Gordon Brown Apologizes to Alan Turing

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?

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.

Logic on Your iPhone

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.

Syllogism 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 hatzicware.com, 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

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.

The Development of Mathematical Logic from Russell to Tarski: 1900-1935

Leila Haaparanta, ed., The History of Modern Logic. New York and Oxford: Oxford University Press, 2009, pp. 318-471 (with Paolo Mancosu and Calixto Badesa)

Reprinted in Paolo Mancosu, The Adventure of Reason. Interplay Between Philosophy of Mathematics and Mathematical Logic, 1900-1940. Oxford: Oxford University press, 2010

The period from 1900 to 1935 was particularly fruitful and important for the development of logic and logical metatheory. This survey is organized along eight “itineraries” concentrating on historically and conceptually linked strands in this development. Itinerary I deals with the evolution of conceptions of axiomatics. Itinerary II centers on the logical work of Bertrand Russell. Itinerary III presents the development of set theory from Zermelo onward. Itinerary IV discusses the contributions of the algebra of logic tradition, in particular, Löwenheim and Skolem. Itinerary V surveys the work in logic connected to the Hilbert school, and itinerary V deals specifically with consistency proofs and metamathematics, including the incompleteness theorems. Itinerary VII traces the development of intuitionistic and many-valued logics. Itinerary VIII surveys the development of semantical notions from the early work on axiomatics up to Tarski’s work on truth.

DOI: 10.1093/acprof:oso/9780195137316.003.0029

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Books by Russell (and others) in Google Books

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).