SUO: Re: Ontology
Thanks for the refs, John.
Unfortunately, I'm temporarily handicapped because I'd recently lent some of
my pertinent sources (primary and secondary) to Randall, or I'd reply
instanter with my own list of refs. More anon, though.
(BTW, Randy, have you finished with those yet? I'm beginning to miss them :)
----- Original Message -----
From: "John F. Sowa" <firstname.lastname@example.org>
To: "Jay Halcomb" <email@example.com>
Cc: <firstname.lastname@example.org>; <email@example.com>;
Sent: Monday, December 22, 2003 15:08
Subject: Re: Ontology
> Please look at Peano's publications of the 1890s
> and compare that notation to the Principia notation.
> Every detail, including the dot notation for showing
> precedence, was in Peano's publications. Whitehead and
> Russell contributed new predicates (W more than R), but
> they made no changes to Peano's syntax -- not a single dot.
Nonsense. The validity of the point depends upon exactly what notations
we're referring to. The PM certainly includes notations (original and
adopted) which neither Peirce or Peano used (at least, used in the same
way). Nicod's '|', for instance, and '!', and the notation for the
representation of types. In the P.M. we're not dealing merely with 'the
calculus of relations', but with the logical system and notation of the
P.M. -- a type theory -- into which Peano's notation is embedded. And, of
course, Russell and Whitehead explicitly credit Peano for those notations
they've adapted. "In the matter of notation, we have as far as possible
followed that of Peano, _supplementing_ [emph. added] his notation, where
necessary, by that of Frege, or by that of Schroder." (Preface, PM). Of
course, they did not change the notation they directly adopted -- that's
tautological. What they changed was the logic.
> > ... Why should logicians not so credit it?
> Because it is a bald-faced lie.
Nonsense. Your own 'bald-faced lie' was that:
JS>But Russell credited only Peano and Frege, and
> omitted any reference to Peirce, who actually invented
> the notation he adopted.
Credited for what, exactly? We've now seen that it's quite untrue that
Russell 'omitted any reference' to Peirce. Incidentally, of course both
Russell and Whitehead (individually and collectively) credited (or
acknowledged or discredited) many earlier authors, for many things, in many
> And I am very familiar with Russell's nonsense on
> p. 23 of his _Principles of Mathematics_, which
> you quoted.
> The calculus of relations, which Russell was criticizing,
> was Peirce's notation of 1870,
Russell wasn't merely criticizing a notation, but a system. See below.
>which was the first advance
> in history beyond monadic predicates. DeMorgan said that
> Peirce's paper was the greatest advance in logic since Boole.
> And after Peirce invented the modern algebraic notation for
> predicate calculus in 1880, he no longer continued to work
> on the relational calculus.
> One of the people who did continue working on the relational
> calculus was Whitehead, who published further work on it
> in his 1898 book in which he credited Peirce and Schroeder.
> Whitehead also included much of that work in the later chapters
> of the Principia (which his student Russell coauthored)
> And by the way, Peirce's relational calculus also happens
> to be the basis for Ted Codd's relational calculus for modern
> databases -- and Codd happened to be a student of Arthur Burks,
> who edited two of the volumes of Peirce's _Collected Papers_.
> And the following part of the quotation from Russell is sheer
> drivel: "but unfortunately, their methods [Peirce and Schroeder's],
> being based, not on Peano, but on the older symbolic logic derived
> (with modifications) from Boole..."
Nonsense. What Russell was here referring to (with 'methods') is a logical
system or systems, not simply to a notation (see your remark following. and
above). In fact, what he was criticizing was the 'calculus of relations'
(considered extensionally). BTW, I should point out that at the time
Russell wrote this remark (probably 1900), he may not have had Peirce's
third system available to him, and, of course, Peirce's last writings
weren't even composed.
> Of course they weren't based on Peano -- because Peano explicitly
> said that he based his notation on Peirce's.
And I'm sure Russell knew the history of the notation. He also said that
both he (and later, both he and Whitehead) adapted notation from Peano.
> And the following continuation of the quotation merely illustrates
> Russell's ignorance: "their method suffers technically (whether
> philosophically or not I do not at present discuss) from the fact
> that they regard a relation essentially as a class of tuples...
> This view is derived, I think, probably unconsciously, from a
> philosophical error..."
Sheer drivel, John. Here again, the point at issue depends upon what text(s)
or notions Russell was derivatively referring to, with the phrase 'their
method'. But Russell was referring to the 'calculus of relations' considered
extensionally. And he was at the business of developing the theory of types
> Peirce was very clear on the point that a relation could be
> considered either intensionally or extensionally. And his
> extensional treatment of a relation as a class of tuples is
> universally accepted today -- unfortunately to the almost total
> exclusion of the intensional view, which Peirce insisted was
> equally important.
That statement is a little inexact, if you consider what 'extensional
treament' might mean -- 'as a class of tuples'. Peirce did not invent formal
set theory, such as ZF, for instance; so that's not 'his treatment'.
Moreover, Peirce's notation is *not* universally accepted today, of course.
However, what is true, as Russell indeed said (P. 23 and 24, Principles), is
that "The [calculus of relations] was first developed by C.S. Peirce. A
careful analysis of mathematical reasoning shows that types [N.B.] of
relations are the true subject-matter discussed.... Peirce and Shroder have
realized the great importance of the subject... " Etc.
Russell was, of course, in the Principles, developing the theory of types --
in contradistinction to the 'calculus of relations' considered
extensionally. Russell and Whitehead were both further concerned to
elaborate it in the Principia. Peirce, of course, did not develop a theory
of types. And that difference is where the most important contrast lies, as
far as this dicussion about credit and acknowledgement goes.
> > Both Whitehead and Russell were certainly acquainted
> > with Peirce and acknowledged the acquaintance in numerous
> > places. They made assessments of Peirce's work which differ
> > from your own and which you dislike.
> Of course I dislike Russell's statement because some people
> who have not done their homework might actually believe it.
Which statement do you dislike again, John?
> But as I have shown (and as anybody who checks the sources
> can verify), all it proves is that Russell was either totally
> ignorant or deliberately distorting the history of his own
> If you don't want to bother checking the originals, you can
> check the following secondary sources, which confirm the
> points I was making.
Don't find them confirmed at all, John. But, as I say, I am also awaiting
the return of other sources. Footnotes anon.
> For further historical information see:
> Putnam, Hilary (1982) "Peirce the Logician" _Historia Mathematica_
> 9:290-301, reprinted in H. Putnam (1990) _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. (1995) _Peirce and Contemporary Thought_, Fordham University Press,
> New York, pp. 23-31.
> Dipert, Randall R. (1995) "Peirce's underestimated place in the history
> of logic," in K. L. Ketner, ed. (1995) _Peirce and Contemporary
> Thought_, Fordham University Press, New York, pp. 32-58.
> Hintikka, Jaakko (1997) The place of C. S. Peirce in the history
> of logical theory, in Brunning, Jacqueline, and Paul Forster, eds.,
> _The Rule of Reason: The Philosophy of Charles Sanders Peirce_,
> University of Toronto Press, Toronto, 1997, pp. 13-33.
> And for further discussion of the history, see my commentary
> to Peirce's MS 514:
> Existential Graphs