Jon AS, List,
For anyone who is not familiar with Peirce's 1911
EGs, see my
introduction to EGs, which is based on the 1911 version.
The first
10 slides are sufficient for an overview. The remaining
slides show
features of the 1911 EGs that make a major advance over
the logics
of the 20th century:
http://jfsowa.com/talks/egintro.pdf
The following comment
shows why Peirce rejected R669 and replaced
it with R670 and L231:
JAS> Peirce had a very good reason for not writing a third rule
at
the end of R 669, and it was not because "he suddenly
realized"
something at that moment in time and
"abruptly" abandoned his
previous train of thought. It was
simply because he had already
stated the third rule a few paragraphs
earlier, and had explicitly
pointed out that it is not an illative
permission; i.e., it is not
a rule of inference.
After
reading that comment, I realized that Peirce's insight on
2 June 1911
was that the adjective 'illative' is irrelevant and
misleading for
all three permissions (rules of inference). The
rules depend only on
negation. They do not depend on a "sign of
illation", such
as a scroll or other symbol for if-then.
In L231, Peirce called
all three rules permissions (without the
adjective 'illative'). I
believe that R669 is the *last* MS in
which he wrote the words
'illative' or 'illation'. I have not
read all his extant MSS, but I
very strongly doubt that he would
continue using a word he had
rejected.
See slides 11 and 12 of egintro.pdf for an
explanation in terms
of the 20th c logics. For the details about
Peirce's five MSS that
document his development of the 1911 EGs and
his rejection R669, see
the attached file eg1911x,pdf.JAS> The
final sentences [of R669] note the inadequacy of automated
reasoning
to apply "the two illative permissions," since they
require
"a living intelligence" (R 669:23-24[21-22], LoF 1:584).
No. Modern theorem provers can use Peirce's rules (and other
rules
derived from them) quite efficiently. For an overview of the
issues,
see the slides in http://jfsowa.com/talks/ppe.pdf . For more
detail,
slide2 of ppe.pdf has a link to a 76-page article in the
Journal of
Applied Logics,
JAS> Unlike
"Prolegomena" (CP 4.569), none of these manuscripts
includes a "4th Permission" expressing "the strange
rule" that Peirce
deemed to be inconsistent with "the
reality of some possibilities" as
affirmed by his pragmatism (CP
4.580-581, 1906), such that he was
ultimately "sceptical as to
the universal validity of" it (RL 477:33[13], 1913).
That
gets into his modal logic, which he intended to replace with Delta
graphs. Any comment about modal issues in 1913 should be evaluated
in terms of the Delta graphs, for which we don't have any MSS.
JAS> deriving negation from... a scroll with a blackened inner
close...
is more analytical because it preserves the fundamental
asymmetry of
reasoning and can thus be easily adapted for
intuitionistic/triadic
logic without excluded middle, which "is
universally true" (R
339:515[344r]).
No. In R670,
negation is a primitive. The scroll is nothing but a
way of drawing
a nest of two negations without raising the pen.
Since negation is a
primitive in R670, it would be absurd to derive
negation from a nest
of two negations plus a pseudograph.
In structure, motivation,
and applications, intuitionistic and
3-valued logic are totally
different from each other and from any
version of Peirce's EGs.
Oostra's choice of the scroll as a marker
for intuitionistic rules
has no similarity to Peirce's use for any
version of EGs. There is
much more to say about these issues, and
I'll write another note
about them.
John
eg1911x.pdf
Description: Adobe PDF document
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