Interview with Hao Wang and Robin Gandy

In 1991, I videotaped talks at the Kurt Gödel Colloquium in Kirchberg (it was supposed to be held jointly with the Wittgenstein Symposium, that got cancelled). I also videotaped a conversation with Hao Wang and Robin Gandy, students and friends, respectively, of Gödel and Turing.  I can’t for the life of me remember who the interviewer was. Anyway, you may find it interesting:

[Photo credit: San and Jane Wang]

Fall 2016 edition of Sets, Logic, Computation

The Fall 2016 edition of the OLP remix Sets, Logic, Computation is ready. As before, it includes the OLP part on sets, relations, and functions; the part on first-order logic (with natural deduction chosen as the proof system); and the part on Turing computability including the unsolvability of the halting and decision problems. The methods chapter on induction and biographies of Cantor, Church, Gentzen, Gödel, Noether, Russell, Tarski, Turing, and Zermelo appear as appendices. At students’ request, problems are now listed at the end of each chapter. Many typos and errors have been corrected, a number of examples and problems have been added, and several proofs rewritten for clarity. I’ve also added chapter summaries and a glossary. There are also a few added sections, notably introduction sections to Chapters 5 and 7, as well as discussion of Russell’s Paradox in both Chapter 1 and 6. You can order a printed copy on Lulu, or download the PDF from the builds page. SLC F16

Line Art Portraits of Logicians

You’ve probably seen some of the line art portraits of logicians we’ve commissioned. They were done by Calgary illustrator and graphic designer Matthew Leadbeater. We’re pleased to release them all now under a Creative Commons BY-NC license: anyone is free to use them in their own work, to create derivative works from them, and to share them, provided (a) credit to Matt Leadbeater is properly given and (see license terms!) (b) they are not used for any commercial purposes. They each come in two versions, one with a line below, and one with the portrait in a circle. You can download the original Adobe Illustrator files. For PNG and PDF formats, we have set up a GitHub repository. Commissioning these illustrations was made possible by a grant from the Alberta OER initiative. We gratefully acknowledge the support. [Bonus: an image file with all of them that tiles nicely, for your desktop background.] Antonelli Barcan Marcus Boole Brouwer Cantor Carnap Church Craig Curry Dedekind Frege Gentzen Gödel Heyting Hilbert Kleene Kripke Lewis Lovelace Noether Péter Post Prior Rasiowa Bowman Robinson Russell Skolem Tarski Turing Zermelo

ASL Spring Meeting at the APA Pacific, Seattle, April 2017

The 2017 Spring Meeting of the Association for Symbolic Logic will be held jointly with the Annual Meeting of the Pacific Division of the American Philosophical Association, April 12-15, 2017, in Seattle. The members of the Program Committee are Wesley Holliday, Audrey Yap, and Richard Zach (Chair).

There will be three Special Sessions:

Modality and Modal Logic

Intuitionistic Mathematics and Logic

Inclusiveness in Logic Eduction

(organized by the ASL Committee on Logic Education)

There will also be a session for contributed talks. Abstracts of contributed talks submitted by ASL members will be published in The Bulletin of Symbolic Logic if they satisfy the Rules for Abstracts. Abstracts must be received by the deadline of September 12, 2016, at the ASL Business Office: ASL, Box 742, Vassar College, 124 Raymond Avenue, Poughkeepsie, New York 12604, USA; Fax: 1-845-437-7830; email: asl@vassar.edu.

Student members of the ASL are eligible for travel awards.

[Photo credit: Howard Ignatius CC BY-NC-ND 2.0]

Student Satisfaction Survey Results

In the Winter term 2016, I taught the University of Calgary’s second logic course from a textbook remixed from the Open Logic Project.  Traditionally, Logic II has used Boolos, Burgess & Jeffrey’s Computability and Logic, and it was taught in Fall 2015 using that book as the required text by my colleague Ali Kazmi, and before that by him, Nicole, and me twice a year from that same book.  One aim Nicole and I had specifically for the OLP was that it should provide a better text for Logic II, since neither we nor our students seemed to be very happy with “BBJ”. In order to ascertain that the OLP-derived text fares better with students, we did something radical: we asked them what they thought of it.  Ali graciously gave permission to run the same textbook survey in his class, so we have something of a baseline.  A direct comparison of the two books as textbooks for the course is not easily made, since Ali and I used the books differently: I stuck closer to my text than he did to BBJ; I assigned homework problems from the text; and we assessed students differently, so it’s difficult to control for or compare teaching outcomes.  With small samples like ours the results are probably also not statistically significant. But the results are nevertheless interesting, I think, and also gratifying. We obtained clearance from the Conjoint Faculties Research Ethics Board for the study.  All students in each section of Logic II in F15 and W16 were sent links to an electronic survey.  As an incentive to participate, one respondent from each group was selected to receive a $100 gift certificate to the University of Calgary bookstore. The surveys were started in the last week of classes and remained open for 3 weeks each.  Response rates were comparable (23/43 in F15, 23/42 in W16). The survey was anonymous and administered by staff from the Taylor Institute for Teaching and Learning; results were not given to us until past the grade appeal deadline in W16. We asked 23 questions.  The first three regarded how students accessed and used the textbooks. In the F15 section, the textbook was not made available electronically, but students were expected to buy their own copy (about $40).  Most respondents did that, although almost a quarter apparently pirated electronic copies.  In W16, the OLP-derived text was available for free in PDF and students had the option to buy a print copy at $10. Over half the respondents still opted to buy a copy.  We asked students how they used the texts in hardcopy and electronic form.
When using the text in hardcopy, do you...
Those using the OLP-derived printed text underlined significantly more than those who used BBJ. I’m guessing the OLP text is better structured and so it’s not as necessary to provide structure & emphasis yourself by underlining. In fact, one student commented on BBJ as follows: “Very little in the way of highlighting, underlining, or separating the information. It was often just walls of text broken up by the occasional diagram.”
When using the text in electronic form, do you...
When using the electronic version (both PDF), students did not differ much in their habits between F15 and W16. More students took notes electronically in F15. I suspect it’s because the PDF provided in W16 was optimized for screen reading, with narrow margins, and so there was little space for PDF sticky notes as compared with a PDF of the print book in F15. Also notable: highlighting and bookmarking is not very common among users of the PDF. The second set of questions concerned the frequency with which students consulted the textbook, generally and for specific purposes.  W16 students used the OLP-derived text significantly more often than F15 students did, and for all purposes.
How often do you consult the text?
The difference is especially striking for the questions about how often students consult the textbook for exams and homework assignments:
Do you read the text in preparation for exams?
Do you consult the text when working on homework problems?
We next asked a series of questions about the quality of the texts. These questions were derived from the “Textbook Assessment and Usage Scale” by Regan Gurung and Ryan Martin. On all but one of these questions, the OLP-derived text scored positive (4 or 5 on a 5-point Likert scale) from over half the respondents. The discrepancy to students’ opinions of BBJ is starkest in the overall evaluations:
How engaging/interesting is the writing?
How understandable/clear is the writing?
The one exception was the question “How well are examples used to explain the material?”:
How well are examples used to explain the material?
This agrees with what we’ve heard in individual feedback: more, better examples! Lastly, we were interested in how students think of the prices of textbooks for Logic II. We asked them how much they’d be willing to spend, how much the price influenced their decision to buy it. Interestingly, students seemed more willing to spend money on a textbook in the section (W16) in which they liked the textbook better. They also thought a free/cheap textbook was better value for money than the commercial textbook.
Is the price of the textbook too high for the amount of learning support it provides?We also asked demographic data. Respondents from both sections were similar: almost all men in each (the course is mainly taken by Computer Science and Philosophy majors), evenly divided among 2nd, 3rd, 4th year students plus a couple of grad students in each (Logic II is required for the Philosophy PhD program). Student in W16 expected higher grades than those in F15, but that may well be just an effect of differences in assessment and grading style rather than better student performance.
If you care, there’s an interactive dashboard with all the graphs, and the raw data.

More Photos of Logicians

As previously mentioned, the Open Logic Project now has a separate repository for photos of logicians to illustrate your OLP-derived materials.  They are automatically included in the biographies that live in content/history.  I’ve just uploaded a whole bunch of photos that don’t have associated biographies (yet).  Some of them are not well-known, even. For the technicalities, I’ll repeat myself from the previous post:
We have a separate repository for photos: github.com/OpenLogicProject/photos. We’ve separated them because (a) the licensing issues are more complicated: some of the photos are under copyright, and we wanted everything in the main repository to be available under a Creative Commons license; (b) the main repository would become very large if it included all these pictures. To use the pictures, clone the photos repository into the assets/ subdirectory of your local OLP clone. There’s a PDF with all the photos on the build site.
Tracking down these pictures and getting permissions was (and continues to be) a surprising amount of work.  Thanks to all the people and archives who provided them and granted permissions: the IAS archives, Princeton University Library, Berkeley’s Bancroft Library, the Russell Archives at McMaster, the Archives of the Universities of Warsaw and Wittenberg-Halle, the ILLC, the Austrian National Library, the NSUB at Göttingen, the National Portrait Gallery, the Oslo Museum, Neil Reid (Julia Robinson’s brother-in-law), Libby Marcus (Ruth Barcan Marcus’s daughter), Kim Heffernan (Haskell Curry’s granddaughter), Eckhardt Menzler-Trott, Craig Smorynski, and Peter van Emde Boas. Detailed photo credits are included with the photos.  Thanks also to the Alberta OER initiative for providing some funding to do this.  And last, but not least, thanks to Joel Fuller for doing an awesome job with PhotoShop restoring some of these photos (the original Curry photo, in particular, had a big tear right through the middle)! More to come!

CfA: Foundations of Mathematical Structuralism

12-14 October 2016
Munich Center for Mathematical Philosophy, LMU Munich

In the course of the last century, different general frameworks for the foundations of mathematics have been investigated. The orthodox approach to foundations interprets mathematics in the universe of sets. More recently, however, there have been other developments that call into question the whole method of set theory as a foundational discipline. Category-theoretic methods that focus on structural relationships and structure-preserving mappings between mathematical objects, rather than on the objects themselves, have been in play since the early 1960s. But in the last few years they have found clarification and expression through the development of homotopy type theory. This represents a fascinating development in the philosophy of mathematics, where category-theoretic structural methods are combined with type theory to produce a foundation that accounts for the structural aspects of mathematical practice. We are now at a point where the notion of mathematical structure can be elucidated more clearly and its role in the foundations of mathematics can be explored more fruitfully.

The main objective of the conference is to reevaluate the different perspectives on mathematical structuralism in the foundations of mathematics and in mathematical practice. To do this, the conference will explore the following research questions: Does mathematical structuralism offer a philosophically viable foundation for modern mathematics? What role do key notions such as structural abstraction, invariance, dependence, or structural identity play in the different theories of structuralism? To what degree does mathematical structuralism as a philosophical position describe actual mathematical practice? Does category theory or homotopy type theory provide a fully structural account for mathematics?

Confirmed Speakers

  • Prof. Steve Awodey (Carnegie Mellon University)
  • Dr. Jessica Carter (University of Southern Denmark)
  • Prof. Gerhard Heinzmann (Université de Lorraine)
  • Prof. Geoffrey Hellman (University of Minnesota)
  • Prof. James Ladyman (University of Bristol)
  • Prof. Elaine Landry (UC Davis)
  • Prof. Hannes Leitgeb (LMU Munich)
  • Dr. Mary Leng (University of York)
  • Prof. Øystein Linnebo (University of Oslo)
  • Prof. Erich Reck (UC Riverside)

Call for Abstracts

We invite the submission of abstracts on topics related to mathematical structuralism for presentation at the conference. Abstracts should include a title, a brief abstract (up to 100 words), and a full abstract (up to 1000 words), blinded for peer review. Authors should send their abstracts (in pdf format), together with their name, institutional affiliation and current position to mathematicalstructuralism2016@lrz.uni-muenchen.de. We will select up to five submissions for presentation at the conference. The conference language is English.

Dates and Deadlines

Submission deadline: 30 June, 2016
Notification of acceptance: 31 July, 2016
Registration deadline: 1 October, 2016
Conference: 12 – 14 October, 2016

For further details on the conference, please visit: http://www.mathematicalstructuralism2016.philosophie.uni-muenchen.de/

Natural deduction for the Sheffer stroke and Peirce’s arrow (and any other truth-functional connective)

Richard Zach, “Natural Deduction for the Sheffer Stroke and Peirce’s Arrow (and any Other Truth-Functional Connective),” Journal of Philosophical Logic 45(2) (2016), pp. 183–197.

Methods available for the axiomatization of arbitrary finite-valued logics can be applied to obtain sound and complete intelim rules for all truth-functional connectives of classical logic including the Sheffer stroke (NAND) and Peirce’s arrow (NOR). The restriction to a single conclusion in standard systems of natural deduction requires the introduction of additional rules to make the resulting systems complete; these rules are nevertheless still simple and correspond straightforwardly to the classical absurdity rule. Omitting these rules results in systems for intuitionistic versions of the connectives in question.

DOI: 10.1007/s10992-015-9370-x

Preprint on arXiv (with errata)

Helmut Veith (1971-2016)

My friend and colleague Helmut Veith died yesterday.  His death is a great and shocking loss to his family and friends, and the logic community, especially in Austria.

I’ve known Helmut since we were undergraduates in computer science at Vienna Technical University in the early 1990s.  We shared a passion for theoretical topics in computer science, a love of Robert Musil; we took many courses together.  In fact, we liked logic so much that together we created a specialized course of study (a studium irregulare) in computational logic.  At the time this still required approval by the federal ministry of science and research, and it was a lot of work, but we got it approved.  It has since morphed into a standard stream in the computer science curriculum at the TU Vienna, and more recently a doctoral program, all in no small part due to Helmut’s tireless organizational work.  I was a year ahead of him, but he was the better student.  He literally had straight As throughout high school and university. In Austria, that earns you a doctorate sub auspiciis praesidentis, and the president of the republic himself hands you your diploma.  His Diplom was on finite model theory; his dissertation on the complexity of database query languages (supervised by Georg Gottlob). Helmut had a stellar career: appointments at TU Munich, TU Darmstadt (two of the centers of computer science in Germany), and finally a full professorship at our alma mater in 2010; add to that an adjunct professorship at Carnegie Mellon. Not only was he the better student, he had the better sense to stay in computer science, and to do something useful with logic. He was one of the leading experts in computer aided verification, especially model checking, with over 120 papers to his name.  After his return to Vienna, he was instrumental in getting the Vienna Center for Logic and Algorithms off the ground, led the organization of the Vienna Summer of Logic, and helmed the Austrian doctoral program on logical methods in computer science.  Helmut wasn’t just an outstanding researcher, he was also passionate about improving undergraduate education in logic and computer science (he served on the ASL’s Logic Education committee, and we co-organized a special session at the 2014 Logic Colloquium), about diversity in the field, and about science policy.

We need more people like him. I miss him.

  • TU Vienna obituary in German and English.
  • A scholarship fund in Helmut’s honour is being set up.  Contributions to the Helmut Veith Award can be made to “Zentrum für Informatikforschung”, IBAN: AT36 1200 0515 8258 2701, BIC: BKAUATWW, reference: “Helmut Veith Award”

[Photo credit: Nadia Meister/VSL]

An Actual Textbook, and: Photos!

(Cross-posted from the Open Logic Project)

Two exciting new things from the Open Logic Project. The first one is another sample textbook. I’ve previously written about how to get your textbook to print, and for my course “Logic II (Phil 379)” this term, I’ve done that. Properly: perfect bound paperbacks, with a nice cover, proper front and back matter, professional illustrations, and an (I think) appealing book design. The source for generating it is on GitHub (of course): github.com/rzach/phil379. If you want to compile it, just clone that repository into the courses/ subdirectory of your local OLP clone. It should compile out of the box.  There are three files you can compile: phil379-screen.tex makes a multi-color PDF suitable for on-screen reading; phil379-print.tex makes a black-and-white PDF suitable for printing via lulu.com.  The third is cover-lulu-quarto.tex, which generates the PDF lulu.com uses for the cover. You can see the product on the builds site:

The second exciting thing is that we’ve started to put photos of logicians into the text. Right now, they’re imported into the biographies. The photos themselves are not in the main repository, however. We have a separate repository for them: github.com/OpenLogicProject/photos. We’ve separated them because (a) the licensing issues are more complicated: some of the photos are under copyright, and we wanted everything in the main repository to be available under a Creative Commons license; (b) the main repository would become very large if it included all these pictures. To use the pictures, clone the photos repository into the assets/ subdirectory of your local OLP clone. (If the files aren’t there, the biographies including them will happily compile but leave out the photos.) There’s a PDF with all the photos also on the build site.

(PS: If you want to buy an actual copy of the Sets, Logic, Computation book, go here. It sells for CAD 9.42 (USD 8.36, EUR 8.55). But be warned; we’ve already corrected a bunch of typos and errors, so that version is not up-to-date.)

Association of Symbolic Logic Abstract Deadline Today!

The deadline to submit abstracts for contributed talks at the ASL Annual Meeting in Storrs, CT this May is today!

There will be a super exciting Special Session on History and Philosophy of Logic, featuring:

  • Teresa Kouri (Ohio State), Carnap on translations
  • Daniel Nolan (ANU), Reflections on Routley’s Ultralogic Program
  • Dave Ripley (UConn), Toward a naive type theory
  • Gil Sagi (MCMP), Invariance criteria: terms and constraints
  • Zeynep Soysal (Harvard), Unfolding the content of the concept of set
  • Sean Walsh (Irvine), The prehistory of the subsystems of second-order arithmetic (joint work with Walter Dean)

[Photo: Manchester Hall CC-BY-ND by Ray Kingston]

Reconsidering Frege’s Conception of Number

Erich Reck and Roy Cook have edited a special issue of Philosophia MathematicaReconsidering Frege’s Conception of Number,” with contributions by Paddy Blanchette, Phil Ebert, Thomas Forster, Roy Cook, and Richard Heck.

It is dedicated to the memory of Aldo Antonelli:

Before launching into the introduction to this issue, we would first like to mention a conclusion of sorts. The end in question is of many friendships; many productive collaborations; many days spent eating good food, drinking good wine (or beer), and talking great philosophy; and an end to a great many other wonderful things. Aldo Antonelli passed away, tragically and too young, on October 11 of 2015, when this special issue was near the end of the long path from initial ideas to eventual publication. We could easily justify dedicating this issue to Aldo based on the role he played in its production. He was involved in various ways from beginning to end, and there is no doubt that the issue would be less ‘special’ had he not added his insights and intelligence, but most importantly his generosity, to the project at various critical points. But that is not the only reason for the dedication. The editors of, and contributors to, this special issue all have fond memories of long conversations with Aldo — often about the very topics discussed in the essays collected here. We are deeply saddened by the fact that we will not have any more opportunities to talk with him about Frege, logicism, and many other things. Thus, we are not dedicating this issue to Aldo just because he was a good philosopher, but also because he was a good friend.

The Reason We Use Symbols

In my second logic course I start with some very basic set theory.  You forget just how confusing symbols can be to students who aren’t used to them. But then you also appreciate how useful they are when you try to explain in “plain English” what they mean. Even something as simple as a proof of X ∩ Y ⊆ Y ∩ X is hard. I tried to write a proof of it in the Up-Goer Five text editor. It’s up top. What do you think?

Diversity Summer Program on Paradoxes

Maureen Eckert is organizing Summer Program for Diversity: Logic at the University of Massachusetts Dartmouth from May 22-28, 2016.  The program is open to undergraduates and recent graduates from underrepresented groups; there are 10 spaces and travel & lodging are provided.  The topic of the program is paradoxes:

Paradoxes present the ultimate challenge—contradictions. Logicians and philosophers work at solving or dissolving paradoxes. This program is an opportunity for students to investigate a range of formal techniques and systems aimed at solving paradoxes.

Guest speakers will address Self-Referential, Set-Theoretic, Epistemic and other types of paradoxes, presenting current research from a variety of perspectives. Classes and workshops are led by visiting faculty and Graduate Assistants.

So far the visiting faculty confirmed are Liam Kofi Bright (Carnegie Mellon University), Margaret Cuonzo (Long Island University), and Gillian Russell (University of North Carolina). Deadline to apply is April 18.