Tuesday, 16 January 2007
A Visit with our Heroes
Following our informal tradition, our first lunchtime speaker of the term is Nicholas Rescher, co-chair of the Center. I do my best to introduce him without consuming all the time available. But what can you say to do justice to him? He has written over 100 books and his academic life extends over half a century to 1951, when, at age 22, he earned a doctorate at Princeton. There is always a faint sense of blasphemy when I acquiesce to his cordiality in calling him "Nick."
The topic is "Goedel, Leibniz, and a bit of Einstein." It is a familiar list of our academic heroes, each of whom lives for us in the bound pages of letter press editions on our bookshelves. But that is no so for Nick. He excuses himself for offering some autobiographical remarks--"a walk down memory lane." For Goedel and Einstein were both working in Princeton when Nick was working on his PhD.
Nick went out to the Institute for Advanced study, where he met with John von Neumann, another hero who makes a brief cameo appearance. And then he went to Goedel's office. The line was so carefully stated that we already knew what came next. ...and Goedel wasn't in. Nick paused and we exhaled. But now we were hungry. He had to give us some taste of our heroes.
Well, von Neummann's office was large and you passed through a long passage to get to his desk. Goedel had been given such an office, but didn't want it. He got himself a much smaller office, the size of a broom closet. It had very spartan furnishings. There were very few books and a reprints on its partially empty shelves.
What of Einstein, we wondered. Nick didn't need telepathy to sense the thought. He'd seen Einstein a few times, once at Paul Oppenheim's. Einstein had come to a talk. There was a hush when Einstein entered. Everyone knew this was Einstein. He looked just like Einstein, Nick reassured us, and somehow this complete truism was informative. When he sat down and his trouser leg lifted, you could indeed see that the legend was true. There were no socks on this leg end.
The remembrances continued. Nick's dissertation had been on Leibniz. He found that few others were borrowing and reading the Leibniz volumes from Princeton's Firestone Library. His major competition was none other than Goedel and Nick had initiated recalls that had reached out to Goedel. In the old system, a patron would sign the book's card. So the Liebniz volumes began to fill with Goedel's and Rescher's signatures.
What was Goedel finding in those volumes? Nick hit the button on the overhead projector and began to show us schematic figures of science. The classical conception has laws explaining observations and those observations leading back to the laws by inductive inference. Leibniz offered Goedel an extra layer. Those laws were in turn underpinned by deeper principles arrived at through a metainductive inference. He began to list the principles: of sufficient reason, of least effort, of least time, continuity, ... there were so many that I was astonished and I couldn't capture even a portion of them. I was overwhelmed. Rational mechanics, that triumph of post Newtonian physics, had come directly from these principles--least action, least time, and so on.
Nick's manner had remained that of the teller of anecdotes. Abruptly it changed. Nicked turned to his manuscript and began to read his paper. He reads well. You have no trouble following. However I couldn't help noticing an urgency in his voice, as if he regretted the time wasted by self-indulgent reminiscences. The self-discipline behind his extraordinary academic productivity was faintly visible.
His principal burden is to explain the affinity of Goedel for Leibniz. Part of it lay in Goedel sharing Leibniz's fascination for deeper metaphysical principles that could underpin the laws of science. And they both partook of the ancient tradition that held that the world must be understood from the vantage point of number. But there needed to be more. Superficially, one would expect a real tension. Leibniz had an innocent enthusiasm for formalizing notions. Goedel, one would think, was the nemesis of such enthusiasms. For, famously, Goedel had shown that no finite, formal axiom system could capture all the truths of arithmetic.
Now it turned out that Leibniz had already sensed a fundamental inadequacy in language. It has, he urged, a kind of finitude that is completely outstripped by the vastness of the detail of the world. Both Leibniz and Goedel shared that sense of the limit of what could be precisely expressed in a formal language and of the presence of deeper truths that were decidable, as Nick put it, "by the supercalculability at the disposal of a Leibnizian God."
Nick was still reading at an urgent pace. But old habits die hard and a typo is not to be tolerated. From time to time, from my close vantage point, I could see that Nick would take a pen from his pocket and make a small mark on his manuscript, without pausing or even slowing his sentence.
Now Nick turned to the denoument, the "bit of Einstein." Under a famous photo of Einstein and Goedel, he recalled for us the close personal friendship that Goedel and Einstein had developed at Princeton. He read the startling quotes from Einstein's later corpus where he confessed to a conversion to a Platonic view. As the talk wound down and we eventually passed over into question time, one could only marvel at the depth of scholarship that allowed Nick to pass with easy familiarity from the arcana of Leibniz's metaphysics, to 18th century rational mechanics, to Goedel's metalogic and on to Einstein's discovery of this gravitational field equations.
Nick fielded his own questions and then called the session to an end with two truths and a question: "You're exhausted; I'm exhausted. Shall we quit?"
John D. Norton
::: Goedel, Leibniz, and a bit of Einstein