Jim Willgoose wrote:
...The "Studies in Logic" would not lose its relevance then as
potential topics for philosophy classes, although the symbolic
portion would be eclipsed by the "Fregean Revolution."<<
That's an accurate summary of my main point.
For example, Bode could have included something of it in his 1910
book if he so chose. On another point, would it be fair to say then
that the Fregean Revolution is as much about the uses to which
symbolism is put, as it is about competing historical traditions?<<
That would certainly be one of the claims for Frege's _Begriffsschrift_
made by van Heijenoort, that among the original contributions to logic
that Frege made in the _Begriffsschrift_, according to van Heijenoort,
was that that it made mathematical or symbolic logic applicable to the
study of philosophy and the sciences in general, and most especially of
language in particular.
In other words, the equal weight of emphasis of a historical
explanation for the eclipse of the algebraic tradition lies with
logicism in the philosophy of mathematics rather than the
superiority of the symbolism and methods. I get the feeling
sometimes that the so called "Fregean" methods are simply superior
and this explains why it won out in terms of the historical
understanding of the writers of the earliest elementary and 1st
order symbolic logic textbooks.<<
The question of the superiority of the methods of the "modern
"symbolic" or "mathematical" logic or logistic -- which more properly
ought to be called function-theoretical -- as compared with that of the
classical Boole-Schröder calculus was a matter of debate from the
instant the reviews of Frege's _Begriffsschrift_ appeared. John Venn,
who in 1880 produced a catalog of the various notations from Leibniz
through Peirce, Schroder, and Frege, in his review of the
_Begriffsschrift_, called Frege's notation "cumbrous", find some two
dozen competing ways of rendering "a is b" (In _Studies in Logic_
Christine Ladd-Franklin explicitly remarked, or shall we better say
complained, that Venn had "collected some two dozen ways in which "a is
b" has been put into logical form". In 1898, Schroder argued the
superiority of Peirce's notation or "pasigraphy" (and by implication
his own, which, with minor exceptions he derived directly from Peirce
and Peirce's student Oscar Mitchell); and Peano and Frege also had
exchanges as to which of their respective notations was the better. The
goal of Norbert Wiener's Harvard doctoral thesis of 1913 was to
demonstrate that the classical Boole-Schroeder calculus has the same
expressive power as the logic of _Principia_.
But a slight alternative historical explanation is simply
sociological, and places greater emphasis on the research program
that dominated in the early decades. Put counterfactually, had
logicism not occurred, the earliest elementary symbolic logic books
with suitable formalization and proof could have developed without
that historical understanding. Nested in here is also the claim that
formaization and proof for textbook presentation could have
developed without the Fregean revolution.<<
Certainly another one of the major characterizations of the
_Begriffsschrift_ that van Heijenoort claimed as original with Frege is
the institution of formalization. Peirce's attitude is well known;
we've more than once in this forum talked about the import (I almost
said "implication" -- how's that for a bad pun?) of his remark about
proof as merely the pavement on which the chariot of mathematics rolls.
Seriously, there is no one sentence answer that I could offer. I have
some 1600 pages on a wordprocessing file in the effort to clarify and
detail the issue, under the cumbrous, or even baroque, title "From
Algebraic Logic to Logistic: How We Stopped Algebraicizing and Learned
to Love Logistic, or, Forgetting the Classical Boole-Schröder Calculus
The Fregean "Revolution" and the Rise of the "Russellian" View of
Mathematical Logic: An Historiographical, Philosophical, and
Sociological Investigation of an Episode in the History of Mathematical
Logic", ... and I don't seriously expect to complete this any time
soon, or even in what's left of my lifetime.
On the more readily accessible and simple question of whether the
_Studies in Logic_ suffered because of the difuseness of the topics,
the previous response I gave is, I think, more than adequate. It
certainly would not have bothered philosophers ill prepared to deal
deal with the mathematics.
That does not speak specifically to the point that Mr. Rooney was
presumably attempting to make, that those with mathematical training
would not, unlike their enumerate or mathophobic cohorts, have been put
off by the mathematical nature of the logic. My response to that part
of the issue would be that, in the post-Principia era, logicians who
had mathematical background gradually gravitated towards the
Frege-Russell approach, towards logistic, or function-theoeric, as
opposed to the algebraic Boole-Peirce-Schröder approach. That, too, is
one of the principal issues that "From Algebraic Logic to Logistic..."
attempts to explain.
It is worth noting:
(1) that _Studies..._ was well appreciated by logicians with strong
mathematical qualifications during Peirce's lifetime; here, we may
point to De Morgan, Venn, Schröder, MacColl, and Charles Lutwidge
Dodgson (a.k.a Lewis Carroll). Thus, for example, as Francine Abeles
demonstrated, it was reading Marquand's contributions to _Studies_ on
logic achines together with Ladd-Franklin's contribution, focusing on
the antilogism, that led Dodgson, in the unpublished-in-his-lifetime to
combine these to develop his version of the falsifiability tree method
for polysyllogisms. Beyond that, even while Bertrand Russell was
pointedly denying that he was familiar with any of Peirce's work in
logic, he was privately writing to Louis Couturat in 1899 recommending
that Couturat read _Studies..._.
(2) As usual, accuracy, exactitude, precision -- "picky, picky, picky"
-- is more complicated than we would sometimes wish. "Und in dem 'Wie',
da liegt der Unterschied." No one would, so far as I am aware, not even
I, claim that algebraic logic vanished altogether from the scene with
the arrival of logistic. It became, along with model theory, recursion
theory, proof theory, set theory, one of the specialized branches of
mathematical logic, beyond general logic (which, incidentally, also
encompasses, in the AMS subject classification scheme, besides prop
calc, FOL, higher-order calculi, non-classical logics, probability
logic -- thus continuing in some repects to justify the "mix" of topics
in intro logic texts for philosophers), and that primarily thanks to
Jan Lukasiewicz, who referred to Peirce's work in his claases at Warsaw
and especially his foremost student, Alfred Tarski. But listen to
Tarski decrying, in 1941, in "The Calculus of Relations" (p. 47) the
lack of attention to algebraic logic during the early post-Principia
period, noting that, "given the wealth of unsolved problems and
suggestions for further research to be found in Schröders _Algebra der
Logik_ [1890-1895]", it is "amazing that Peirce and Schröder did not
have many followers." Tarskis analysis of this situation and the
reasons for it appear to rest on the assumption that the absorption of
algebraic logic into Whitehead and Russells logical system was at the
cost of ignoring the mathematical content of the algebraic theory.
Tarski then wrote [1941, 74] that: "It is true that A.N. Whitehead and
B. Russell, in _Principia mathematica_, included the theory of
relations in the whole of logic, made this theory a central part of
their logical system, and introduced many new and important concepts
connected with the concept of relation. Most of these concepts do not
belong, however, to the theory of relations proper but rather establish
relations between this theory and other parts of logic: _Principia
mathematica_ contributed but slightly to the intrinsic development of
the theory of relations as an independent deductive discipline. In
general, it must be said that -- though the significance of the theory
of relations is universally recognized today -- this theory, especially
the calculus of relations, is now in practically the same stage of
development as that in which it was forty-five years ago."
The survival of algebraic logic as a specialized subfield may be due
preeminently, if not exclusively, as much as any factor, to the work of
Tarski and the generations to logicians that he taught and promoted at
U Cal Berkeley from the 1940s to his death.
(3) Since Mr. Rooney spoke of logic at the University of Illinois in
the 1950s, perhaps it would be worth remarking that in the mid-1930s,
one had to take logic, as did my father and Paul Halmos, in the
philosophy department with Oskar ("Oscar") Kubitz, who used the
then-brand-new Cohen & Nagel as the textbook for the course. Kubitz was
a Millian, and the author of the _Development of John Stuart Mill's
System of Logic_ (Urbana: Univ. of Illinois, 1932). My father was a
chem major, and enjoyed Kubitz's logic course (I inherited his copy of
Cohen & Nagel); Halmos was double majoring in philosophy and
mathematics, and his disaffection with that logic course and the drills
in syllogistic was one of the factors in deciding him to become a
mathematician.
(4) For those unafraid of mathematics, between 1910 and 1930, there
were few options in the immediate post-Principia era for studying the
"new" symbolic logic other than to do as Quine did, and that was to
find a professor willing and able to join him in working through
_Principia Mathematica_. The first textbooks began appearing in the
1923s, led off by Carnap's Abriss; in English, Clarence Irving Lewis
and Cooper Harold Langford co-authored the first modern symbolic logic
textbook in English, their _Symbolic Logic_ (1932; 2nd ed., 1959). This
was followed by Susanne K. Langer's textbook, _An Introduction to
Symbolic Logic (1937; 2nd ed., 1953); in the first edition of her book,
she mistakenly claimed it to be the first modern symbolic logic
textbook in English, but she corrected this error in the second
edition, reminding her readers of Lewis and Langfords textbook.
Tarski's _O logice matematycznej i metodzie dedukcyjnej_ appeared in
1936, his _Einführung in die mathematische Logik und in die
Methodologie der Mathematik_, in 1937, and the English edition in 1941.
John Cleveland Cooley worked out his lecture notes as Quine's T.A., to
produce his own _Primer of Formal Logic_ (1942; reprinted: 1946; 1949).
The next step was for professors, for more sophisticated treatments, to
hand out mimeographed copies of their typescripts, as Alonzo Church did
at Princeton for his students (Kleene among them), of what eventually
became Church's _Introduction to Mathematical Logic_ (1956)Carnap's
_Einführung in die symbolische Logik_ didn't appear until 1954.
----- Message from [email protected] ---------
Date: Fri, 4 May 2012 12:09:13 -0500
From: Jim Willgoose <[email protected]>
Reply-To: Jim Willgoose <[email protected]>
Subject: RE: [peirce-l] Not Preserving Peirce
To: [email protected]
Thank you Irving. The "Studies in Logic" would not lose its relevance
then as potential topics for philosophy classes, although the
symbolic portion would be eclipsed by the "Fregean Revolution." For
example, Bode could have included something of it in his 1910 book if
he so chose. On anther point, would it be fair to say then that the
Fregean Revolution is as much about the uses to which symbolism is
put, as it is about competing historical traditions? In other words,
the equal weight of emphasis of a historical explanation for the
eclipse of the algebraic tradition lies with logicism in the
philosophy of mathematics rather than the superiority of the
symbolism and methods. I get the feeling sometimes that the so
called "Fregean" methods are simply superior and this explains why it
won out in terms of the historical understanding of the writers of
the earliest elementary and 1st order symbolic logic textbooks. But a
slight alternative historical explanation is simply sociological, and
places greater emphasis on the research program that dominated in the
early decades. Put counterfactually, had logicism not occurred, the
earliest elementary symbolic logic books with suitable formalization
and proof could have developed without that historical understanding.
Nested in here is also the claim that formaization and proof for
textbook presentation could have developed without the Fregean
revolution.
> Date: Thu, 3 May 2012 15:31:15 -0400
From: [email protected]
To: [email protected]
CC: [email protected]
Subject: RE: [peirce-l] Not Preserving Peirce
Jim,
I suggest -- assuming I have not missed the import of your question --
that it would be far more accurate to propose that "Studies in Logic",
like most of the work of the algebraic tradition of the
"post-Principia" era was a victim rather of the so-called "Fregean
revolution" which, when not ignoring algebraic logic, rejected it
altogether as "inferior" to the modern logistic. If, for example, on
examines introductory logic textbooks from the mid-20th century, in
particular those aimed at philosophy students, one continues to find
inductive logic and scientific method ensconced in the same
introductory textbooks as deductive logic, although then the deductive
logic includes propositional calculus (and, depending upon the level of
the textbook, first-order predicate calculus), along with syllogistic
logic. One of the earliest, popular, post-Principia intro texts aimed
at philosophy students was Cohen & Nagel's "Introduction to Logic and
Scientific Method", which first appeared in 1934 and still had a strong
following until well into the 1960s at least. If differed from newer
intro logic textbooks aimed at philosophy students such as Copi's
"Introduction to Logic", appearing twenty years later and still going
strong, only in preferring the axiomatic approach to prop calc and FOL
rather than Copi-style natural deduction. They differ from an older
"pre-Principia" textbook such as -- to pull one off the shelf here,
Boyd Henry Bode's 1910 "An Outline of Logic" only in that deductive
logic meant syllogisms. Even in Peirce's day, few philosophers would
touch algebraic logic, taking the tack of Jevons in wanting to get rid
of the "mathematical dress" of classical algebraic logic.
On a related matter: The fact is, that the classical Boole-Schröder
calculus was simply too technically difficult, both in its day and
since, to fair well at appealing to any but those with mathematical
training. Examine the American Mathematical Society's and Zentralblatt
für Mathematik's Mathematical Subject Classification (any edition will
do): what you will find is that algebraic logic is listed as a
specialty, on a par with model theory, recursion theory, proof theory,
set theory, rather than as belonging to general logic that includes
propositional calculus, FOL, and the sorts of topics you might expect
to find in introductory textbooks.
Sorry if this doesn't speak more explicitly to the question you had in mind.
----- Message from [email protected] ---------
Date: Wed, 2 May 2012 14:41:18 -0500
From: Jim Willgoose <[email protected]>
Reply-To: Jim Willgoose <[email protected]>
Subject: RE: [peirce-l] Not Preserving Peirce
To: [email protected], [email protected]
>
> Irving and Jon; I wonder if the "Studies in Logic" did not suffer, in
> part, from a retrospective lack of unity. In other words, from the
> vantage point of 1950, the various topics (quantification, induction,
> Epicurus etc.) did not fit the 20th century development of a more
> narrow-grained classification into history of philosophy of science
> or formal deductive logic, or philosophy of language and meaning.
> Another conjecture might be that the first two decades of the 20th
> century dealt with the formalization and sytematizing of deductive
> logic for textbook presentation. Only after sufficient time had
> passed could the book be retrieved for historical and philosophical
> interest. Of course, there is always the nefarious possibility of an
> 'institutional apriori" authority having its way. Jim W
> > Date: Wed, 2 May 2012 11:48:14 -0400
>> From: [email protected]
>> Subject: Re: [peirce-l] Not Preserving Peirce
>> To: [email protected]
>>
>> Jon,
>>
>> I couldn't have said it better myself!
>>
>> Kneale & Kneale, to which Jack referred, was originally written in the
>> late 1950s and published in 1962, and in terms of respective
>> significance pays more attention to Kant even than to Frege, and is
>> best, thanks to Martha Kneale's expertise, on the medievals. Trouble
>> was, in those days, and pretty much even today, it is about all there
>> is in English.
>>
>> My joint paper with Nathan Houser, "The Nineteenth Century Roots of
>> Universal Algebra and Algebraic Logic", in Hajnal Andreka, James Donald
>> Monk, Istvan Nemeti (eds.), Colloquia Mathematica Societatis Janos
>> Bolyai 54. Algebraic Logic, Budapest (Hungary), 1988
>> (Amsterdam/London/New York: North-Holland, 1991), 1-36, includes a
>> brief analysis of what's WRONG with Kneale & Kneale and its ilk.
>>
>> When Mendelson's translation of Styazhkin's History of Mathematical
>> Logic came out in 1969, it should really have come to serve as a decent
>> supplement to Kneale & Kneale for K & K's grossly inadequate treatment
>> of Boole, Peirce, Schröder, Jevons, Venn, and Peano to help fill in the
>> serious gaps in Kneale & Kneale.
>>
>> Even if one looks at the hugh multi-volume Handbook of the History of
>> Logic under the editorship of Dov Gabbay and John Woods that is still
>> coming out, it's a mixed bag in terms of the quality of the essays,
>> some of which are historical surveys, others of which are attempts at
>> reconstruction based on philosophical speculation.
>>
>>
>> Irving
>>
>> ----- Message from [email protected] ---------
>> Date: Wed, 02 May 2012 11:15:05 -0400
>> From: Jon Awbrey <[email protected]>
>> Reply-To: Jon Awbrey <[email protected]>
>> Subject: Re: Not Preserving Peirce
>> To: Jack Rooney <[email protected]>
>>
>>
>> > Jack,
>> >
>> > All histories of logic written that I've read so far are very weak
>> on Peirce,
>> > and I think it's fair to say that even the few that make an
>> attempt to cover
>> > his work have fallen into the assimilationist vein.
>> >
>> > Regards,
>> >
>> > Jon
>> >
>> > Jack Rooney wrote:
>> >> Despite all this there are several books on the history of logic eg
>> >> Kneale & Kneale[?].
>> >
>> > --
>> >
>> > academia: http://independent.academia.edu/JonAwbrey
>> > inquiry list: http://stderr.org/pipermail/inquiry/
>> > mwb: http://www.mywikibiz.com/Directory:Jon_Awbrey
>> > oeiswiki: http://www.oeis.org/wiki/User:Jon_Awbrey
>> > word press blog 1: http://jonawbrey.wordpress.com/
>> > word press blog 2: http://inquiryintoinquiry.com/
>> >
>>
>>
>> ----- End message from [email protected] -----
>>
>>
>>
>> Irving H. Anellis
>> Visiting Research Associate
>> Peirce Edition, Institute for American Thought
>> 902 W. New York St.
>> Indiana University-Purdue University at Indianapolis
>> Indianapolis, IN 46202-5159
>> USA
>> URL: http://www.irvinganellis.info
>>
>>
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>
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Irving H. Anellis
Visiting Research Associate
Peirce Edition, Institute for American Thought
902 W. New York St.
Indiana University-Purdue University at Indianapolis
Indianapolis, IN 46202-5159
USA
URL: http://www.irvinganellis.info
----- End message from [email protected] -----
Irving H. Anellis
Visiting Research Associate
Peirce Edition, Institute for American Thought
902 W. New York St.
Indiana University-Purdue University at Indianapolis
Indianapolis, IN 46202-5159
USA
URL: http://www.irvinganellis.info
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