, but an infinite collection of
> lattices, with each truth concept lattice truth-lattice(L) indexed by a
> 1st-order language L. Moreover, it is important to observe that this
> indexing extends to morphisms, with the theory lattices linked by morphisms
> of theories: for each 1st-order interpretation
> I : L1 --> L2
> from 1st-order language L1 to 1st-order language L2, there is a truth
> concept lattice morphism.
> truth-concept-morphism(I) : truth-lattice(L1) --> truth-lattice(L2)
> that maps theories to theories.
>
> truth : Language* ==> CONCEPT LATTICE
>
> Internally, each truth concept lattice orders its theories by the set
> inclusion of their closures. But externally, concept lattices are linked by
> concept morphisms. More precisely, truth concept lattices are situated in
> the cocomplete quasicategory CONCEPT LATTICE of large concept lattices and
> concept morphisms. See page 5 in the document
> http://suo.ieee.org/IFF/versions/20020515/IFFClassificationOntology.pdf
> for the current version of the IFF Upper Classification Ontology. The
> colimit operation, which fuses diagrams of concept lattices and concept
> morphisms into a single concept lattice, can perhaps profitably be thought
> of as an internalization operator.
>
> colimit : Diagram(CONCEPT LATTICE) ==> CONCEPT LATTICE
>
> It is just a guess, but perhaps some of the notions "supervenience",
> "non-monotonicity", "language games", "language use", "shifts of meaning",
> "acquired information", and "paradigm shifts in science" can be modeled
> primarily as external transformations in the quasicategory CONCEPT LATTICE,
> and only secondarily (by colimiting fusion) as internal transformations
> within an internalized lattice of theories.
>