Gary F, Jeff BD, Kirsti, Jon A,
I didn't respond to your previous notes because I was tied up with
other work. Among other things, I presented some slides for a telecon
sponsored by Ontolog Forum. Slide 23 (cspsci.gif attached) includes
my diagram of Peirce's classification of the sciences and discusses the
implications. (For all slides: http://jfsowa.com/talks/contexts.pdf )
Among the implications: The sharp distinction between "formal logic",
which is part of mathematics, from logic as a normative science and the
many studies of reasoning in linguistics, psychology, and education.
Peirce was very clear about the infinity of mathematical theories.
As pure mathematics, the only point to criticize would be the clarity
and precision of the definitions and reasoning. But applications may
be criticized as irrelevant, inadequate, or totally wrong.
Gary
as late as 1909 Peirce was still trying (apparently without success)
to get Lady Welby to study Existential Graphs. And the graphs he sent
her to study look pretty much the same as the graphs he introduced
in the Lowell Lecture 2: nested cuts, areas defined by the cuts,
and no shading.
That failure may have been one of the inspirations for the 1911
version,
which he addressed to one of her correspondents.
[JFS] The rules are *notation independent*: with minor adaptations
to the syntax, they can be used for reasoning in a very wide range
of notations...
[GF] This does not explain why Peirce was dissatisfied with algebraic
notations (including his own) and invented EGs for the sake of their
optimal iconicity
On the contrary, simplicity and symmetry enhance iconicity and
generality. See the examples in http://jfsowa.com/talks/visual.pdf :
1. Shading of negative phrases in English (slides 28 to 30) and the
application of Peirce's rules to the English sentences.
2. Embedded icons in EG areas (Euclid's diagrams, exactly as he drew
them) and the option of inserting or erasing parts of the diagrams
according to those rules (slides 33 to 42).
3. And the rules can be generalized to 3-D virtual reality. I
couldn't
draw the examples, but just imagine shaded and unshaded 3-D blobs
that contain 3-D icons (shapes) with parts connected by lines. I'm
sure that Peirce imagined such applications when he was writing
about stereoscopic equipment (which he could not afford to buy).
Gary
“Peirce said that a blank sheet of assertion is a graph. Since it's
a graph, you can draw a double negation around it.” — Eh? How can
you draw anything around the sheet of assertion, which (by Peirce’s
definition) is unbounded??
But note Jeff's comments about projective geometry and topology
(which Peirce knew very well):
Jeff
My reason for picking this example of a topological surface is that
it provides us with an example of a 2 dimensional space in which
a path can be drawn all of the way "around" the surface...
Yes. And that infinite space bounded by its infinite circle can be
mapped -- point by point -- to a finite replica on another sheet.
In any case, the formal logic does not depend on the details of any
representation. We can just use the word 'blank' to name an empty
sheet of assertion or any finite replica of it.
Gary
I’m reluctant to apply topological theories to EGs if they’re going
to complicate the issues instead of simplifying them.
For a mathematician, Jeff's method is an enormous simplification.
Finite boundaries in mathematics and computer science are always
a nuisance. But when you're teaching EGs to students, you can just
use the word 'blank' for an empty area. A pseudograph is just an
enclosure that contains a blank.
Gary
John appears to regard all graphs, all partial graphs and all areas
as being on the sheet of assertion. But Peirce says explicitly that
neither the antecedent nor the consequent of a conditional can be
scribed on the sheet of assertion...
My diagrams (with or without shading) are isomorphic to Peirce's.
Talking about sheets doesn't generalize to other logics or to 3-D
icons. It makes the presentation more complex and confusing.
Kirsti
I attended Hintikka's lectures on game theory in early 1970's.
No shade of Peirce. I found them boring.
Game theoretical semantics (GTS) is just a mathematical theory.
As pure mathematics, Peirce would not object to it.
Kirsti
it hurts my heart and soul to read a suggestion that Peirce's
endoporeutic may have or could have been a version of Hintikka's
game theoretical semantics.
Jon
Peirce's explanation of logical connectives and quantifiers
in terms of a game between two players attempting to support
or defeat a proposition, respectively, is a precursor of many
later versions of game-theoretic semantics.
Risto Hilpinen (1982) showed that the formal theory of Peirce's
endoporeutic is equivalent to GTS. As a formal theory, Peirce
would have no objection to GTS or to any proof of formal
equivalence.
Peirce's motivation was the similarity to his theory of inquiry:
a dialog between two parties, one who proposes a theory and one
who is skeptical. The proposer is trying to find evidence for it,
and the skeptic is trying to find evidence against it.
Hintikka's applications had some similarities and some differences.
But that's a topic that goes beyond the EG issues.
John
