I first came across Raymond Smullyan’s work — surely like many of my sort of vintage — through his wonderfully inventive and illuminating short(ish) paper “Languages in which self-reference is possible” which was reprinted in Hintikka’s 1969 *The Philosophy of Mathematics *(in the Oxford Readings series). Still more than worth reading, after all this time. And that paper led me to look out his *First-Order Logic* over forty years ago. I think it took me a while to really appreciate that classic: certainly, I kept battling on teaching first-year students Lemmon-style natural deduction for while before I was fully gripped by the loveliness of trees! I had occasion to read the first half of *First-Order Logic* again a few months ago, and it is such a delight.

But perhaps even more elegant, clear, readable, illuminating, getting-to-the-heart-of-things, there’s Smullyan at his very best in the three Oxford Logic Guides he published in quick succession — *Gödel’s Incompleteness Theorems* (1992), *Recursion Theory for Metamathematics* (1993), and *Diagonalization and Self-Reference* (1994). They give the lie to G.H. Hardy’s bitter remark that “Exposition, criticism, appreciation, is work for second-rate minds.” Smullyan’s expositions and re-organizations and novel re-appreciations and inventive drawings-out of new connections are surely the work of a first-rate mind.

And then, as a late coda, there is that other great book that Smullyan wrote with Melvin Fitting, *Set Theory and the Continuum Hypothesis *(1996). Those of us past the first, second, and even third flush of youth can’t but be encouraged and cheered to see Smullyan getting perhaps to the very top of his game, as far as the writing of serious logical texts is concerned, as he moves into his seventies. (The very late books like *Logical Labyrinths* and *A Beginner’s Guide to Mathematical Logic *are perhaps too uneven and quirky to really work, but still have fun and instructive episodes.)

I can’t think of a single logician whose writings I have *enjoyed* reading and working through more than Smullyan’s, and whose elegant lucidity I’d more like to be able to emulate. And there are few logicians that I’ve learnt as much from. So I wanted to mark Smullyan’s passing, as others have, with very warm appreciation and gratitude.

“But what about all the puzzle books? You haven’t mentioned them!” Well, I know that many others have loved them, but I very much prefer my logic served straight up: and I think it would be a sad if Smullyan is mainly remembered for them. I don’t seem to have the kind of mind that is drawn to puzzle books, to magic tricks, or Taoism: but that’s uptight Englishness for you!

Jan von PlatoAdd Feynman with his Lectures on Physics to the second-raters. Hardy must have been quite a silly person.

Peter SmithOh, I don’t think we can ever call Hardy

silly: just that his standards for a “first-class mind” were rather stratospheric!André GargouraCalling Hardy “silly” is certainly an abuse of language… Hardy’s remark, put back in its context, simply meant that criticism must be based on solid counterarguments and at the same level — usually high when Hardy is concerned — as that of the theory one tries to falsify…

I think K. Popper would fully agree with Hardy !!

Cheers,

André

David AuerbachThe first work of Smullyan’s that I read was Theory of Formal Systems (the orange Princeton edition). It was a slog for me at the time, but a treasure to me on later re-reading. But I first met Smullyan in 1970. I was between undergraduate and graduate school ( & teaching junior high school math). In the Fall semester I had taken an advanced logic course at CUNY (using Robbin) and in the Spring a set theory course with Smullyan. The bombing of Cambodia led to a student strike, so part way through the semester we started meeting at Smullyan’s house, which contained a couple of grand pianos (one for him, one for Blanche) and a harpsichord. The set theory was mixed with music, magic and chess puzzles. I found it all very wonderful and a glimpse into a another world.