SUO: Re: Ontology
Jay,
Since Cathy Legg already covered many of your questions,
I'll just respond to the ones she didn't address.
The following passage you quoted is an example of what I
had previously called "nonsense". But I admit that is
a loaded word. Instead, I'll use the more precise
technical term: "lie".
BR> "In Paris, in 1900, I was impressed by the fact that, in all
> discussions, Peano and his pupils had a precision which was
> not possessed by others. I therefore asked him to give me his
> works, which he did. As soon as I had mastered his notation,
> I saw that it extended the region of mathematical precision
> backwards towards regions which had been given over to
> philosophical vagueness. Basing myself on him, I invented
> a notation for relations."
If you look at the original publications by Peano, you will
see that Russell added *nothing* to Peano's notation. Even
the dot notation for showing precedence, which is used
throughout the Principia, was invented by Peano in 1889.
And if you look at Peano's publications, you will see that he
gives full credit to his predecessors. In his first publication
on the application of logic to arithmetic in 1889, Peano says
"The logical symbols and propositions contained in parts II,
III, and IV, except for a few, are to be traced to the works
of many writers, especially Boole." In a footnote, he cites
the publications by Boole, Schroeder, Jevons, MacColl, and
Peirce's two papers "On the Algebra of Logic", 1880 & 1885.
Peano was unaware of Frege's work until he was asked to review
a paper by Frege, which he described negatively as using an
unreadable notation. Frege wrote a reply to Peano, which
initiated a correspondence between them -- but Peano insisted
that Frege translate his Begriffsschrift notation into the
algebraic form before P. would read F's letters.
BR> "Whitehead, fortunately, agreed as to the importance of the
> method, and in a very short time we worked out such matters
> as the definitions of series, cardinals, and ordinals, and
> the reduction of logic to mathematics."
That is an odd claim, because the reduction of logic to
mathematics is what Frege and Peirce had already done 20
years earlier. What Frege and Russell were unsuccessfully
trying to do is to reduce mathematics to logic. What W.
and R. did in the Principia is to define mathematics in
terms of set theory, which is today considered a part of
mathematics, not a part of logic.
BR> "For nearly a year, we had a rapid series of quick
> successes. Much of the work had already been done by
> Frege, but at first we did no know this..."
This is one more example where Russell tries to make it
seem that he (with a little help from Whitehead) discovered
independently what others had accomplished 20 years earlier.
But Peano's publications, which Russell read, contained many
long lists of results, which, as Peano always acknowledged,
came from others, including Frege, Peirce, Schroeder, etc.
Competent mathematicians, as Whitehead and Russell certainly
were, can take a list of results and quickly reconstruct
the proofs for themselves. That is not considered
"groundbreaking research".
JH> No, the Principles was original, including new and careful
> discussion of Frege's Contradiction and the beginning
> formulations of Type Theory. The Principles, which Whitehead
> proofed, led to the P.M.
I agree that Russell did contribute some original points,
such as a version of type theory and his observation of the
contradiction in Frege's system. But the bulk of it was a
reconstruction of "well known results" from Peano's long lists
of formulas that he, his students, and the many predecessors
he cites had discovered.
BR> "In June 1902, this period of honeymoon delight came to
> an end. Cantor had a proof that there is no greatest cardinal;
> in applying this proof to the universal class, I was led to
> the contradiction about classes that are not members of
> themselves. It soon became clear that this is only one of
> an infinite class of contradictions. I wrote to Frege,
> who replied with the utmost gravity that 'die Arithmetik
> ist ins Schwanken geraten.'"
Russell deserves credit for discovering a contradiction that
Frege had overlooked. But that problem only creates a difficulty
for Frege's set theory -- it certainly does not cause arithmetic
to totter (Schwanken). I agree with Kronecker, Peirce, and many
others that arithmetic is far more solid than set theory. And
what Goedel did is the opposite of what Frege and Russell were
trying to do: Goedel numbering models logic in arithmetic,
which has a far more reliable foundation than logic.
JH> Zermelo didn't publish his thoughts on Frege at the time
> that Russell did. How is that a fault of Russell's?
Neither Peirce nor Zermelo considered that contradiction
to be a big deal. What Zermelo published were axioms that
avoided the contradiction. If you use ZF set theory, you
have a simpler foundation without the theory of types.
I was not blaming Russell. I was just pointing out that
the mainstream of logic and set theory in continental
Europe was based on Peirce and the logicians who built on
his work -- including, Schroeder, Peano, Hilbert, Zermelo,
Loewenheim, Tarski, etc. If Frege and Russell had never
existed, the technical achievements in logic would not have
slowed down at all -- in fact, they might have advanced
more rapidly because Tarski had to fight an uphill battle
against the entrenched Frege-Russellism to get model
theory accepted.
These points are confirmed by the references I thought I
had given, but they are also listed in my commentary on
Peirce's MS 514. In any case, I add a copy at the end
of this note.
Some other comments:
JH> ... I have fairly frequently heard Peirce's logic discussed
> in academic settings. Just a short while ago, in fact, although
> it's true that Peirce comes up less often than many others.
> But Peirce is discussed extensively, for instance, in Kneale
> and Kneale's Development of Logic, which is a standard historical
> work in logic.
Two points: (1) In 1989, there was a one-week conference
at Harvard to celebrate Peirce's 150th birthday; that event
helped spur a minirevival of interest in Peirce, but that
was long after I was in college. (2) I have a high regard
for the scholarship done in the two major histories of logic:
the one by Kneale and Kneale, which you cited, and another
one by Bochenski. But both of them have blind spots, partly
caused by the harsh light cast by Russell's all-pervasive
publicity.
As examples, I'll quote some typical passage from Bochenski's
_History of Formal Logic_:
Page 347: In discussing quantification, Bochenski says
"Hence it must have been developed independently of Frege
by Mitchell (1883), Peirce (1885), and Peano (1889)."
Those last three are independent of Frege, but they are not
independent of one another. Mitchell was Peirce's student,
whom Peirce graciously credited with reinterpreting P's
own symbols Pi and Sigma as quantifiers in 1883. But P.
had introduced Pi and Sigma in a logically equivalent form
in 1880 without interpreting them as quantifiers. And as
I said, Peano cited Peirce, not Frege, as a source for
his notation.
Page 349: Bochenski says "Peirce's notation was adopted by
Schroeder and today is still used in Lukasiewicz's symbolism.
But Peano's is more widely established since its essentials
were taken over in the Principia."
Two problems with that point: Peano explicitly gave credit to
Peirce and Schroeder from whom he took over the "essentials",
but made a different choice of symbols. Russell took over
Peano's notation unchanged -- in detail and essentials.
JS> In my first publication on conceptual graphs in 1976,
> I was trying to combine the AI work on semantic networks
> with a solid logic foundation, but I was not completely
> happy with the combination.... Peirce had done it all
> in a very elegant form, and nobody else in AI (or in
> any of my logic courses) had noticed.
JH> Peirce had done what 'all'?
By "all", I meant exactly what I said in the first sentence
of that paragraph: Establish a solid logic foundation for
semantic networks with an elegant proof theory and a
model-theoretic semantics. I have been citing the following
web page with citations for those points in almost every
note I wrote on this topic. Please look at the references:
http://www.jfsowa.com/peirce/ms514.htm
Existential Graphs
JH> Invented the Theory of Types, for instance? Found the
> conradiction in Frege? Invented the semantical definition
> of truth? Proved the Completeness Theorem? Invented Godel
> numbering? Proved the Incompleteness Theorem? None of these.
> Shall I mention the Contradiction in Frege again?
JH> Let me again mention Type Theory and the Contradiction in Frege.
See Cathy's comments. As for Russell's theory of types, that
was demolished by both Wittgenstein and Frank Ramsey to the
point where both Russell and Whitehead admitted that it had to
be completely rewritten for the second edition of the Principia
-- but neither of them had the time to do it. See Ray Monk's
biography and his citations for more detail.
JS> And of course Russell referred to Peirce, but only
> to disparage him instead of giving him credit.
JH> Wrong. Check the originals. He did though, point out errors
> or infelicities in Peirce, as well as commend him.
I read a library copy of R's P. of M., so I can't check the
citations now. But R did not point out any "errors" in Peirce,
and the "infelicities" were in Peirce's 1870 paper, which was
was the first publication that went beyond monadic predicates.
And R. certainly did *not* credit Peirce with inventing the
notation he was using -- in fact, Russell lied in claiming
that he had improved upon Peano.
JH> And, finally, the History is *delightfully* critical of many
> philosophers. Including the pragmatists Dewey and James, BTW,
> which I suspect galls pragmatists particularly. Again, see:
> <http://www.sonic.net/~halcomb/Russell_Pragmatism_Power.html>
I did follow that pointer, and I own a copy of R's _History
of Western Philosophy_ (which I bought for $1 at a book sale).
But my terms "travesty" and "nonsense" are mild compared to what
professional philosophers wrote about HoWP. The following is
from vol. 2 of Ray Monk's biography:
RM> p. 279 HoWP "was greeted with almost universal disdain
> by the academic philosophers who reviewed it. Even C.D. Broad,
> an ex-pupil and admirer of Russell's who had played a hand in
> getting him back to Cambridge, could not bring himself to
> overlook the book's outrageous and cavalier superficialities
> and simplifications. Nevertheless, despite its many flaws
> (or perhaps to some extent because of them), the book became
> a runaway best-seller and placed Russell's finances on a
> secure footing for the rest of his life."
Russell's other attempt to get back into serious philosophy
was _Human Knowledge: Its Scope and Limits_, which did
not fare any better among professional philosophers.
RM> p. 295: "He was particularly hurt by a review of _Human
> Knowledge_ by Norman Malcolm, Wittgenstein's friend and
> disciple, which ended by saying:
>
> Anyone who feels grateful, as I do, for the splendid
> work he did in philosophy and logic during the first
> twenty years of this century, is likely to regard the
> present book with considerable regret.
>
> Malcolm accused Russell of slipshod language and careless
> thought, and of not even *trying* to think through the
> philosophical questions seriously: 'The style is jaunty and
> bouncy and reminds me of the patter of a conjurer who wishes
> to entertain, dazzle and bewilder the customers. I have the
> impression that the author, after writing philosophy for so
> many years, is not tired, but callous.'
>
> Malcolm's review was especially harsh, but the view that
> _Human Knowledge_ was inferior to Russell's earlier work was,
> and still is, almost unanimously held by professional
> philosophers...."
And following is the review of HoWP:
RM> p. 296 "He kept a copy of Malcolm's review of _Human Knowledge_,
> which he annotated, and a copy of an even more scathing review,
> this time of _History of Western Philosophy_, written by another
> of Wittgensteins friends and disciples, Yorick Smythies. HoWP,
> Smythies wrote, 'embodies what seem to me the worst features of
> Lord Russell's previous more journalistic works, but it is of
> poorer quality than any of these'. Severly criticizing both
> the style and the content of the book, Smythies concluded:
> 'I fear that Lord Russell's book will teach successfully a
> a popular substitute for thinking and for knowledge, and that
> it will both appeal to and stimulate slipshod thinking.'"
Russell gave a brief summary of his prejudices in a radio
broadcast during the time he was writing HoWP:
"I think philosophy has suffered four misfortunes in the
world's history -- Plato, Aristotle, Kant, and Hegel. If
they were eliminated, philosophy would have done very well."
(quoted by Monk, vol. 2, p. 255).
Hegel is more controversial, but Plato, Aristotle, and Kant are
in most lists of the greatest philosophers of all time. With
such company, it would be an honor to be disparaged by Russell.
John
________________________________________________________________
References that correct the histories by Bochenski and by Kneale
and Kneale:
Hintikka, Jaakko (1997) "The place of C. S. Peirce in the history
of logical theory," in Brunning & Forster, eds. (1997) _The Rule
of Reason: The Philosophy of Charles Sanders Peirce_, University
of Toronto Press, Toronto. pp. 13-33.
Putnam, Hilary (1982) "Peirce the Logician" Historia Mathematica
9:290-301, reprinted in Putnam, _Realism with a Human Face_,
Harvard University Press, Cambridge, MA. pp. 252-260.
Quine, Willard Van Orman (1995) "Peirce's logic," in K.L. Ketner,
ed., _Peirce and Contemporary Thought_, Fordham University Press,
New York. pp. 23-31.