SUO: Re: Thirdness vs Local Inconsistencies; was Ontology, Epistemology,Semiotics
Tom,
I realize that the "There you go again" reponse can be too
easily applied a lot the comments that Jon and I have been
making about Peirce. I get a similar response when I tell
people who are working on knowledge representation that
they have to study logic. People who are "professionals"
in a field do not like to be told that they don't know
the rudiments of their own subject.
JS> And that gets to my major complaint about Vulgar Rortyism:
> Rorty was exposed to Peirce, but he was too puffed up with his
> own reflection to recognize the goldmine he was digging in.
TJ> I believe you've said the same thing about Quine. And I believe
> I found a similar comment about William James, in the Haack
> article you sent. It almost sounds like Conspiracy Theory
> Meets Modern Philosophy.
Actually not. The original conspirators were Russell and Quine,
and some of us are fighting an uphill battle to undo the damage.
And by the way, I have read nearly all of Quine's works, but I
can't stomach Rorty's. Both Haack and I have a high regard for
William James. James was Peirce's closest friend, but he was
not a mathematician (not even close), and he was never able
to understand the logic. I can excuse James because his lack
of comprehension was not from a lack of trying. But I can't
excuse Rorty.
First, let me start with a bit of history:
1. Frege published his Begriffsschrift in 1879, and it was
almost completely ignored by everybody. Carnap was one
of the very few students who attended Frege's lectures,
and even he switched to the Principia notation after 1910.
2. Peirce published his two articles "On the Algebra of Logic"
in 1880 and 1885. The 1880 article wasn't as complete as
Frege's, but the 1885 article became the foundation for
all subsequent work on predicate calculus. Ernst Schroeder
wrote a review of Frege's Begriffsschrift, in which he
compared Frege's notation unfavorably to Peirce's (and in
that, he was absolutely correct). Frege paid more attention
to the syntactic details than Peirce (for which he deserves
credit). But Peirce's 1885 article contained the following:
a) Sound and complete rules of inference for first-order logic.
b) Model-theoretic arguments for the soundness of his rules
of inference (his presentation was not as rigorous as
modern treatments, but this was the first publication
of modern predicate calculus).
c) Examples of proofs, in which he recommended that formulas
should be converted to prenex normal form before doing
the proofs. (But he didn't use the term "prenex".)
d) Examples of second-order logic, including the first
formal definition of x=y as (for every predicate P,
P(x) if and only if P(y)). That definition is usually
credited to Russell, but Peirce published it over
20 years earlier.
e) The terms "existential quantifier" and "universal
quantifier" (Frege had only a universal quantifier,
and he did not give a name to it) as well as "first
intentional" and "second intentional" logic, which
Schroeder translated into German as erste und zweite
Ordnung, which Russell translated back into English
as "order".
3. Schroeder adopted Peirce's notation, which he used for
his three volume "Vorlesungen ueber die Algebra der Logik",
which became the primary textbook on logic until the
Principia came out in 1910. Hilbert, Zermelo, Loewenheim,
and Tarski published their early work on logic and set
theory using Peirce's notation.
4. Peano adopted the notation from Peirce and Schroeder,
but he changed the symbols to keep the math and logic
symbols distinct. Peano gave full credit to Peirce and
Schroeder and said that Frege's notation was unreadable.
After Peano published an unfavorable review of Frege's
work, Frege began a correspondence with Peano, but
Peano insisted that Frege translate his diagrams into
Peirce-Peano notation before he would read them.
5. Russell said that he first learned logic from Peano at
the Paris conference in 1900. Then he published his
Principles of Mathematics using Peano's notation in 1903.
In a review of that book, Peirce wrote "A good compendium
of well-known results." But in a private note to Lady Welby,
he called it "superficial to the point of nauseating me."
He was right in saying both of those statements.
6. In the Preface to the Principia Mathematica (1910), Russell
credits Peano and Frege, but ignores Peirce and Schroeder.
That notation is usually called Peano-Russell notation,
despite the fact that Peano credited it to Peirce and
Schroeder, and Russell did not change anything in Peano's
notation (even that dot convention for showing operator
precedence was Peano's invention).
7. In their 1926 introduction to logic, Hilbert and Ackermann
give a brief, but fair summary that credits Frege, Peirce,
Schroeder, and Peano. Everybody else follows Russell's
practice.
If you want to know why I am so angry at Quine, I suggest that
you look at van Heijenoort's _Sourcebook in Mathematical Logic_.
The first article is Frege's complete Begriffsschrift of 1879,
and the second article is an excerpt from Peano's 1889 work.
The first mention of Peirce in that book is in a footnote
on page 86, and it is not in a commentary by van Heijenoort
-- it is in a footnote by Peano, who gives credit to Peirce,
but not to Frege.
In the preface to that book, van Heijenoort thanks Quine
who "generously contributed" his time in helping van H.
"select the texts." Meanwhile, all of Peirce's collected
manuscripts were sitting in the Harvard library under
Quine's nose.
What is especially galling is that van Heijenoort's book
is repeatedly praised for its historical scholarship.
I bought it myself in 1968, and I was also misled into
thinking it was good. And it wasn't until ten years
later that I discovered that it was a deliberate act
of historical malpractice (but I blame Quine more
than I blame van H.).
Re Whitehead: Yes, I also have a very high regard for
Whitehead, who really deserves more credit for what is
good about the Principia Mathematica. Whitehead, by
the way, did not take part in the second edition, and he
wrote a letter to _Mind_ disavowing the new introduction
by Russell. I think he was right to disavow it.
John