Volume 1, Issue 7: A Solvable Problem: Buying or Not Alonzo Church’s Collected Works

A Decidable Problem: Buying or Not Alonzo Church’s Collected Works

The Collected Works of Alonzo Church. Edited by Tyler Burge and Herbert Enderton. Cambridge, MA., London: The MIT Press, 2019, pp. xxxvi + 1189. Hardcover ISBN 978-0-262-02564-5. $135.

Parceling up the intellectual history of western science into diverse and well-defined fields is not a new thing at all. Nonetheless, the studies in recent years about philosophy and science show an even more stratified picture of the historical dimension of knowledge production. Among philosophers, special attention has been given to philosophy of science, theory of knowledge, and to some extend to the philosophy of language. Even though the history of logic has its own journal (History and Philosophy of Logic), its own handbook series (under the general editorship of Dov M. Gabbay), if you ask someone about the subject, she will tell you only a few things. Perhaps something about Gottlob Frege’s Begriffsschrift, Bertrand Russell and Alfred N. Whitehead’s Principia Mathematica, about Carnap’s many-faced contributions, and finally – and mainly – Alfred Tarski’s theory of truth.

                  Even though new and fascinating interpretations occur with more details of Frege’s and Russell’s works, their views have been sufficiently discussed in the last few decades. Tarski is a more challenging task, as he also has a secured place in the history of logic and many noteworthy books have appeared about his life and works, but they are still not comparable in number and depth to Frege and Russell-studies. Carnap is also a hard nut to crack, but for another reason. Presumably, every student of analytic philosophy knows a lot about Carnap’s works and associates his name to symbolic or formal logic. Carnap has indeed published three textbooks on formal logic (one in 1929, a refined German edition was published in 1954, and its English translation in 1958). During the 1940s, his books on semantics, formalization and modal logic had a wide-ranging reputation and recognition; his inductive logic received significant attention too. It would be harder though, to name any of his actual views and conceptions that were followed by many. Carnap’s significance is unquestionable; nonetheless, his influence on the actual history of logic (as a developing discipline) is not measurable with regard to Tarksi’s, or, for that matter, to Alonzo Church’s.

                  And now we have arrived at the subject of this review, namely to Alonzo Church. As his collected works were published during the summer of 2019 by MIT Press, under the editorship of Tyler Burge and Herbert Enderton, Church shall get some new and refreshing attention from scholars of logic and philosophy.

                  Alonzo Church was an American mathematician, logician and philosopher of the first rank, having a wide-ranging international reputation in all these fields. He studied mathematics at Princeton and obtained a Ph.D. under Oswald Veblen in 1927 and spent then a year in Europe mainly Göttingen and Amsterdam where Hilbert and other prominent mathematician-logicians were staying that time. Church was teaching mathematics and formal logic at Princeton until 1967 (first as an Associate Professor and after 1947 as a Professor). When he retired from Princeton after almost forty years of teaching, he went to the University of California at Los Angeles and became Professor of Philosophy and Mathematics. He retired there the second time in 1992, that is, after more than six decades of continuous teaching. He published papers until 1995 and stopped conducting research only shortly before his death in the same year.

                  Church’s move from Princeton to UCLA was connected to one of his main organizational brainchild, namely to The Journal of Symbolic Logic (JSL). The journal – edited by Church and C. H. Langford, with C. A. Baylis as managing editor – was established in 1936 and it was published and supported by the Association for Symbolic Logic. JSLwanted to serve as a tool for achieving basically two goals: (1) to provide a suitable institutional and academic frame for the canonization of the diversified investigations of symbolic logic while at the same time propagating the upshot of the results, (2) and to facilitate research in the field by critically investigating the publications of philosophers and mathematicians.

                  These aims were served not only by the first half of the journal with the standard article section but by the Review section as well, which was sometimes two or three times longer than the article section. The Review section had been edited from the first number on by Church. Now, his move from Princeton to UCLA was partly connected to some financial problems of the JSL: after the 1961 grant from the National Science Foundation has ended and Church retired in 1967, the fate of JSL was sealed. Finally, the support from UCLA (both financially and institutionally) made the undisturbed work possible. The term of this, however, was that the aging Church had to edit the review section, and he indeed completed this task until 1979. 

                  The education and research field of Church provided suitable capacities for him to extend the basic goals of JSL to the review section and to edit and look after it for almost four decades. Before his 1979 leave, Church tried to resign several times but the Association for Symbolic Logic refused to let him and encouraged him to continue his work. Since Church continued teaching until 1990 and made further research and publications until his death in 1995, the reason behind the resignation in 1979 was presumably that the journal could not follow its original aims and principles (in the 1970s so many works appeared about logic that it wasn’t possible to represent and review all of them in the journal in a comprehensive manner without arbitrary choices).

                  The Review section, similarly to the journal, was organized around two basic goals: (1) it had to overview all the works in the field of symbolic logic from January 1, 1936 (outside the English speaking world as well – among the reviewed works we found German, French, Polish, Dutch, Italian, Swedish, Finnish, Portuguese and Spanish writings). Listing the titles of the relevant works would have been enough to mark the boundaries of the field, but Church’s aims were more ambitious. (2) The reviewers had to produce a critical review of the given book, article or review, i.e. besides presenting the content of their subjects, they had to evaluate them by the given scientific and logical standards. The goal was “to defend the field and to separate wheat from chaff” (editorial introduction, p. xv).

                  Church decisively rejected the idea that the Review section should be restricted merely to abstracts that summarize the given work, while the critical writings would be published as separate articles. He thought that if the journal tries to redefine itself in such a manner then he would withdraw from the whole enterprise, because he has not “sufficient interest in a program of publishing mere abstracts” (Church to Carnap, September 8, 1950, p. 1069). In 1975 the journal had to face a similar inner controversy when it gave up reviewing articles and restricted itself to the critical investigation of books. The Review section formed a part of JSL until March 2000 and after that, the other journal of the Association for Symbolic Logic, the Bulletin of Symbolic Logic ensured a place for it. 

                  The Review section under the editorial work of Church acquired a significant reputation thanks to his commitment to take both of the mentioned principles seriously, and by providing ample space in JSL for the reviews to actually review all of the relevant works. On the other hand, Church’s personal relationships and acquaintances also played an important role in upholding the quality of the reviews over the decades. Thus Church went through all of the manuscripts before publication (or rejection) and commented on their content and style.

                  Furthermore, Church asked the most prominent scholars of logic for reviewing – this means that in certain cases Church invited someone for one special review, but he also worked with a regular team whose members gained an extra status. They were ‘consulting editors’ with their names on the cover of the journal along with the editors undertaking the task of reporting constantly about the newest results in symbolic logic (of course, Church also made reviews, approximately five hundred; seemingly a complete list of these reviews – alphabetically with the authors of the reviewed work – is provided in the volume on pp. 1106-1142). Among the consulting editors and reviewers, one finds Evert W. Beth, Paul Bernays, Max Black, Robert Feys, Frederic B. Fitch, Carl G. Hempel, Leon Henkin, László Kalmár, S. C. Kleene, J. C. C. McKinsey, Ernest Nagel, W. V. O. Quine, Rózsa Péter, Arthur N. Prior, Thoralf Skolem and Alfred Tarski.

                  Summing up these features of JSL and especially its Review section’s, one could state that the aim of the reviews was indeed to define the territory of symbolic logic. A review in itself, of course, did not mean acceptance into the canon since the goal of the process was to review everything and decide afterward what will be permanent and what will go off the map.

                  Thankfully, the editors collected and included many of Church’s most important reviews. Some of them (e.g. about Principia Mathematica, Carnap’s Foundations of Logic and Mathematics, Introduction to Semantics, Formalization of Logic) are listed separately, while there is also a longer and more robust selection (consisting of more than forty items) in the last third of the volume (pp. 934-985). There are some rarities and some more well-known papers: reviews of Alan Turing, Emil Post, Leon Chwistek, W.V.O. Quine, Marvin Farber (his The foundations of phenomenology is discussed), Ernest Nagel, Alexadre Koyré, Franz Brentano, A.J. Ayer’s second edition of Language, Truth and Logic, G.E.M. Anscombe, and even an entry from the New Catholic encyclopedia).

                  There are some obvious and less obvious advantages of having these reviews in a collection: (1) they show the wide-ranging interest of Church and the depth of his knowledge of the field, (2) we get a glimpse on what Church thought about his colleagues and the development of the field; (3) it represents a major part of his oeuvre and workload, thus omitting tgem would have resulted in a highly biased volume; (4) finally, they contain many important logical and philosophical insights. Just to give you one typical and well-known example: Church reviewed Quine’s papers on modal logic and the modalities (pp. 941-945) and laid there some foundations for his own logic of sense and denotation. The volume contains a 1968 postscript (published originally in a Brazil periodical).

                  That’s for the reviews. Church is known, and perhaps known mainly, for his work in logic and mathematics. The editors of the volume distinguished three separate fields of his contributions, namely (a) calculability, (b) set theory and foundations, (c) philosophy and intensional logic. His work is described in some details by the editors (pp. xvii-xxiv) and one could open up Church’s Festschrift from 2001 (Logic, Meaning and Computation: Essays in Memory of Alonzo Church, eds. C. A. Anderson and M. Zelëny, Dordrecht, Kluwer). The mathematical and logical parts of Church work are represented in volume by such pieces as his famous papers on the Entscheidungproblem and unsolvable problems, but the book contains the Introduction to his Introduction to Mathematical Logic, Volume I (along with two unpublished chapters from the projected second volume.

                  Church’s philosophical work is well known among logicians. The reason is, as the editors said, “[f]ollowing the examples by Frege and Russell, Church took developments in mathematical logic as a basis for philosophical reflection, and approached philosophy as a subject continuous with parts of mathematical science” (p. xx.). In fact, though it mirrors some of the best works in twentieth-century analytic philosophy, it had a more explicit and solid background in mathematics and logic. This can be easily seen from Church’s writings in the volume already at first glance, but also from Church’s life of securing his field and laying down the foundations for a logically consistent and updated work in philosophy.

                  Nonetheless, what could be even more interesting and important for philosophers are Church’s papers from the 1950s. There we find some really well written pieces about logic and mathematics without using any formalization (“Ontological Commitment”, “Misogyny and Ontological Commitment”, “Logic and Analysis”, “Logic, Arithmetic, and Automata”, “Mathematics and Logic”). Further, there are Church’s papers on intensional logic (also from the 1950s) and his debate with Carnap on the modalities; finally, having a look at Church’s encyclopedia and dictionary articles on logic (pp. 448-530 and 692-747) one might see how rigorous Church was in setting the standards for logicians and philosophers both in their own fields and in communicating the main points of the field to the educated public.

                  But the volume contains much more important and special materials! Besides the already mentioned list of Church’s review, there is a list of his doctoral students (p. 1105), and a small amount of his professional correspondence is reproduced as well. We got letters from Oswald Veblen, Paul Bernays, Stephen C. Kleene, Emil Post, Rudolf Carnap, and W.V.O. Quine. The editors have claimed, “letters that formed coherent and interesting groups were chosen for this collection” (p. ix). The Church-Gödel correspondence was already published in the Gödel Collected Works. At the beginning of every correspondence, the editors explain why it was included; though some of them are complete as they stand, in other cases (Post, Carnap) it is told that the further letters “were judged to be of lesser philosophical and mathematical interest” (p. 1005).

                  And why these letters are important, besides their intrinsic value for intellectual history? “Church’s contribution to philosophy, though extremely influential, have not been as influential – nor are they as wide-ranging – as those of his contemporaries, Quine and Carnap. However, Church’s work has a depth and integrity that promise long life. One sees in it, and in his correspondence, a clarity and power of mind that are certainly not surpassed, and possibly not equaled, by any of his contemporaries, with the lone exception of Gödel” (editors, p. xx, original emphasis). While everyone has to decide for herself/himself, it is certainly true that the volume contains such a rich material that is exceptional in the history of twentieth-century logic and logical philosophy 

                  Finally, some words shall be told here about the edition itself. While the editors explicitly aimed to respect Church’s predilection for simplicity, austerity and purity, the reader’s predilection for having in his/her hands an aesthetically attractive and cozy volume has not been taken really into consideration. Having a quick look at the cover one might get the feeling that he/she is dealing with the final proof-stage version for internal circulation; this is just reassured by the book’s spine (and by the strange contrast of the baby blue textile spine with the shining white hardcover). Although the young Church’s photo might give us some relief from the weight of the volume (as do all the photos that are included, starting with the three-year-old Church and ending with the eighty-seven years old), it is especially bothersome to twist, leaf through and carry it anywhere in your bag. The volume is robust, heavy and hard to grab for late-night reading (not just intellectually, but physically as well). The only advantage of the book’s huge format is that there is plenty of space on the margins for internal notes. With its index of subjects, names and long bibliography, the volume is, after all, 1200 pages long, so its hugeness shall not surprise the reader at all. Nonetheless, perhaps it would have been wise somehow to break down it into two volumes (but it is hard to see how that could have been done if not by making a more logical and a more philosophical volume, which would have perhaps gone against Church’s conception of the field).

                  So, all in all, The Collected Works of Alonzo Church is a nicely edited, important document that cannot be bypassed by historians, philosophers and especially logicians in the forthcoming years. Hopefully, historians of analytic philosophy will devote more attention to Church too: not knowing where to start cannot be an excuse anymore. It has been provided by MIT Press and the editors. So buy it!

Adam Tamas Tuboly

Supported by the MTA BTK Lendület Morals and Science Research Group and by the MTA Premium Postdoctoral Scholarship.