ONT Re: Extension x Comprehension = Information
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CP = Charles Peirce
RK = Robert Kent
RK: Heavens to Murgatroid Jon, from all of these recent
excerpts I am beginning to believe that CSP was the
first Formal Concept Analyst!
actually, much of the language that peirce is using here --
the duality between "individuals" and "simples", what
birkhoff called "atoms" and "anti-atoms", but fuzzy
on that memory -- cames straight out of leibniz, but
i think the that ex-in-tensorial symmetry-breaking
by way of the information integral is peirce's.
rule of thumb. all ideas are older than anybody thinks.
CP: | With me -- the 'Sphere' of a term is all the things we know that
| it applies to, or the disjunctive sum of the subjects to which
| it can be predicate in an affirmative subsumptive proposition.
| The 'content' of a term is all the attributes it tells us,
| or the conjunctive sum of the predicates to which it can
| be made subject in a universal necessary proposition.
RK: The IFF Classification Ontology:
http://suo.ieee.org/IFF/versions/20020102/IFFClassificationOntology.pdf
is in one sense categorical rendition of the basic theorem of
Formal Concept Analysis -- it is a distillation and axiomatization
of my Relmics'6 paper "Distributed Conceptual Structures"
http://www.kub.nl/faculteiten/fww/medewerkers/swart/conference/rmcs2001.html
very interesting confab. one of my advisors does work in rel prop:
http://www.secs.oakland.edu/~mili/index.htm
http://www.secs.oakland.edu/~mili/publication.htm
RK: A central aspect of the basic theorem of FCA is that the instances
of a classification are join-dense, and that the types are meet-dense,
in the corresponding concept lattice. This fact is concentrated on
page 35 of the IFF Classification Ontology. There you see a formula
that states that every formal concept (element in the concept lattice
of a classification) is both the join (disjunctive sum) of the objects
(= instances) below it, and the meet (conjunctive sum) of the attributes
(= types) above it.
CP: | The maxim then which rules explicatory reasoning
| is that any part of the content of a term can
| be predicated of any part of its sphere.
RK: By derivation, (the formal concept generated by) any object (part of CSP's sphere)
of a formal concept (CSP's term) is below (the formal concept generated by) any
attribute (part of CSP's content) of a formal concept.
is "derivation" here meant to evoke the algebraic sense?
jon awbrey
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