csp-frege-revolu

HOW PEIRCEAN WAS THE “‘FREGEAN’ REVOLUTION” IN LOGIC? 42
34 Sluga [1987, 95] disagrees with van Heijenoort only in arguing the relevance of the question of the claimed universality
for the logic of the Begriffsschrift; in Frege, Sluga argues, concepts result from analyzing judgments, whereas in Boole, judgments
results from analyzing concepts. [Korte 2010, 285] holds, contrary to all other suggestions on the question of why the Begriffsschrift
properly is a language, that it is so because of Frege’s logicism, and nothing else.
In attempting to understand Peirce’s position with regard to whether his logic of relatives is a language or a calculus, we are
therefore returned to the debate regarding the question of whether, and if so, how and to what extent, Peirce was a logicist in the
sense of Frege and Peano; see supra, n. 18.
35 Peirce tended to conflate Russell and Whitehead even with respect to Russell’s Principles of Mathematics, even prior to
the appearance of the co-authored Principia Mathematica [Whitehead and Russell 1910-13], presumably because of their earlier
joint work “On Cardinal Numbers” [Whitehead 1902] in the American Journal of Mathematics, to which Russell contributed the
section on, a work with which Peirce was already familiar.
36 I owe this historical point to Nathan Houser.
37 [Zerman 1977, 30] refers, imprecisely, to the English translation at [van Heijenoort 1967a, 13] of [Frege 1879], but not to
Frege’s original, and does not explain the nature of Frege’s failure to distinguish logic as proof-theoretic from semantic. The reference
is to the discussion in [Frege 1879, §4].
38 [Zeman 1977, 30] has in mind [Gödel 1930; 1931].
39 The problem of the existential import thus became a major issue of contention between traditional logicians and mathematical
or symbolic logicians; [Wu 1962] is a brief history of the question of existential import from Boole through Strawson.
40 I would suggest that it is in measure precisely against this backdrop that Russell became so exercised over Meinongian
propositions referring to a non-existent present bald king of France as to not only work out his theory of definite descriptions in “On
Denoting” [Russell 1905], but to treat the problem in The Principles of Mathematics [Russell 1903] and in Principia Mathematica
[Whitehead & Russell 1910], as a legitimate problem for logic as well as for philosophy of language and for metaphysics.
41 See, e.g. [Michael 1976a] on Peirce’s study of the medieval scholastic logicians. [Martin 1979] and [Michael 1979b] treat
individuals in Peirce’s logic, and in particular in Peirce’s quantification theory. [Dipert 1981, 574] mentions singular propositions in
passing in the discussion of Peirce’s propositional logic.
42 In a letter to Jourdain of March 15 1906, Russell wrote (as quoted in [Russell 1994, xxxiii]: “In April 1904 I began working
at the Contradiction again, and continued at it, with few intermissions, till January 1905. I was throughout much occupied by the
question of Denoting, which I thought was probably relevant, as it proved to be. ...The first thing I discovered in 1904 was that the
variable denoting function is to be deduced from the variable propositional function, and is not to be taken as an indefinable. I tried
to do without i as an indefinable, but failed; my success later, in the article “On Denoting”, was the source of all my subsequent
progress.”
43 We cannot entirely discount the relevance of Peirce’s isolation from his academic colleagues following his involuntary
resignation from his position at Johns Hopkins University in 1884 (see, e.g. [Houser 1990/1991, 207]). This may perhaps underline
the significance of Schröder’s seeking, in his letter to Peirce of March 2, 1897 (see [Houser 1990/1991, 223], to “to draw your attention
to the pasigraphic movement in Italy. Have you ever noticed the 5 vols. of Peano’s Rivista di Matematica together with his
“Formulario” and so many papers of Burali-Forti, Peano, Pieri, de Amicis, Vivanti, Vailati, etc. therein, as well as in the reports of
the Academia di Torino and in other Italian periodicals (also in the German Mathematische Annalen).”
44 Reviews of the Begriffsschrift have been collected and published in English in [Frege 1972]; the introductory essay
[Bynum 1972] presents the familiar standard interpretation that Frege’s work was largely ignored until interest in it was created by
Bertrand Russell; more recent treatments, e.g. [Vilkko 1998], argue that Frege’s work was not consigned to total oblivion during
Frege’s lifetime.
45 [Gray 2008, 209] would appear to suggest a strong influence “of the algebraic logic of Boole, Jevons, and others” on
Frege, who thought that “a deep immersion [in their work] might drive logicians to new and valuable questions about logic.” There
is no virtually evidence for accepting this supposition, however.
46 See [Wehmeier & Schmidt am Busch 2000] on the fate of Frege’s Nachlaβ.
47 [Macbeth 2005] is clearly unaware of [Russell ca. 1900-1901], Russell’s notes on [Peirce 1880] and [Peirce 1885].
48 See [Russell 1983] for Russell’s log “What Shall I Read?” covering the years 1891–1902.
References
ANELLIS, Irving H. 1990/1991. “Schröder Material at the Russell Archives”, Modern Logic 1, 237–247.
_______. 1991. “The Löwenheim-Skolem Theorem, Theories of Quantification, and Proof Theory”, in Thomas Drucker (ed.), Perspectives
on the History of Mathematical Logic (Boston/Basel/Berlin: Birkhäuser), 71–83.