SUO: Re: Sociology of Citations
Fred,
Thanks for the reference to Badesa's book.
For anybody who is interested in the history of logic,
I strongly recommend the sample chapter of the book
by Calixto Badesa (which can be downloaded for free).
It includes some good observations about the work of
Boole, Jevons, Peirce, and Schroeder.
I haven't yet seen the full book, but from the way
the author is proceding, it sounds as if it presents
Loewenheim's anticipations of Tarski's model theory,
using the logic developed by Peirce and Schroeder.
As Hintikka and Hilpinen showed, Peirce more than
anticipated Tarski -- he developed a better version.
Peirce's endoporeutic is equivalent to Hintikka's
game-theoretical semantics.
Following are some interesting points in Badesa's first
chapter (the free download). The first is on page 2:
Boole classifies the propositions of interest to logic
into primary and secondary (Laws, pp. 53 and 160). Primary
propositions are the ones that express a relation between
things. Secondary propositions express relations between
propositions, or judgments on the truth or falsity of a
proposition. For example, “men are mortal” is a primary
proposition (because it expresses a relation between men
and mortal beings), but “it is true that men are mortal”
is secondary.
This shows that Boole drew a distinction between first-order
logic (primary propositions) and second-order logic (secondary
propositions). Boole wasn't the first to make that distinction,
since it was familiar to Ockham and the medieval logicians.
But it is important to note that one can make the distinction
even without having quantifiers.
Badesa summarizes some points from Peirce's papers of 1870,
1880, and 1885 in pp. 12 to 17. In pages 17 to 31, he discusses
Schroeder's work, comparisons to Peirce, and the correspondence
between Peirce and Schroeder. Note the following on p. 17:
...Moreover, the lengths to which Schroeder goes to quote
the origin of the results of other logicians and the
discussions that frequently accompany their presentation make
the Vorlesungen a valuable source for the historian of logic.
This is an admirable characteristic that is very different from
Russell's slipshod treatment of citations. As an example, see
the following footnote in Hilary Putnam's paper:
Subsequent to writing this essay I discovered that, in
"Whitehead and Principia Mathematica," Mind (1948), p. 137,
Russell says that Whitehead contributed the notion for the
universal quantifier.
If Russell had really paid any attention to Peirce's paper of 1885,
he could not have missed the term "universal quantifier" (which
Peirce had coined). Furthermore, Whitehead had cited Peirce's 1885
paper in his 1898 book on Universal Algebra.
On page 20, footnote 33, Baseda makes the following point, which
indicates that Russell's simple theory of types wasn't exactly
a major breakthrough (especially since Russell claimed to have
read Schroeder's work):
In [1976] Church noticed that Schroeder’s hierarchy of
manifolds anticipates Russell’s simple theory of types.
As for Russell's discovery of the contradiction in Frege's
work, Peirce said that it was an obvious result of Cantor's
work. And Zermelo, who discovered it independently, didn't
even think that it was worth publishing -- instead, Zermelo
spent his time developing axioms for set theory that avoided it.
(And Z. had expressed his axioms in Peirce-Schroeder notation.)
I think that it's rather safe to say that Peirce's review of
Russell's 1903 book, in which he called it "a compendium of
well-known results", was accurate. And Peirce's private remark
("superficial to the point of nauseating me") was, for somebody
who had been working on the subject for over 30 years, justified.
John Sowa
_____________________________________________________________
> Hi,
>
> I am not sure if this newly published book has been
> mentioned on the cg-list before, but I thought some might
> be interested in it in light of recent discussions to do
> with the history of logic. The first chapter is online
> and deals with Boole, Pierce and Schroder in some detail,
> (at first glance, supporting John's standpoint).
>
> http://pup.princeton.edu/chapters/s7795.pdf
>
> The book is called:
> The Birth of Model Theory:
> Lowenheim's Theorem in the Frame of the Theory of Relations
> February 2004, Princeton University Press
> Author: Calixto Badesa (Associate Professor of Logic and
> History of Logic at the University of Barcelona)
>
> For more details, visit:
> http://pup.princeton.edu/titles/7795.html
>
> Regards
>