The Abnormal Distribution

A bit of intellectual biography, prompted by a couple of days’ free time leading me to a paper written 27 years ago by a pal, which I have just read. I say a little of what’s in the paper, to encourage others to read it. And then I comment on a couple of disappointing aspects of the WWW, and of academic work here in Bielefeld.

I am reading a collection of papers on The Law of Non-Contradiction, edited by Priest, Beall and Armor-Garb (Oxford University Press, 2004, reprinted 2011), for a seminar I offer on the subject of paraconsistent logics. Amongst them is a paper by Vann McGee, an MIT logician and philosopher, on Frank Ramsey’s Dialethism. Dialethism is the position that there are logically incompatible assertions that are true. In this case, says McGee, “…sometimes Ramsey is willing to count each of two classically logically incompatible theories as true”.

I am interested in such phenomena because I am interested in reasoning in general, and have been induced by a Bielefeld student, Daniel Milne, who has been following such matters for some time, to become interested in reasoning about and reasoning in stories – fiction. For, one could say, one of the ways in which much fiction works is to induce us to reason about situations invented by the author, who may well not be constrained in general by the “laws” of reasoning applying to the physical world. One can imagine a story in which, while I am sitting listening to you present a paper on dialethism in my seminar, you are simultaneously off waterboarding a tax collector. You cannot be in two different places at once physically, but in a story you can be so without the story appearing to be incoherent. But other stories are incoherent – think of Finnegan’s Wake. How to mark a difference?

Further, many stories involve people and objects which are not real, which are invented. Do these people and objects “exist” in some way? If so, then certainly not in the way in which you or I exist, for we are “real”, “actual”, or however you might like to describe us, and the invented entities not – they don’t have an address or an ID card or pay radio licence fees and nobody is going to go looking for them to insist they sign up for any of these. But we can’t just say “anything goes”, that we can reason about such invented entities any way we like. What about that superficial referring phrase itself, “invented entities”? Does it refer? In one sense, obviously it does: you know exactly what I am talking about, because I told you: things invented by people to occur in stories they write. In Fregean logic, modern formal logic, or on Russell’s interpretation of putatively-referring terms, however, the term doesn’t refer. But singular or plural terms in “classical” formal logic (that is, the post-Frege traditional complete formulations of propositional and predicate logic) must refer. What, then, does this term do and how does it do it? And what logic, if definitely not classical as just noted, is involved in reasoning concerning it? Say, in helping to explain what this very paragraph means?

I was in grad school at Berkeley with Vann McGee, who entered a year later than I did – or was it two years? We were in the Group in Logic and Metholodology of Science, started by Tarski and having 15 or so graduate students pursuing PhDs, and about four times that many faculty members, some of whom we never saw, such as the game theorist John Harsanyi, who was to win a Nobel Prize. Vann entered at the same time, I think, as Shaughan Lavine, a loquacious logician interested in physics – at that time Shaughan wanted to solve the riddle of the intellectual incoherence of quantum mechanics, but thought it would take decades and thus the enterprise couldn’t really start until one had tenure, so he considered it wise to pick lower-hanging fruit for PhD and pre-tenure work. Shaughan left Berkeley after a couple of years because he didn’t see how it was actually possible to get a PhD degree in the Group in the environment prevailing in the 1970′s. He worked as an editor for the Physical Review, and came back at the end of the decade to work on a technical problem in mathematical model theory which he thought he could crack in a couple of years (in fact, it took him eight more years, underlining the accuracy of his earlier observation).

I was very interested in mathematical logic. In fact, I came to Berkeley being most interested in the Scott semantics for the lambda calculus, but I found nobody else there interested in them, except a young Japanese scholar, Reiji Nakajima, working with a temporary faculty member in the Computer Science Department who was applying it to programming languages with recursive constructs, so I thought. My interest in computation was theoretical – Turing machines, recursive functions and the like, and I came from a university which had a research group in programming languages, but no department doing work in computing science – the Oxford Computing Laboratory was largely for people who wanted to solve applied-math problems numerically and I was utterly uninterested in those at the time (things would change!). I classified the Berkeley Computer Science Department in that shoebox – one of the many and varied intellectual mistakes I have made in my career, and this one took me a decade to correct.

Even then, I think I was equally or more interested in questions in philosophical logic than in set theory or model theory, but there were more people doing the hard math and I didn’t think you could get a job doing philosophical logic. Further, the math seemed “hard” and the philosophical logic “soft”. The math was hard – it proved too hard for me in the end. But I was worried about career prospects in philosophical logic. I knew some physicists in the mid-1970′s who had told me that at that time there was just one tenure-track academic job in theoretical physics offered in the whole of the US. I thought philosophical logic was going the same way. So rather than follow my inclinations away from math, I went into it even more – I even taught myself and taught others numerical analysis (at both the undergrad and grad levels) because I thought I’d have more chance of a job doing something related to what I enjoyed. I didn’t realise that the South Bay was about to explode into Silicon Valley and help logic become one of the largest applications of mathematics after calculus and numerical algebra and analysis. But the varied non-logic mathematical skills I learned have proved invaluable to me; I don’t regret at all the time spent developing them.

Back to Vann. Vann was quiet in classes and conversation, but his observations and conjectures were pertinent and incisive when he made them and he was obviously both very clever and very able. As well as giving us the impression of being quite other-worldly. None of us at that time in the mid-1970′s knew how to get out of Berkeley with our PhD degree (indeed, the university itself was to recognise the fact that too many clever graduate students were often having too much demanded of them, and was to initiate change), but Vann gave me the impression of not caring about it that much, as long as he could carry on thinking about technical matters in measurement theory and conditionals and all those problems ignored by the logicians in the Math Department. He finished in 1985, having written not only a thesis on Truth and Necessity in Partially Interpreted Languages, but also having done work in the Theory of Measurement (one of Ernie’s Adams’s interests, as well as one of Pat Suppes’, down the road at Stanford) and in the Logic of Conditionals (the major Adams theme along with Probability Logic). Some of his work on conditionals was published the year he was awarded his PhD, in the Journal of Philosophy, a – some say the – leading journal.

I just read the paper, after 27 years. Which is part of what prompted this note.

Me, I’d gone “applied”, having taught math and computer science at two California State Universities, San Francisco and then Hayward to try to support myself while working on my degree in the copious free time left to me on a full teaching schedule at a teaching university. I managed to reprove a result of Humberstone in algebraic logic without realising it, as Johan van Benthem noted when I explained my result. My resolution to “stop reading and get down to working!” had been taken two papers too soon . “It shows what you can do!” said Johan helpfully, but it didn’t seem any consolation at the time after that couple of years’ work. I got my first real break in mid-1984, with a temporary job in SRI’s Computer Science Lab. That helped me write half a thesis on eliminating quantifiers in naive set theories, but that effort ended some months later when my job ran out. The second break was at my next job, at the Kestrel Institute starting in late 1985, where I was put to work on devising a computational system for reasoning about time. Cordell Green pointed me at James Allan’s work on intervals in interpretation of reasoning about time in natural languages, and I recognised a Relation Algebra, which is something I knew something about in algebraic logic, and about which my pal Roger Maddux knew much more. We got some significant new mathematical results (largely his) as well as data structures and algorithms (largely mine, some implemented). I had a book contract with MIT Press Bradford Books together with Pat Hayes (which remains to this day unrequited), submitted my thesis and was awarded my PhD degree in 1987. My code, written in the now defunct language REFINE, which was very modular and mostly declarative, persuaded me of the value of declarative languages with strong typing and rigorous modularity. I spent six months writing code to perform calendrical calculations according to my data structure (to computer scientists a “model”, but not to logicians), for the Project Manager part of the Knowledge-Based Software Assistant project of the USAF. I gave the code along with API to the integrator of the KBSA-PM. She spotted one error (a boundary value) inside a couple of hours of testing – and then the code ran seamlessly for demo at AAAI in 1986 and in the KBSA-PM delivered to the Air Force, for the next ?few years? as far as I know. In the last twenty-five years, we have not gone forward much in industrial programming languages. All the issues I was able to avoid seamlessly by using REFINE still occur all the time in the industrial systems I am acquainted with.

Shaughan finished a year later, in 1988. He had solved a major technical problem in admissible model theory and was successful in his job search at the very time that philosophical logic was suffering the fate of physics a decade earlier – I think he got the one tenure-track job in philosophical logic available at the end of the 1980′s. He was at Stanford – although I was in Palo Alto at my job most days in the week, I never met up with him there – and then went to Columbia, where he wrote his book Understanding the Infinite (Harvard University Press, 1994, reprinted 1998). I haven’t seen Shaughan for twenty years, nor Vann for thirty.

Man, what a paper that is which Vann published in 1985! A Counterexample to Modus Ponens. Tim Williamson in The Philosophy of Philosophy (Blackwell, 2007) calls Vann a “distinguished logician” while explaining one of these results (see for example, this citation).

Let A and B be things you assert (sentences, say, or propositions or statements, if you believe in those and can say what they are). “Assert” means something like “claim to be true”. Modus Ponendo Ponens is the inference rule whereby, from an assertion of A and an assertion that if A then B, you may infer B.

According to the Stanford Encyclopedia of Philosophy, Aristotle discussed a forerunner of Modus Ponens called Theophrastus, whereby from the premises if something is F, it is G and x is F one may infer x is G. Modus Ponens concerns general assertions, whereas Theophrastus is concerned with objects having properties or characteristics, and properly belongs to the logic of predicates rather than to propositional logic.

So, what is an inference rule? What are doing when you “infer”? One common explanation, the “classical” explanation (although “classical” here means largely the 150-year-old Fregean tradition) is that asserting A and A implies B or if A then B means you are taking these sentences to be true. Inference then means that you take the third sentence B also to be true on the basis of the truth of the first two. The rule is said to “preserve truth”. A rule of inference which preserves truth is said to be valid.

There are two main ways of formulating the logic of whole sentences, propositional logic. One is to give a set of axioms – a collection of logical truths (sentences guaranteed to be true just in virtue of their form, such as A implies A, or (A and B) implies B) and just two inference rules: Substitution and Modus Ponens. Substitution says you may replace any schematic letter, such as “A” in the two logical truths just given, by any sentence whatever. This is truth-preserving, because the logical truths are so because of their form, not their content, so no matter what “A” is, something of the form “A implies A” will be true. That “no matter what” phrase is another way of expressing Substitution. No one queries Substitution; it is one of the basic mechanisms of logic as truth/assertability according to form and not content. It looks to be significant for this century-and-a-half-long conception of logic that Modus Ponens may not be truth-preserving when “if…then….” is used in natural-language reasoning! The other way of formulating logic consists of giving no axioms, but plenty of rules of inference, indeed some (“introduction” rules and “elimination” rules) for each logical constant. Modus ponens is the “introduction rule” for the conditional in this formulation. So either way Modus Ponens is key. (The first type of system is popularly ascribed to the German mathematician David Hilbert, the second to the German logician Gerhard Gentzen.)

In fact, when “implies” is taken to be what is called the “material conditional”, Modus Ponens is truth-preserving, as Vann points out. The material conditional is the intepretation of “implies” whereby “A implies B” is taken to be equivalent to saying “either Not-A or B”. One interpretation of logic, one explanation of the meaning, takes the “logical constants” in propositional logic, the connectives “and”, “or”, “implies” and “not” to be purely functions of the truth or falsity of the sentences they combine. This, along with the claim that every sentence whatever either is true or is false, constitute the basis of what is called classical propositional logic (that is, the common propositional logic since Frege).

It is easy to see that, when “implies” is the material conditional, Modus Ponens is truth-preserving, as follows. You assert A. A is taken to be true. You assert A implies B, that is, either Not-A or B. So this is taken to be true. But you have taken A to be true, so it follows that you cannot take Not-A to be true as well, for you would be contradicting yourself (the so-called Law of Non-Contradiction is another foundational principle of classical logic, but exactly what it means can be questioned – see the more than 240 different variations pointed out by Patrick Grim’s article in the eponymous op. cit.). If the “Not-A” part of the true either Not-A or B isn’t true, then it must be the “B” part that is true. That shows that Modus Ponens is truth-preserving, because B is exactly what Modus Ponens infers from the first two sentences.

People using formal logic in mathematics generally take “implies” to mean the material conditional when they are using logic or talking about it. And they take this to be settled. But they also infer, as a professional activity: they prove theorems from other mathematical “facts” (theorems). It is prima facie apparent that inference of this sort may well not be the same kind of activity as when, looking out from my room, I see your shadow on the street and infer that the sun is shining. For that is defeasible – somebody may have turned a searchlight on you on a cloudy day. Whereas mathematical theorems are not usually taken to be defeasible in the same way – they taken to be wrong only if their author has made a technical mistake in reasoning, not if the phenomenon they assert is valid but otherwise explained.

When Vann points out apparent counterexamples to Modus Ponens, he is noting that there are conditionals, “if…then…”-statements, in the language we use, and if one is trying to formulate truth-preserving inferences using those notions of implication, then formal Modus Ponens doesn’t preserve truth.

On the face of it, he’s right. “On the face of it” means that the arguments he uses are formally of the Modus Ponens form (except for a couple of minor typographical differences which are assumed to be contingently grammatical and not substantial). The question is how to explain the phenomenon. Vann suggests it is crucial that the “B” part of his counterexamples is itself a conditional. That is, there is an “if ….. then….” as the “then”-part of an “if….then…..”; known as “nested conditionals”.

There is a substantial amount of work on the logic of conditionals. They seem to be quite tricky, so it is really not surprising that phenomena such as Vann identified have remained unnoticed for so long. Ernie Adams wrote an influential eponymous book on the logic of conditionals, published in 1975. David Lewis addressed it in a number of seminal papers as well as a book, Counterfactuals (Havard U.P./Blackwell’s 1973, reissued Blackwell’s 2001). Jonathan Bennet has an extensive survey of some 380 substantial pages (A Philosophical Guide to Conditionals, Clarendon Press, Oxford, 2003). One locus classicus is a set of papers edited by Frank Jackson (Conditionals, Oxford University Press 1991, unfortunately out of print).

Vann considers also the interpretation of if A then if B then C as if A and B then C and vice versa (he calls this the “law of exportation”, the “law of importation” being the interpretation of the second as the first), and notes that, if these laws are correct interpretations of conditionals, the difficulty is “basic”: that you are stuck with taking “if … then …” to be the material conditional (which it can’t be, because if so there would be no counterexamples to Modus Ponens) or the logically most powerful conditional called “strict implication”, whereby “if A then B” is true only if in every possible world in which A is true, B is also true. Which wouldn’t seem right: “if I have my brown jacket on, then my grey jacket is at the cleaner’s” tells you something about my clothing habits in this world in which we actually live, and tells you nothing about another world, odd but possible, in which I have a pathological hatred specifically of wearing grey jackets and would never do so, even if there were fifty in my closet and I only had my brown one otherwise.

That is a powerful and surprising result.

He goes further, in showing that Robert Stalnaker’s account of a certain kind of conditionals called subjunctive or counterfactual conditionals (conditionals in which the antecedent, the part following the “if” and before the “then” are not actually true but hypothetical) is “inaccurate” (Stalnacker’s account is in A Theory of Conditionals, in Studies in Logical Theory, American Philosophical Quarterly, Monograph 2, 1968, reprinted in Jackson op. cit.). He means wrong, if the law of exportation holds. This is also a significant result, for at the time the Stalnaker and closely-related Lewis semantics for counterfactual conditionals were held to be the best accounts. (They are still the best available for many purposes. Forty years on, we use the Lewis semantics for counterfactual conditionals in my technique for causal analysis of accidents, Why-Because Analysis, where it works very well in the context of complex engineered sociotechnical systems.) The issues with counterfactual conditionals in particular were, I believe, first raised by Nelson Goodman in a paper The Problem of Counterfactual Conditionals, Journal of Philosophy XLIV(5), February 27, 1947, available through JSTOR to those with access. It is also reprinted as Chapter 1 of his book Fact, Fiction and Forecast (Harvard University Press, 1984).

There is much, much more in this short paper. I am so glad I read it finally.

On to my second theme, somewhat distressing. As I have written before, I thought in the mid-1990′s that the advent of the World-Wide Web would render the business models of traditional academic publishing obsolete. That hasn’t happened, to my regret as well as sometimes to my annoyance. But the WWW has led to on-line discussions, and there are various software available to format ongoing discussions of any and all subjects on the WWW. Instead of searching out a bunch of like-minded people to meet to discuss raising blue goldfinches, you can find them right there in the blue-goldfinch forum! What a wonderful enrichment of our lives.

I looked for discussion of Vann’s paper. I only found two discussions in forums on the first few pages of the Google search. The second entry in the Google search for the paper was a discussion on TalkRational: A Republic of Free Thought. A “moderator” brings up McGee’s paper in 2010, a quarter-century after publication. Kudos for drawing attention to it, one might think, but consider hisher comment:
“

(1) I think that the most obvious problem with McGee’s argument is that he equivocating between two radically different ways of construing the relevant statements. Are there any other problems with the argument that you see?
(2)Is Vann McGee retarded? Seriously, is there any reason whatsoever why his argument should be persuasive?

which is partly personally abusive. Heshe says in a later note:

McGee has basically become a rock star in philosophical logic because of this argument, too. It’s a pretty tragic statement on the condition of contemporary philosophy.

The discussion goes downhill from there, quite steeply. Most people seem to want to deprecate McGee personally, as the moderator implictly does.

Such a combination of incomprehension and abuse is unfortunately rife on WWW forums. It doesn’t seem to happen to anything like the same extent on subscription-only e-mailing lists. This is one area in which e-mail seems to serve a function which the WWW does not, contrary to what one might have anticipated. I regret, and am frustrated by, the low standard of such forum discussion. Recall that this is a discussion which appears high on the Google list responding to the query “vann mcgee modus ponens”.

I wish for a different world, a world in which papers and arguments can be presented and discussed on the WWW the way they are presented and discussed in colloquia, conferences and the better journals. We are unfortunately a long way from that.

On to my third theme.

The first PhD to graduate whom I advised in Bielefeld was Thorsten Scherer. Thorsten built a mobile robot to perform lab assays automatically. I became his advisor after his original advisor left Bielefeld and Thorsten didn’t want to follow. His robot worked in a biotechnology lab. It drew samples from a large (industrial-scale) fermenter, which was producing cells, took them to and installed them in a centrifuge, started the centrifuge, removed them when it stopped and took the results to and installed them in an assay machine. These devices were distributed around the lab. Thorsten had developed the robot to such a degree of reliability that it worked at night when nobody was around. It only spilled stuff one time, near the beginning of development.

I was very impressed by this piece of system engineering. Thorsten had put together algorithms – recognition, motion and control algorithms – some of which he had gleaned from the literature and many of which he had devised himself and had integrated them in a piece of hardware which performed its chosen task to a demonstrated high level of reliability (achieving the task as wished) and safety (avoiding spills, collisions, breakages).

Readers will appreciate that most academic contraptions of this sort are “proof of concept”, that is, their devisers can get it to do what it is supposed to do some of the time, at least once or twice. Adding dependability to such “proof of concept” devices comes out to around ten times as much work, as an industrial rule of thumb. It is very frustrating to those of us who work in the area that, with some notable exceptions, dependability issues are largely ignored in academic computer science, for they are not intellectually trivial. Most of us end up spending far more time talking with industrial engineers than we do with fellow academics.

I thought this superb work, and proposed Thorsten for a summa cum laude designation. So did his second thesis reviewer, his ex-boss. But it was vetoed by the Chair of his committee (as thesis advisor, I could not be Chair) on the basis that he had taken too long – seven years, I think.

Another example. I had an Indonesian scholar in my group, I Made Wiryana. Made’s thesis was on what I would call practical requirements engineering in culturally very different situations from those in the West. Indonesia has many different cultures, information technology is helpful and very much needed, but some ways we have of engineering these systems just don’t fit local cultures there, which are many and varied. Made devised a means of performing dynamic adjustments to sociotechnical system requirements through causal analysis of cultural issues that came up during initial system development and prototyping. Again, unlike most academic work, this was serious “grown-up” engineering. The examples in his thesis included designing and implementing the system to run the blog of the Indonesian president, whom he had personally advised, and designing and implementing the warning-message function associated with the tsunami early-warning system installed with international help after the 2004 December tsunami.

Again, I thought this work worthy of a summa cum laude designation, as indeed Made’s committee decided. But before the defence, I had a brief chat with one of my colleagues, multiple times Dean of our faculty, known for his very effective fund-raising, and now Rector of my university, who opined strongly that it was inappropriate to consider awarding a summa cum laude to someone who had “taken too long” (Made had been working with my group about a decade).

To my mind, the quality of a PhD lies solely in its achievement. Both of these scholars had achieved way beyond what most German PhDs in computer science achieve, in that they had devised and implemented systems with demonstrated dependability. As I noted, that simply takes longer. Made had to work with a number of organisations, including government, to get his results. Anyone setting a clock ticking on government work anywhere is liable to run out of clock batteries.

Why am I saying this here? By means of contrast. Vann took ten or eleven years to get his PhD. Shaughan took 13, as did I. Was ten years worth that one seminal paper of Vann, let alone a PhD? In my view yes, most certainly! Read it, and I bet you’ll agree. But in Germany he would have “taken too long”………

Martyn Thomas chaired a committee convened by the UK Royal Academy of Engineering on infrastructure vulnerabilities to GPS disturbances. The committee reported in March 2011 and Martyn was briefly on the front page of UK news media on March 10, 2011 until the Tohoku event happened the day after.

What Martyn’s committee found was astonishing. For example, critical infrastructure functions whose builders and operators were convinced had no connection with any GPS functionality – and which stopped working when a GPS jammer was activated. The Committee’s report is well worth reading all the way through. Its remit includes all SatNav systems, not just GPS.

Martyn gave a Keynote talk at the 20th Safety-Critical Systems Symposium in Bristol a couple of weeks ago. A Google preview of Martyn’s paper is available, as well as an IET.tv film of his talk. (The Institution of Engineering and Technology, IET, filmed many of the presentations. You can check out my Keynote on the Fukushima Daiichi accident as well if you like )

It is amazing to me that anyone wouldn’t take Martyn’s observations very seriously indeed.

However, we do appear to have a few journalists that poo-poo it, for example Lewis Page again recently in The Register after his commentary a year ago upon the report’s release, just as we had an astonishing number of journalists who made public their opinion that Y2K was never a big deal. A very silly point of view. As Martyn points out in his talk, the reason Y2K was not a big deal is that people such as himself worked very hard to eliminate as many as possible of the Y2K vulnerabilities discovered in our critical infrastructure, and were obviously quite successful. He knows what they were, since he was the senior technical advisor for some of that work (for example, UK air traffic services provision), and knows what would have happened had they not been taken care of.

The main social point here is, I think, people who worry versus people who don’t. If we didn’t have people who worried, then we wouldn’t be able to operate because things would be continually going wrong, such as possibly UK air traffic services at the turn of the millenium had NATS not worked very hard to eliminate those vulnerabilities. And on the back of such successful effort there are journalists who say “everything’s OK, isn’t it? Why worry?”. Yes, things are OK. Why worry? Because if some of us didn’t, they wouldn’t be.

Here is an example of a daily vulnerability that bit. It’s also old hat. But it happened to me two days ago, and most of those involved are a professional computer scientists with a PhD (or about to obtain one) and decades of experience of such matters.

I have used my e-mail system as a memo system very effectively for the last few decades. I am based on IMAP, so it’s what people now call “in the cloud” but used to be called “stored on a server“. Over the years, when a subject or task occurs to me, I have got pretty good at remembering the context in which it occurred and indexing into e-mail (I send quite a few messages just to myself). It works for me very well. For decades.

Until Tuesday. I was writing an email, and the longish memo I was writing started losing characters backwards from where I had been typing, at the similar repetitive rate to that deriving from, say, a stuck delete key. It took a few seconds to realise what was happening. Then I went into the menu-strip at the top of the screen (I use the Apple OS+environment) and tried to quit my mail client (Thunderbird – Apple Mail apparently does not work well with IMAP. I lost all my mail for about a year at one point a few years ago and it took a couple of days to generate a solution from backup. The second time it happened, I switched to Thunderbird). The menu would come down, but disappeared again as I moved the mouse onto it. This happened repeatedly. I tried the same on the Apple main menu (so I could “Force Quit” the mail client) but the same happened there. I tried a hardware shutdown – the OS refused because Thunderbird would not quit and it advised me to quit Thunderbird and then try again. I have never actually tried to log in as root and am not sure I remember the root password, so trying that, and if successful getting the process number and performing “kill -9” didn’t seem like a good option given the urgency.

So, hardware kill: press the “off” switch and hold until the machine powers down. Good news for me: this worked.

When it came back up and I fired up the mail client, it showed me that all the messages from Wednesday 15 February at 16:35 (15:35 UTC) until that Tuesday morning, 21 February, were no longer there. There are a bunch of important interventions that had disappeared.

So I asked the faculty computer services to restore the mails from backup. One of the two officers is Jan Sanders, with whom I have worked closely for over a decade; he also works with Causalis (people from SSS2012 may remember him from the booth) and will shortly finish his Ph.D. with me. And he installed and maintains this blogging system. These two people, along with 50-75% more help from assistants, manage the Technology Faculty’s (TechFak) computer systems, which account for over half the data volume per day of the entire university. A couple of years ago, we purchased backup hardware for some €30,000 because the university computer center proved to be unable to provide backup services as needed by some high-data-volume colleagues. The university is trying to centralise as many “routine” computing services as possible, and this situation was and is a major negotiating point over the future organisation of research computing services in the university.

Well, our backup HW+SW didn’t work. Jan + colleagues were unable to extract my e-mail Inbox directory alone. They ended up rebuilding the entire TechFak mail-server IMAP file system on a restore disk, some seven hundred gigabytes or so to be restored from main+incremental backup tapes. Estimate on Tuesday lunchtime was Wednesday morning. But on Wednesday morning, when they came in to work, the job had terminated with an error, and then only had up to 6 February cleanly restored.

Moral: the cloud is vulnerable in the ways that people concerned with the provision of computing services have known about for a long time. This is not the first time this has happened to me (indeed, the third time I have lost amounts of mail in five years). There are obvious ways to avoid specific problems, but there is mostly neither time nor resources to implement and manage all those solutions perfectly all the time. In this case, there were (at least) two failures, and it is clearly impractical for the faculty computing services to check continuously whether they can effectively restore data through such two failures, as well as all the other possible failures that could occur. This is a resource-intensive on-demand function and it is combinatorially impossible to check regularly the execution of all such functions in even a moderately complex system such as e-mail backup.

When someone comes up with easy ways to solve any digital-computational vulnerabilities, say to GPS interference, that is less than half the tale. The rest of the tale concerns whether those solutions are implemented, and also continuously and effectively maintained.

There is a lot of superb computer science behind this nowadays. Versions of Leslie Lamport’s Paxos algorithms are enabling Google’s servers to provide us with our daily informational bread (Paxos logically serialises distributed database transactions).

Most journalists and digital-services marketing people have not heard of, let alone understand, the combinatorial impossibility of checking and maintaining all your on-demand functions, or even routinely how the various Paxos variants work and three-phase commit doesn’t. To find out what is possible and what is not, in other words, you still have to talk to computer scientists with authoritative knowledge. Such as Martyn and his GPS-vulnerability team from the Royal Academy of Engineering. And be wary of what is said in thoughtful articles about “cloud computing” in news media unless it comes from such people.

What actually happened to me? I don’t know. The “stuck delete key” hypothesis seems to me to be implausible (it has worked fine since). And a software glitch in my mail client alone would not explain why the windowing system pull-down menus failed to operate as expected. I am not unfamiliar with forensic analysis of this sort (indeed we do it for major accidents) but this is not the first time an explanation has eluded me and I doubt it will be the last.

Michael. Everyone knew him as Michael.

I was a freshman at Oxford in mathematics, interested in logic. I had been reading Chomsky in my first quarter because I had been told Chomsky had mathematised language. My tutor in algebra, Ian Macdonald (same jacket as in the picture!), an algebraic geometer, suggested I could look at a logic textbook he recommended (which I read with some difficulty over the Christmas break). Derek Goldrei, a graduate student tutoring in logic at my college Magdalen, suggested I listen to Michael’s lectures in set theory.

Michael didn’t lecture. Michael thought out loud. He distributed notes telling his listeners what he was going to be thinking about during that appointment. I learnt, by watching and listening, how to think. About set theory. About inference rules. About non-classical logic (Michael was drawn to intuitionist thinking about mathematics, because he thought it was right to base your assertions on the concrete evidence you had).

I had been attending freshman mathematics lectures, which went “Theorem” “Proof” “Let x be…” and had despaired of ever being the kind of person who thought like that. Then I attended Michael’s thinking-out-loud sessions and understood what really went on in people’s minds; how the symbols were shorthand for notating thoughts. And, in my second year, I could do it! Just like Michael! Actually, not just like Michael. Not anywhere near “just like Michael”. For, as John Mackie is reported to have said in The Times’s obituary, Michael was a genius. Michael was ineffable.

Michael was different. A mass of wavy white hair, he would array himself longitudinally on a bench in the lecture hall and clean his cigarette holder while leaning on an elbow, with his head just above the seat backs, and crack jokes about his friends and colleagues while waiting for the lecture to begin. At which point the jokes would reduce in number as he concentrated on what was being said. If there is anything any undergraduate wished to be in the course of study he had in large part created, Maths and Philosophy, it was to be “just like Michael”.

Simply put, Michael taught me how to think, in logic; by extrapolation, in mathematics. About the deep philosophical questions concerning truth, mathematics, the use of language. Differently put, I learned how to think by watching and listening to him.

When I graduated in 1973, I attended a ceremony in the Sheldonian Theatre, in Latin, much foreshortened from the original, during which my degree was conferred. A ceremony designed over centuries to give its recipients the indelible impression: you have done it! I had done it! I felt it and they’d said it in Latin! After the ceremony, I went straight across the road in my academic dress to purchase a copy of Michael’s new book, on Frege’s philosophy of language. Michael had shown how to think about these matters in pellucid English prose.

I went right afterwards to the other side of the Northern Hemisphere, to Berkeley in California. Michael had helped me get there, for he had written me a recommendation for graduate school. I have no idea what he said, but I it can’t have been all disastrous. (I can imagine: “Ladkin is mortal and does OK for one. But I’m afraid I don’t really know much about mortals.”)

I was required at the end of my first year by Bill Craig, my advisor in Berkeley, he of Craig’s Interpolation Theorem, to take the qualifying exam in philosophy. I protested and threw tantrums and all that, but you know you can’t really rebel. Bill said “you will do it” so I did it. I read Michael’s book, and its seemingly impenetrable prose. And I read it again. And understood more. And again. And more. And again. It wasn’t that Michael’s prose was impenetrable. Michael wrote exactly what he was thinking and his thinking was non-trivial and exact. It took me a while to absorb his train of thought. His prose was, indeed, pellucid. When I had done so, I went into the exam room (actually the philosophy library) for six hours and wrote exactly what I thought about the matters about which I had learned from reading Michael’s book so carefully. Non-trivially and exactly. I think Ernie Adams graded the exam. I passed. Turns out I was the first student in the history of Tarski’s program to pass the philosophy exam in my first year. Thank you, Michael!

(You have to understand – I was rotten at written exams. I got so nervous I couldn’t even read the questions straight. It’s a miracle I ever got into and out of Oxford, at which assessment is based on a student’s brilliance at written exams.)

I saw Michael in Berkeley once. He gave an evening lecture which I attended. I did get to exchange a brief word, amongst all the others earnest to talk with him.

I saw him again in 2009, at the 40th anniversary reunion of Maths and Philosophy graduates in Oxford, of the course which he had done so much to establish, and to which I owe my subsequent career. Derek Goldrei was the First Graduate (he switched in his final year; graduating in 1969 when the course was established). I in 1973. I was one of only two or three from that era at the reunion and felt quite The Establishment. Michael was there, and Dana Scott. Michael was old and frail. Gave an endearing and well-constructed speech. When I approached him after the dinner, he didn’t remember who I was, but then so many had passed through the gate since I had. I simply thanked him. He accepted graciously.

Michael is gone, on 27 December 2011. For me, he was Philosophy. When he was with us, Philosophy was alive. Now he is gone, Philosophy is gone. Maybe not, but it sure feels like it. It turns out I seem to have assumed he was immortal. Apparently not. It is -let me say- hard for me to adjust.

Here is The Guardian’s take. The Times has a fine obituary, forwarded to me by Chris Miller, but it lies behind a paywall, just as now Michael does, though with a currency which I only wish I had. As an atheist without this currency, I can only say: God be with you, as you wished.

Some Coincidences.

Racism. Two of the killers of Stephen Lawrence were convicted in early January 2012. Here is a poem about it by Poet Laureate Carol Ann Duffy. Michael and his wife Ann devoted themselves to race relations in 1960′s and early 1970′s Britain, efforts well documented in the obituaries. He only returned to philosophical work after he felt the efforts to turn Britain away from racist habits had failed. But they haven’t failed, Michael, and neither had you.

Brains. Apparently some people claim now that our brains start to go downhill at age 45 It is not clear this is news: The Guardian had something about it 12 years ago. Michael published his first book at 48, and there followed many more, all of them worth reading very carefully indeed.

Note Added 11.01.2012

It’s not just philosophy. Thinking it over, there are three fundamental developments in technical elementary logic which I have kept coming back to throughout my career. Things which are simple, clear, brilliant, which increase one’s understanding almost instantly, and continually prove to be useful. One is Dana Scott’s Consequence Relations, a formulation of logics which, to me, turns out to be the most efficient way to perform formal deductions, the raw material of logic. I keep meaning to translate into LaTeX the mimeographed notes which Dana handed out almost 40 years ago now. Another is Saul Kripke’s possible-worlds semantics for normal modal logics, and his similar epistemic-worlds semantics for logics of belief and evidence, such as inference in intuitionistic mathematics, and the inferences of Pen Maddy’s “Second Philosopher”. I learnt these partly from Michael. The third is Michael’s and John Lemmon’s formal correspondence between the modal logics from S4 to S5 and the propositional logics between intuitionist and classical.

Second Note Added 11.01.2012

Timothy Williamson, Michael’s successor in the Wykeham chair of Logic (David Wiggins came between Michael and Tim), pointed me to a series of tributes in the New York Times Opinionator blog last week.

John McCarthy has died. The great John McCarthy. Brilliant and entertaining, fun to be around, accessible unlike many of his stature, who carried an aura about him which blessed you with the feeling, if you came within it, that you were doing the Thinking That Really Mattered. Even if you were just flapping around at a loss for ideas.

The German Wikipedia describes him as a logician and computer scientist. The English version as a computer scientist and cognitive scientist. The German has it right.

John used to be quite happy to get in discussions with everyone about anything and became well known for it as Internet news groups really got started in the mid-1980′s. He had a knack for posing simple questions that turned out to be hard to answer.

And not just in AI. For example, check out his proposal for a new civil right on what counts for him as his personal page:

Remark: Ideally one would put all the information that one considers public about oneself on a page like this. When asked to fill out a form, one would simply put down the URL in place of any information that is on the page and tell the recipient of the form to just look it up.

One step beyond that is that any program needing this public information would just take it from the somewhat standardized web page.

More precisely, here’s a proposed new civil right. No Government agency, educational institution or business should ever be able to require anyone to supply anew information that the institution already has or is publicly available.

Typically for John, it is simple, doable, but somehow not done, and has significant social consequences. Let’s consider it a little further.

There are inadvertent violations. I tried to hand in a technical review of a paper submitted to an IEEE Transactions to the IEEE ScholarOne “system” (I use the word loosely) and found it wouldn’t let me do it without requiring me to fill in a lot of personal information. (I sent the review by email, and someone else has now tweaked the system enough to let me file, apparently.)

But the phenonemon is also used – and this, I suspect, is an insight of John – for political purposes. I had been asked on five or six occasions in the last year by a grant-supported institution with which I am associated to deliver information about activities (publications and talks and so on). Always the same stuff, but somehow not in quite the right format, or not quite the right selection. I began to suspect that someone is looking for a “reason” to ease me out, and so it turned out. Bureaucracy-overload as a political instrument; and of course always deniable.

The focus of this institution is, well, the successor “discipline” (I use the word loosely) to AI. John would have loved it!

Jon Hind informed a mailing list on Tuesday 25th October of the Guardian obituary that had just come out. There is a joint obituary with Dennis Ritchie in The Economist which appeared in the Novermber 5th print edition.

The Economist suggests that John did not suffer fools gladly. That is not quite how it was, as I recall. He engaged with all sorts of people – students mouthing off on Internet bulletin boards, for example, which nobody else did at the time. But he didn’t condescend. Anyone could talk to and argue with John, but he didn’t adjust his intellect to your capabilities – you had to adjust yours to his; for almost everyone an impossibly tall order. As well as being exactly what bright Stanford students need.

The Guardian article seems to me to miss most of what John was about during the 1980′s and 1990′s (the Economist, unusually, even more). Of course, after the invention of LISP, still the longest living programming language with over half a century of use (C, eleven years its junior, still has to catch up), one could regard anything else as a coda. But it was just a start. I’ll talk about the decade I know about, from the mid-1980′s to the mid-1990′s.

John had discovered, or invented, the Frame Problem, with Pat Hayes, and then came up with the cleanest purely technical proposal for solving it, Circumscription. Unfortunately, Circumscription didn’t turn out to solve the Frame Problem sui generis, but it did start a little industry all of its own. This little industry frustrated people such as Danny Bobrow, then-editor in the 1980′s of the premier journal in the field, Artificial Intelligence. Danny is a programmer through and through, who feels that to do AI you have to build stuff, that is, to program. The Circumscription industry consisted of a largish collection of mostly ex-Eastern European logicians, many of them eminent and all of them both capable and productive, who wrote great technical papers in mathematical logic and sent them to the Artifical Intelligence journal- where of course they had to be sent off to be refereed by other members of the group, and they took over about the third of the journal with all that ***** Math!! All good stuff no doubt, but it didn’t seem to some as if much was getting built………

It mirrored a significant split in AI, indeed in all computer science, which continues to this day. There are people who incline to solve problems intellectually before they solve them practically, and there are people who attempt practical solutions and solve, or resolve, issues as they come up to them. In AI in the 1980′s, they were known respectively as “neats” and “scruffies”. The neats have it right in that you cannot program solutions you do not have. The scruffies have it right in that a computational solution to a problem consists in an implementation. You might imagine that they could agree on a division of labor, but research is a little messier than that. The neats have it wrong in that abstraction is also a fine way of subtly changing the problem to fit the solution you happen to have, and the scruffies have it wrong in that a clever programmer can build wonderful programs which fail to solve the problem they set themselves, but “almost” do – the permanent, ineffable “almost”, which turns out to mean “never”.

John’s view on progress was that you knew a field was technically mature when you couldn’t understand the work of someone working on a different problem from you. Let’s turn that on itself. In some sense the division of AI research into neats and scruffies, say Danny’s frustrated view of all that math, could thereby have constituted a proof of some sort of maturity, although the way the squabbles were conducted left many wondering if that was the word for it! Maybe that was John’s point?

And John was the living contradiction to this view on progress. Of course. He could explain to anyone with a modicum of understanding of propositional calculus exactly what he was interested in and what problems he thought were worth solving. Check it out at his group WWW site. They were all so simple! Until you realised that, John being John, if they were really as simple as they looked, he would have solved them already. I recall one evening after dinner at the IJCAI conference in Detroit in 1989 when a bunch of us formal people were chatting away after late dinner. Along comes John. Says, “you know, I was thinking about this…… do you know how to do it?” and posed, as usual, what appeared to be a simple problem in propositional logic. Well, after a few minutes, everyone else made their excuses and left. I couldn’t solve it. Then came another problem. And another. All simple, all propositional logic, all needing to be solved if machines were going to mimic human decision capabilities. And, of course, AI meant that machines should be able to do this, somehow, so even if you programmed them with genetic algorithms or neural-network problem solvers, they would still just have been solving John’s “easy” problems in propositional logic. Surely a problem posed in logic can be solved in logic? Well, sometimes.

This went on for an hour and longer. At such sessions one could choose to feel stupid and frustrated at not being able to solve anything, or to revel in the creativity exhibited before your very eyes. For anyone can solve problems, but very, very few people know how to ask exactly the right questions. John was one. Astonishing performances, puzzles rolling off his tongue as if he were discussing the bus timetable. Anyone – and there were many – who claimed that “symbolic AI” was dead just hadn’t been listening properly. Symbolic AI wasn’t and isn’t “dead”. John’s simple problems need to be solved one way or another. But no longer by him, unfortunately.

Circumscription? Let me have a go. Circumscription is a syntactic (and therefore computationally feasible) way of doing the following. Say you have a description of part of the world in front of you, and what is going on in it. Say your description is in some language which allows deductive inference. Circumscription is a way of drawing rich inferences about features (“predicates”) of that scenario under the supposition that the world doesn’t have anything else in it but those objects expressly described plus whatever else needs to be there for the description to be accurate. Not just rich inferences, more than you could obtain with deduction alone, but rich, correct inferences. To logicians, it is a set of inference rules about what is true in certain minimal models of the set of sentences.

That is logically very important. Modern logic arose with Frege considering the logic of arithmetic, of counting and adding and so on. But in Frege’s logic, it turns out that you can’t just restrict your talk to the positive whole numbers. Circumscription was a way of trying to do just that for “worlds” which had a finite number of objects in them. It resolves many of the issues in the Frame Problem (maybe more appropriately called the Framing Problem), by implicitly defining what you are framing. However, it doesn’t neatly resolve the conundrum posed in 1986 by Steve Hanks and Drew McDermott and known as the Yale Shooting Problem. That was first resolved by using other principles. The conundrum it posed has now dropped out of fashion, as far as I know.

To see the rich the tradition around Circumscription, one may look at the Stanford Encyclopedia of Philosophy entries on Non-Monotonic Logic, on Defeasible Reasoning, on Logic and Artificial Intelligence, on the Frame Problem, on Ceteris Paribus laws (that is, rules based on “all other things being equal”).

John was not concerned merely with mimicking intelligence with machines, but with the more elusive reasoning phenomenon of common sense, which occurred in the title to a collection of his papers in 1990. There was a whole branch of AI research devoted to “common-sense” reasoning about the world; which in turn spawned a branch of reasoning called Qualitative Physics: how the world works ; check out for example this book chapter by Ken Forbus. (John, though, would have distinguished common-sense physics from qualitative physics.) If you put a round ball on a slanting table, it will roll down the slope and drop off the edge and hit the floor just beyond the edge, and how far beyond depends largely on its speed relative to the table when it drops. This phenomenon is known to every two-year-old a couple of decades before they can understand the Newtonian version, but we adults have far more trouble getting a handle on the qualitative reasoning than we do on Mr. Newton’s mathematics. Yet another delicious irony.

And one could go on. Maybe without end. Qualitative physics will not end; it’s a phenomenally hard problem. It may go out of fashion, but it’ll come back. And somebody will have to solve all those common-sense physics problems as well, and maybe differently. Circumscription didn’t solve the Yale Shooting Problem, but it did open up the study of rigorous forms of defeasible reasoning.

And always there was an irony, a delightful little joke in the tail. Somehow, you never quite knew whether you were thinking about a new subject or an elaborate joke. Look closely at the picture in the Guardian. Can you, also, maybe, see the slight smirk that I always thought I saw? Maybe, just maybe, AI was his very biggest joke of all…..