SUO: Re: Ontology
Once more, then, John, since some of your remarks are not factual, nor are
they comprehensive. More below.
Jay
----- Original Message -----
From: "John F. Sowa" <sowa@bestweb.net>
To: "Jay Halcomb" <jhalcomb8@attbi.com>
Cc: <meena@hbcse.tifr.res.in>; <cg@cs.uah.edu>;
<standard-upper-ontology@ieee.org>
Sent: Saturday, January 10, 2004 12:22
Subject: Re: Ontology
> Jay,
>
> I apologize for any slurs I may have cast on your mother's
> beloved teacher. And please realize that I also bought
> the _World of Mathematics_ when I was in high school, and
> that is where I first learned about Russell, Whitehead,
> and symbolic logic. In my freshman year at MIT, I took
> a course on symbolic logic, in which I was dutifully
> taught that it all came from Frege, Peano, Russell,
> and Whitehead. In that same year, I read William James'
> book on pragmatism, in which he mentioned his friend
> Charles Sanders Peirce -- but nobody mentioned any
> connection between Peirce and modern logic.
>
> Then for many years I used symbolic logic in what they
> told me was "Peano-Russell" notation. I took a lot more
> courses on the subject, but nobody ever mentioned Peirce.
That's unusual, John, since 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.
> In 1968, I bought the _Sourcebook on Mathematical Logic_
> by van Heijenoort, which jumped straight from Frege
> to Peano, with no mention of Peirce (except in Peano's
> footnote about Peirce as the inventor of the notation).
>
> 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. But in 1978, Martin Gardner
> wrote about Peirce's existential graphs in his column
> in the Scientific American. I followed the references,
> and it was a total revelation. Peirce had done it all
> in a very elegant form, and nobody else in AI (or in
> any of my logic courses) had noticed.
Peirce had done what 'all'? 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? There have been many developments in logic since Peirce -- and
since Russell and Whitehead, for that matter.
>
> As Russell himself said, he did not learn about symbolic
> logic until he went to the conference in Paris in 1899.
> That was 20 years after Frege and Peirce had invented
> the subject and quite a few years after Schroeder had
> published his 3-volume textbook (1890 to 1895), which
> used Peirce's notation throughout.
This is not accurate nor complete. Russell was still in his 20s (born 1872)
when he went to Paris, so in a certain sense he'd only 'just learned about
symbolic logic' (Peano's) -- he was still a young man, one who'd read Euclid
at 11 and Hegel's Logic in his teens.
What he specifically learnt about in Paris was the work of Peano, and what
he said was (for instance):
"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. 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. 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... 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.'"(My
Philosophical Development, Russell).
Russell was evidently a quick and brilliant learner, since he discovered
what Frege had overlooked.
BTW:
"In Mathematics, my chief obligations, as is indeed evident, are to Georg
Cantor and Professor Peano. If I had become acquainted sooner with the work
of Professor Frege, I should have owned a great deal to him, but as it is I
arrived independently at many results which he had already established... In
the endeavour to cover so wide a field, it has been impossible to acquire an
exhaustive knowledge of the literature. There are doubtless many important
works with which I am unacquainted; but where the labour of thinking and
writing necessarily absorbs so much time, such ignorance, however,
regrettable, seems not wholly avoidable." (Principles of Mathematics,
Preface)
Any lack of acquaintance, though, does not extend to Pierce, as shown by
Russell's references to Peirce -- although, beyond Russell's remarks, we do
not know entirely with what of Peirce's Russell was acquainted, and with
what he was not. More on this point further below.
> That was 20 years after Frege and Peirce had invented
> the subject and quite a few years after Schroeder had
> published his 3-volume textbook (1890 to 1895), which
> used Peirce's notation throughout.
What is 'the subject' which Frege and Peirce had invented? Logic? Ab initio?
What Frege (and Peirce, independently) had importantly done was to introduce
variable-binding quantifiers. See the discussion by the Kneale's, below.
After acknowledging the importance of Frege to logic, BTW, and remarking
upon Frege's influence upon Russell, Kneale and Kneale also add, very
reasonably (P. 528, Development of Logic): "This is not to say that the
history of logic in the twentieth century is merely a record of the
assimilation of [Frege's] work into the body of accpted doctrine, for there
have been some very important innovations of which he never dreamt." Or, of
course, of which Peirce had never dreamt also. Such innovations as those of
Russell, Tarski, Godel, Zermelo, and many more. Frege's own notation,
though, was much too cumbrous.
>
> Since Russell read and spoke German fluently,
Russell, BTW, actively promoted Leibniz, whose reputation had languished to
some extent by that time, at least in England. He travelled to Germany and
did translations and commentary.
>there
> is no way that he could have missed Schroeder's book,
> which had become the standard textbook on the subject.
> But he did not refer to either Peirce or Schroeder as
> the inventors of the notation he used.
Russell often referred to Peano with particular commendation; Peano in turn,
as you pointed out, in turn credited Peano, in part. Russell also in
numerous places referred to and discussed many other authors, including
Schroder, Frege, and a host of others. Schroder, for example, is mentioned
ten times in the Principles. One remark is: "By far the most complete
account of the non-Peanesque methods will be found in the three volumes of
Schroder."
>As you pointed
> out, his only reference to Peirce was a disparaging
> mention of P's 1870 work on relations with more than
> one argument (which DeMorgan hailed as the "greatest
> advance in logic since Boole").
No, I did not point out that 'his only reference to Peirce was a disparaging
one.' I pointed out that the Principles contains several references to
Peirce (which you had denied) -- some of them critical, and some
complimentary. In fact, the Principles contains seven references to Peirce.
Check the original, and check my own remark, too.
>
> Then Russell published his _Principles of Mathematics_
> in 1903 -- just four years after he first learned the
> subject from Peano.
Russell had not 'just learned' the subject of logic, except in the sense of
finding Peano -- who did indeed open his eyes, as he stated. What he then
begun to *invent* was type theory.
>In his published review of that
> book, Peirce wrote "a compendium of well-known results",
> but in a letter to Lady Welby, he called it "superficial
> to the point of nauseating me." What else would you
> expect Peirce to say? R. had just learned the subject
> and tossed off a book immediately after learning about it.
> No matter how brilliant R. might be, the book was certainly
> superficial by the standards of Frege, Peirce, Schroeder,
> Hilbert, and others who had been working on it for years.
Let me again mention Type Theory and the Contradiction in Frege.
>
> JH> I don't believe that Putnam, Quine or Hintikka ever
> > wrote that Russell was simple-minded, or that they said
> > that his work was nonsense or a travesty or unthoughtful,
> > or showed no spark of originality, or any other of those
> > loaded remarks you're fond of making, or even that he
> > never referred to Peirce, which is simply factually
> > egregious, as we've seen.
>
> Please let me try to put those words back into the
> context in which I wrote them.
>
> Putnam, Quine, and Hintikka were doing the same thing
> that I am doing now -- making brief historical remarks
> to set the record straight.
I don't believe Putnam, Quine, or Hintikka used the kind of scurrilous
language in connection with Russell you have liked to use, but I'm still
waiting to learn otherwise. No page references have been forthcoming on that
point, but -- speaking of contexts -- I see that you've deleted my previous
request for such references.
>
> The term "simpleminded" was Whitehead's, whose words I
> quoted, in which W. referred to himself as "muddleheaded"
> and R. as "simpleminded". Those are indeed disparaging
> terms, but W. used them to characterize both himself and
> R. in the same slightly disparaging, but humorous way.
> I observed that those terms, when taken in that sense,
> are a good way of describing the difference between
> the two. In doing so, I did not say that R. was not
> "thoughtful" in an absolute sense, but that he was
> more likely than W. to resort to witty remarks than
> detailed, thoughtful analyses.
That above of yours is all a rather different, kindlier spin than the last
time around, John. I'm glad to see you getting off the pedal to some extent.
>
> I did apply the words "nonsense" and "travesty" to
> R's _History of Western Philosophy_ because it is a
> highly distorted presentation that is (a) historically
> inaccurate (see, for example, R's misrepresentation
> of the history of logic), (b) unsympathetic to most of
> the philosophers he describes, and (c) heavily dependent
> on secondary sources rather than the original material.
>
The History isn't concerned with logic -- it's concerned with philosophy in
general, and hardly treats logic at all. It's a history of philosophy, not
of physics, or logic, or mathematics. And philosophy, like religion, is
endlessly controversial.
The book is Russell's account of the history of philosophy from his own
viewpoint, and designedly critical of other philosophers on just that basis.
It's particularly concerned with the social context in which philosophy is
done, and of course deliberately involves Russell's own interpretation of
those contexts.
The book isn't heavily dependent on secondary sources, though, any more than
any other such history. In fact some of it is based, for example, on the
translations of Leibniz which Russell made in Germany.
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>
> And of course Russell referred to Peirce, but only
> to disparage him instead of giving him credit.
Wrong. Check the originals. He did though, point out errors or infelicities
in Peirce, as well as commend him.
> I did not say that R. "showed no spark of originality",
> but that Whitehead believed that his more "muddleheaded"
> students were more likely to be the creative ones.
> There is certainly nothing new in R's _Principles of
> Mathematics_, which a good textbook, but not original
> research.
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 also said that two of Russell's most famous
> discoveries had been done better by others:
>
> 1. R's 1905 work on definite descriptions had been
> anticipated by Ockham in a form that is more
> complete and thorough, although written in Latin
> instead of symbolic logic.
'Anticipated in Latin' covers a multitude of sins. Without the symbolic
logic -- variable binding quantifiers -- which hadn't been invented, the
significance of Russell's analysis is lost.
>
> 2. R's discovery of the contradiction in Frege's work
> had been noticed by Zermelo, who did not publish
> the contradiction in a separate paper. Instead,
> he published his axioms for set theory that avoided
> the contradiction.
And....? Zermelo didn't publish his thoughts on Frege at the time that
Russell did. How is that a fault of Russell's?
>
> Russell deserves credit for discovering these points
> independently, but he was not a groundbreaking pioneer.
> I might also mention that the so-called "DeMorgan's Laws"
> for relating the Boolean operators AND and OR, were also
> stated in Latin by Ockham.
I will mention once again that Peirce did not invent the Theory of Types,
nor discover
the Contradiction. Nor invent set theory, for that matter.
>
> All of these points are factual observations, which are
> documented in the literature. This is not a hatchet
> job on Russell, but a necessary correction of historical
> oversights.
>
> John
>
Your remarks remain selectively factual, when they are not wrong, and are
skewed, tendentious, 'unsympathetic', and frankly, some of them have been
absurd. Most of your suggestions are not documented as such in any
literature I've seen. Although, of course, it is quite true that Russell has
been criticized for many things, some of which he's actually been guilty of
(and has acknowledged, BTW, such as the implausibility of the Axiom of
Reducibility, or the confusion between language and object in the P.M.).
Mine is a correction of your revisionism. For myself, I both credit Peirce
with originality and insight, and fault him for his fogginess and mysticism,
and for his peculiar theory of truth, and his odd vocabulary, and so on.
No more do I believe that Russell or Whitehead did the deepest or most
important work in modern logic. Much of greater significance has been
learned since Russell, and both he and Whitehead quit working in the heavily
symbolic field after their monumental efforts. But at the time, their work
was a very important stimulus which led directly to important developments,
e.g., in modern versions of type theory..
Here are some other historical reflections on Peirce, which you may have
read but which perhaps some others haven't:
"Unfortunately Peirce was like Leibniz, not only in his originality as a
logician, but also in his constitutional inability to finish the many
projects he conceived." (P.410), Kneale and Kneale, The Development of
Logic)
Speaking of the logic of relatives: "Is [this] result a natural extension of
Boolean algebra? ... although there are some analogies between the three new
and the three old operations, anyone who studies the details in the work of
Schroder may well doubt whether this attempt [Peirce's] to present the
theory of relations as an algebra is worth the trouble it involves.... When
his earlier suggestions had been worked out in detail by Schroder, Peirce
himself came to appreciate this point." (P. 430, Kneale and Kneale, The
Development of Logic)
[Neither Peirce nor Russell invented, say, cylindric algebras, nor polyadic
Boolean algebras, nor category theory, nor set theory. There are many
developments in logic. Why do you seem to feel that there is too little
credit to go around? Are there not enough problems of interest remaining to
exhaust many lifetimes? Isn't it comforting to know that "we'll never run
out of work"?]
"In his paper of 1883 and his more detailed study of 1885, Peirce gave the
credit for these new devices [quantifiers] to O.H. Mitchell. This pupil of
his had indeed used relational signs with indices and the operators Pi and
Sigma in his contribution to Johhs Hopkins Studies in Logic, but not in
conjunction with or with the senses which Peirce gave to them." (P. 431,
Kneale and Kneale, The Development of Logic)
[Should we not be referring to the Mitchell notation, then? Although what
Peirce did was notable and 'original' (as far as hnew), he too, like
everyone else, built upon the work of others -- and credited them, BTW. His
work, though, didn't achieve much recognition in his lifefime; somewhat
ironically, he was unpopular among his peers. Perhaps because of remarks
like that one about his nausea?]
"We cannot, it is true, give Peirce the credit of being the first to
conceive a comprehensive theory of general logic; for that honour belongs to
Frege, who published his Begriffschrift in 1870. But, so far as is known,
Peirce had mever heard of Frege when he published his paper on The Logic of
Relatives in 1883, and his achievement therefore deserves commemoration."
(P. 432, Kneale and Kneale, The Development of Logic)
"Working on some suggestions of De Morgan, Perice explored this new field,
and shortly after the publication of the Begriffschrift he even produced
independently a doctrine of functions with a notation adequate for
expressing all the principles formulated by Frege; but he never reduced his
thoughts to a system nor set out a number of basic principles like those
given [by Frege]. (P. 510, Kneale and Kneale, The Development of Logic)
"Of all the novelties which Frege introduced his use of quantifiers was the
most important. In our account of Peirce's contribution to logic we have
already drawn attention to the significance of this step, but it is proper
at this point to emphasize once more that use of quantifiers to bind
variables is the main distinguishing feature of modern logical formalism,
and the device which gives it superiority not only over ordinary language
but also over symbolism of the type used by Boole." (P. 511, Kneale and
Kneale, The Development of Logic)
In a nutshell: Russell was principally concerned at that time, along with
Whitehead, to develop the theory of types, as a response to Russell's
discovery of the Conradiction. In the process Russell made a different
assessment of Peirce's work in logic (and philosophy) than you care for, as
you are enamoured of Peirce. That's fine with me; at least, until we
consider the details. But your`s is very much a minority opinion, as Google,
for instance, demonstrates: "Bertrand Russell" - 236,000; "Charles Peirce" -
6,250. (Unsurprisingly, neither one compares well with "Bill Gates" -
2,270,000). I usually have myself a certain kind of sympathy for minority
opinions, but not when they're absurd.
Now, why don't you perhaps take up (modern versions of) type theory, and
discuss the technical merits and shortcomings of those? This might be
fruitful. Or, if you want to argue the philosophy, argue the philosophy
directly.
Jay