Jon, I think your posts in this thread and its predecessors are the most
valuable contributions to the list that we’ve seen in the past year or so.
You’ve illuminated one of Peirce’s most philosophically important contributions
to logic, one that I must admit I had previously overlooked, and reawakened my
interest in Peirce’s graphs. I think we owe thanks to you, Pietarinen,
Bellucci, and Shafiei for doing the spadework on this. I’m particularly
interested in the phenomenological aspects of the work you cited previously,
Peirce and Husserl: Mutual Insights on Logic, Mathematics and Cognition
(https://books.google.com/books?id=xjK0DwAAQBAJ). But even the logical aspects
alone seem to me one of Peirce’s major contributions.
It’s clear that Peirce himself never repudiated that contribution, or John Sowa
would have given evidence of that by now. What puzzles me is why John wants to
repudiate these Peircean insights, when his argument is based solely on his
claim to absolute authority “in mathematics and logic”.
Gary f.
} It is a characteristic of wisdom not to do desperate things. [Thoreau] {
<https://gnusystems.ca/wp/> https://gnusystems.ca/wp/ }{ living the time
From: Jon Alan Schmidt <[email protected]>
Sent: 8-Feb-21 20:39
To: [email protected]; Peirce List <[email protected]>
Cc: [email protected]; [email protected];
[email protected]; [email protected]
Subject: Re: [PEIRCE-L] Scroll vs Nested Ovals (was Existential Graphs in 1911)
John, List, All:
JFS: Thank you for emphasizing the fact that Peirce's only comments in favor of
the scroll came before June 1911.
Indeed, his "only" comments in favor of the scroll are in numerous passages
from his extensive writings about EGs between late 1896 and June 1911.
Nevertheless, as far as I know--please provide a citation if I am
mistaken--there is no passage whatsoever in his entire vast corpus where he
repudiates those favorable comments, nor his underlying analysis of inference.
As I keep pointing out, omission is not rejection.
JFS: In Peirce's writings after that date, the scroll is "equivalent" to a nest
of two negations.
Actually, he never uses the word "scroll" in any of those writings, and he
states that a figure showing nested ovals "is equivalent to" one showing a
scroll (without calling it that) exactly once. It is in a draft manuscript for
a lecture that would have introduced EGs to an audience not previously familiar
with them, where it occurs in the context of explaining why shading is a much
better alternative to thin lines for distinguishing oddly and evenly enclosed
areas. Again, as far as I know--please provide a citation if I am
mistaken--there is no passage whatsoever in his entire vast corpus where he
repudiates the philosophical basis for taking consequence (scroll) as a
primitive, such that negation (cut/oval) is derived from it.
Moreover, even in June and December 1911, he remains consistently adamant about
his primary objective in developing and promoting EGs.
CSP: I wish to draw your attention, in the most emphatic way possible, to the
purpose this Syntax is intended to subserve; since anybody who did not pay
attention to that statement would be all but sure, not merely to mistake the
intention of this syntax, but to think that intention as CONTRARY to what it
really is as well he could. Namely he would suppose the object was to reach the
conclusion from given premisses with the utmost facility and speed, while the
real purpose is to dissect the reasoning into the greatest possible number of
distinct steps and so to force attention to every requisite of the reasoning.
The supposed purpose would be of little consequence, and it is the business of
the mathematicians to furnish inventions to attain it; but the real purpose is
to supply a real and crying need, although logicians are so stupid as not to
recognize it and to put obstacles in the way of meeting it. (RL 231, NEM 3:168,
1911 Jun 22)
CSP: The ultimate purpose of contriving this diagrammatic syntax, is to enable
one with facility to divide any necessary, or mathematical, reasoning into its
ultimate logical steps. (RL 376, R 500:3, 1911 Dec 6)
As I discussed previously (
<https://list.iupui.edu/sympa/arc/peirce-l/2021-02/msg00019.html>
https://list.iupui.edu/sympa/arc/peirce-l/2021-02/msg00019.html), Shafiei's
example of ex falso quodlibet conclusively demonstrates the vast superiority of
scrolls over cuts/ovals for fulfilling the real and ultimate purpose of EGs,
even when employed in accordance with classical logic.
Regards,
Jon Alan Schmidt - Olathe, Kansas, USA
Structural Engineer, Synechist Philosopher, Lutheran Christian
www.LinkedIn.com/in/JonAlanSchmidt <http://www.LinkedIn.com/in/JonAlanSchmidt>
- twitter.com/JonAlanSchmidt <http://twitter.com/JonAlanSchmidt>
On Mon, Feb 8, 2021 at 9:21 AM John F. Sowa <[email protected]
<mailto:[email protected]> > wrote:
Jon AS,
Thank you for emphasizing the fact that Peirce's only comments in favor of the
scroll came before June 1911.
In Peirce's writings after that date, the scroll is "equivalent" to a nest of
two negations. In mathematics and logic, equivalence means freely
interchangeable in all contexts without any change in meaning.
Other people may choose to use a scroll for any purpose they please, but their
choices have no effect on the logic or on anything Peirce wrote.
John
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