Paul Bernays Lectures 2013

The Paul Bernays Lectures are a new, annual and three-part honorary lecture series about the philosophy of the exact sciences.

The series will alternate between the philosophy of logic or mathematics and the philosophy of physics. This lecture series is established in honor of the eminent logician, mathematician and philosopher of logic and mathematics Paul Bernays who was engaged in teaching and research at the ETH from 1933 to 1959.
Within the framework of the Paul Bernays lectures outstanding philosophers of logic, mathematics or physics will be invited to speak about their pioneering research. The first lecture will present the research topics for a wider audience, the second lecture will address the research community, and a final seminar will offer to the members of the research community the opportunity to discuss with the invited speaker selected research topics and ideas.

Prof. Robert B. Laughlin, Stanford University, USA Nobel Prize in physics (1998)

Robert B. Laughlin is the Anne T. and Robert M. Bass Professor of Physics and Applied Physics at Stanford University. Macroscopical quantum phenomena belong to his main field of research. In 1998 he received the Nobel Prize for Physics for his contribution to the theoretical explanation of the fractional quantum Hall effect. In his popular scientific books he also deals with epistemological questions concerning the future and the knowledge strategy of physics („A Different Universe: Reinventing Physics from the Bottom Down“) as well as with political and social questions concerning the energy future („Powering the Future: How We Will (Eventually) Solve the Energy Crisis and Fuel the Civilization of Tomorrow“).

 

Lecture 1:

A DIFFERENT UNIVERSE

Tuesday, Sept. 10, 2013, 17:00 h, Auditorium F3, HG

Lecture 2:

THE METER STICK OF LIFE

Wednesday, Sept. 11, 2013, 14:15 h, Auditorium F3, HG

Lecture 3:

BOND CURRENT ANTIFERROMAGNETISM

Wednesday, Sept. 11, 2013, 16:30 h, Auditorium F3, HG

 

Lecture 1

A different universe

Tuesday, Sept. 10, 2013, 17:00 h, Auditorium F3, HG

It sometimes seems obvious that the universe should be ruled by law-relationships among measured quantities that are always accurately true -but it actually isn't. It's a miracule that only look obvious because of one's cultural and religious prejudices, specificially the idea from Greek stoic philosophy that Nature, Logic and God should all be the same thing. The power of this idea makes it notoriously difficult for us to ask where law might come from. But it turns out that many of the most useful laws -rigidity of solids, for example, the electrical properties of metals or the rules of heat- definitely do come from somewhere. They are organizational, and they emerge from chaos as the system size grows larger the way political consensus might, or the way a Monet painting does as one steps away. The growing body of experimental evidence accumulated in the last 60 years has demonstrated explicitly that many engineering laws fail when the system size gets small. But there is also accumulating evidence at the level of big science that ALL physical laws known to science may be in this category, including those of Newton (which emerge from quantum mechanics) and those of the empty vacuum of space-time. This observation has the disturbing implication that entire idea of fundamental law, and the search for the theory of everything based on it, may be ideological, and thus not science at all.

 

Lecture 2

The meter stick of life

Wednesday, Sept. 11, 2013, 14:15 h, Auditorium F3, HG

It is not known how living things measure their lengths. They clearly do so, for organisms have characteristic sizes and shapes that are the same down to very small details. But it is a conundum nonetheless because the experimental means at our disposal are not very good at addressing this question. Elementary mass action in chemistry is very good for making clocks, but not so good at making lengths, especially ones that can be tuned and scaled proportionately as an organism grows. In this talk I shall discuss the various options available for dealing with this problem, including Turing reaction-diffusion, none of which is completely satisfactory. One's inability to write down equations that describe how cells do this highly quantitative thing is not an unimportant detail of interest only to physicists but unambiguous evidence that at least one important idea is missing.

 

Lecture 3

Bond current antiferromagnetism

Wednesday, Sept. 11, 2013, 16:30 h, Auditorium F3, HG

In this talk I will review the growing body of evidence that a previously unknown order parameter, bond antiferromagnetism, is present in cuprate superconductors in a glassy form and is responsibile for much of their perplexing behavior, including particularly their pseudogap, doping asymmetry, weak spin polarization and violenty varying superfluid density. I shall argue that bond-current order competes with d-wave superconductivity in the cuprates the same way structural phase transitions compete with s-wave superconductivity in conventional metals, the ordered bond antiferromagnet being essentially a crystal of d-wave Cooper pairs. Its relevance to the cuprates is thus mainly as an impediment to achieving higher superconducting transition temperatures. However, it has wider relevance to engineering through oxide resistive memory, a vastly more important phenomenon presently of great interest to electronics manufacturers on account of its potential to replace flash memory.

 

Paul Bernays Lectures 2012

Prof. Solomon Feferman, Stanford University, USA

Solomon Feferman is the Patrick Suppes Professor of Humanities and Sciences, Emeritus, and Professor of Mathematics and Philosophy, Emeritus, Stanford University. His main interests are in mathematical logic (especially proof theory and the theory of computation), the foundations of mathematics (especially constructive and semi-constructive approaches), the philosophy of mathematics and the history of modern logic. He was awarded the Rolf Schock prize in logic and philosophy in 2003.

Opening address by Prof. E. Engeler

Tuesday, Sept. 11, 2012, 16:30 h, Auditorium C14, CHN

Lecture 1
Bernays, Gödel and Hilbert's consistency program

Tuesday, Sept. 11, 2012, 17:00 h, Auditorium C14, CHN

Paul Bernays was brought from Zurich to Göttingen in 1917 by David Hilbert - the leading mathematician of the time - to assist him in developing his consistency program for the foundations of mathematics. The major exposition of that work appeared in the 1930s in the two volume opus by Hilbert and Bernays, Grundlagen der Mathematik, whose preparation was due entirely to Bernays. In the meantime, Kurt Gödel, a precocious doctorate in Vienna, had discovered his remarkable incompleteness theorems which threatened to undermine Hilbert’s program. Though Hilbert refused to accept that, Bernays undertook to absorb the significance of those theorems through correspondence with Gödel. This led to a lifelong deep personal and intellectual relationship between the two of them whose high points will be traced in the lecture.

Lecture 2
Is the Continuum Hypothesis a definite mathematical problem?

Wednesday, Sept. 12, 2012, 14:15 h, Auditorium C14, CHN

Georg Cantor established the modern theory of sets with his theory of transfinite cardinal and ordinal numbers, which began with his proof that the set of real numbers has greater cardinality than the set of natural numbers; Cantor’s Continuum Hypothesis (CH) states that there is no intermediate cardinal number. The call to establish CH was the first in the famous list of twenty-three challenging mathematical problems that Hilbert posed at the International Congress of Mathematicians in 1900. Yet, a century later, it did not appear on the list of the seven Millennium Prize Problems worth a million dollars each, despite the fact that no solution to it has been found in the mean time. In this lecture I will discuss the evidence for my view (contrary to Gödel above all) that CH is not a definite mathematical problem, despite the fact that it is formulated in terms of concepts that have become an established part of mathematics.

Lecture 3
Foundations of Unlimited Category Theory

Wednesday, Sept. 12, 2012, 16:30 h, Auditorium C14, CHN

Following a discussion of various forms of set-theoretical foundations of category theory and the controversial question of whether category theory does or can provide an autonomous foundation of mathematics, this lecture concentrates on the question whether there is a foundation for “unlimited” or “naïve” category theory. I proposed four criteria for such some years ago. This lecture describes how much had previously been accomplished on one approach to meeting those criteria, then takes care of one important obstacle that had been met in that approach, and finally explains what remains to be done if one is to have a fully satisfactory solution.