[Inquiry] Re: Futures Of Logical Graphs -- Discussion

[Jon Awbrey]

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FOLG.  Discussion Note 30

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Re: KS 7.  http://stderr.org/pipermail/inquiry/2005-November/003187.html
In: KS.    http://stderr.org/pipermail/inquiry/2005-November/thread.html#3183

Peirce List,

Because we were just talking about the anticipated transition to Beta level
logical graphs, very roughly tantamount to what is called first order logic,
the logic of quantifications, or the predicate calculus, it might be useful
to comment on a not-just-terminological point that has just raised its head
in our reading of Peirce's "Kaina Stoicheia".

The Alpha level graphs are commonly interpreted to rule the realm
of subject matter that is variously known as zeroth order logic,
the logic of propositions, or the sentential calculus, and it
does not seem like the various communities of interpretation
are likely to budge in their usage of these terms even when
they do condescend to accord some measure of diplomatic
recognition to other communities of interpretation.

Therefore, we must get used to the word "proposition" being used
in many different senses, each of which will have to spelled out
whenever the intended range of uses fails to be clear in context.

Peirce's definition of a "proposition" as "a sign which separately,
or independently, indicates its object" reflects an observation of
critical importance for many of the discussions that are currently
under way, both here and about.  This is a characterization of the
species of proposition covered at the Beta level of logical graphs,
a complete, complex, or compound type of proposition that is taken
up in first order logic, the logic of quantified relations, or the
predicate calculus, all of which species descended or evolved from
the material that was classically treated under the heading of the
so-called "subject-predicate" form.

The upshot is that we'll need to be sensitive to these distinct
but related types of propositions and propositional expressions.

Jon Awbrey

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inquiry e-lab: http://stderr.org/pipermail/inquiry/
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