SUO: Re: Thirdness vs Local Inconsistencies
Tom,
There are many complex reasons why the history of logic turned
out the way it did, and it really isn't a conspiracy. It is
more the result of large numbers of historical accidents,
trends, fads, personal grudges, and just plain oversights.
1. Peirce was really in the center of the scientific
world during the 1870s and 1880s when he was actively
corresponding with and visiting Schroeder, De Morgan, and
others. At that time, he was teaching at Johns Hopkins,
where he had some very good students, and he was working
at the US Coast and Geodetic Survey, which paid him to
travel around the world to measure gravity and perform
other experiements.
2. Besides his fame in logic, he was simultaneously
famous in physics and mathematics. He was the first
US scientist to be invited to lecture at international
congresses in Europe, he invented instruments of his
own design for measuring gravity with greater precision
than had ever been done before, and he was not only
the first person to propose that the standard for
length be based on a wavelength of light, he actually
built the apparatus to use light waves to measure the
length of his pendulum arms. In mathematics, he was
a colleague of Cayley and Sylvester (from whom he got
many of his ideas about graphs), and he edited his
father's pioneering book on linear algebra, to which
he added a number of new theorems of his own.
3. But some serious reversals in his fortuntes occurred,
partly caused by the death of his father, partly caused
by his divorce and remarriage, and partly caused by
incredible villany on the part of Simon Newcomb, a
former student of his father's, who had been jealous
of Peirce's greater fame as a scientist. As a result,
Peirce lost his job at the USC&GS and at Johns Hopkins
and was blackballed at every university where he applied
for a job (primarily because Simon Newcomb, his former
superior at the USC&GS wrote a highly negative review
to everyone who might hire him). He had to support
himself with many part-time jobs, including his role
as associate editor of the Century Dictionary, for which
he wrote, revised, or edited over 16,000 definitions.
4. As late as 1902, he tried to get support to write a
book on his logic from the new Carnegie Foundation,
which was giving money to support science projects.
He had letters of recommendation both from a senator
from New York and from President Teddy Roosevelt.
But Simon Newcomb, the head of the committee that
was distributing the funds, rejected his application
on the grounds that logic was not science.
This is a brief summary of the much greater detail that
can be found in the biography by Joseph Brent.
Meanwhile, the old logicians who had known Peirce were
dying off, including his strongest backer, Ernst Schroeder.
Peirce had no money to travel, no academic affiliation,
and no new students to pursue his research further.
Whitehead cited Peirce's papers on the algebra of logic
in his 1898 book on Universal Algebra, but Russell was
trying to make a name for himself, and he had no reason
to advertise the work of his predecessors (especially
if they had invented the same things earlier -- as
Donatus said, "Pereant qui ante nos nostra dixerunt").
In the late 1920s, Quine went to Harvard to study with
Whitehead, and after he got his PhD, he won a fellowship
to go to Europe, where he spent some time with the
Vienna Circle and became a close friend of Carnap,
from whom he learned that Frege had invented everything
there was to know about logic. Then for the next 70
years, Quine was Frege's loudest cheerleader at the
most prestigious university in the US.
Another reason why Quine might have been cool
on Peirce is that in his early days at Harvard,
he was quarreling with C. I. Lewis, who was
a very strong advocate of Peirce's work.
The editing of Peirce's Collected Papers was
initiated by Lewis and done by two of Whitehead's
graduate students, Hartshorne and Weiss (neither
of whom was strong in logic -- and a better title
for that work would be "Collected Excerpts").
Meanwhile in the UK, Dummet was churning out book
after book about Frege, while ignoring everything that
occured on the other side of the pond. Most other
logicians are not historians, and most historians
know nothing about logic. When logicians go back
into history, the oldest book they look at is
the Principia Mathematica, in which they see
Russell's note about Peano and Frege.
> 1) I believe that Kneale and Kneale have published what
> is acknowledged as the standard history of logic. Have
> they got the story right?
They mention Peirce as somebody who invented FOL
shortly after Frege, but neither the Kneales nor
Bochenski (who says much more about the early history
than the Kneales) says that it was Peirce's notation
that everyone adopted rather than Frege's. They
all say that the notation came from Peano, but
they don't mention (or at least don't emphasize)
that Peano got it from Peirce and Schroeder. In
any case, van Heijenoort's book is the major source
for most logicians, and it skips from Frege directly
to Peano with nothing in between.
> 2) There is a good history of the work on logic done by Russell
> and Quine in particular. It's by Hao Wang, an important logician
> in his own right. The book is "Beyond Analytic Philosophy"
> (MIT Press, 1988). His only mention of Peirce is in a brief
> section "Pragmatism and C. I. Lewis". So the cover-up (or
> oversight? or a little of both?) has been pretty extensive,
> and has fooled a serious logician writing a history of that period.
Wang was a close friend of Goedel's, who came on the
scene after Russell and Carnap had already begun to
dominate the logical scene, and Wang would have had no
reason to go digging in the earlier work. As I said,
there was no organized cover-up. People were just
promoting themselves and their buddies.
The last logician of that generation who was seriously
interested in Peirce was Frank Ramsey, who recommended
Peirce to Wittgenstein. For more on that encounter,
see the paper by Jaime Nubiola:
http://members.door.net/arisbe/menu/library/aboutcsp/nubiola/scholar.htm
I always wondered what might have happened to the history
of logic and philosophy if Ramsey had not died so young.
> 3) Could it be more oversight than cover-up, an oversight
> based perhaps on what I yesterday called the "hermeneutic"
> character of Peirce's writings, and the "high cost of entry"
> to hermeneutic systems?
As I said, Peirce was very much in the mainstream during
the 1870s and 1880s, but in his later years, he had no
job, no money, no students, and no one with whom he
could discuss his ideas. He continued writing many
pages of manuscripts, mostly unpublished, which are
highly idiosyncratic. Most Peircean scholars regard
his later work as the most revolutionary and the most
profound. Unfortunately, the Collected Papers, which
were not edited by logicians, do not bring out the
connections between Peirce's logic and the rest of his
philosophy, which Peirce, Haack, and I believe are
his most important contributions to modern (i.e., 21st
century philosophy, logic, and artificial intelligence).
In any case, Peirce's background in mathematics, physics.
logic, and lexicography gave him a breadth and depth
that is rare, if not unique, in the history of philosophy.
And I even forgot to mention that Peirce boasted of having
the largest collection of medieval manuscripts on logic
in the Boston area -- even more than Harvard library.
That background led him to put more emphasis on language
than Frege, Schroeder, Peano, Russell, Hilbert, or Goedel.
That is another reason why Peirce's combination of logic
and semeiotic is so much more valuable than the work by
logicians whose only applications are to mathematics.
(And it's also another reason why they ignore him.)
John