[Inquiry] Re: Fractured Frege Tales -- Discussion
Jon Awbrey
jawbrey at att.net
Mon Mar 28 14:40:53 CST 2005
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FFT. Discussion Note 4
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Theresa,
Was that here, or maybe the CG or SUO list?
At any rate, it's something of a stretch to lump
George Spencer Brown in with Frege and Russell,
since GSB's "Laws of Form" is more closely akin
to Peirce's Alpha Graphs, especially in the
entitative interpretation, as Peirce wrote
it up in his "Qualitative Logic" in NEM.
As far as I know the only connection
between GSB and Russell is that GSB
self-reportedly showesd his work to
Russell shortly before the latter's
death, and Russell GSB-repoirtedly
said that it was an improvement
over his stop-gap measures in
the theory of types. WIW.
Jon Awbrey
Theresa Calvet wrote:
>
> Thanks for your reply. For some reason or other this sort of reminded me of
> a previous thread in 2001 (and I did enjoy what John Sowa wrote then to you),
> and also what John Sowa wrote to Tom Johnston in 2003:
>
> "From: "John F. Sowa"
> Date: Tue, 27 Mar 2001
>
> Jon,
>
> Your calculus is interesting, but I disagree with your approach,
> which follows in the tradition of Frege-Russell-Spencer-Brown:
> it treats the rules of inference as primitives that are not
> justified by their effects on truth conditions:
>
> >When it comes down to this
> >very primitive level of formal structure, I find it important to note
> >and I even tend to stress the formal significance of the circumstance
> >that this formal system is a "very abstract calculus" (VAC), devoid of
> >meaning in the usual logical sense. I cannot speak for how this works
> >out or what it might mean beyond this point, on the next levels of form.
>
> Peirce and Tarski followed the Aristotelian-Scholastic
> tradition of treating logic as "the formal conditions for
> the truth of representations", as CSP stated it. As I pointed
> out in my commentary on Peirce's MS 514, there is a continuous
> line of descent from Aristotle to the medieval Scholastics to
> Peirce and Tarski. In that tradition, Frege and Russell stand
> out as aberrations, which have mercifully been put to rest.
> Spencer-Brown's approach is an unfortunate throwback to Frege.
>
> For a brief review of the justification in terms of
> truth conditions, click on the following URL and search
> for the text beginning with the word "Ockham":
>
> http://www.jfsowa.com/peirce/ms514.htm
>
> >The first theorem is known as the "Double Negation Theorem" (DNT).
> >The proof that succeeds it is derived from the one that was given
> >by George Spencer Brown in his book 'Laws of Form', and credited
> >to two of his students, John Dawes and D.A. Utting. This result
> >is annotated as "Consequence 1" (C1) or as "Reflection" in LOF.
>
> Ockham, Peirce, Tarski, and others proved it in terms of its
> effects on truth conditions. GSB, like Frege and Russell,
> just played with meaningless symbols.
>
> There is nothing wrong with developing a formal calculus,
> but to justify the rules of inference as anything more than
> a meaningless game, you have show what effects they have on
> truth conditions.
>
> John Sowa
> ----------------------------------------------------------------------------
> From: "John F. Sowa"
> Date: Thu, 28 Jun 2001
>
> Jon,
>
> > Yes, but there seem to be reasons - of the unconsciously enculturated
> > sort - why certain types of patterns just keep on happening, for all
> > our pretenses of e-lightenment.
>
> As a good scholarly starting point, it would make a fascinating story
> to explore exactly why Peirce has been systematically expunged from
> every philosophy text or course written in the analytic tradition.
> Some references with comments:
>
> 1. Coffa, J. Alberto (1991) The Semantic Tradition from Kant to Carnap,
> Cambridge University Press, Cambridge.
>
> This book starts with Kant, presents Bolzano as the beginning of
> what Coffa calls "the semantic tradition", shows how Bolzano
> "invented" a three-way distinction (surprisingly similar to
> Aristotle's), shows how it influenced Frege, discusses Frege as
> the big hero, and then goes on to Russell, early Wittgenstien,
> Tarski, and the Vienna gang.
>
> There is not a single mention of Peirce, Aristotle, or any of
> the Scholastic crowd; Schröder is mentioned once and dismissed as
> a "computationalist". Perhaps it didn't occur to the author that
> Bolzano, as a Catholic priest, might have read something about
> signs and triads in the Aristotelian tradition.
>
> The blurbs on the back of the book quote a couple of philosophers
> who spout phrases like "Its history is meticulous" and "rigorous
> and sophisticated from both an historical and a technical point
> of view."
>
> 2. Dummett, Michael (1993) Origins of Analytical Philosophy, Harvard
> University Press, Cambridge, MA.
>
> This is one of many Dummett tomes, which manage to idolize Frege
> without ever mentioning the fact that the commonly used notation
> for predicate calculus is based on Peirce's algebraic notation,
> and no one but Frege ever used his Begriffsschrift notation.
>
> 3. van Heijenoort, Jean, ed. (1967) From Frege to Gödel, Harvard
> University Press, Cambridge, MA.
>
> This book is a useful collection of many early papers on logic,
> with one egregious failure: it skips from Frege (1879) to
> Peano (1895) without giving a single excerpt from Peirce.
> The obvious paper to include is Peirce (1885), which Schröder,
> Peano, and Whitehead cited as sources for their work. It could
> also have mentioned Schröder's three volume Vorlesungen, which
> served as the main textbook on logic from 1895 to 1910, and whose
> notation is based directly on Peirce and which was used by Hilbert,
> Zermelo, Tarski, and all the other major logicians until 1910.
>
> The editor thanks some Harvard philosophers, Quine and Dreben,
> for their advice and guidance. For more about Harvard, see #4.
>
> 4. The courses taught by the Harvard philosophy department. For the
> latest listing, see
>
> http://www.registrar.fas.harvard.edu/Courses/Philosophy.html
>
> When I was at Harvard (in the late 1960s), I was talking with a
> friend of mine who was writing a dissertation on Frege. It didn't
> occur to me then to ask about Peirce because no one at Harvard ever
> talked about Peirce, despite the fact that his collected papers were
> lodged in the Havard library, under the ostensible sponsorship of
> the philosophy dept. However, there was always a course on Frege
> taught by Quine, but no course on Peirce and no one who ever thought
> that it might be interesting to write a dissertation that compared
> the approaches by Peirce and Frege. Even today, the following two
> course listings explicitly mention Frege, but none mentions Peirce:
>
> Philosophy 141. Frege, Russell, and the Early Wittgenstein
> Catalog Number: 6807
> Warren Goldfarb
> Half course (fall term). Tu., Th., at 10. EXAM GROUP: 12
>
> An examination of the beginnings of analytic philosophy, with
> primary interest in the reformulation of traditional philosophical
> problems by these three authors and the analytic and logical
> methods they introduced to treat them.
>
> Philosophy 245. Demonstratives: Seminar
> Catalog Number: 2142
> Susanna Siegel
> Half course (spring term). Th., 2-4. EXAM GROUP: 16, 17
>
> An examination of demonstrative reference and of related
> mental states. Topics to include formal theories of
> demonstrative reference; proposals about what Fregean
> senses of demonstratives might be; arguments that there
> are no such things.
>
> This last course is almost ridiculous. Instead of speculating on
> what Frege might have said about demonstratives, why doesn't the
> instructor talk about what Peirce did say? Or does she perhaps
> think that Frege invented the term "indexical", as some philosophers
> have said? I tried clicking on the course title to see what was
> being discussed (as one can in other courses), but for this course,
> that information is in a password-protected "secure document".
>
> John Sowa
> ----------------------------------------------------------------------------
>
> From: "John F. Sowa"
> Date: Thu, 07 Aug 2003
>
> Tom,
> [...]
>
> Re Peirce: Since Frege and Peirce were contemporaries, who invented
> their systems of logic at nearly the same time (1879 for Frege's
> Begriffsschrift and 1880 and 1885 for Peirce's two papers on the
> Algebra of Logic), I would expect any student of either Frege's or
> Peirce's logic to have more than a passing familiarity with the
> work of the other and be able to compare and contrast their
> approaches. I consider someone like Michael Dummet, who has
> published volume after volume on Frege without mentioning a word
> about Peirce to be guilty of philosophical malpractice.
>
> As a result of such malpractice, most students of logic are
> totally unaware of the fact that the notation they use every day
> was not in any way influenced by Frege's Begriffsschrift and
> is a direct descendant of Peirce's notation of 1880 and 1885
> - as presented by Ernst Schröder in his three weighty tomes
> "¨ber die Algebra der Logik" and adopted by Peano (with a
> change of symbols) for his notation of 1895, which was adopted
> without alteration by Russell & Whitehead for the Principia.
>
> (Peano cited both Peirce and Schröder and declared Frege's
> notation to be "unreadable". After Peano wrote an unfavorable
> review of Frege's work, Frege began a correspondence with
> Peano, but Peano insisted that Frege translate his diagrams
> into Peano's notation before he would comment on them.)
>
> Another malpractitioner was Willard Van Orman Quine, who taught
> generation after generation of students about Frege, even while
> he was sitting on top of Peirce's original manuscripts, which
> Peirce's widow had donated to the Harvard library. Quine never
> suggested that any of his students who churned out dissertations
> on Frege should look at Peirce's manuscripts to see whether they
> might suggest some thesis topic that compared the systems of
> the two co-founders of modern logic.
>
> [...]
> John Sowa
> ----------------------------------------------------------------------------
>
> From: "John F. Sowa"
> Date: Wed, 10 Sep 2003
>
> Tom,
> [...]
>
> 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 Schröder
> 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
> Schröder translated into German as erste und zweite
> Ordnung, which Russell translated back into English
> as "order".
>
> 3. Schröder adopted Peirce's notation, which he used for
> his three volume "Vorlesungen ¨ber die Algebra der Logik",
> which became the primary textbook on logic until the
> Principia came out in 1910. Hilbert, Zermelo, Löwenheim,
> and Tarski published their early work on logic and set
> theory using Peirce's notation.
>
> 4. Peano adopted the notation from Peirce and Schröder,
> but he changed the symbols to keep the math and logic
> symbols distinct. Peano gave full credit to Peirce and
> Schröder 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 Schröder.
> That notation is usually called Peano-Russell notation,
> despite the fact that Peano credited it to Peirce and
> Schröder, 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,
> Schröder, 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
> ----------------------------------------------------------------------------
>
> From: "John F. Sowa"
> Date: Wed, 10 Sep 2003
>
> 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 in the center of the scientific world
> during the 1870s and 1880s when he was actively
> corresponding with and visiting Schröder, 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 Schröder.
> 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
> occurred 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 Schröder. 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 Gödel'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, Schröder, Peano, Russell, Hilbert, or Gödel.
> 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
>
> You probably have read all this before, so do excuse me for reproducing it here.
>
> Theresa Calvet
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