This is a preprint version of the paper that appeared in definitive form in From Dedekind to Gödel, J. Hintikka (ed.), Dordrecht: Kluwer, 1995, pp. 97-118. The published version should be consulted for all citations.
Gottlob Frege's isolation is almost legendary. Michael Dummett portrays him as having been a man who was perhaps too original to have ever been capable of working with others, "of sailing on any sea on which other ships were in sight. ...", and someone who "never seems to have learned from anybody, not even by reaction. ...". Dummett's Frege felt isolated, misunderstood and unlistened to in the philosophical and mathematical world of his time, led a "life of disillusionment and frustration". In addition to this, we have Bertrand Russell's well-known claims that Frege's work had gone virtually unnoticed until Russell discovered it in 1900.
There is certainly a good deal of truth in such accounts of Frege's life. Born in 1848, Frege entered the University of Jena at age twenty-one. He left Jena for the couple of years he needed to be obtain his doctorate at Göttingen and then returned to Jena when he was twenty- six, remaining there until he retired forty years later. Outside of his own work, little, if anything, of lasting interest transpired there in his field during his tenure. And in any case, Frege apparently eschewed all personal contact with the academic community, both in Jena and elsewhere. Although Jena is just a few hours by train from the Universities of Göttingen, Berlin, Leipzig and Halle where Karl Weierstrass, David Hilbert, Georg Cantor, Ernst Zermelo and others were making breakthroughs in Frege's field, he was little inclined to travel. Hilbert chided him about this in a letter saying that it was a shame that Frege had missed two recently held professional meetings. "Since rail travel is so comfortable today", he wrote, "personal communication is surely preferable to the written kind". From Frege's correspondence we also know that he turned down opportunities to speak at the International Congress of Philosophy held in Paris in 1900 (PMC pp. 6-7), and to take part in a Mathematical Congress in Cambridge. In the latter case he cited "weighty reasons" for his
going to Cambridge, but mysteriously cited "something like an insuperable obstacle" that was keeping him from it (PMC p. 170). Lothar Kreiser has even suggested that Frege seemed almost to have made it a principle not to speak at all to others about mathematics or logic, behaviour which is perhaps nor so surprising on the part of one who was so worried about "the many illogical features ...at work in language" (PW p. 266), and who so often and so vociferously voiced his complaints about the imperspicuous and imprecise character of investigations conducted in words (PMC pp. 33, 57-58).
Perhaps it was this aloofness on Frege's part which has made it seem possible that he was unknown and unappreciated until Bertrand Russell discovered him and that he was, as Michael Dummett claims, totally oblivious to the work of others. Frege's correspondence, however, tells another story. Frege actually left behind a valuable record in the form of letters of exchanges he had engaged in with the leading people in his field. Bertrand Russell was perhaps just too young in 1900 to have heard of the older Frege who by 1900 had acquired enough of an international reputation to have, since the 1880s, engaged in significant written, if not personal, exchanges with, among others, the Italian logician Giuseppe Peano (PMC pp. 108-129), the future phenomenologist Edmund Husserl (PMC pp. 61-65), the French philosopher Louis Couturat (PMC pp. 6-8), the extensionalist logician Ernst Schröder, mathematicians David Hilbert (PMC pp. 31-43) and Georg Cantor, and several noted members of Franz Brentano's Austrian school (PMC pp. 61, 99, 171).
Most of the exchanges cited above were epistolary and many of the letters exchanged as well as some of the information we have about them are found in the English edition of Frege's correspondence, which is abridged. Unfortunately, many of the letters to and from Frege have been lost. Brian McGuinness, the abridger of the English edition, however, consoles readers who might mourn the loss by advising them that it "would be unphilosophical, and perhaps improbable, to suppose that what we have lost must have been more interesting than what remains to us" (PMC p. xvii). He further informs readers that the abridged English text only includes the actual surviving texts considered by him to be of scientific interest and that he has eliminated what he dismisses as "laundry lists". ln fact, he has left out what information we still have about the missing letters, omitting in particular the dates we have for them and what in one case he calls "tantalizingly jejune notes" made by Heinrich Scholz, who had actually read much of the now missing material. ln addition, McGuinness admits to having "heavily abridged" the notes found in the German edition along with much pertinent information about the letters (PMC p. xvii). For example, he has eliminated twelve of the twelve and a half pages of introduction to Russell's correspondence with Frege (BW pp. 200-211), and five pages of information about each the Frege- Wittgenstein correspondence (BW pp. 64-268) and the Frege-Löwenheim correspondence (BW pp. 157-161) so that anyone wishing anything more than a superficial introduction to questions raised or resolved by studying Frege's correspondence is obliged to turn to German editions.
In fact, very close study of the content of the letters we do have and of what we actually know about the letters we do not have makes McGuinness's remarks seem presumptuous and his abridging unscholarly. Frege wrote "detailed, substantial" letters (his correspondents commented upon this: PMC pp. 23, 64, 106) in which he tried to explain some of his most basic and important ideas. ln them, he discoursed at length about such matters as sense and meaning (PMC pp. 61-64, 79-80, 152-154, 163-165), the paradoxes of set theory (PMC pp. 130-169), identity (PMC pp. 95-98, 113-116, 126-127), and the foundations of geometry (PMC pp. 32-51, 90-93). The portion of the correspondence presently available in published form has already played an important role in discussions concerning the influence Frege may have had on Edmund Husserl's thought and the originality of Frege's distinction between Sinn and Bedeutung. Frege's correspondence records his reactions to Russell's discovery of the paradox and to the solutions Russell proposed for it (PMC pp. 130-169). It has shed light on the origins of the analytic tradition in philosophy. It has shown the extent to which Russell and Frege disagreed (PMC pp. 78-84, 135, 155-156, 159, 163, 165, 168-169) and Frege's keenness in pointing out problems in Russell's reasoning (PMC p. 166). It clearly shows that Frege's works were known, read and appreciated in the nineteenth century (PMC pp. 6, 64-65; BW p. 145). An 1882 letter indicates that Frege was already aware then of the very problems associated with determining the extension of a concept, with language's fatal tendency to transform concept words into proper names, and with confusions about concepts and objects (PMC pp. 100-101) which he, once he had struggled with Russell's paradox, would ultimately blame for the failure of his project to logicize arithmetic (PMC pp. 55, 191). The same letter also clearly shows (PMC p. 99, 171) that Russell was wrong to think with regard to the Begriffsschrift that he was "the first person who ever read it more than twenty years after its publication".
Moreover, what the letters divulge about what Frege thought on these matters is often consistent in quality with the discussions found in his published writings, to which the letters provide an illuminating complement. Frege had, in fact, wanted to publish his correspondence with Hilbert concerning the foundations of geometry (PMC p. 48) "because", he said, "of the importance of the questions discussed in it" (PMC p. 92), and "because reading this correspondence would have been the most convenient way of introducing someone into the state of the question, and it would have saved me the trouble of reformulating it" (PMC p. 32). Frege and Löwenheim had at one time intended to publish their twenty letter exchange of ideas on formalism (BW pp. 158, 161). Letters Frege and Peano exchanged actually were published in the Rivista di matematica in 1896 (PMC pp. 112-120). ln addition, Frege left among his papers an impressive number of drafts of the letters he sent, a fact consistent with his striving for rigor and exactness which indicates that he took his letter writing seriously. Fortunately, some of these drafts (or often fragments of them) have survived, often comprising all we now know about letters of which no other trace remains.
So I am arguing that it is rather probable to suppose that what we have lost was quite interesting, and that it too could shed light on questions Frege's work raises which may have remained unresolved until now because we have not been in full possession of the facts. So, in the next pages I propose to engage in the "unphilosophical" task of systematically trying to piece together what we actually can know about the philosophical content of the letters that have been lost. I must begin by going over the story of the fate met by Frege's literary estate.
1. THE STORY OF THE LETTERS
In 1919 a chemist, Ludwig Darmstaedter, asked Frege whether he might contribute letters addressed to him to an autograph collection. Frege actually selected several letters to be set aside for this collection and upon his death in 1925, Alfred Frege, his adopted son, handed "a not very extensive collection of letters to Frege" over to the Prussian National Library which housed Darmstaedter's collection (PMC pp. xi-xii). Although the English edition has been cleansed of most of the information regarding the fate of the individual letters, by piecing together the notes in the unabridged German edition we find that a little more than half of the one hundred and twenty one letters published there were part of this autograph collection which seem to have remained largely intact.
As one might expect of a person choosing letters for an autograph collection, Frege principally chose letters that were signed by well-known people, but which were relatively void of philosophical or personal content. Often the se were the "requests for an offprint, refusals to print an article, apologies for not writing" that McGuinness has qualified as "laundry lists" (PMC p. xvii). With only one or two exceptions, the collection consists entirely of letters written to Frege, not by him. By far the most important letters Frege contributed were those that Bertrand Russell had written to him, including the 1902 letter in which Russell informed Frege of the famous paradox. Frege's reasons for consigning Russell's letters to him to an autograph collection are not known.
In the 1930s the German logician Heinrich Scholz began collecting Frege's unpublished writings and correspondence with the intention of publishing them in a three volume work. He succeeded in finding the letters written to Frege that had been preserved in the autograph collection. At the International Congress of Scientific Philosophy held in Paris in 1935, he appealed for help in locating letters written by Frege to others (PMC pp. xi-xv). Again he was fortunate enough to acquire valuable material. In exchange for photographic copies, Bertrand Russell provided him with nine letters (BW p. 200). Leopold Löwenheim made available another ten letters (BW p. 159). Additional letters came from Edmund Husserl (BW p. 93), David Hilbert (BW p. 57) and other distinguished correspondents.
From Frege's adopted son, Alfred Frege, Scholz managed to acquire most, perhaps all, of the philosophically interesting papers and letters the older Frege had left in his son's care. Besides Frege's unpublished writing, the papers included letters Löwenheim, Wittgenstein, Husserl, Hilbert and others had written which Frege had not judged suitable for an autograph collection, and many drafts Frege had made of the letters he wrote. Scholz also examined and sent back to Alfred Frege some letters of a purely personal nature. Wittgenstein declined to make Frege's letters to him available. Others had not kept their correspondence (PMC pp. xii-xiii).
Not including the autograph collection, Scholz was all in all able to obtain approximately one hundred letters. In collaboration with others, he then went to work preparing the material for publication (PW p. x). However, World War II intervened with disastrous consequences. For safekeeping, Scholz fatefully placed the materials he had collected in the University of Münster library. The building was bombed on March 25, 1945 and Scholz collection was lost. Fortunately, Scholz had typed copies of some of the material. He had also catalogued and made notes on the content of other materials of which there is now no longer any trace. Scholz's lists and the copies he made of about fifteen of the letters survived the war (PMC p. xiii wrongly seems to imply that they all survived), as did the autograph collection. However, more than three-fourths of the letters Scholz had gathered, along with any copies he may have made of them, have vanished. For example, Scholz had worked particularly hard on Frege's correspondence with Löwenheim. Unfortunately, the twenty Frege-Löwenheim letters Scholz had managed to acquire, a complete transcript of all twenty letters, plus two forty-seven page thick typed copies of the correspondence up to the beginning of the fourteenth letter, some drafts of letters and comments on a 1908 letter from Frege to Löwenheim all disappeared from Scholz's Münster archive (BW p. 159). None of this would be apparent to readers of the English edition which only mentions Löwenheim once in passing (PMC p. xvii).
Scholz resumed his work after the war and following his death in 1956 others eventually set about to retrieve, as much as possible, what had been lost and complete what he had begun (PW pp. xii-xiii). Efforts made to determine whether anything of value might have remained in Alfred Frege's possession proved to be in vain. He was killed in 1944 while serving as a soldier in France. The house he had inherited from his father was requisitioned for use by the Soviet army, repeatedly plundered and then used to house refugees. Alfred Frege's own house was completely destroyed by bombing in 1943 (PMC pp. xiv-xv).
Using what evidence remained at hand, extensive efforts were also made to locate additional letters. These endeavors were sometimes crowned with success and over the years approximately fifty more letters were found that had been preserved in other archives, published, or kept by Frege's correspondents or their families.
Frege's correspondence was finally published in 1978, more than twenty years after Scholz died and more than forty years after he had begun his work on it. All in all, scholars have been able to relocate more than half of the approximately two hundred and fifty that have been identified as having been written to or by Frege. Unfortunately, over a hundred letters and their copies seem to be irremediably lost, and even where copies or drafts survive, they often contain frustrating gaps.
2. THREE PERIODS
Losing the letters of a philosopher, even those of an important philosopher, is not in and of itself a reason for great dismay. Much, perhaps most, of what learned people write in letters is of little abiding interest. I have, however, tried to provide some reasons why Frege's correspondence may be an exception to this. Now I want to argue that the close study of the letters we have and what we can know about the letters we do not have actually discloses some very interesting, and not immediately apparent, facts about the latter. To make my point I need first to divide Frege's thought into the following three periods:
1. The first period extends from the publication of Frege's Begriffsschrift in 1879 until June 1902, when Russell first wrote to Frege about the contradiction now commonly known as Russell's paradox. Almost all Frege's works were written and published during this period. Even the 1903 Basic Laws II was already in the press when Frege received Russell's letter. Approximately one fourth of the nearly two hundred and fifty letters Frege is known to have exchanged date from this period. With a few quite interesting exceptions, the surviving letters were among those relegated by Frege to the autograph collection, and so have survived and been published.
2. The second period encompasses the brief time from June 1902 through 1906, during which, as Dummett has argued, Frege continued his logical work still hoping to find solutions to the questions Russell's finding raises. Basic Laws II appeared in 1903 and while working on Basic Laws III, Frege published little else. We know of approximately fifty letters exchanged during this period. Two thirds of these belonged to the autograph collection which housed the ten important letters Russell sent to Frege between 1902 and 1904. These have survived along with a letter and a postcard found by Grattan-Guinness at the Mittag-Leffler Institute in Sweden, copies Scholz made of two letters Frege wrote to Husserl, and Russell's photographic copies of Frege's letters. The remaining letters were collected by Scholz and are lost.
3. The third period ranges from 1907 until Frege's death in 1925. During the year 1906 Frege apparently abandoned his work on the third volume of the Basic Laws, utterly persuaded that his logical work was irremediably flawed. Well over half of the letters to and from Frege that have been inventoried over the years were written during these yearsin which Frege wrote very little else. Frege in fact wrote substantially more pages of letters during these years than he did pages of published works. Though the letters we know something of only represent a portion of Frege's epistolary output during this time, they alone already indicate that. Moreover, the fact that the dates of twenty-one letters and cards from Frege to Wittgenstein found in Austria in the late 1980s do not correspond with the dates Scholz recorded for the fifteen letters from Wittgenstein to Frege once housed in his Münster Archive indicates that many Frege-Wittgenstein letters are still missing.
Two-thirds of the approximately one hundred and fifty letters we presently know Frege exchanged during the last nineteen years of his life were acquired by Scholz and they, along with all but a handful of the copies Scholz was able to make (not all of them complete) were lost in the Münster bombing. Unfortunately, there is reason to believe that it is precisely the most interesting letters that are missing from these last two, crucial periods for which we have so little other indication of what Frege was thinking. It is, after all, only reasonable to conjecture that Frege would have selected less important letters for an autograph collection, keeping the letters he deemed to be particularly significant among papers which he thought would one day be valued more highly than they were at the time of his death (PW p. IX). ln what follows, however, I wish to put such conjectures aside and to set out some philosophical reasons for considering the lost letters to be significant.
3. SUBJECTS TREATED
The principal reason, I contend, for believing that the missing correspondence dealt with matters of particular interest to twentieth century philosophy is that, studying the letters written after 1902 that have survived and reflecting on the notes Scholz left regarding the letters he once had in his possession, one cannot help but notice that the now missing materials repeatedly dealt with certain specific, intimately related subjects of prime importance. These subjects are: the paradoxes of set theory and possible solutions to them: extensionality and classes: the differences between concepts and objects; identity (or equality since Frege considered them to be the same); and Frege's opinion of the work of his contemporaries.
Interestingly, many other materials on these same subjects have disappeared in distressing ways, a fact that I shall partially document as I go along.
The way these subjects are interconnected and their significance for Frege at that crucial time in his life during which he abandoned his logical work becomes apparent when one considers that when Russell informed him of the famous paradox of set theory (PMC pp. 130-131), Frege immediately traced the origin of the contradiction to his axiom of extensionality, Basic Law V of the first volume of Basic Laws (PMC p. 132). ln an appendix to the second volume Basic Laws, then in the press, Frege proposed a solution which involved the modification of Basic Law V. For Frege, Russell's contradiction indicated:
...that the transformation of an identity into an identity of ranges of values (sect. 9 of my Basic Laws) is not always permissible, that my law V (sect. 20, p. 36) is false ... the collapse of my law V seems to undermine not only the foundations of my arithmetic but the only possible foundation of arithmetic as of the generality of an identity into an identity of ranges of values so as to retain the essential of my proofs (PMC p. 132).
Frege himself had never been completely satisfied with Basic such. And yet, I should think it must be possible to set up conditions for the transformation Law V and he more than once admitted that he had formulated it because he saw no other way of logically grounding arithmetic other than by appealing to the extensions of concepts he reticently began using in §68 of his 1884 Foundations. In the brief overview of that book which figures on the closing pages of the work, Frege acknowledged that appealing to extensions would not "meet with universal approval" and claimed to "attach no decisive importance even to bringing in extensions of concepts at all." When he published the first volume of Basic Laws in 1893, he was more explicit about his reservations: "If anyone should find anything defective", he wrote there, "he must be able to state precisely where, according to him, the error lies… A dispute can arise, so far as I can see, only with regard to my Basic Law concerning courses of values (V). ..." This is where, he believed, the decision would be ultimately made.
By transforming "a sentence in which mutual subordination is asserted of concepts into a sentence expressing an equality", Basic Law V would permit logicians to pass from a concept to its extension, a transformation which, Frege held, could "only occur by concepts being correlated with objects in such a way that concepts which are mutually subordinate are correlated with the same object". However, Frege never believed that any proof could be supplied that would sanction such a transformation "in which concepts corresponded to extensions of concepts, mutual subordination to equality". So he devised Basic Law V to mandate that it was true.
In 1912, having already given up trying to save his logic, Frege wrote for an article by Philip Jourdain:
And now we know that when classes are introduced, a difficulty, (Russell contradiction) arises… Only with difficulty did I resolve to introduce classes (or extents of concepts) because the matter did not appear to me to be quite secure -and rightly so as it turned out. The laws of numbers are to be developed in a purely logical manner. But numbers are objects… Our first aim was to obtain objects out of concepts, namely extents of concepts or classes. By this I was constrained to overcome my resistance and to admit the passage from concepts to their extents… I confess… I fell into the error of letting go too easily my initial doubts. (PMC p. 191)'
Six years earlier, Frege had written of this transformation which he considered to be so vital to this theories that if it had been "possible for there to be doubts previously, these doubts have been reinforced by the shock the law has sustained from Russell's paradox" (PW p. 182). Frege was convinced that "everybody who in his proofs has made use of extensions of concepts, classes, sets", was in the same position he was.
4. SMART BOMBS
In order to carry my argument concerning the importance of the lost letters further, I need to take a close look at the fate of specific letters dating from the last two periods and at how the important subjects discussed above figured in Frege's epistolary exchanges once he was confronted with Russell's paradox.
ln June 1902, Frege received Russell's letter regarding the paradox. Frege replied, pinpointing the exact place he believed the error to be. Over the next two years, Russell and Frege exchanged several letters in which each proposed and critically discussed possible solutions to the problems Russell's finding unearthed. Scholz acquired all the letters known to have been part of this exchange and his collaborators, Friedrich Bachmann and Marga Titz set to work writing about them. The letters Russell had furnished were lost in the Münster bombing and only sixteen pages of Bachmann and Titz's commentary on them have survived (BW pp. 210-211). In 1963, however, Scholz's successors managed to retrieve the photographic copies Scholz had made for Russell, so these Frege letters now number among the few letters from Scholz's archive that are available today (BW p. 200).
Immediately upon receiving Russell's letter regarding the contradiction, Frege replied writing that, though he was surprised beyond words and left thunderstruck by the discovery of the contradiction, "it may perhaps lead to a great advance in logic, as undesirable as it may seem at first sight" (PMC p. 132). In September 1902, Frege replied to a letter from Philip Jourdain, who was then writing a book on the history of set theory. In the letter Frege mentions that Russell had called his attention to the fact that Basic Law V was in need of restriction, but Frege still displays the same confidence that a satisfactory solution would be found (PMC p. 73). This letter (a draft of which once existed in the Münster archive) and a March 1904 postcard Frege sent to Jourdain were eventually found in the Mittag-Leffler Institute in Sweden (BW pp. 109-112). In the postcard, Frege alludes to a letter from Jourdain. An entry in Jourdain's notebooks records a letter written to Frege at that time about "getting over Russell's and Burali-Forti's contradiction by limitation on conception of class - so that mathematical conceptions can apply to it". This letter is now missing (PMC p. 74n.).
During those years, Jourdain also corresponded with Georg Cantor, Russell, Ernst Zermelo, Giuseppe Peano, John Venn, Arthur Schönflies about their work, and with G. H. Hardy regarding Cantorian set theory. Unfortunately, although many of the letters survived, Jourdain's manuscripts have vanished and anything Jourdain's widow may have had in her possession was destroyed in 1940 and 1946.
In 1902, Frege also replied to a letter sent by the American mathematician, Edward Huntington (PMC p. 57). A draft of Frege's letter was housed in Scholz's archive and a typed copy of it survived the war (BW p. 88). The copy, however, contains a frustrating gap precisely at the point at which Frege discusses his project of basing arithmetic solely on logic and the justification of inference by appealing to purely logical laws. Frege's letter picks up again with the words: "what I call endless, namely the number of all finite numbers, and show that endless is not a finite number" (PMC p. 57). These words tantalizingly recall Russell's words in a second 1902 letter to Frege which tells of Russell's having been led to the contradiction while studying Cantor's proof that there is no greatest cardinal number.
In January 1903, Moritz Pasch, a mathematician interested in the logical and methodological problems of mathematics (PMC p. 103), wrote to Frege to inquire as to how Frege proposed to explain infinitely distant points. According to a later latter from Pasch, Frege responded in a letter which contained an "in depth discussion of infinitely distant elements". Though none of Frege's letters to Pasch have ever been found, a fragmentary draft Frege composed in reply to Pasch's question was once in Scholz's hands. According to Scholz's notes regarding that portion of the letter, Frege held that one could define infinitely distant points by considering extensions of concepts as classes as set out in §68 of The Foundations of Arithmetic (PMC p. 106; BW pp. 172-173). As mentioned above, this was the very section of Foundations in which Frege introduced the extensions of concepts and classes which become codified in the problematic Basic Law V of the first volume of Basic Laws of Arithmetic. It is also in a note to this section that Frege brings up two possible objections to his identifying concepts with their extensions: The first objection, he maintains, would be that in so identifying them he would seem to be contradicting his previous statement that the individual numbers are objects, not concepts. The second objection would concern the fact that concepts can have identical extensions without coinciding.
Two 1903 letters and a postcard from Alwin Korselt to Frege were preserved in the autograph collection. ln the first letter, Korselt proposes a solution to Russell's paradox concerning which he concludes: "All we need to do is hold on to the fact that a class is not a concept but the object of a concept and that a concept is not a class, a fact which you demonstrated in your essay 'On Concept and Object' (PMC p. 86). Frege immediately replied to Korselt's letter, but the reply was unfortunately among the letters once entrusted to Scholz's care and is now lost. According to Scholz's notes, Frege's letter concerned the unacceptableness of Korselt's proposed solution (BW p. 142; PMC p. 85). Any attempts to find letters from Frege or relevant information regarding their exchange among Korselt's papers have proved fruitless as it seems Korselt's papers were burned by their owner in 1962.
A 1903 postcard from David Hilbert to Frege also made its way into the autograph collection. ln it Hilbert acknowledges receipt of Basic Law II and informs Frege that Russell's paradox was already known to his circle in Göttingen as Ernst Zermelo had discovered it three or four years earlier. Hilbert further claims that he himself had "found other convincing even more convincing contradictions as long as four or five years ago" (PMC p. 51).
Four years earlier Hilbert had actually been corresponding with Frege on the significance of contradictions in axiomatic systems (PMC pp. 34-51), and Scholz managed to obtain from Hilbert three letters Frege wrote to him on that subject in 1899 and 1900. Frege had hoped these letters would be published (PMC pp. 48, 92). Scholz copied them and returned the originals to Hilbert. The copies survived the war, but the originals are nowhere to be found (BW p. 57). Scholz also apparently acquired a late 1899 letter Hilbert had written to Frege that was part of this same exchange. This letter has disappeared, but copies Hilbert and Frege made of parts of it have survived and are published (PMC pp. 38-43). Edmund Husserl also had access to the letters and the notes he made on three of the letters have been published.
In 1900, Frege sent Heinrich Liebmann copies of the correspondence with Hilbert (PMC pp. 50, 92), and wrote to Liebmann criticizing Hilbert's views on axiomatization, once again bringing up the subject of contradictions and charging Hilbert, among other things, with blurring the distinction between first and second level concepts (PMC p. 91). Frege then went on to discourse on the radical difference between concepts and objects and the essentially predicative nature of the former. "An object can never be predicated of anything. When I say 'the evening star is Venus', I do not predicate Venus but coinciding with Venus" (PMC p. 92). These letters were published in 1940 and so have survived. Apparently Liebmann never replied.
During 1906, Frege exchanged letters with another philosopher and mathematician who was participating in Hilbert's and Zermelo's discussions of the foundations of mathematics and the paradoxes of set theory, Edmund Husserl. Husserl had thoroughly studied Frege's Foundations of Arithmetic in his 1891 Philosophy of Arithmetic, a book he had written in the company of Georg Cantor and Carl Stumpf, a man Frege had once appealed to for help in making the Begriffsschrift known (PMC pp. 171-172). The most significant of Husserl's 1891 criticisms of Frege's work had been directed toward §§62-68 of Foundations where Frege had spelled out the very views on identity and extensionality which led to the formulation of Basic Law V and which Frege apparently decided were irremediably flawed in 1906. ln 1900, Husserl had moved to Göttingen where, as a 1902 note from Zermelo shows, Husserl was privy to Zermelo's discovery of the paradox that has come to bear Russell's name. In 1912 and 1920, Husserl, in fact, worked intensively on finding a solution to Russell's paradox.
From Alfred Frege and Husserl, Scholz managed to acquire five Husserl-Frege letters dating from late October 1906 to mid-January 1907. Scholz made typescripts of the two letters Frege wrote to Husserl. These typescripts have survived and are remarkably similar in content to the brief survey Frege apparently made in 1906 of his own logical doctrines now published with posthumous writings (PW pp. 197-202). However, the three letters Husserl wrote to Frege have disappeared. According to Scholz's notes these letters dealt with, among other things "the paradoxes" (PMC p. 70).
In The Interpretation of Frege's Philosophy, Michael Dummett argues that Frege's posthumously published writings strongly suggest that in 1906 Frege became persuaded that attempts to resolve Russell's paradox raises would meet with failure. During that year, Frege had begun to write an article in which he discussed Schönflies's and Korselt's work on the paradoxes of set theory and the inadequacy of the remedies they were proposing for them (PW pp. l76-183). Dummett considers that the presence in Frege's outline for the article 'Concepts which coincide in their extension although this extension falls under the one but not under the other' indicates that Frege was then still pursuing the solution to Russell's paradox proposed in the appendix to the second volume of the Basic Laws. The short twenty line plan Dummett refers to in fact indicates that Frege's article would have dealt exclusively with the themes I have been discussing. The outline plainly states that Russell's contradiction cannot be eliminated in Schönflies's way, that the remedy from extension of second level concepts is impossible, and that set theory is "in ruins" (PW p. 176). The unfinished article itself specifically deals with Russell's paradox, and problems with extensions and Basic Law V (PW pp. 181-182). At one point, Frege alludes to the shock Basic Law V had sustained from Russell's paradox, but suggests that his readers put these doubts temporarily aside and carry out the operation the problematic law would mandate (PW p. 182). It seems, however, that at this point, Frege was himself no longer able to put his doubts aside. "Tantalizingly little of the article survives…", Dummett writes, "very probably it represents the very moment at which Frege came to realize that the attempt was hopeless".
Nothing Frege wrote after 1906 indicates that he ever again tried to salvage the specific logical doctrines he concluded had led to the paradoxes of set theory. Indeed, very little on that subject survives at alI. Less than half of the material Scholz had in his possession before the war is now available and many of the materials missing specifically dealt with the reasons Frege's logic leads to Russell's paradox and Frege's despair concerning proposed solutions to the problems. With the exception of the incomplete draft of the Schönflies article discussed above and other incomplete draft of a 1925 article which is discussed below, all the unpublished writings dated after 1906 in which Frege refers to Schönflies, Korselt, extensions, identity, and Russell's paradox are missing. For example, missing since the bombing are a piece entitled 'Basic Law V Replaced By Basic Law V" and a 1906 piece entitled 'Two Noteworthy Concepts'. According to Scholz's report to the 1935 International Congress of Scientific Philosophy these represented two attempts on Frege's part to reconstruct his system once confronted with Russell's paradox and were connected with the solution proposed in the appendix on the paradox that Frege wrote for the second volume of Basic Laws.
Moreover, Frege's earlier unpublished writings on the same subjects are missing. As I noted above, Frege had already expressed reservations about extensions in his 1884 Foundations and in the 1893 volume of Basic Laws. This means he must have been struggling with the matter as he wrote the three celebrated articles, 'Function and Concept', 'On Sense and Meaning', and 'On Concept and Object', which appeared in 1891 and 1892. All indications as to the nature of this struggle, however, disappeared in the Münster bombing. Manuscripts Scholz once had of these articles, along with excerpts from three of Frege's letters to Hilbert which Frege had filed with them are now lost. Two bundles of papers dating from that time which contained Frege's thoughts on Schröder's work on extensional logic have disappeared. According to the contents listed by Scholz, the papers discussed precisely the issues that have been the focus of the present paper. About the manuscript Scholz had noted that there were sections on, among other things: "Identity and the corresponding second level relation. What two concept-words mean is then and only then the same when the extensions of their respective concepts coincide." The only portions of these papers that have survived have been published posthumously as 'Comments on Sense and Meaning' (PW pp. 118-125). In the now published material, Frege discourses at length about extensionality, arguing that, as Basic Law V would mandate, "concepts differ only in so far as their extensions are different… If an object falls under a concept, it falls under all concepts with the same extension... just as proper names can replace one another salva veritate, so too can concept-words, if their extension is the same" (PW p. 118).
Another missing sheaf of papers from the 1880s contained critical questions regarding §§63-69 of Foundations, the very sections on identity and extensions Husserl had criticized in 1891. These papers also apparently contained reflections concerning conceiving numerical equality as strict identity, and notes on Frege's early attempts to define extensions of concepts. Tyler Burge has conjectured "that in the Foundations manuscript Frege was reconsidering the whole question of whether numbers were objects…, contemplating a contextual definition of such singular terms (roughly in the spirit of Russell's 'no-class' theory)", similar to an alternative Frege would consider in his 1902 appendix on Russell's paradox.
The absence of so many documents concerning Frege struggles with some of the most fundamental issues his logical work raises only aggravates the loss sustained by the destruction of approximately hundred post-1906 letters, many of which plainly dealt with these same matters. From a copy of a draft of a letter Frege wrote to philosopher Paul Linke in 1919, we know that in a now lost 1916 letter Linke had written to Frege asking him for his views as to "whether the mathematical equals sign means equality or identity" (BW pp. 152-153). A copy of a partial draft of a letter Frege sent to the mathematician Karl Zsigmondy survived the destruction of Scholz's archive (BW p. 269). ln the draft Frege says that his efforts to "get clear about what we mean by the word 'number' ...have been a complete failure" (PMC p. 176), and discusses his conviction that mathematics "regards numbers as objects, not as properties. It uses number words substantivally, not predicatively" (PMC p. 178). ln addition, Scholz inventoried, but lost, a 1921 card from Carnap concerning Frege's article 'Concept and Object' (BW p. 16). A now missing 1920 card Korselt wrote to Frege concerned axioms as definitions (BW p. 144), recalling Frege with Hilbert.
Particularly regrettable is the loss of all twenty letters Leopold Löwenheim and Frege wrote to each other from 1908 to 1910. In the late thirties, Löwenheim wrote to Paul Bernays that the exchange had concerned Frege's and Thomae's views on formalism and, in particular, the comparison with chess as found in § 90 of the second volume of Basic Laws (BW p. 161). According to Scholz's report before the International Congress of Scientific Philosophy, Löwenheim and Frege had engaged in an extensive epistolary exchange which they had intended to publish and in which Löwenheim succeeded in convincing Frege of the possibility of establishing secure foundations for formal arithmetic (BW p. 158). As mentioned above, the entire correspondence, along with remarks and drafts Frege had made, and all Scholz's copies were lost. Interestingly, the last letter Löwenheim wrote to Frege was found unopened among Frege's papers (BW p. 161).
Other materials which could shed light on the nature of this exchange are also missing. For example, Scholz's inventory of Frege's papers shows that the Münster archive once housed several sheaves of papers written between 1907 and 1910 which contained Frege's view's on Thomae's and Korselt's work on formalism. These now missing papers contained a detailed 1907 article written by Frege on Thomae's views and a letter refusing to publish it. One, apparently inconsequential letter from Thomae to Frege has also been lost (BW p. 258). Any hopes of finding additional clues as to the nature of the exchange among Thomae's papers were dashed when they, like Korselt's papers, were destroyed. In the last days of World War Il, Thomae's daughter burned all his papers. Attempts to locate relevant material from among Löwenheim's papers have likewise proved utterly futile; Löwenheim was presumed dead for the last seventeen years of his life and anything of interest that may have remained in his possession would most probably have been lost when his Berlin apartment was destroyed in a bombing raid in 1943 (BW pp. 158-159).
Ten letters Frege and Jourdain exchanged between 1909 and 1914 have survived. Almost all of them belonged to the autograph collection and are inconsequential. Much of the correspondence concerned Jourdain's various efforts to make Frege's work known in the English-speaking world. ln particular, Jourdain was preparing an article on Frege's logical and mathematical theories. Frege sent Jourdain his comments, most of which Jourdain published (PMC pp. 179-206). ln a 1913 letter, Jourdain refers to an unknown letter in which Frege "spoke about working at a theory of irrational numbers". Jourdain notes that he and Wittgenstein were rather disturbed by this "because the theory of irrational numbers - unless you have got a quite new theory of them - would seem to require that the contradiction has been previously avoided" (PMC pp. 76-77). There is no indication as to whether Frege replied to this. Two drafts of the last letter Frege is known to have written to Jourdain were found in the autograph collection (BW pp. 126, 129). ln them Frege had discoursed at length on problems with Russell's Principia (PMC pp. 78-84). Scholz at one time had a copy of Jourdain's last letter to Frege. According to Scholz's notes the 1914 letter from Jourdain to Frege concerned Wittgenstein and Russell's Principia (BW p. 133).
So few letters from the last eighteen years of Frege's life have survived that their number almost doubled with the recent discovery of twenty-one cards and letters written by Frege to Wittgenstein between 1914 and 1920. In 1936, having acquired twenty-four letters Wittgenstein (or his sister on his behalf) had written to Frege, Scholz wrote to Wittgenstein inquiring into any letters from Frege that Wittgenstein might still have. Wittgenstein replied saying that, though he did have some cards and letters from Frege, they would not be of any value to a collection of Frege's writings as they were purely personal in nature and devoid of philosophical content (BW p. 265). ln the 1980s fifteen of these cards and six letters from Frege to Wittgenstein were found and published. The last four letters are of interest to philosophers in that they contain Frege's quite harsh pronouncements regarding Wittgenstein's Tractatus which Frege did not hesitate to condemn as unclear and incomprehensible. He, in fact, had nothing good to say about it at all.
Wittgenstein had wanted Frege to recommend the work to Bruno Bauch and Arthur Hoffmann for publication. The five letters from Hoffmann to Frege and the eight letters Bauch wrote to Frege that Scholz once had are lost, but it is apparent from Scholz's notes that some of them concerned the Tractatus (BW pp. 8-9,81-82). C. K. Ogden finally translated the Tractatus into English and it was published in 1921. Scholz inventoried a late 1921 letter from Ogden to Frege, though there is no indication that the letter concerned Wittgenstein (BW p. 168). Also missing from Scholz's archive are four pages of notes by Frege on some of Wittgenstein's views and a package of drafts of replies to Wittgenstein which included drafts of two letters Frege wrote in response to Wittgenstein's requests for his opinion of the Tractatus (BW p. 265).
In 1925, Bruno Bauch had further occasion to correspond with Frege. This time their correspondence concerned an article entitled 'The Sources of Knowledge in Mathematics and the Mathematical Sciences' that Richard Hönigswald had asked Frege to write. Bauch had agreed to act as an intermediary between Frege and Hönigswald. All six letters Hönigswald and Frege are known to have exchanged were in Scholz's possession and are missing. Scholz, however made a copy of a letter Hönigswald wrote to Frege on April 24th and of Frege's reply. These copies have survived, along with part of the article Frege was preparing.
On April 24th, Hönigswald wrote Frege to thank him for the manuscript Bauch had forwarded and to ask Frege whether he might not expand his discussion of certain particularly significant topics. Hönigswald specifically requested more information on the paradoxes of set theory and Frege's reasons for believing set theory to be untenable, on functions, axiomatization, and the concept of number. Finally he asks for Frege's view regarding Russell's, Zermelo's and Hilbert's work. Frege responded immediately by letter to Hönigswald's questions. On May 7th, having received Frege's reply, Hönigswald wrote him once again concerning the expanded version of the article. This last letter is missing (BW p. 87), as are the additional pages Frege had prepared in compliance with Hönigswald's request. Frege died two months later. The unfinished article was published for the first time in his posthumous writings (PW pp. 267-274).
There is, of course, nothing very conclusive that one can say about the contents of documents which have had a history like the one described above. Moreover, pure speculation as to significance of such documents is really pointless. In this case, however, more can be known than first meets the eye, and that is what I have tried to show here.
Frege was a man so impressed by the inherently defective character of natural language that he made it his life's work to free thought from its fetters. His apparent preference for written exchanges is wholly consistent with his convictions in this regard. He wrote long, detailed letters on important subjects. He made drafts of his letters. He wrote many of his letters with the intention of publishing them and letters of his that have been retrieved and published have already proven to be worthy complements to his published writings.
Dummett has written of Frege's total obliviousness to the work of others, and has noted that "there is not a trace in Frege's published or unpublished writing of any notice on his part of the work that was going on in the field he had opened up". In particular, Dummett cites the "many profound contributions from Russell and Whitehead, Hilbert, Zermelo, and Löwenheim". Though Dummett does well to note the dearth of materials available to scholars, it should be clear from what I have said above that Frege was not oblivious to the work of his contemporaries. However, it is precisely those documents that could shed light on Frege's opinion of their work that are missing.
A close look at Frege's correspondence in fact gives lie to many other false ideas about Frege's isolation. Russell was neither the first to read Frege's Begriffsschrift, nor to discover his other works. Frege's work was known to his contemporaries and he did exchange ideas with them. The paradoxes of set theory did not, as Russell has stated, follow "from premisses which were not previously known to require limitations". From the very beginning Frege himself had reservations about the ideas that went into the making of Basic Law V, and Husserl (as Alonzo Church has been almost alone in pointing out) was studying problems in Frege's basic premises ten years before Russell even read Frege.
Of prime importance, as well, must be the fact that practically all the missing letters, and many of the other materials, destroyed in the bombing of the Münster library, were written after Russell's discovery of the paradox and broadly concerned Frege's views on what the problem was and why he found the solutions his contemporaries were proposing unacceptable. These letters presumably could have provided information about a subject concerning which distressingly little can now be known because so little remains to indicate what Frege was thinking about matters of the most vital importance to him at this most crucial time in his intellectual career. What indeed could Frege himself have considered more important than those very issues which brought his life's work to an end and led him to conclude that his efforts complete failure?