New Textbook on Incompleteness

I made a textbook on incompleteness for my Logic III course. See it/read about it over at the Open Logic Project.

CfP: Quantifiers and Determiners (part of ESSLI 2017)

QUAD: QUantifiers And Determiners

http://www.lirmm.fr/quad

Toulouse, Monday  July 17 — Friday July 21:  17:00-18:30

ESSLLI 2017 workshop

Schedule:

deadline for submissions:  17 March 2017
submission website: https://easychair.org/conferences/?conf=quad2017
notification to authors:  15 April 2017
final version due: 19 May 2017
conference: 17-21 July 2017

Presentation:

The compositional interpretation of determiners relies on quantifiers  — in a general acceptation of this later term which includes generalised quantifiers, generics, definite descriptions i.e. any operation that applies to one or several formulas with a free variable, binds it  and yields a formula or possibly a generic term  (the operator is then called a subnector, following Curry). There is a long history of quantification in the Ancient and Medieval times at the border between logic and philosophy of language, before the proper formalisation of quantification by Frege.

A common solution for natural language semantics is the so-called theory of generalised quantifiers. Quantifiers like « some, exactly two, at most three, the majority of, most of, few, many, … » are all described in terms of functions of two predicates viewed as subsets.

Nevertheless, many mathematical and linguistic questions remain open.

On the mathematical side, little is known about generalised , generalised and vague quantifiers, in particular about their proof theory. On the other hand, even for standard quantifiers, indefinites and definite descriptions, there exist alternative formulations with choice functions and generics or subnectors (Russell’s iota, Hilbert-Bernays, eta, epsilon, tau). The computational aspects of these logical frameworks are also worth studying, both for computational linguistic software and for the modelling of the cognitive processes involved in understanding or producing sentences involving quantifiers.

On the linguistic side, the relation between the syntactic structure and its semantic interpretation, quantifier raising, underspecification, scope issues,…  are not fully satisfactory. Furthermore extension of linguistic studies to various languages have shown how complex quantification is in natural language and its relation to phenomena like generics, plurals,  and mass nouns.

Finally, and this can be seen as a link between formal models of quantification and natural language,  there by now exist psycholinguistic experiments that connect formal models and their computational properties to the actual way human do process sentences with quantifiers, and handle their inherent ambiguity, complexity, and difficulty in understanding.

All those aspects are connected in the didactics of mathematics and computer science: there are specific difficulties to teach (and to learn) how to  understand, manipulate,  produce and  prove quantified statements, and to determine  the proper level of formalisation between bare logical formulas and written or spoken natural language.

This workshop aims at gathering  mathematicians, logicians, linguists, computer scientists  to present their latest advances in the study of quantification.

Among the topics that wil be addressed are the following :

  • new ideas in quantification in mathematical logic, both model theory and proof theory:
    • choice functions,
    • subnectors (Russell’s iota, Hilbert’s epsilon and tau),
    • higher order quantification,
    • quantification in type theory
  • studies of the lexical, syntactic and semantic of quantification in various languages
  • semantics of noun phrases
  • generic noun phrases
  • semantics of plurals and mass nouns
  • experimental study of quantification and generics
  • computational applications of quantification and polarity especially for question-answering.
  • quantification in the didactics of mathematics and computer science.

Some recent relevant references:

  • Anna Szabolcsi Quantification Cambridge University Press 2010
  • Stanley Peters and Dag Westerstahl Quantifiers in Language and Logic Oxford Univ. Press 2010
  • Mark Steedman Taking Scope – The Natural Semantics of Quantifiers MIT Press 2012
  • Jakub Szymanik. Quantifiers and Cognition, Studies in Linguistics and Philosophy, Springer, 2015.
  • Vito Michele Abrusci, Fabio Pasquali, and Christian Retoré. Quantification in ordinary language and proof theory. Philosophia Scientae, 20(1):185–205, 2016.

Submissions:

The program committee is looking for  contributions introducing new viewpoints on quantification and determiners,  the novelty being either in the mathematical logic framework or in the linguistic description  or in the cognitive modelling. Submitting purely original work is not mandatory, but authors should clearly mention that the work is not original, and why they want to present it at this workshop (e.g. new viewpoint on already published results)

Submissions should be

In case the committee thinks it is more appropriate, some papers can be accepted as a poster with a lightning talk.

Final versions of accepted papers may be slightly longer. They will be published on line. We also plan to publish postproceedings

Programme committee:

  • Christian Retoré (Université de Montpellier & LIRMM-CNRS)
  • Mark Steedman (University of Edinburgh)
  • Vito Michele Abrusci (Università di Roma tre)
  • Mathias Baaz (University of Technology, Vienna)
  • Daisukke Bekki (Ochanomizu University, Tokyo)
  • Oliver Bott (Universität Tübingen)
  • Francis Corblin (Université Paris Sorbonne)
  • Martin Hakl (Massachusetts  Institute of Technology, Cambridge MA)
  • Makoto Kanazawa (National Institute of Informatics, Tokyo)
  • Dan Lassiter (Stanford University)
  • Zhaohui Luo (Royal Holloway College, London)
  • Alda Mari (CNRS Institut Jean Nicod, Paris)
  • Wilfried Meyer-Viol (King’s college, London)
  • Michel Parigot (CNRS IRIF, Paris)
  • Anna Szabolcsi (New-York University)
  • Jakub Szymanik (Universiteit van Amsterdam)
  • Dag Westerstahl (Stockholm University)
  • Bruno Woltzenlogel Paleo  (University of Technology, Vienna)
  • Richard Zach (University of Calgary)
  • Roberto Zamparelli (Università di Trento)

Jack Howard Silver, 1942-2016

From the Group in Logic and the Methodology of Science:

It is with great sadness that we announce that Professor Jack Howard Silver died on Thursday, December 22, 2016. Professor Silver was born April 23, 1942 in Missoula, Montana. After earning his A.B. at Montana State University (now the University of Montana) in 1961, he entered graduate school in mathematics at UC Berkeley. His thesis, Some Applications of Model Theory in Set Theory, completed in 1966, was supervised by Robert Vaught. In 1967 he joined the mathematics department at UC Berkeley where he also became a member of the Group in Logic and the Methodology of Science. He quickly rose through the ranks, obtaining promotion to associate professor in 1970 and to full professor in 1975. From 1970 to 1972 he was an Alfred P. Sloan Research Fellow. Silver retired in 2010. At UC Berkeley he advised sixteen students, three of whom were in the Group in Logic (Burgess, Ignjatovich, Zach).

 

His mathematical interests included set theory, model theory, and proof theory. His production was not extensive but his results were deep. Professor Silver was skeptical of the consistency of ZFC and even of third-order number theory. As Prof. Robert Solovay recently put it: “For at least the last 20 years, Jack was convinced that measurable cardinals (and indeed ZFC) was inconsistent. He strove mightily to prove this. If he had succeeded it would have been the theorem of the century (at least) in set theory.”

 

He will be greatly missed.

Jack’s contributions to set theory, according to Wikipedia (used under CC-BY-SA):

Silver has made several deep contributions to set theory. In his 1975 paper “On the Singular Cardinals Problem,” he proved that if κ is singular with uncountable cofinality and 2λ = λ+ for all infinite cardinals λ < κ, then 2κ = κ+. Prior to Silver’s proof, many mathematicians believed that a forcing argument would yield that the negation of the theorem is consistent with ZFC. He introduced the notion of master condition, which became an important tool in forcing proofs involving large cardinals. Silver proved the consistency of Chang’s conjecture using the Silver collapse (which is a variation of the Levy collapse). He proved that, assuming the consistency of a supercompact cardinal, it is possible to construct a model where 2κ++ holds for some measurable cardinal κ. With the introduction of the so-called Silver machines he was able to give a fine structure free proof of Jensen’s covering lemma. He is also credited with discovering Silver indiscernibles and generalizing the notion of a Kurepa tree (called Silver’s Principle). He discovered 0# in his 1966 Ph.D. thesis. Silver’s original work involving large cardinals was perhaps motivated by the goal of showing the inconsistency of an uncountable measurable cardinal; instead he was led to discover indiscernibles in L assuming a measurable cardinal exists.

[Photo ©Steven Givant. Picture taken on the occasion of the Tarski Symposium at UC Berkeley in 1971.]

Courant’s Home Movies

Legendary mathematicians: They’re just like us!

Bjarni Jónsson, 1920-2016

Sad news via the FOM list today:

Published in Tennessean on Nov. 6, 2016

Bjarni Jónsson, originally of Draghals, Iceland, passed away in Cincinnati, OH on
Friday, September 30, 2016 at the age of 96. Beloved husband of the late Harriet P.
(nee Parkes) Jonsson. Devoted father of Eric (Kaye) Jonsson, Meryl (Bob) Runion Rose
and Kristin (Rick) Porotsky. Loving grandfather of Elisabeth (Terry) Winslow, David
Runion, and Brent, Gena, Aaron, Billy and Cole Porotsky. Former resident of Nashville,
Tennessee. He was Vanderbilt’s first Distinguished Professor of Mathematics. A leader
in his field and author of 89 technical papers, he received many commendations for his
work, including the Earl Sutherland Prize for Academic Research as well as the Knights
Cross awarded by the President of Iceland.

Please send donations in his honor to:

Bjarni Jonsson Research Prize
Department of Mathematics
1326 Stevenson Center
Vanderbilt University
Nashville, TN 37240.

Noted algebraist Bjarni Jónsson dies
by David Salisbury, Oct. 12, 2016
https://news.vanderbilt.edu/2016/10/12/noted-algebraist-bjarni-jonsson-dies/

Bjarni Jónsson, Vanderbilt’s first Distinguished Professor of Mathematics, died Sept.
30 at the age of 96.

Born in Iceland, Jónsson earned his bachelor’s and doctoral degrees from the
University of California-Berkeley and also received an honorary degree from the
University of Iceland. He was internationally recognized as a leading authority on
universal algebra, lattice theory and algebraic logic.

In his career, Jónsson authored 89 technical papers and served on the editorial board
of several major mathematics journals, including Algebra Universalis. He presented
numerous invited talks at mathematics conferences around the world. In 1974, he was an
invited speaker at the International Congress of Mathematicians. In 2012 he was
elected an inaugural fellow of the American Mathematical Society. He was also the
recipient of Vanderbilt’s Harvie Branscomb Distinguished Professor Award in 1974 and
the Earl Sutherland Prize for Achievement in Research in 1982.

“Bjarni Jónsson was a remarkable mathematician who made field-defining and path-
breaking contributions in universal algebra, lattice theory and algebraic logic.
Anyone who had the fortune to know him admired his integrity, kindness and immense
respect for colleagues and friends. His influence on my personal and mathematical life
has been enormous, and it is a great privilege that I have had the opportunity to work
with and learn from him,” said Professor Constantine Tsinakis, a long-term colleague
and a former chair of the mathematics department.

“To me Bjarni will always be a legend, who in his quiet, sincere, unassuming ways
continues to inspire uncountably many algebraists, raising questions and re-examining
areas that he feels would benefit from an algebraic approach,” wrote Peter Jipsen, one
of the doctoral students that Jónsson advised, on the occasion of his 70th birthday.
“While some mathematicians almost revel in stringing together long complex arguments,
Bjarni has constantly sought to simplify and illuminate the subjects dear to him,” the
professor of mathematics at Chapman University added.

Jónsson came to Vanderbilt in 1966 and taught here until his retirement in 1993. When
he arrived, mathematics was mostly an undergraduate teaching department. He was
instrumental in establishing the department’s graduate program, which presently ranks
among the top departments in the nation, according to the latest evaluation by the
National Research Council. Jónsson also formed a research group in algebra that
attracted mathematicians from around the world and contributed substantially to the
high research profile that the department currently enjoys.

Algebra is the study of mathematical objects and the rules for manipulating them.
Jónsson made his most important contributions in the area of universal algebra. It is
one of the most abstract subfields of algebra because it studies algebraic structures
in general, as opposed to specific classes of algebras, such as groups and fields. The
importance of his contributions is reflected by the fact that a number of mathematical
objects are named for him, including Jónsson and Jónsson-Tarski algebras, Jansson
cardinals, Jónsson terms, the Jónsson lemma and the Jónsson-Tarski duality.

During his tenure, Jónsson supervised 14 Ph.D. students. In letters they wrote for a
symposium in honor of his 70th birthday, which took place in Iceland in 1990, his
former students all expressed a deep appreciation for him as a “respected mathematical
guide and personal friend.”

One of the first students he supervised, Steven Monk, now professor emeritus at the
University of Washington, recalled advice that he received from Jónsson regarding
teaching: “Adventure is not in the guidebook and beauty is not on the map. The best
one can hope for is to be able to persuade some people to do some traveling on their
own.”

“Bjarni’s work and scholarly contributions will have a lasting legacy. His name will
forever be interwoven in the history of our department. We are honored to have had
him as a colleague,” noted the current department chair, Professor Mike Neamtu.

[Photo ©Steve Givant]

(SEP ∧ SSHAP) → Calgary

In May 2017, both the Society for Exact Philosophy and the Society for the Study of the History of Analytic Philosophy will hold their annual meetings at the University of Calgary. Come for one, stay for the other, or come for both and stay for Banff National Park in the Canadian Rockies! Keynotes will be given by Juliet Floyd, Robin Jeshion, and Bernie Linsky at SSHAP and Catarina Dutilh Novaes, Louise McNally, and Dorit Ganson at SEP.

 

Immediately before SEP, the Calgary Graduate Student Conference will also be held; the topic will be “Ethics in the Age of Science.” Keynote speakers will be Katrina Sifferd and Gregg Caruso.

My First Paper!

I went through old floppies when I went back home over the summer and found the first logic paper I ever wrote! It was on proof theory and general algebra (I guess I must have taken courses in both at the time–1992). For your amusement: A Paedagogical Example of Cut-Elimination

A paedagogical Example of Cut-Elimination