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Leibniz's Influence on 19th Century Logic

Submitted by Richard Zach on Sat, 09/12/2009 - 9:16pm

Volker Peckhaus has a new entry in the Stanford Encyclopedia on the influence of Leibniz on the development of logic in the 19th century.

Library Book Dedication

Submitted by Richard Zach on Sat, 09/12/2009 - 8:56pm

I got Herbert Feigl's Theorie und Erfahrung in der Physik from the library, and on the front flyleaf there's a handwritten dedication to Karl Menger that reads "Herrn Professor Menger ergebenst überreicht vom Verf., 13. VI. 1929."

Turing Machine Robot in LEGO

Submitted by Richard Zach on Fri, 09/11/2009 - 5:33pm

Wow. Four students (Sean Geggie, Martin Have, Anders Nissen, Mikkel Vester) at the University of Aarhus, Denmark, constructed a Turing Machine tape read/write assembly in LEGO. This was a final project for the course Embedded Systems - Embodied Agents, taught by Ole Caprani of the LEGO Lab at Aarhus. On their blog Lego of Doom, they describe the initial idea as follows:

The "Turing Machine" will need to traverse a track of some kind, reading marks on the track and altering them. Reading and altering bits on a track entails three things: Detecting that the machine is over a cell, detecting the state of the cell and altering the state of the cell. These three problems will each be solved by careful application of various sensors. Many solutions exist for each problem and much experimentation will be needed to find out which yields the most stable results.

Architecturally speaking, the Turing Machine robot could be in contact with a PC via bluetooth connection. Via this connection, the robot could leave some calculations to the PC which would send back instructions. One example of this could be that the PC handles all the "boring" Turing Machine calculations while the robot itself could be in charge only of cell and bit state detection as well as motor control.

The main part of this project would be getting the robot to accurately read and set the bits on the track. The implementation of the turing machine itself is trivially accomplished. The "meat" of the project is embedding the program in a machine that actually performs computations in a physical environment.

They did all that and then they made an awesome movie about it:


HT: Francesco Berto/Andrea Sereni

Review of Symbolic Logic Published Two of Ten Best Papers of 2008

Submitted by Richard Zach on Fri, 09/11/2009 - 3:13am

The new journal of the Association for Symbolic Logic, the Review of Symbolic Logic, started up in 2008. Two of the papers in that first volume were selected for the Philosopher's Annual, vol 28, which each year "attempts to select the ten best papers in philosophy published in each year". They are:

  • Thomas Forster, The Iterative Conception of Set, Review of Symbolic Logic 1:1 (2008), 97-110
  • Penelope Maddy, How Applied Mathematics Became Pure, Review of Symbolic Logic 1:1 (2008), 16-41

Only the Phil Review also had more than one (viz., three) papers selected. The selected papers also include another logic paper:

  • Fabrizio Cariani, Marc Pauly & Josh Snyder, Decision Framing in Judgment Aggregation. Synthese 163 (2008), 1-24

You can read the papers online (and free) at the Philosopher's Annual website. Congratulations to all the authors!

Gordon Brown Apologizes to Alan Turing

Submitted by Richard Zach on Fri, 09/11/2009 - 1:57am

In response to the petitions mentioned recently, the UK government has issued an apology. The statement in full, as published on the 10 Downing St website:

Alan Turing2009 has been a year of deep reflection - a chance for Britain, as a nation, to commemorate the profound debts we owe to those who came before. A unique combination of anniversaries and events have stirred in us that sense of pride and gratitude which characterise the British experience. Earlier this year I stood with Presidents Sarkozy and Obama to honour the service and the sacrifice of the heroes who stormed the beaches of Normandy 65 years ago. And just last week, we marked the 70 years which have passed since the British government declared its willingness to take up arms against Fascism and declared the outbreak of World War Two. So I am both pleased and proud that, thanks to a coalition of computer scientists, historians and LGBT activists, we have this year a chance to mark and celebrate another contribution to Britain’s fight against the darkness of dictatorship; that of code-breaker Alan Turing.

Turing was a quite brilliant mathematician, most famous for his work on breaking the German Enigma codes. It is no exaggeration to say that, without his outstanding contribution, the history of World War Two could well have been very different. He truly was one of those individuals we can point to whose unique contribution helped to turn the tide of war. The debt of gratitude he is owed makes it all the more horrifying, therefore, that he was treated so inhumanely. In 1952, he was convicted of ‘gross indecency’ - in effect, tried for being gay. His sentence - and he was faced with the miserable choice of this or prison - was chemical castration by a series of injections of female hormones. He took his own life just two years later.

Thousands of people have come together to demand justice for Alan Turing and recognition of the appalling way he was treated. While Turing was dealt with under the law of the time and we can’t put the clock back, his treatment was of course utterly unfair and I am pleased to have the chance to say how deeply sorry I and we all are for what happened to him. Alan and the many thousands of other gay men who were convicted as he was convicted under homophobic laws were treated terribly. Over the years millions more lived in fear of conviction.

I am proud that those days are gone and that in the last 12 years this government has done so much to make life fairer and more equal for our LGBT community. This recognition of Alan’s status as one of Britain’s most famous victims of homophobia is another step towards equality and long overdue.

But even more than that, Alan deserves recognition for his contribution to humankind. For those of us born after 1945, into a Europe which is united, democratic and at peace, it is hard to imagine that our continent was once the theatre of mankind’s darkest hour. It is difficult to believe that in living memory, people could become so consumed by hate - by anti-Semitism, by homophobia, by xenophobia and other murderous prejudices - that the gas chambers and crematoria became a piece of the European landscape as surely as the galleries and universities and concert halls which had marked out the European civilisation for hundreds of years. It is thanks to men and women who were totally committed to fighting fascism, people like Alan Turing, that the horrors of the Holocaust and of total war are part of Europe’s history and not Europe’s present.

So on behalf of the British government, and all those who live freely thanks to Alan’s work I am very proud to say: we’re sorry, you deserved so much better.

Gordon Brown

Why Study Formal Logic?

Submitted by Richard Zach on Thu, 09/03/2009 - 12:59am

Next week it's back to the classroom for me, and I'm teaching intro logic again. I've been thinking a bit about what to do on the first day, especially in the "why you should take this course" department. There's the obvious reason: it's required (at least for philosophy and CS majors). So I'm really talking about "why you should want to take this course". And here, the textbooks usually don't do such a good job. First there's the "you'll learn how to think correctly and identify logical errors" line. The examples there are usually a valid and an invalid syllogism, examples that I suspect anyone with any chance getting a decent grade in the class can already identify as good and bad instances of reasoning. Second, there's the "important applications in logical circuit design" story. But, honestly, any logic design course can cover the logic they need for combinational circuits in a week. Third, there's the "taking this course will train your analytic and abstract thinking skills". Ok, maybe, but that's not really a good selling point.

So I'm looking for concrete, real-life examples where some of the things that you learn in a formal logic class are useful: examples that are relatively easy to describe, where it's obvious that these are "really relevant" to whatever discipline they're taken from, and where you can reasonably claim that you need to be able to deal with a formal language, understand relations and multiple quantification, or use logical methods like formal proofs or model-building techniques to avoid errors or solve a problem.

One of the examples I think I'll use is SNOMED CT. That's a health-care terminology database (aka an "ontology") with over 300,000 concepts organized by over 1,000,000 rules. These rules could be formulated in a fragment of first-order logic (some description logic suffices, I'm not sure which). One example I've seen mentioned here is this: In SNOMED CT, an leg amputation is defined as a procedure with method amputation and procedure-site-direct lower limb structure; and a toe amputation as a procedure with method amputation and procedure- site-direct toe structure. Now SNOMED CT also knows that the toe is a part of the lower limb, so that if a procedure happens in the toe, it eo ipso happens in the lower limb. Therefore, a toe amputation is also a leg amputation. But of course you wouldn't want a surgeon to take off your entire leg if you have a gangrened toe! On the other hand, if you have a pain in your temple, then since the temple is part of the head, you have a headache, and you do want SNOMED to know that. So here you need all kinds of logic: you need a formal language in which to express these concepts and relations, it needs to be expressive enough so that you can express everything you want to express, you need logical methods to tell you a) what follows from SNOMED (queries), b) wether SNOMED is consistent, c) where the errors are and how to remove them. (I learned about SNOMED CT from Frank Wolter's talk at the Logic Colloquium, "Mathematical logic for life science technologies".)

Of course, all of this is just a particular case of the various important applications of logic in AI and databases, but I thought it was a nice example that wasn't just a toy database. Also, I like the "mistakes that logic helps avoid or correct" flavor.

I'd also like examples like that from philosophy and mathematics. For mathematics I was thinking of talking about Cauchy's "erroneous" proof of the uniform convergence theorem, and pointing out the importance of the order of quantifiers. That has the problem that (as we know from Lakatos) Cauchy didn't really overlook the necessary requirement of uniform convergence, and also it might be a bit too difficult (to explain in a short amount of time). For philosophy, I thought of maybe using Skorupski's argument for the principle of moral categoricity from Ethical Explorations, which I found in a post by Doug Portmore on PEA Soup. I like it because it's simple, and recent, and from ethics, which is often considered by students to be next to the opposite of logic( as far as courses are concerned).

Do you have other ideas? Better ideas? Ideas applying in other disciplines?

I think it would be nice to have an example where a famous mathematician or philosopher committed a more-or-less elementary logical error that can be diagnosed or avoided by formalization.

Hermann Weyl in the SEP

Submitted by Richard Zach on Wed, 09/02/2009 - 9:00pm

Logic on Your iPhone

Submitted by Richard Zach on Wed, 09/02/2009 - 4:15pm

David Johnston, of the University of Victoria Philosophy Department, has just released three apps for the iPhone (and iPod Touch), which will be of interest to students (and teachers) of introductory logic courses:

Logic 100

These utilities for truth-functional logic allow you to check syntax, construct truth tables, and test for consistency and validity. Notation can be set to match any logic textbook.


These utilities for categorical logic allow you to construct syllogisms, test them for validity, and display their Venn diagrams.

Logic 101

This app helps you construct derivations based on the system SD from The Logic Book. It checks the syntax of each line and automatically applies derivation rules. Completed derivations, including line justifications, can be emailed directly from the app.

I guess we'll have to be more vigilant about students having cellphones on them when they take a logic exam! But, in the words of Hans von Ditmarsch, "anyone who gets people to do logic while waiting for their bus, wasting time otherwise, ..., deserves praise!" Read more about these apps on, try them out, and let us (and him) know what you think!

Incidentally, these apps are versions of David's Logician's Toolkit, which lets you do all these things inside a Java applet on his website. Useful especially if you use the Logic Book.

Apology for Alan Turing

Submitted by Richard Zach on Tue, 09/01/2009 - 4:16pm

As you probably know, logic pioneer Alan Turing invented the Turing machine model of computation, proved the undecidability of the halting problem and (independently of Church) the undecidability of the decision problem, and played an important role in the work at Blechley Park that broke various German ciphers during World War II. He was also gay, and committed suicide following his criminal conviction for "gross indecency" and the chemical castration he was forced to undergo. There are now two petitions circulating, calling for a formal apology from the British Government for Turing's treatment: one for British citizens and an international petition.

Books by Russell (and others) in Google Books

Submitted by Richard Zach on Tue, 09/01/2009 - 1:45am

I had to look up a Russell quote the other day, and that's when I noticed that many of his books -- including the Foundations of Geometry, Our Knowledge of the External World, Introduction to Mathematical Philosophy, Analysis of Mind, Principles of Mathematics, Mysticism and Logic, and Principia Mathematica (annoyingly, only vol. II) -- are available in their full glory through Google Books. There are lots of other gems, including Hilbert's Grundlagen der Geometrie, the Tractatus, etc. But beware: the Google metadata are unreliable, to say the least (see Geoff Nunberg on Google Books: A Metadata Trainwreck).

Job Prospects for Philosophy Students

Submitted by Richard Zach on Fri, 08/28/2009 - 3:34pm

Here's another article in the "you might not have thought it but philosophy undergrads are actually doing well in careers in business and law" mold, from a Canadian perspective.

Philosophy’s makeover: Why job prospects for philosophy grads are brightening, by Daniel Drolet

T-Rex on Vagueness

Submitted by Richard Zach on Fri, 08/28/2009 - 3:24pm

Carbone on the Genus of Proofs

Submitted by Richard Zach on Mon, 08/24/2009 - 5:19pm

A long time ago I posted on Richard Statman's dissertation work on the geometrical complexity of proofs: take a proof in natural deduction, interpret the formulas in it as nodes of a graph with edges going from premise to conclusion of an inference and from assumption to the (conclusion of the) inference where it is discharged. The genus of that graph is an interesting complexity measure. Ale Carbone has also worked on this complexity measure, and now has an exciting paper entitled "Logical structures and genus of proofs" forthcoming in the Annals of Pure and Applied Logic. Here's the introduction:

The objects of our analysis are proofs. We shall not ask why we prove a statement, nor how to show a statement, but how difficult it is to prove it. An answer to the third question might give insight into the second.

At present, there is no notion that captures well how difficult it is to prove a theorem. Measures employed to grasp this idea are the number of steps and symbols used in a deduction, and these measures are far too rough: proofs containing no cuts/lemmas usually have a larger number of steps and symbols than proofs with cuts, but their combinatorial structure is simple, essentially a tree; on the other hand, the combinatorial structure of proofs with cuts can be quite intricate, and lemmas might be very hard to guess. Despite this, in practice, we look for lemmas in order to show a theorem.

Here we consider the genus of a proof as a measure of proof complexity and we discuss a few geometrical properties of logical flow graphs of proofs, with and without cuts, with the purpose of representing how complicated a cut-free proof can be. The main result of the article says that arbitrarily complicated non-oriented graphs, that is graphs of arbitrarily large genus, can be encoded in a cut-free proof. This fact was proved by Richard Statman in his thesis written in the early seventies and never published. Here, we reformulate Statman’s result in a purely graph theoretical language and give a proof of it. We show that there are several ways to embed non-oriented graphs of arbitrary complexity into cut-free proofs and provide some other direct embeddings of arbitrarily complex non-oriented graphs into proofs possibly with cuts. We also show that, given any formal circuit, we can codify it into a proof in such a way that the graph of the circuit corresponds to the logical flow graph of the encoding proof.

Logic (and Other Fun Stuff) on BBC Radio 4

Submitted by Richard Zach on Mon, 08/03/2009 - 9:26pm

The BBC 4 radio program "In Our Time," presented by Melvyn Bragg, has archives of previous features on a range of topics, including some relevant to logic. Haven't had the time to listen to them, but it you do, let me know what you think. Might be the kind of thing you can tell your relatives to listen to when they want to know what you are interested in.

HT: Chris Green

New Open Access Logic Books from the ASL

Submitted by Richard Zach on Sun, 08/02/2009 - 10:21pm

Exciting developments! The Association of Symbolic Logic has made the now-out of print volumes in the Lecture Notes in Logic (vols. 1-12) and Perspectives in Mathematical Logic (vols. 1-12) open-access through Project Euclid. This includes classics like

I'm especially excited about the Hájek/Pudlák and Barwise/Feferman volumes, which are chock-full of useful material! Check out the full list of volumes available (click on the "Series Contents" link on the right side). For now it's available in nicely scanned and OCR'd PDF format, perhaps there will also be a print-on-demand way of getting a bound copy.

Most Logical Countries in the World

Submitted by Richard Zach on Tue, 07/14/2009 - 7:49pm

For your amusement: a list of all countries with at least 5 members of the Association for Symbolic Logic, rank-ordered by number of logicians per 10,000,000 inhabitants. Bonus info: percentage of women logicians in these countries.

Country # ASL members % Women per 10,000,000
New Zealand 17 0% 39.5
Switzerland 25 4% 32.5
Israel 22 18% 29.7
Norway 13 0% 27.1
USA 806 12% 26.3
Netherlands 43 21% 26.1
Canada 85 11% 25.2
Belgium 23 4% 21.5
Finland 10 10% 18.9
United Kingdom 100 10% 16.4
Denmark 9 0% 16.4
Sweden 15 20% 16.3
Singapore 7 17% 14.6
Greece 16 25% 14.3
Austria 11 9% 13.3
Croatia 5 0% 11.4
Germany 87 8% 10.6
Portugal 9 33% 8.5
Australia 17 6% 7.8
Spain 35 11% 7.6
Italy 42 24% 7.0
France 40 11% 6.2
Japan 63 12% 5.0
Czech Republic 5 0% 4.8
Poland 12 8% 3.1
Brazil 40 13% 2.1
Colombia 8 25% 1.8
Argentina 6 33% 1.5
South Africa 6 0% 1.2
Iran 5 0% 0.7
Russia 8 25% 0.6
Mexico 5 20% 0.5
China 14 0.1
India 8 20% 0.1

Women in Philosophy of Logic and Philosophical Logic

Submitted by Richard Zach on Fri, 06/26/2009 - 4:24pm

Catarina Dutilh Novaes sent the following important message to PHILOS-L last weekend, reposted here with her permission:

Dear all,

Recently (and admittedly very late!), I started thinking more seriously about the lack of gender balance in the areas in which I do most of my research, namely history and philosophy of logic and philosophical logic. What got me thinking was probably the (positive) noise being made at Feminist Philosophers. One of the issues raised by the Feminist Philosophers is the low proportion of women in most philosophy conferences (in particular as invited/keynote speakers); I realized that in the workshop I am organizing, there are only three women as speakers, including myself! So I think this is a matter that deserves further attention.

Richard Zach had a blog entry a while ago on the staggeringly low number of women publishing in the journals of the area (his data concerned the Journal of Philosophical Logic). From this sort of data it is all too easy to conclude that there simply aren't enough women around working in (philosophy of) logic and philosophical logic so as to redress the imbalance seen in conference lineups. But here again the usual analysis applies: the lack of female speakers at such conferences reinforces the idea that the area is just not 'for women', which in turn does not encourage young female students to pursue interests they might have in the area. Absence of female keynote speakers may also be a discouraging factor for other female researchers to submit papers to such conferences. Sally Haslanger has a wonderful piece on how vicious these mechanisms can be, which can be found here: Changing the Ideology and Culture of Philosophy: Not by Reason (Alone)

So the purpose of this message now is to question the widespread impression that there are not (or very few) prominent female logicians and philosophers of logic, people with the standing to be keynote speakers at major conferences. I was thinking it might be useful to compile a list of such people, sort of a handy device that could help those organizing conferences in the area to ensure a better gender balance among the speakers. Please send me names off list, and I will post the results to the whole list once we have a significant number of names. Just to give you an idea of what I have in mind, here are some women that would obviously be on such a list: Juliet Floyd, Penelope Maddy, Gila Sher, Delia Graff Fara. I’m sure there are many more such talented women working in the philosophy of logic and philosophical logic, so I look forward to many reactions!


cdutilhnovaes at yahoo dot com

Please respond to Catarina at the email address above!

UPDATE: Results of the effort are collected "women in philosophy of logic and philosophical logic" on the Logic and Rational Interaction blog.

PM@100: Logic from 1910 to 1927

Submitted by Richard Zach on Wed, 06/24/2009 - 1:28am
Call for Papers
PM@100: Logic from 1910 to 1927

21 – 24 May, 2010
Bertrand Russell Research Centre
McMaster University
Hamilton, Ontario

The Bertrand Russell Research Centre in 2010 will host a conference to celebrate the 100th anniversary of the publication of the first volume of Russell and Whitehead’s Principia Mathematica.

The publication in 1910 of the first of the three volumes of Russell and Whitehead’s Principia Mathematica was a landmark in the development of logic, the foundations of mathematics, and the application of logic in philosophy. The rapid development of these fields in the two decades after 1910 owes perhaps more to Principia Mathematica than to any other work. Subsequently, however, its lessons learnt in different ways by different people, it becomes more difficult to determine exactly what the world owes to this gigantic piece of work. Daunting both for its size and its technical difficulty, the book is now known more by reputation than by detailed study. Russell himself maintained, no doubt with some exaggeration, that he knew of only six people besides the authors who had read the entire three volumes. He remained dissatisfied with the foundations of the work and attempted a major revision (this time without Whitehead’s help) in a second edition published in 1925–27, which further complicated its historical legacy.

A century after its first appearance, a great deal has changed. Many of Russell’s working papers on the problems it addressed have been published, and this has led to significant re-interpretations of the work itself. Enough time has now passed to make it possible to evaluate what contributions it made, or failed to make, to philosophy, logic, and the foundations of mathematics.

Presenters Include: Patricia Blanchette, Charles Chihara, Warren Goldfarb, Ivor Grattan-Guinness, Leila Haaparanta, Allen Hazen, David Kaplan, Gregory Landini, Peter Simons, Alasdair Urquhart, and Richard Zach.

Submissions to the conference are sought in all areas relating to Principia Mathematica or to the development of logic and to the philosophy and foundations of mathematics in the years between the two editions.

Contributors are asked to submit two copies of an essay suitable for 30–45 minute presentation with an abstract no later than 1 January 2010 to:

Professor Nicholas Griffin, Director
The Bertrand Russell Research Centre
1280 Main Street West
Hamilton, Ontario

FAX: 905-577-6930

Graduate students are also encouraged to submit. Announcements of acceptances for the program will be made by the end of February 2010.

Conference Co-Organizers:

Nicholas Griffin
The Bertrand Russell Research Centre
McMaster University

Bernard Linsky
Department of Philosophy
University of Alberta
bernard.linsky@ualberta. ca

Server Problems

Submitted by Richard Zach on Fri, 06/19/2009 - 6:40pm

My website people changed something on the server and now this blog isn't displaying properly and my website is completely down. Sorry. If you want to get to my website, try instead of