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.