Richard Zach
http://www.ucalgary.ca/rzach
enWrote Something New!
http://www.ucalgary.ca/rzach/blog/2015/03/wrote-something-new.html
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"> <p>I wrote something about Quine's paradox and Gödel's theorem on the new blog.</p>
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</ul>Tue, 31 Mar 2015 03:39:25 +0000Richard Zach688 at http://www.ucalgary.ca/rzachhttp://www.ucalgary.ca/rzach/blog/2015/03/wrote-something-new.html#commentsThe LogBlog is Moving!
http://www.ucalgary.ca/rzach/blog/2015/03/logblog-is-moving.html
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"> <p>I've decided to move the blog to WordPress. It now lives at <a href="http://richardzach.org/">richardzach.org.</a></p>
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</ul>Sun, 22 Mar 2015 16:16:41 +0000Richard Zach686 at http://www.ucalgary.ca/rzachhttp://www.ucalgary.ca/rzach/blog/2015/03/logblog-is-moving.html#commentsAcademic Genealogy Graphed
http://www.ucalgary.ca/rzach/blog/2015/02/academic-genealogy-graphed.html
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"> <p>The <a href="http://genealogy.math.ndsu.nodak.edu/index.php">Mathematics Genealogy</a> project is a huge database of mathematicians, where and when they got their degrees, and who their advisors were. (There's also a wiki-based <a href="https://philosophyfamilytree.wikispaces.com/Philosophy+Family+Tree">Philosophy Genealogy</a>.) Nice pastime when the polar vortex keeps you from leaving the house: find famous people in your academic family tree.</p>
<p>If you're in the Mathematics Genealogy, you can use <a href="http://www.davidalber.net/geneagrapher/">Geneagrapher</a> by <a href="http://www.davidalber.net/">David Alber</a> to produce a graphical genealogy. It's pretty amazing. Here is mine (click for full size):</p>
<p><a href="http://www.ucalgary.ca/rzach/files/rzach/ancestry.png"><img src="http://www.ucalgary.ca/rzach/files/rzach/ancestry.png" height="597" width="700" /></a></p>
<p>TIL: Mersenne and Copernicus are in that tree.</p>
<p><a href="//www.pinterest.com/pin/create/extension/" style="height: 20px; width: 40px; position: absolute; opacity: 0.85; z-index: 8675309; display: none; cursor: pointer; background-color: transparent; background-image: url('data:image/png;base64,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');"></a></p>
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</ul>Sat, 21 Feb 2015 21:47:32 +0000Richard Zach685 at http://www.ucalgary.ca/rzachhttp://www.ucalgary.ca/rzach/blog/2015/02/academic-genealogy-graphed.html#commentsCfP: Hilbert’s Epsilon and Tau in Logic, Informatics and Linguistics
http://www.ucalgary.ca/rzach/blog/2015/02/cfp-hilberts-epsilon-and-tau-in-logic-informatics-and-linguistics.html
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"> <div>
<p>Dates: June 10-12, 2015<br />Location: Montpellier, France<br />Submission deadline: April 1, 2015</p>
<div>
<p>This workshop aims at promoting work on Hilbert’s epsilon calculus in a number of relevant fields ranging from Philosophy and Mathematics to Linguistics and Informatics. The Epsilon and Tau operators were introduced by David Hilbert, inspired by Russell's Iota operator for definite descriptions, as binding operators that form terms from formulae. One of their main features is that substitution with Epsilon and Tau terms expresses quantification. This leads to a calculus which is a strict and conservative extension of First Order Predicate Logic. The calculus was developed for studying first order logic in view of the program of providing a rigorous foundation of mathematics via syntactic consistency proofs. The first relevant outcomes that certainly deserve a mention are the two "Epsilon Theorems" (similar to quantifiers elimination), the first correct proof of Herbrand’s theorem or the use of the Epsilon operator in Bourbaki’s Éléments de Mathématique. Nowadays the interest in the Epsilon substitution method has spread in a variety of fields: Mathematics, Logic, Philosophy, History of Mathematics, Linguistic, Type Theory, Computer science, Category Theory and others.</p>
<h2>Submission</h2>
</div>
<div>
<p>The workshop welcomes submissions of up to 4 (but not less than 2) pages. Usual spacing, font and margin should be used (single-spaced, 11pt or larger, and 1 inch margin on A4 or letter size paper). Abstracts should be submitted by April 1st, 2015 as pdf files through the EasyChair conference system ( <a href="https://easychair.org/conferences/?conf=epsilon2015" target="_blank">https://easychair.org/conferences/?conf=epsilon2015</a>). An indicative list of themes that are of particular interest to the conference are (non-exhaustive):</p>
<ul><li>History of Logic</li>
<li>Philosophy</li>
<li>Proof theoryModel theory</li>
<li>Category theory</li>
<li>Type theory</li>
<li>Quantification in Natural language</li>
<li>Noun-Phrases Semantics</li>
<li>Proof Assistants (e.g. Coq, Isabelle, ... )</li>
<li>Other subnectors (e.g. Russell's iota, μ-operator, ... )</li>
</ul></div>
<div>Abstracts will be reviewed by members of the program committee, and, where appropriate, outside reviewers. The organizers will be responsible for making decisions partly in consultation with the program committee. Notifications will be made by May 1st, 2015. Selected papers from the workshop will appear as a special volume in Journal of Logics and their Applications
<h2>Important dates</h2>
<p>April 1, 2015: Submission deadline<br />May 1, 2015: Notification of acceptance<br />June 10-12, 2015: Workshop</p>
<h2>Invited speakers</h2>
<div>
<p><a href="http://wirth.bplaced.net/" target="_blank" rel="nofollow">Claus-Peter Wirth</a> (University of Saarland): The descriptive operators iota, tau and epsilon - on their origin, partial and complete specification, model-theoretic semantics, practical applicability (with the support of the Hilbert Bernays Project (sponsored by IFCoLog)).</p>
<p><a href="http://www.uniroma3.it/persona.php?persona=v9rdc8l/v34h57mDvlwB1jjlJFqAH%2B3Or9wKcvkvgtI%3D" target="_blank" rel="nofollow">Vito Michele Abrusci</a> (University of Roma Tre): Hilbert's tau and epsilon in proof theory.</p>
<p><a href="https://www.socrates.uwa.edu.au/Staff/StaffProfile.aspx?Person=hartleyslater" target="_blank" rel="nofollow">Hartley Slater</a> (University of Western Australia): Linguistic and philosophical ramifications of the epsilon calculus.</p>
<h2>Program Committee</h2>
</div>
<div>
<p><a href="http://researchmap.jp/bekki/" target="_blank" rel="nofollow">Daisuke Bekki</a> (Ochanomizu University)<br /><a href="http://www.stergioschatzikyriakidis.com/" target="_blank" rel="nofollow">Stergios Chatzikyriakidis</a> (LIRMM-CNRS & University of Montpellier)<br /><a href="http://fcorblin.free.fr/" target="_blank" rel="nofollow">Francis Corblin</a> (University of Paris-Sorbonne & Institut Jean Nicod CNRS)<br />Michael Gabbay (University of Cambridge)<br /><a href="http://research.nii.ac.jp/%7Ekanazawa/" target="_blank" rel="nofollow">Makoto Kanazawa</a> (National Institute of Informatics of Tokyo)<br /><a href="http://www.kcl.ac.uk/artshums/depts/philosophy/people/staff/associates/emeritus/kempson/index.aspx" target="_blank" rel="nofollow">Ruth Kempson</a> (King's College, London)<br /><a href="http://lumiere.ens.fr/%7Eamari/" target="_blank" rel="nofollow">Alda Mari</a> (CNRS Institut Jean Nicod & ENS & EHESS)<br /><a href="http://cl-informatik.uibk.ac.at/users/georg/" target="_blank" rel="nofollow">Georg Moser</a> (University of Innsbruck)<br /><a href="http://www.logic.at/staff/bruno/" target="_blank" rel="nofollow">Bruno Woltzenlogel Paleo</a> (Vienna University of Technology)<br />Michel Parigot (CNRS-PPS & University of Paris Diderot 7)<br /><a href="https://www.i2m.univ-amu.fr/spip.php?page=pageperso&nom=PASQUALI&prenom=Fabio" target="_blank" rel="nofollow">Fabio Pasquali</a> (University of Aix-Marseille & I2M CNRS)<br /><a href="http://www2.lirmm.fr/%7Eretore/" target="_blank" rel="nofollow">Christian Retoré</a> (University of Montpellier & LIRMM-CNRS)<a href="http://homepages.inf.ed.ac.uk/steedman/" target="_blank" rel="nofollow">\<br />Mark Steedman</a> (University of Edimburgh)<br /><a href="http://www.ucalgary.ca/rzach/" target="_blank" rel="nofollow">Richard Zach</a> (University of Calgary)</p>
<h2>Organizers / workshop co-chairs</h2>
<p>Stergios Chatzikyriakidis, LIRMM-CNRS, University of Montpellier <br />Fabio Pasquali, University of Marseille<br />Christian Retoré, University of Montpellier & LIRMM-CNRS</p>
<div>Host: I2M-CNRS and University of Montpellier</div>
</div>
</div>
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</ul>Fri, 20 Feb 2015 16:01:48 +0000Richard Zach684 at http://www.ucalgary.ca/rzachhttp://www.ucalgary.ca/rzach/blog/2015/02/cfp-hilberts-epsilon-and-tau-in-logic-informatics-and-linguistics.html#commentsIn Memoriam: Grigori Mints
http://www.ucalgary.ca/rzach/blog/2015/02/in-memoriam-grigori-mints.html
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"> <ul><li><a href="http://www.grishamints.net/home"><img style="float: right; margin-left: 20px;" src="http://www.ucalgary.ca/rzach/files/rzach/grisha.jpg" height="454" width="350" /></a> A <a href="http://www.grishamints.net/home">memorial site has been set up</a> to honor Grisha's memory.</li>
<li>A <a href="http://www.pdmi.ras.ru/EIMI/2015/LC/index.html">memorial conference in honor of Grisha Mints</a> will be held at the Third St.Petersburg Days of Logic and Computability, August 24-26, 2015, at the Euler International Mathematical Institute, St. Petersburg, Russia.</li>
<li>The following obituary was included in the January 2015 Newsletter of the <a href="http://aslonline.org/">Association for Symbolic Logic</a>:</li>
</ul><p>Grigori (“Grisha”) Mints died unexpectedly at Stanford on May 29, 2014. Born on June 7, 1939 in what is now St. Petersburg, Russia, Mints studied at the then Leningrad State University, obtaining a Masters degree in mathematics in 1961 with a thesis on proof search in classical predicate logic, a Ph.D. in 1965 with the thesis On Predicate and Operator Variants for Building Theories of Constructive Mathematics , and a D.Sc. in 1990 with Proof Transformations and Synthesis of Programs. From 1961 to 1979, Mints was a researcher at the Leningrad Branch of the Steklov Mathematics Institute. In 1980 he was appointed to a research position at the Institute of Cybernetics in Tallinn, Estonia. In 1991 he became a professor of philosophy and, by courtesy, of mathematics and computer science at Stanford University. Mints was elected to the Estonian Academy of Sciences in 2008 and to the American Academy of Arts and Sciences in 2010.</p>
<p>Mints’ research spanned several areas, with many interconnections. The grand unifying theme in his oeuvre was proof theory and constructivism, but entangled with this came a lifelong interest in computational logic as well as special attention for two specific areas: intuitionistic logic and modal logic.</p>
<p>Mints was trained in the Russian school of constructive mathematics of Markov and of his teacher Nikolai Shanin. In this paradigm, all mathematical objects should be defined in a finite language, and every proof of existence should provide an algorithm, where properties of the algorithm are to be proved by constructive principles including Markov’s schema. In tandem with this foundational view concerning mathematics, Shanin’s group at Steklov also worked on practical automated reasoning, with an emphasis on generating natural proofs, where ‘natural’ included making sense from the perspective of a human agent. This mixture of proof theory and computation led to inventions such as the inverse method, a style of analyzing provability similar to resolution, developed in 1964 by Sergei Maslov, a close friend of Mints.</p>
<p>Combining proof theory and computation naturally leads to a study of intuitionistic logic, and the most significant results of Mints’ first period concern this interface. They include an extension of Herbrand’s theorem to intuitionistic predicate logic (1962), and a proof of the undecidability of intuitionistic predicate logic with a single unary predicate (1965, a classical paper joint with Maslov and Orevkov). Some of these results are still under active investigation. Mints’ paper of 1968 on decidability of a certain fragment of the Gentzen system LJ introduced what is now called the “Mints hierarchy” of intuitionistic first-order formulas. Complexity properties of Mints classes are still under investigation (e.g., in recent works by Schubert, Urzyczyn, et al.), since they are important to understanding constructive type-theoretic proof assistants such as Coq. Also noteworthy is Mints’ proof in 1974 that familiar procedures for extracting programs from existence proofs in intuitionistic arithmetic produce equivalent algorithms.</p>
<p>In subsequent years, Mints turned to the study of relationships between proof theory and category theory. He used proof-theoretic methods to simplify proofs in category theory and to prove new theorems. Three key papers appeared in 19771980 in Russian (English translations in G. Mints, <em>Selected Papers in Proof Theory</em>, Bibliopolis and North-Holland, 1992). In particular, Mints gave a clear exposition of Lambek’s results connecting Cartesian closed categories and intuitionistic logic using a novel technique of encoding proofs as explicit proof-terms, an idea that has entered categorical logic itself, and that reemerged in modern manifestations such as Artemov’s justification logic. Important results obtained by Mints with this style of analysis include normalization and coherence theorems.</p>
<p>Mints retained his fundamental proof-theoretic interests throughout, witness his longstanding work on Hilbert’s epsilon calculus to subsystems of analysis right through his Stanford period.</p>
<p>During his stay in Estonia, Mints was actively involved with automated deduction. While in Tallinn, he studied the mathematical principles behind the program synthesizer PRIZ, designed by a group at the Institute of Cybernetics led by Enn Tyugu. Mints came up with an example that PRIZ could not handle, leading to an improvement of the algorithm for which Mints established completeness (1982, joint with Tyugu).</p>
<p>This applied work was based on Mints’ earlier research in proof theory for intuitionistic logic. But he also proved a large number of pure results in the area of intuitionism. These include his proof of Novikov’s hypothesis that a Tarski-style translation from Heyting arithmetic to modal arithmetic is faithful (1978). This result fits in an important line of system embeddings, whose later highlights include Flagg and Friedman (1984). Another long-standing interest of Mints in this area were interpolation theorems. An error in the interpolation proof by Lopez-Escobar for intuitionistic first-order logic with constant domains was found by him in 1983, and a recent joint paper with Olkhovikov and Urquhart (2012) finally produced a concrete and instructive counter-example. Mints’ book <em>A Short Introduction to Intuitionistic Logic</em> (2000) is a delightful introduction to the field with many original perspectives.</p>
<p>A natural step leads from intuitionism to modal logic. Mints was the first logician in the Soviet Union to work in modal logic, an exotic area in the 1960s. His first papers (1968-1969) addressed proof theory and decidability of first-order modal logics: in particular, he gave a cut-free sequent calculus for first-order S5 with equality. He also independently introduced the standard translation from modal to classical formulas, one of the main tools in contemporary modal logic. In 1974 he wrote an overview of modal logic in the period 1965-1973 including some of his own results (later transformed into the book <em>A Short Introduction to Modal Logic</em>, 1992).</p>
<p>In the 2000s, Mints proposed a study of basic laws of topology and of dynamical systems over these in a modal language. His results from this period include new proofs (some with Ting Zhang) of the completeness of S4 for the open unit interval and for Cantor space, and for the completeness of the basic dynamic topological logic S4C in Cantor space. Much of this work was collected in a chapter in the <em>Handbook of Spatial Logics</em> (2007), written by Mints and his collaborator Phil Kremer, which put this research program on the map. Recent new directions in his work included work on cut-elimination in fragments of the modal mu-calculus (2012).</p>
<p>Looking back at Mints’ work one sees a unity of themes and style that connected logic, mathematics, and computer science in many innovative ways. In addition he had a unique charm, formed by Russian and later on also by American culture, and a generous and encouraging intellectual attitude that exerted a strong positive influence on his colleagues, from America to Russia, and on successive generations of students until this very period. Many people owe him great ideas that set them on their paths, which he gave unstintingly, as well as help at crucial stages in their career. </p>
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</ul>Thu, 12 Feb 2015 17:59:17 +0000Richard Zach683 at http://www.ucalgary.ca/rzachhttp://www.ucalgary.ca/rzach/blog/2015/02/in-memoriam-grigori-mints.html#commentsPreviously Unknown Turing Manuscript Going to Auction
http://www.ucalgary.ca/rzach/blog/2015/02/previously-unknown-turing-manuscript-going-to-auction.html
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"> <p><img style="float: right; margin-left: 20px;" src="http://www.ucalgary.ca/rzach/files/rzach/22795_turing.png" height="438" width="347" />You may have heard that a notebook by Alan Turing, which he left to Robin Gandy, is going to <a href="http://www.bonhams.com/press_release/18431/">auction in April</a>. Bonham's, the auction house, has kindly permitted me to share the <a href="http://www.ucalgary.ca/rzach/files/rzach/22795_turing.pdf">auction catalog</a>.</p>
<p>The notebook apparently dates from around 1944. The mathematical content is divided into two parts, one on Peano's axioms (judging from the few samples in the catalog, in what looks like <em>Principia</em> notation), the other on "notation," specifically variables. He quotes from Weyl's 1939 book <em>Classical Groups</em>, where Weyl introduces polynomials as "a formal expression $f(x) = \sum_{i=0}^n \alpha_i x^i$ involving the 'indeterminate' (or variable) $x$ whose coefficients $\alpha_i$ are numbers in a field $k$." Turing writes:</p>
<p style="padding-left: 30px;">The idea of of an "indeterminate" is distinctly subtle, I would almost say too subtle. It is not (at any rate as van der Waerden sees it) the same as a variable. Polynomials in an indeterminate $x$, $f_1(x)$ and $f_2(x)$, would not be considered identical if $f_1(x) = f_2(x)$ all $x$ in $k$, but the coefficients differed. They are in effect the array of coefficients, with rules for multiplication and addition suggested by their form.</p>
<p style="padding-left: 30px;">I am inclined to the view that this is too subtle and makes an inconvenient definition. I prefer the indeterminate $k$ [possibly should be $x$?] be just the variable.</p>
<p>Turing's worry is clear enough. If the $x$ in the polynomial is a variable, then the polynomial is determined by its values for all variables, essentially, as a function on $k$. But identity conditions for polynomials are more fine grained. I'm not sure, though, why he thinks this is "too subtle" or why he prefers "the indeterminate be just the variable." Anyway, it <em>is</em> subtle, and I don't know if logicians (or algebraists for that matter) by that time commonly made the distinction clearly. When did people start talking about free algebras on generators $\{x, \dots\}$?</p>
<p>The other detail from the manuscript included in the catalog concerns Leibniz's $dy/dx$ notation. Here, too, he seems to be concerned essentially with the role the symbol "$x$" plays in mathematical notation: is it a variable, so that this notation, as he puts it, has "laid down a relation between $x$ and $y$" (i.e., between their values), and that a polynomial is just a special kind of specification of a function? Or are they indeterminate symbols, and polynomials are certain sequences involving these variables? In other words, do the variables belong to the mathematical metalanguage used to describe mathematical objects, or are they symbols in a formal object language?</p>
<p>Frustrating that we don't have more to look at! If you have a few mil lying around and are going to buy this, please share with the poor scholars.</p>
<p><a href="//www.pinterest.com/pin/create/extension/" style="height: 20px; width: 40px; position: absolute; opacity: 0.85; z-index: 8675309; display: none; cursor: pointer; background-color: transparent; background-image: url('data:image/png;base64,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');"></a></p>
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</ul>Tue, 10 Feb 2015 23:47:22 +0000Richard Zach682 at http://www.ucalgary.ca/rzachhttp://www.ucalgary.ca/rzach/blog/2015/02/previously-unknown-turing-manuscript-going-to-auction.html#commentsCarnap (and Goodman and Quine) and Linguistics (Guest post by Darin Flynn)
http://www.ucalgary.ca/rzach/blog/2015/02/carnap-and-goodman-and-quine-and-linguistics-guest-post-by-darin-flynn.html
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"> <p><img style="float: right; margin-left: 20px;" src="http://www.ucalgary.ca/rzach/files/rzach/carnap.jpg" height="469" width="350" /> (This is a guest post by my linguistics colleague <a href="http://www.ucalgary.ca/dflynn/">Darin Flynn</a>)</p>
<p>I was intrigued by <a href="http://www.ucalgary.ca/rzach/blog/2015/02/carnap-on-syntax-vs-semantics.html">your last post</a>—that Carnap (apparently) gave serious consideration to suggestions by Gödel and Behmann that he use “semantics” rather than “syntax” in the title of his <a href="http://books.google.ca/books?id=j6RqQtU0OKkC&lpg=PP1&pg=PA1#v=onepage&q&f=false">1934 book</a>. The story we’re told in linguistics is that Carnap learned to love semantics (e.g. 1939, 1942, 1947/1956) only after logicians (notably Tarski) showed it to be competitive with logical syntax, but his goal in the early 30s was precisely to develop a formal theory of language (though not of natural language) based on syntax rather than semantics—not just because the latter had a less reputable scientific status at the time, but also because Carnap considered only the first part of the familiar linguistic form/meaning dichotomy to be properly formal:</p>
<blockquote><p>“A theory, a rule, a definition, or the like is to be called formal when no reference is made in it either to the meaning of the symbols (for example, the words) or to the sense of the expressions (e.g. the sentences), but simply and solely to the kinds and order of the symbols from which the expressions are constructed.” <a href="http://books.google.ca/books?id=j6RqQtU0OKkC&lpg=PP1&pg=PA1#v=onepage&q&f=false">(p. 1)</a></p>
</blockquote>
<p>Some of America’s most important theoretical linguists—notably Leonard Bloomfield, Zellig Harris and Noam Chomsky—believed linguistics to be about form rather than meaning, so were impressed by Carnap’s semantics-free theorizing, and by his first example, “Pirots karulize elatically” (p. 2). The latter demonstrated that a sentence could be analyzed as well-formed phonologically, morphologically and syntactically in the absence of meaning. Carnap also used this pseudo-sentence to illustrate “logical syntax” (e.g. deduction): “A is a Pirot” ∴ “A karulizes elatically”. Crucially, “neither the meaning of the words nor the sense of these three sentences need be known” (p. 3).</p>
<p>Chomsky was suspicious of Carnap’s “syntactically” defined logical deductions (semantics in sheep’s clothing?), but was otherwise (like his former mentor, Harris) a careful and appreciative reader of Carnap, and of Goodman’s and Quine’s takes on Carnap. As Heitner (2005) describes in “<a href="http://www.ibrarian.net/navon/page.jsp?paperid=2331410">An odd couple: Chomsky and Quine on reducing the phoneme</a>”:</p>
<blockquote><p>“Chomsky’s early philosophical interaction with Nelson Goodman (1906–1998) and Morton White (b. 1917)—two prominent figures within analytic philosophy of language deeply suspicious of an uncritical reliance on “meaning” in philosophy—with whom he took graduate classes with as an undergraduate is no doubt also relevant. After all, it was Goodman who recommended Chomsky for a Junior Fellowship in the Society of Fellows at Harvard where Chomsky would come into close contact with an elite Harvard philosophical circle revolving around Goodman and Quine... Chomsky recalls how “studying at Penn with Zellig Harris and Nelson Goodman was a highly stimulating experience”; a “remarkable opportunity” where he spent “a good deal of time in courses, seminars, discussions, primarily with philosophers at Harvard—Quine, Austin (who was visiting Harvard then), White, and others... a very lively and stimulating period in the Cambridge area for a student with my particular interests” (p. 17). … [I]n addition to these interpersonal relations, others have also detected a significant line of intellectual descent connecting Chomsky to Quine through the influence of Goodman, and through Goodman and Quine, to the philosophical heritage of Rudolph [sic] Carnap (1891–1970)—one of the leading positivist figures of the Vienna Circle of Logical Empiricism. For while Otero (1994, vol. II) reports that among non-American philosophers, it was only Rudolf Carnap whom Chomsky read as a student (p. 3), Tomalin (2002, <a href="http://www.ibrarian.net/navon/page.jsp?paperid=2835099">2003</a>) has more recently provided valuable research documenting the distinctive Carnapian aspirations and “constructive nominalist” methodology adopted throughout Chomsky’s early formulations of generative grammar as reflected in <em>The Logical Structure of Linguistic Theory</em> (1955/1975) and his first published paper “Systems of Syntactic Analysis” (1953). According to Tomalin, Chomsky’s early commitment to constructing formal systems of syntactic analysis independent of semantic information is traceable to the empiricist methodology of Carnap and the meta-mathematical efforts of Goodman and Quine to devise a formal system for mathematics without appeal to abstract objects (2003, p. 1236). (See Newmeyer (1996, p. 15) for similar considerations.) In fact, in “<a href="http://www.ibrarian.net/navon/page.jsp?paperid=18956557">Logical Syntax and Semantics, Their linguistic relevance</a>” Chomsky (1955a, p. 36) favorably references Quine’s (1953) extremely influential critiques of meaning, and even explicitly defends Quine’s anti-mentalistic philosophy in <em>The Logical Structure of Linguistic Theory</em>.” (p. 2-3)</p>
</blockquote>
<p>For instance, compare Carnap’s quotation above with Chomsky’s in <em>The Logical Structure of Linguistic Theory</em> (the title of which may plausibly be construed as a mashup of Carnap’s <em>The Logical Structure of the World</em> & <em>The Logical Syntax of Language</em>): “In the strict sense of the word, an argument, a characterization, a theory, etc. is ‘formal’ if it deals with form as opposed to meaning, that is, if it deals solely with the shape and arrangement of symbols” (1955/1975, p. 83). Compare, too, Chomsky’s “Colorless green ideas sleep furiously” with Carnap’s pseudo-sentence. According to <a href="http://books.google.ca/books?id=XbjFag2qCygC&lpg=PP1&pg=PP1#v=onepage&q&f=false">Tomalin (2006)</a>, these are examples among many of Carnap’s influence on Chomsky and on his former mentor, Harris. Another notable example: “the transformations developed by Harris and Chomsky were related to the transformation rules presented in (the English translation of) Carnap LST” (p. 168).</p>
<p>Tomalin’s research on the philosophical and historical background of transformational generative grammar is fascinating—particularly his original attention to Carnap, and Goodman’s modifications. For critical reviews, see especially Scholz & Pullum (2007) “<a href="http://www.lel.ed.ac.uk/~gpullum/bcscholz/Tracking.pdf">Tracking the origins of transformational generative grammar</a>” and Seuren (2009) “<a href="http://www.jbe-platform.com/content/journals/10.1075/hl.36.1.05seu">Concerning the roots of transformational generative grammar</a>” [sorry, this one's paywalled :( -RZ].</p>
<p><a href="//www.pinterest.com/pin/create/extension/" style="height: 20px; width: 40px; position: absolute; opacity: 0.85; z-index: 8675309; display: none; cursor: pointer; background-color: transparent; background-image: url('data:image/png;base64,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'); top: 22px; left: 423px;"></a></p>
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</ul>Mon, 09 Feb 2015 22:52:11 +0000Richard Zach681 at http://www.ucalgary.ca/rzachhttp://www.ucalgary.ca/rzach/blog/2015/02/carnap-and-goodman-and-quine-and-linguistics-guest-post-by-darin-flynn.html#commentsCarnap on "Syntax" vs "Semantics"
http://www.ucalgary.ca/rzach/blog/2015/02/carnap-on-syntax-vs-semantics.html
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"> <p>Carnap's <em>Logical Syntax of Language</em> actually deals with semantic notions such as "analytic." Why, then, didn't he call it "semantics"? </p>
<p>When the project was still in its early stages, Carnap sent a manuscript entitled "Metalogik" to Heinrich Behmann. Behmann objected to the title and suggested as alternatives first "Logic of Language" and then "Semantics." Carnap replied:</p>
<blockquote><p>I like the term "semantics"; Gödel also suggested it. Neurath, on the other hand, thinks it is unappealing and pedantic; he suggests "syntax." In order to avoid confusion with syntax in philology, one would probably have to often call it "logical syntax."</p>
<p>Der Terminus "Semantik" sagt mir zu; auch Gödel schlug ihn gleichzeitig vor. Neurath aber findet ihn unsymphatisch und gelehrtenhaft; er schlägt "Syntax" vor. Zur Vermeidung der Verwechslung mit der philologischen S. müsste man dann wohl häufig "logische Syntax" sagen.</p>
<p>(Carnap to Behmann, April 17, 1932)</p>
</blockquote>
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</ul>Sat, 07 Feb 2015 18:02:09 +0000Richard Zach680 at http://www.ucalgary.ca/rzachhttp://www.ucalgary.ca/rzach/blog/2015/02/carnap-on-syntax-vs-semantics.html#commentsCfP: Tools For Teaching Logic TTL2015
http://www.ucalgary.ca/rzach/blog/2015/01/cfp-tools-for-teaching-logic-ttl2015.html
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"> <p><a href="http://ttl2015.irisa.fr/"><img style="float: right; margin-left: 20px;" src="http://ttl2015.irisa.fr/ttl2015_poster.png" height="353" width="250" />Tools for Teaching Logic</a> (June 9-12, 2015, Rennes, France) is seeking original papers with a clear significance in the following topics (but are not limited to): teaching logic in sciences and humanities; teaching logic at different levels of instruction (secondary education, university level, and postgraduate); didactic software; facing some difficulties concerning what to teach; international postgraduate programs; resources and challenges for e-learning logic; teaching argumentation theory, critical thinking and informal logic; teaching specific topics, such as modal logic, algebraic logic, knowledge representation, model theory, philosophy of logic, and others; dissemination of logic courseware and logic textbooks; teaching Logic Thinking.</p>
<p>Abstracts are due on February 13, full papers on February 20. More details on the website: <a href="http://ttl2015.irisa.fr/">http://ttl2015.irisa.fr/</a></p>
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</ul>Sat, 31 Jan 2015 19:55:49 +0000Richard Zach679 at http://www.ucalgary.ca/rzachhttp://www.ucalgary.ca/rzach/blog/2015/01/cfp-tools-for-teaching-logic-ttl2015.html#commentsSkolem's 1920, 1923 Papers
http://www.ucalgary.ca/rzach/blog/2015/01/skolems-1920-1923-papers.html
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"> <p><img style="float: right; margin-left: 20px;" src="http://upload.wikimedia.org/wikipedia/commons/thumb/3/3e/ThoralfSkolem-OB.F06426c.jpg/319px-ThoralfSkolem-OB.F06426c.jpg" height="376" width="250" />In case you need the original 1920 or 1923 papers by Skolem, and you don't have <em>Selected Works in Logic</em> handy, here are PDFs extracted from the digital version of <a href="http://www.biodiversitylibrary.org/bibliography/14789#/details"><em>Skrifter utgit av Videnskapsselskapet i Kristiania. I, Matematisk-naturvidenskabelig klasse</em></a> made available by the Biodiversity Heritage Library and the Internet Archive.</p>
<p>Thoralf Skolem, "<a href="https://www.ucalgary.ca/rzach/files/rzach/skolem1920.pdf">Logisch-kombinatorische Untersuchungen über die Erfüllbarkeit oder Beweisbarkeit mathematischer Sätze nebst einem Theorem über dichte Mengen</a>", <em>Skrifter utgit av Videnskapsselskapet i Kristiania. I, Matematisk-naturvidenskabelig klasse</em> 1920, no. 4, pp. 1–36</p>
<p>Thoralf Skolem, "<a href="https://www.ucalgary.ca/rzach/files/rzach/skolem1923.pdf">Begründung der elementaren Arithmetik durch die rekurrierende Denkweise ohne Anwendung scheinbarer Veränderlichen mit unendlichem Ausdehnungsbereich</a>", <em>Skrifter utgit av Videnskapsselskapet i Kristiania. I, Matematisk-naturvidenskabelig klasse</em> 1923, no. 6, pp. 1–38.</p>
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</ul>Sat, 31 Jan 2015 17:45:07 +0000Richard Zach678 at http://www.ucalgary.ca/rzachhttp://www.ucalgary.ca/rzach/blog/2015/01/skolems-1920-1923-papers.html#commentsChanges at the J for History of Analytic Philosophy
http://www.ucalgary.ca/rzach/blog/2015/01/changes-at-j-for-history-of-analytic-philosophy.html
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"> <p>We have some <a href="http://sshap.org/2015/01/27/new-issue-and-changes-at-jhap/">new editors at the <em>Journal for the History of Analytic Philosophy</em></a>.</p>
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</ul>Sat, 31 Jan 2015 16:27:38 +0000Richard Zach677 at http://www.ucalgary.ca/rzachhttp://www.ucalgary.ca/rzach/blog/2015/01/changes-at-j-for-history-of-analytic-philosophy.html#commentsCfP: 2015 Logic Colloquium in Helsinki
http://www.ucalgary.ca/rzach/blog/2015/01/cfp-2015-logic-colloquium-in-helsinki.html
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"> <h3 style="text-align: center;">First Announcement & Call for Abstracts</h3>
<h2 style="text-align: center;">Logic Colloquium 2015<br />European Summer Meeting of the Association for Symbolic Logic</h2>
<p style="text-align: center;">Helsinki, Finland, 3-8 August 2015<br /><a href="http://www.helsinki.fi/lc2015" class="moz-txt-link-freetext">http://www.helsinki.fi/lc2015</a></p>
<p>The annual European Summer Meeting of the <a href="http://www.aslonline.org/index.htm" target="_blank">Association for Symbolic Logic</a>, the Logic Colloquium 2015 (LC 2015), will be organized in Helsinki, Finland, 3-8 August 2015. Logic Colloquium 2015 is co-located with the 15th Conference of Logic, Methodology and Philosophy of Science, <a href="http://clmps.helsinki.fi" target="_blank">CLMPS 2015</a>, and with the <a href="http://www.helsinki.fi/sls2015">SLS Summer School in Logic</a>. </p>
<h3>Plenary lectures</h3>
<p><a href="http://researchmap.jp/tosarai/" target="_blank">Toshiyasu Arai</a> (Chiba) <br /><a href="http://www.gc.cuny.edu/Page-Elements/Academics-Research-Centers-Initiatives/Doctoral-Programs/Philosophy/Faculty-Bios/Sergei-Artemov" target="_blank">Sergei Artemov</a> (New York)<br /><a href="http://www.andrew.cmu.edu/user/awodey/" target="_blank">Steve Awodey</a> (Pittsburgh) <br /><a href="https://staff.fnwi.uva.nl/j.vanbenthem/" target="_blank">Johan van Benthem</a> (Amsterdam and Stanford) <br /><a href="http://www.chernikov.me" target="_blank">Artem Chernikov</a> (Paris) <br /><a href="http://www.math.yorku.ca/%7Eifarah/" target="_blank">Ilias Farah</a> (York) <br /><a href="http://www.haverford.edu/philosophy/dmacbeth/" target="_blank">Danielle Macbeth</a> (Haverford)<br /><a href="http://math.nsc.ru/%7Easm256/" target="_blank">Andrei Morozov</a> (Novosibirsk) <br /><a href="http://math.haifa.ac.il/kobi/" target="_blank">Kobi Peterzil </a>(Haifa) <br /><a href="http://wwwmath.uni-muenster.de/logik/Personen/rds/" target="_blank">Ralf Schindler </a>(Münster)<br /><a href="http://en.wikipedia.org/wiki/Saharon_Shelah" target="_blank">Saharon Shelah</a> (TBC) (Jerusalem and Rutgers) <br /><a href="http://www.math.ru.nl/%7Eterwijn/" target="_blank">Sebastiaan Terwijn</a> (Nijmegen)</p>
<h3>Tutorials</h3>
<p><a href="https://logic.rwth-aachen.de/People/Graedel/" target="_blank">Erich Grädel</a> (Aachen)<br /><a href="http://settheory.mathtalks.org/speaker/menachem-magidor/" target="_blank">Menachem Magidor</a> (Jerusalem).</p>
<h3>Special sessions</h3>
<p><strong>Set Theory</strong>, organized by Heike Mildenberger (Freiburg)</p>
<p><strong>Model theory, </strong>organized by Dugald Macpherson (Leeds)</p>
<p><strong>Computability Theory, </strong>organized by Russell Miller (New York) and Alexandra Soskova (Sofia)</p>
<p><strong>Proof Theory, </strong>organized by Benno van den Berg (Amsterdam) and Michael Rathjen (Leeds)</p>
<p><strong>Philosophy of Mathematics and Logic, </strong>organized by Patricia Blanchette (Notre Dame) and Penelope Maddy (Irvine)</p>
<p><strong>Logic and Quantum Foundations, </strong>organized by Samson Abramsky (Oxford)</p>
<h2>Travel Awards and Contributed Talks</h2>
<p>Travel awards for students and young researchers have been made available by the organizers. In some cases full compensation of expenses is possible. The website includes detailed information about the awards, instructions of how to apply, and an electronic form which may be used for the application. </p>
<p>The Logic Colloquium will include contributed talks of 20 minutes' length. Abstracts on contributed talks are published in the <em>Bulletin of Symbolic Logic</em>.</p>
<p>The deadline for travel award applications and abstract submission is <strong>Tuesday, May 3, 2015</strong>. Please see <a href="http://www.helsinki.fi/lc2015/submission.html">http://www.helsinki.fi/lc2015/submission.html</a> for information about applying for travel awards and for submitting an abstract.<br /><br /><br /></p>
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</ul>Sun, 18 Jan 2015 15:25:57 +0000Richard Zach676 at http://www.ucalgary.ca/rzachhttp://www.ucalgary.ca/rzach/blog/2015/01/cfp-2015-logic-colloquium-in-helsinki.html#commentsJohn Shepherdson, 1926-2015
http://www.ucalgary.ca/rzach/blog/2015/01/john-shepherdson-1926-2015.html
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"> <p>Sad news from Philip Welch at Bristol: John Shepherdson has died.</p>
<blockquote><p>I deeply regret having to impart the very sad news that John Shepherdson died in Bristol on Thursday of an inoperable sarcoma.</p>
<p>John was a founder of the BLC (together with Robin Gandy if I remember rightly). His own work was in many areas, starting with set theory, then recursion theory (inventing the register machine in a paper with Sturgis), models of arithmetic, incompleteness phenomena, and towards the end of his career working on PROLOG and fuzzy logic. Besides all this, he made Bristol a centre for mathematical logic in the UK, with many prestigious visitors in the early years. In particular it became a training ground in the 50s, 60s for many who went on to academic careers, as well as in the 70's through its MSc in Mathematical Logic and Theory of Computation. He spent his whole working career at the Bristol department arriving there in 1946.</p>
<p>He always struck me as an exceptionally kind person, an amusing and intelligent companion to be with, and most modest, as well as self-effacing in the best sense. He will be much missed.</p>
<p>A fuller appreciation will be composed at some point. There will be no funeral, but his family have indicated there will be a Memorial Service or Occasion at a date in the future, when a full tribute can be paid to him.</p>
<p>Philip Welch</p>
</blockquote>
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</ul>Fri, 16 Jan 2015 17:36:56 +0000Richard Zach675 at http://www.ucalgary.ca/rzachhttp://www.ucalgary.ca/rzach/blog/2015/01/john-shepherdson-1926-2015.html#commentsBrilliance and Other Causes of Academic Gender Gaps
http://www.ucalgary.ca/rzach/blog/2015/01/brilliance-and-other-causes-of-academic-gender-gaps.html
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"> <p>Every mathematician and philosopher should watch this video by <a href="https://www.princeton.edu/~sjleslie/index.html">Sarah-Jane Leslie</a> (Philosophy, Princeton) on her study with <a href="http://www.psychology.illinois.edu/people/acimpian">Andrei Cimpian</a> (Psych, Illinois). Takes just 11 minutes.</p>
<p><iframe src="//www.youtube.com/embed/FM6mbSiD3eA" frameborder="0" height="315" width="560"></iframe></p>
<p>Then you can go and read the <a href="http://www.sciencemag.org/content/347/6219/262.abstract">original study</a> in <em>Science</em> or any of the writeups in, e.g., the <a href="http://news.sciencemag.org/education/2015/01/belief-some-fields-require-brilliance-may-keep-women-out">Science news blog</a>, <a href="http://chronicle.com/article/Disciplines-That-Expect/151217/">Chronicle</a>, <a href="http://dailynous.com/2015/01/15/raw-intellectual-talent-and-academias-gender-gaps/">Daily Nous</a>, etc.</p>
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</ul>Fri, 16 Jan 2015 15:35:05 +0000Richard Zach674 at http://www.ucalgary.ca/rzachhttp://www.ucalgary.ca/rzach/blog/2015/01/brilliance-and-other-causes-of-academic-gender-gaps.html#commentsLogical Operators in the SEP
http://www.ucalgary.ca/rzach/blog/2015/01/logical-operators-in-sep.html
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"> <p>The Stanford Encyclopedia of Philosophy now has entries on:</p>
<ul><li><a href="http://plato.stanford.edu/entries/negation/">Negation</a> (Laurence R. Horn and Heinrich Wansing)</li>
<li><a href="http://plato.stanford.edu/entries/disjunction/">Disjunction</a> (Ray Jennings and Andrew Hartline)<a href="http://plato.stanford.edu/entries/disjunction/"></a></li>
<li><a href="http://plato.stanford.edu/entries/conditionals/">Indicative Conditionals</a> (Dorothy Edgington)</li>
<li><a href="http://plato.stanford.edu/entries/quantification/">Quantifiers and Quantificiation</a> (Gabriel Uzquiano)</li>
<li><a href="http://plato.stanford.edu/entries/identity/">Identity</a> (Harold Noonan and Ben Curtis)</li>
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</ul>Fri, 09 Jan 2015 20:54:36 +0000Richard Zach673 at http://www.ucalgary.ca/rzachhttp://www.ucalgary.ca/rzach/blog/2015/01/logical-operators-in-sep.html#commentsIvor Grattan-Guinness, 1941-2014
http://www.ucalgary.ca/rzach/blog/2015/01/ivor-grattan-guinness-1941-2014.html
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"> <p><img style="float: right; margin-left: 20px;" src="http://upload.wikimedia.org/wikipedia/commons/thumb/4/45/Grattan-Guinness_1.jpg/170px-Grattan-Guinness_1.jpg" height="194" width="170" />I learned today that <a href="http://en.wikipedia.org/wiki/Ivor_Grattan-Guinness">Ivor Grattan-Guinness</a>, the historian of mathematics and logic, died last month.</p>
<p>Obituaries:</p>
<ul><li><a href="http://www.theguardian.com/education/2014/dec/31/ivor-grattan-guinness">Guardian</a></li>
<li><a href="http://bibnum.hypotheses.org/671">BibNum</a></li>
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</ul>Wed, 07 Jan 2015 14:02:50 +0000Richard Zach672 at http://www.ucalgary.ca/rzachhttp://www.ucalgary.ca/rzach/blog/2015/01/ivor-grattan-guinness-1941-2014.html#commentsNerlim: a Master Bibliography Style that Allows Books to have both Authors and Editors
http://www.ucalgary.ca/rzach/blog/2014/12/nerlim-master-bibliography-style-allows-books-to-have-both-authors-and-editors.html
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"> <p>If you're using BibTeX and LaTeX and are doing any kind of scholarly/humanistic work, I'm sure you've run into this annoying problem: BibTeX always complains when a book has both an author and an editor. That's a problem when, say, you want to include</p>
<p style="padding-left: 30px;">Gödel, K., 1986. <em>Collected Works</em>, vol. I. S. Feferman et al., eds. Oxford: Oxford University Press.</p>
<p>There is a wonderful package that allows you to generate new BibTeX bibliography styles based on a large number of customization options: <a href="http://www.ctan.org/pkg/custom-bib">custom-bib</a>. It comes with one big master bibliography style merlin.mbs from which your custom style is generated. I've produced a <a href="https://github.com/rzach/nerlim">modified file</a> which will also print both author and editor for a book that has both. </p>
<p>Merry Christmas.</p>
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</ul>Mon, 22 Dec 2014 20:09:32 +0000Richard Zach671 at http://www.ucalgary.ca/rzachhttp://www.ucalgary.ca/rzach/blog/2014/12/nerlim-master-bibliography-style-allows-books-to-have-both-authors-and-editors.html#commentsHalbach & Visser: Self-reference in arithmetic
http://www.ucalgary.ca/rzach/blog/2014/12/halbach-visser-self-reference-in-arithmetic.html
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"> <p>New in the <em>Review of Symbolic Logic</em> (<a href="http://dx.doi.org/10.1017/S1755020314000288">part 1</a>, <a href="http://dx.doi.org/10.1017/S175502031400029X">part 2</a>)</p>
<blockquote><p>A Gödel sentence is often described as a sentence saying about itself that it is not provable, and a Henkin sentence as a sentence stating its own provability. We discuss what it could mean for a sentence of arithmetic to ascribe to itself a property such as provability or unprovability. The starting point will be the answer Kreisel gave to Henkin’s problem. We describe how the properties of the supposedly self-referential sentences depend on the chosen coding, the formulae expressing the properties and the way a fixed points for the formulae are obtained. This paper is the first of two papers. In the present paper we focus on provability. In part II, we will consider other properties like Rosser provability and partial truth predicates.</p>
</blockquote>
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</ul>Sun, 14 Dec 2014 14:19:00 +0000Richard Zach670 at http://www.ucalgary.ca/rzachhttp://www.ucalgary.ca/rzach/blog/2014/12/halbach-visser-self-reference-in-arithmetic.html#commentsStorify'd Michael Beaney's Vienna Circle Lecture on Susan Stebbing
http://www.ucalgary.ca/rzach/blog/2014/12/storifyd-michael-beaneys-vienna-circle-lecture-on-susan-stebbing.html
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"> <div class="storify">
<iframe src="//storify.com/RrrichardZach/michael-beaney-s-vienna-circle-lecture-on-susan-st/embed?border=false" frameborder="no" height="750" width="100%"></iframe><p></p><noscript>[<a href="//storify.com/RrrichardZach/michael-beaney-s-vienna-circle-lecture-on-susan-st" target="_blank">View the story "Michael Beaney's Vienna Circle Lecture on Susan Stebbing" on Storify</a>]</noscript></div>
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</ul>Sat, 13 Dec 2014 13:19:01 +0000Richard Zach669 at http://www.ucalgary.ca/rzachhttp://www.ucalgary.ca/rzach/blog/2014/12/storifyd-michael-beaneys-vienna-circle-lecture-on-susan-stebbing.html#commentsMore on Shatunovsky, Kagan, and Yanovskaya
http://www.ucalgary.ca/rzach/blog/2014/12/more-on-shatunovsky-kagan-and-yanovskaya.html
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"> <p>In response to my post about "<a href="http://www.ucalgary.ca/rzach/blog/2014/12/some-lesser-known-to-me-russiansoviet-logicians.html">lesser known Russian/Soviet logicians</a>", <a href="http://www.mi.ras.ru/~bekl/">Lev Beklemishev</a> commented:</p>
<blockquote><p>Dirk van Dalen was interested in Shatunovsky's work and at his request I procured a copy of his book on the development of algebra on the basis of what can be called rudimentary constructivist ideas. This was, of course, pre-Brouwerian, and the ideas of Shatunovsky were perhaps more in line with Kronecker's. In any case, this was interesting to see, but it never came to a publication on it with Dirk.</p>
<p>Yanovskaya was his most well-known student, and she was well-respected among the mathematical logicians in Moscow, for whom she effectively provided some sort of ideological cover in the later years. She worked at the department of mathematics at MSU and is well-remembered there.</p>
<p>A good informative article on Shatunovsky is his obituary written by Chebotarev and published, I think, in Uspekhi matematicheskih nauk [<a href="http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=rm&paperid=7108&option_lang=eng">link</a>].</p>
</blockquote>
<p>By email, <a href="http://www.snd-sorbonne.org/themes-membres/liste-membres/mark-van-atten/">Mark van Atten</a> wrote:</p>
<blockquote><p>A marginal note: There was a brief epistolary exchange between Kagan and Brouwer. They had been put in contact by Mrs Ehrenfest-Afanassjewa. Kagan's letter to Brouwer of June 22, 1922 can be found in <em>The Selected Correspondence of L.E.J. Brouwer</em> (ed. Van Dalen, Springer 2011), <a href="https://books.google.at/books?id=rLZq9sTT5gAC&lpg=PP1&pg=PA290&redir_esc=y#v=onepage&q&f=false">pp. 290-291</a>. In that letter Kagan also mentions Schatunowsky (as he, writing in German, spells it) and the latter's work on the development of algebra without the excluded middle.</p>
<p>The date as given by Van Dalen there is 1925. The online-edition of the correspondence at <a href="http://extras.springer.com/2011/978-0-85729-527-9">extras.springer.com</a>, which contains all of Brouwer's remaining correspondence (but untranslated), contains that letter twice, once dated 1922, once 1925. 1922 seems to me to be correct as Ehrenfest-Afanassjewa's request to Brouwer to send some material to Kagan was made in that year.</p>
<p>That online edition also includes a short second letter from Kagan, dated Feburay 8, 1925 (on Alexandrov and Urysohn, but without specifically scientific content).</p>
<p>The online edition mentions Shatunovsky once more, in a letter from Alexandrov to Brouwer of March 15, 1927. Commenting on a paragraph in a letter from Brouwer to him, apparently lost, of December 27 [1926], Alexandrov writes: `Im Absatz 8 äussern Sie mir Ihre Meinung über den unsinnigen Artikel von Schatunowski. Da diese Meinung im Stillen auch immer die meinige war, sah ich keinen Grund mich irgendwie dazu zu äussern, und habe mich begnügt, dieselbe an Frau Ehrenfest zur gefälligste Kenntnisnahme mitzuteilen.'</p>
<p>Alas, the online edition contains no mention of Schönfinkel.</p>
</blockquote>
<p>Lev responded:</p>
<blockquote><p>This is an interesting exchange. Is there a way to find out which paper of Shatunovsky was mentioned by Brouwer and Alexandroff as non-sensical? In any case, this assessment could actually be true. From a rather superficial reading of his long work I got the impression that it was a specific way of presenting rather ordinary algebra, without anything revolutionary, accompanied by an introduction stating some philosophical pre-constructivist motivations. The case for doing all this was not a very strong one. But it could well be that they mention some other work that could be either more or less non-sensical that this.</p>
<p>By the way, Kagan was the grandfather of <a href="http://en.wikipedia.org/wiki/Yakov_Sinai">Yakov Sinai</a>, this year's Abel laureate. I have just watched his interview where he told some story about his grandfather and his friend Shatunovsky from their time in Odessa. Apparently he knows a lot about their lives! These coincidences are quite curious...</p>
</blockquote>
<p>Mark responded to Lev's question:</p>
<blockquote><p>The edition of Brouwer's correspondence does not carry an annotation on this point, unfortunately. Perhaps an educated guess can be made from a full bibliography. Is there one?</p>
</blockquote>
<p><a href="http://youtu.be/Ui_Q-iphmXU">The interview Lev mentioned is on youtube</a>. It's in Russian, and Google Translate didn't do a very good job on the transcript, probably because of missing punctuation. I'm attaching it here in case someone wants to play with it.</p>
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</ul>Sat, 13 Dec 2014 12:51:54 +0000Richard Zach668 at http://www.ucalgary.ca/rzachhttp://www.ucalgary.ca/rzach/blog/2014/12/more-on-shatunovsky-kagan-and-yanovskaya.html#commentsSome Lesser Known (to me) Russian/Soviet Logicians
http://www.ucalgary.ca/rzach/blog/2014/12/some-lesser-known-to-me-russiansoviet-logicians.html
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"> <p>I'm working on a paper that features Moses Schönfinkel, so I was reading through a manuscript of his where he rattles off a long list of important logicians. In addition to the usual suspects, it features the names "Schatunowski, Sleschinski, Kahan, Poretski." I spent the better part of a day trying to figure out to whom he was referring:</p>
<p style="padding-left: 30px;" class="firstHeading" lang="en" xml:lang="en"><a href="http://en.wikipedia.org/wiki/Samuil_Shatunovsky">Samuil Osipovich Shatunovsky</a> (1859-1929) was a mathematician working in Odessa who, so Wikipedia, "independently from Hilbert, he developed a similar axiomatic theory and applied it in geometry, algebra, Galois theory and analysis."</p>
<p style="padding-left: 30px;" class="firstHeading" lang="en" xml:lang="en"><a href="http://en.wikipedia.org/wiki/Ivan_%C5%9Aleszy%C5%84ski">Iva</a><a href="http://en.wikipedia.org/wiki/Ivan_%C5%9Aleszy%C5%84ski">n</a><a href="http://en.wikipedia.org/wiki/Ivan_%C5%9Aleszy%C5%84ski"> Vladislavovich </a><a href="http://en.wikipedia.org/wiki/Ivan_%C5%9Aleszy%C5%84ski">Sleshinsky</a> (1854-1931), or Jan Śleszyński in Polish, was an analyst who also wrote on logic who worked in Odessa, where Schönfinkel was his student, and later Krakow. He also translated Couturat's book <i>The algebra of logic</i> into Russian.<b><br /></b></p>
<p style="padding-left: 30px;" class="firstHeading" lang="en" xml:lang="en"><a href="http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Poretsky.html">Platon Sergeevich Poretsky</a> (1846-1907) worked on Boolean algebraic logic, teaching in Kazan. He's credited with being the first mathematician to teach logic in Russia.</p>
<p class="firstHeading" lang="en" xml:lang="en">Kahan was a little harder to track down, but apparently Kahan is an alternative transcription of <span>Ка́ган:</span></p>
<p style="padding-left: 30px;" class="firstHeading" lang="en" xml:lang="en"><span><a href="https://en.wikipedia.org/wiki/Veniamin_Kagan">Veniamin Fedorovich Kagan</a> (1869-1953) was a geometer and expert on Lobachevsky, who studied in Odessa, Kiev, and St. Petersburg, and worked in Moscow. He grew up in the same city as Schönfinkel, <span class="mw-redirect">Yekaterinoslav</span> (now Dnipropetrovsk).<br /></span></p>
<p><img style="float: right; margin-left: 20px;" src="http://www.ucalgary.ca/rzach/files/rzach/janovskaya2.jpg" height="290" width="200" />In the process of googling about I also happened on <a href="http://en.wikipedia.org/wiki/Sofya_Yanovskaya">Sofya Aleksandrovna Yanovskaya</a> (1896-1966). She studied in Odessa at the same time as Schönfinkel and, like him, was a student of Shatunovsky. She was active in the revolution, and earned a doctorate in 1935 from Moscow State University, where she taught from 1931. In 1943 she founded the the seminar in mathematical logic. According to some sources, she became the first chair of the newly created Department for Mathematical Logic in 1959, however, others as well as the <a href="http://lpcs.math.msu.su/eng/history.htm">webpage</a> of the institute have A. A. Markov as the first chair, 1959-1979. From <a href="http://projecteuclid.org/euclid.rml/1204835787">this biography</a>, in addition to her teaching and research in mathematics, she was influential in other interesting ways:</p>
<blockquote><p>Her work in history and philosophy of mathematics included preparation of a Russian edition of Marx's mathematical manuscripts and the study of Marx's philosophy of mathematics, as well as more general study of philosophy of mathematics. She was interested, for example, in the history of the concept of infinitesimals and her work along these lines included a study of Rolle's contributions. She also paid special attention to the role of Descartes, and in particular to his <i>La Géométrie</i>, in the development the axiomatic approach to mathematics. Her contributions to history and philosophy of logic included work on the problematics of mathematical logic, including problematics related to cybernetics. In the latter regard, an example can be found in the Russian translation of Alan Turing's essay "Can A Machine Think?", which she edited, and in whose introduction she contributed to the discussion of problems in the philosophical aspects of cybernetics through her original analysis of the comparison of the potentialities of man versus machine. She was also instrumental in acquainting Soviet logicians with the work of their Western colleagues through the translation program which she organized, that included the textbooks on mathematical logic of Hilbert and Ackermann, Goodstein, Church, Kleene, and Tarski, and for which she provided important interpretive introductions. She also wrote important and massive historical-expository surveys of Soviet work in mathematical logic and foundations of mathematics.</p>
</blockquote>
<p>A <a href="http://projecteuclid.org/euclid.rml/1204835624">special issue of <em>Modern Logic</em></a> was devoted to her life and work on the occasion of her centenary in 1996; it includes highly interesting articles on her work as well as some smaller biographical items (all open access). Another interesting paper is <a href="http://staff.ulsu.ru/bazhanov/russian/yanovs.pdf">here</a>.</p>
<p>UPDATE: <a href="https://www.ucalgary.ca/rzach/blog/2014/12/more-on-shatunovsky-kagan-and-yanovskaya.html">Follow-up here</a>.</p>
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</ul>Tue, 09 Dec 2014 15:42:41 +0000Richard Zach667 at http://www.ucalgary.ca/rzachhttp://www.ucalgary.ca/rzach/blog/2014/12/some-lesser-known-to-me-russiansoviet-logicians.html#commentsGraduate Programs in Philosophical Logic
http://www.ucalgary.ca/rzach/blog/2014/12/graduate-programs-in-philosophical-logic.html
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"> <p><a href="http://standefer.weebly.com/">Shawn Standefer</a> has done us all a great service by starting and populating a <a href="http://philwiki.net/logic/index.php/Philosophical_Logic_PhD_Programs">Wiki of PhD programs in Philosophical Logic</a>!</p>
<blockquote><p>This wiki provides an unranked list of PhD (and (eventually) terminal M.A.) programs that have strengths in philosophical logic. Links are provided to the websites, CVs, and PhilPapers profiles of the relevant faculty at each program. Additionally, when known, the specialities and willingness of faculty members to work with new graduate students are noted. The primary intended audience is prospective or current graduate students with interests in philosophical logic who want to get the lay of the land by seeing who works where, and on what. This wiki is modeled on Shawn A. Miller’s <a href="http://philbio.net" class="external text" rel="nofollow">PhilBio.net</a> wiki.</p>
</blockquote>
<p>It's a wiki, so you can edit it: add programs, faculty in your program, edit your own specialities, add a link to your PhilPapers page, etc.!</p>
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</ul>Mon, 08 Dec 2014 14:29:20 +0000Richard Zach666 at http://www.ucalgary.ca/rzachhttp://www.ucalgary.ca/rzach/blog/2014/12/graduate-programs-in-philosophical-logic.html#commentsOne person's modus ponens...
http://www.ucalgary.ca/rzach/blog/2014/12/one-persons-modus-ponens.html
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"> <p><img style="float: right; margin-left: 20px;" src="http://www.famous-mathematicians.com/images/julia-robinson.jpg" height="147" width="300" />...is another's modus tollens.</p>
<blockquote><p>[W]hen I was nine years old, I came down with scarlet fever. [...] During that year there was nothing in the world which I wanted so much as a bicycle. My father assured me that when I got well I would get one but, childlike, I interpreted this as meaning that I was not going to get well.</p>
</blockquote>
<p>Julia Robinson, in: Constance Reid, <a href="http://www.maa.org/programs/maa-awards/writing-awards/the-autobiography-of-julia-robinson">The Autobiography of Julia Robinson</a>. <i>The</i> <i>College Mathematics Journal</i>, Vol. 17, No. 1, (1986), pp. 3-21</p>
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</ul>Sat, 06 Dec 2014 18:06:21 +0000Richard Zach665 at http://www.ucalgary.ca/rzachhttp://www.ucalgary.ca/rzach/blog/2014/12/one-persons-modus-ponens.html#commentsAdolf Lindenbaum
http://www.ucalgary.ca/rzach/blog/2014/12/adolf-lindenbaum.html
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"> <p><img style="float: right; margin-left: 20px;" src="/rzach/files/rzach/lindenbaum.png" alt="Adolf Lindenbaum in 1927 (age 23)" height="389" width="300" />Jan Zygmunt and Robert Purdy have a paper ("<a href="http://link.springer.com/article/10.1007/s11787-014-0108-2">Adolf Lindenbaum: Notes on his Life, with Bibliography and Selected References</a>", open access) in the latest issue of <em>Logica Universalis</em> detailing what little is known about the life of Adolf Lindenbaum (1904-1941). It includes a complete bibliography of Lindenbaum's own publications and public lectures, as well as a bibliography of articles in which results are credited to Lindenbaum. Another paper on Lindenbaum's mathematical contributions is in the works.</p>
<p>The entire issue is dedicated to Lindenbaum. Jean-Yves Beziau gives this poignant quote in the introduction:</p>
<blockquote><div data-canvas-width="486.64179418541994">A mathematician, a modern mathematician in particular, is, as it would be said, in a superior degree of conscious activity: he is not only interested in the question of the what, but also in that of the how. He almost never restricts himself to a solution <em>tout court</em> of a problem. He always wants to have the most ??? solutions. Most what? The easiest, the shortest, the most general, etc.</div>
</blockquote>
<div data-canvas-width="486.64179418541994">Lindenbaum was murdered by the Nazis in 1941, at age 37.</div>
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</ul>Sat, 06 Dec 2014 16:25:16 +0000Richard Zach664 at http://www.ucalgary.ca/rzachhttp://www.ucalgary.ca/rzach/blog/2014/12/adolf-lindenbaum.html#commentsKennedy's Interpreting Gödel Out Now
http://www.ucalgary.ca/rzach/blog/2014/12/kennedys-interpreting-godel-out-now.html
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"> <p><em><a href="http://books.google.ca/books?id=ulw3BAAAQBAJ&printsec=frontcover#v=onepage&q&f=false">Interpreting Gödel: Critical Essays</a></em>, edited by Juliette Kennedy, was just published by Cambridge. It looks extremely interesting, with an all-star cast of contributors:</p>
<p>1. Introduction: Gödel and analytic philosophy: how did we get here? Juliette Kennedy<br /><strong>Part I. Gödel on Intuition:</strong><br />2. Intuitions of three kinds in Gödel's views on the continuum, John Burgess<br /> 3. Gödel on how to have your mathematics and know it too, Janet Folina<br /><strong>Part II. The Completeness Theorem:</strong><br />4. Completeness and the ends of axiomatization, Michael Detlefsen<br /> 5. Logical completeness, form, and content: an archaeology, Curtis Franks<br /><strong> Part III. Computability and Analyticity:</strong><br />6. Gödel's 1946 Princeton bicentennial lecture: an appreciation, Juliette Kennedy<br /> 7. Analyticity for realists, Charles Parsons<br /><strong>Part IV. The Set-theoretic Multiverse:</strong><br />8. Gödel's program, John Steel<br /> 9. Multiverse set theory and absolutely undecidable propositions, Jouko Väänänen<br /><strong>Part V. The Legacy:</strong><br />10. Undecidable problems: a sampler, Bjorn Poonen<br /> 11. Reflecting on logical dreams, Saharon Shelah.</p>
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</ul>Tue, 02 Dec 2014 14:56:30 +0000Richard Zach663 at http://www.ucalgary.ca/rzachhttp://www.ucalgary.ca/rzach/blog/2014/12/kennedys-interpreting-godel-out-now.html#commentsTwo New(ish) Surveys on Gödel's Incompleteness Theorems
http://www.ucalgary.ca/rzach/blog/2014/11/two-newish-surveys-on-godels-incompleteness-theorems.html
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"> <p><img style="float: right; margin-left: 20px;" src="http://upload.wikimedia.org/wikipedia/commons/c/c1/1925_kurt_g%C3%B6del.png" height="386" width="300" />Gödel's incompleteness theorems have many variants: semantic vs. syntactic versions, which specific theory is taken as basic, what model of computability is used, which logical system is assumed to underlie the provability relation, how syntax is arithmetized, what hypotheses the theorem itself uses (soundness, consistency, $\omega$-consistency, etc.). These result in trade-offs regarding simplicity of the proof, but also scope of application and consequences that can be drawn.</p>
<p>There are two new(ish) and super-useful surveys of proofs of Gödel's incompleteness theorem that review these versions and their limitations and scope. The first is by <a href="http://www.mi.ras.ru/~bekl/">Lev Beklemishev</a>:</p>
<p style="padding-left: 30px;">Л.Д. Беклемишев (2010). <a href="http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=rm&paperid=9378&option_lang=rus" target="_top">Теоремы Гёделя о неполноте и границы их применимости. I.</a>, Успехи Математических Наук 65(5) 61-104. <a href="http://www.mi.ras.ru/%7Ebekl/Papers/goedel-uspehi.pdf" target="_top">PDF</a>.</p>
<p>English translation:</p>
<p style="padding-left: 30px;">L. D. Beklemishev (2010). <a href="http://iopscience.iop.org/0036-0279/65/5/R03/">Gödel incompleteness theorems and the limits of their applicability. I.</a><em>,</em> <em>Russian Mathematical Surveys </em> 65(5) 857-898. <a href="http://www.mi.ras.ru/%7Ebekl/Papers/goedel-en.pdf" target="_top">PDF</a></p>
<p>The second is by <a href="http://users.ipfw.edu/buldtb/">Bernd Buldt</a>:</p>
<p style="padding-left: 30px;">B. Buldt (2014). <a href="http://link.springer.com/article/10.1007/s11787-014-0107-3">The scope of Gödel’s first incompleteness theorem</a>, <em>Logica Universalis</em>. forthcoming. <a href="http://opus.ipfw.edu/cgi/viewcontent.cgi?article=1297&context=philos_facpubs">PDF preprint</a></p>
<p>Lev's is mathematically more exhaustive and more technical; Bernd's is less technical and also goes into philosophically relevant aspects such as Gödel's theorems for system with non-classical underlying logics.</p>
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</ul>Fri, 28 Nov 2014 17:49:35 +0000Richard Zach662 at http://www.ucalgary.ca/rzachhttp://www.ucalgary.ca/rzach/blog/2014/11/two-newish-surveys-on-godels-incompleteness-theorems.html#commentsPossible Postdoc on Genesis of Mathematical Knowledge
http://www.ucalgary.ca/rzach/blog/2014/11/possible-postdoc-on-genesis-of-mathematical-knowledge.html
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"> <div>Via the APMP list:</div>
<blockquote><div>Expressions of interest are invited for a postdoc grant (financed by Junta de Andalucia) associated with the following research project: </div>
<div></div>
<div>“THE GENESIS OF MATHEMATICAL KNOWLEDGE: COGNITION, HISTORY, PRACTICES” (P12-HUM-1216). IP: <a href="http://personal.us.es/josef/">Jose Ferreiros</a></div>
<div>Contact: <a href="mailto:josef@us.es">josef@us.es</a></div>
<div></div>
<div>The grant consists in a 2-year research contract to be held at the University of Sevilla. Salary is in the range of 84000 euros for 24 months. Holders must have obtained their PhD <span style="text-decoration: line-through;"> before start of the grant,</span><strong> [update:] by 2014</strong> and at most 10 years ago (exceptions apply in case of motherhood). They will be doing research along the lines of this interdisciplinary project -- devoted to philosophy of mathematics, links between cognition and mathematical practice, and the interactions logic/mathematics and physics/mathematics. Knowledge of Spanish is desirable, although it is not a formal requirement.</div>
<div></div>
<div>The call for these grants, issued by Junta de Andalucia, will be open from early December, allowing for only 15 days. Applications will be made to the Junta de Andalucia, but we invite candidates to get in touch with the project IP in advance, so that we can coordinate and assist you. If you are interested in applying, please contact the IP by email as soon as possible, explaining briefly your situation and interests. Keep in mind that the selection will be made on the basis of fit between the candidate's research project and the topic of the project.</div>
</blockquote>
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</ul>Fri, 28 Nov 2014 15:52:37 +0000Richard Zach661 at http://www.ucalgary.ca/rzachhttp://www.ucalgary.ca/rzach/blog/2014/11/possible-postdoc-on-genesis-of-mathematical-knowledge.html#commentsKalmár's Compleness Proof
http://www.ucalgary.ca/rzach/blog/2014/11/kalmars-compleness-proof.html
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"> <p>Dana Scott's <a href="blog/2014/11/dana-scotts-favorite-completeness-proof.html">proof</a> reminded commenter "fbou" of Kalmár's 1935 completeness proof. (<a href="http://www.inf.u-szeged.hu/kalmar/pdf/35_act_sci_math.pdf">Original paper</a> in German on the Hungarian <a href="http://www.inf.u-szeged.hu/kalmar/index.php">Kalmár site</a>.) Mendelsohn's <em><a href="http://books.google.ca/books?id=ZO1p4QGspoYC&lpg=PT54&vq=kalmar&pg=PT54#v=onepage&q&f=false">Introduction to Mathematical Logic</a></em> also uses this to prove completeness of propositional logic. Here it is (slightly corrected):</p>
<p>We need the following lemma:</p>
<blockquote><p>Let $v$ be a truth-value assignment to the propositional variables in $\phi$, and let $p^v$ be $p$ if $v(p) = T$ and $\lnot p$ if $v(p) = F$. If $v$ makes $\phi$ true, then \[p_1^v, \dots, p_n^v \vdash \phi.\]</p>
</blockquote>
<p>This is proved by induction on complexity of $\phi$.</p>
<p>If $\phi$ is a tautology, then any $v$ satisfies $\phi$. If $v$ is a truth value assignment to $p_1, \dots, p_n$, let $\Gamma(v,k) = \{p_1^v, \dots, p_k^v\}$. Let's show that for all $v$ and $k = n, \dots, 0$, $\Gamma(v, k) \vdash \phi$. If $k = n$, then $\Gamma(v, n) \vdash \phi$ by the lemma and the assumption that $\phi$ is a tautology, i.e., true for all $v$. Suppose the claim holds for $k+1$. This means in particular $\Gamma(v, k) \cup \{p_{k+1}\} \vdash \phi$ and $\Gamma(v, k) \cup \{\lnot p_{k+1}\} \vdash \phi$ for any given $v$. By the deduction theorem, we get $\Gamma(v, k) \vdash p_{k+1} \to \phi$ and $\Gamma(v, k) \vdash \lnot p_{k+1} \to \phi$. By $\vdash p_{k+1} \lor \lnot p_{k+1}$ and proof by cases, we get $\Gamma(v, k) \vdash \phi$. The theorem then follows since $\Gamma(v, 0) = \emptyset$.</p>
<p>Notes:</p>
<ul><li>The inductive proof of the lemma requires as inductive hypothesis both the claim and the corresponding claim for the case where $v$ makes $\phi$ false (i.e., that then $p_1^v, \dots, p_n^v \vdash \lnot \phi$). Kalmár did not include the constants $T$ and $F$ in the language, but if you would, then Scott's (iii) would be a special case of the lemma.</li>
<li>Scott's proof does not require the deduction theorem, but does require proof of substitutability of equivalents.</li>
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</ul>Wed, 19 Nov 2014 02:05:28 +0000Richard Zach660 at http://www.ucalgary.ca/rzachhttp://www.ucalgary.ca/rzach/blog/2014/11/kalmars-compleness-proof.html#commentsDana Scott's Favorite Completeness Proof
http://www.ucalgary.ca/rzach/blog/2014/11/dana-scotts-favorite-completeness-proof.html
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"> <p>Last week I gave my decision problem talk at Berkeley. I briefly mentioned the 1917/18 <a href="http://www.ucalgary.ca/rzach/papers/bernays.html">Hilbert/Bernays completeness proof</a> for propositional logic. It (as well as Post's 1921 completeness proof) made essential use of provable equivalence of a formula with its conjunctive normal form. Dana Scott asked who first gave (something like) the following simple completeness proof for propositional logic:</p>
<blockquote><p>We want to show that a propositional formula is provable from a standard axiomatic set-up iff it is a tautology. A simple corollary will show that if it is not provable, then adding it as an axiom will make all formulae provable.<br /></p><ol style="list-style-type: upper-roman;"><li>If a formula is provable, then it is a tautology.</li>
</ol><p>Because the axioms are tautologies and the rules of inference (substitution and detachment) preserve being a tautology. The argument is by induction on the length of the proof.</p>
<ol style="list-style-type: upper-roman;"><li value="2">If a formula is not provable, then it is not a tautology.</li>
</ol><p>We need three lemmata about provable formulae. The symbols $T$ and $F$ are for true and false. We write negation here as $\lnot p$.</p>
<ol style="list-style-type: lower-roman;"><li>$\vdash p \rightarrow [\phi(p) \leftrightarrow \phi(T)]$.</li>
<li>$\vdash \lnot p \rightarrow [\phi(p) \leftrightarrow \phi(F) ]$.</li>
<li>If $\phi$ has no propositional variables, then either $\vdash \phi \leftrightarrow T$ or $\vdash \phi \leftrightarrow F$.</li>
</ol><p>All these are proved by induction on the structure of $\phi$ and require checking principles of substitutivity of equivalences. And I am claiming here this is less work than formulating and proving how to transform formulae into conjunctive normal form.</p>
<p>From (i) and (ii) it follows that: \[\vdash \phi(p) \leftrightarrow [ [ p \rightarrow \phi(T) ] \land [\lnot p \rightarrow \phi(F)] ],\] because we can show generally: \[\vdash \psi \leftrightarrow [ [ p \rightarrow \psi ] \land [ \lnot p \rightarrow \psi ] ].\] Thus, we can conclude: if $\vdash \phi(T)$ and $\vdash \phi(F)$, then $\vdash \phi(p)$. Hence if $\phi(p)$ is not provable, then one of $\phi(T)$, $\phi(F)$ is not provable.</p>
<p>So, if a formula $\phi$ has no propositional variables and is not provable, then by (iii), $\phi \leftrightarrow F$. So it is not a tautology. Arguing now by induction on the number of propositional variables in the formula, if $\phi(p)$ is not provable, then one of $\phi(T)$, $\phi(F)$ is not a tautology. And so $\phi(p)$ is not a tautology. QED</p>
</blockquote>
<p>I don't know the answer. Do you?</p>
<p>The only thing it reminded me of was <a href="http://www.ucalgary.ca/rzach/papers/eqschema.html">this old paper</a> which shows that all tautologies in $n$ variables can be proved in $f(n)$ steps using the schema of equivalence. It uses a similar idea: evaluate formulas without variables to truth values, and then inductively generate the tautologies by induction on the number of variables and excluded middle. You could turn that proof into a completeness proof by establishing for a given calculus that the required equivalences and formulas are provable. </p>
<p>Dana's proof is a lot simpler, though. Thanks to him for allowing me to post his question here.</p>
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</ul>Mon, 17 Nov 2014 00:15:06 +0000Richard Zach659 at http://www.ucalgary.ca/rzachhttp://www.ucalgary.ca/rzach/blog/2014/11/dana-scotts-favorite-completeness-proof.html#commentsLectures on the Epsilon Calculus
http://www.ucalgary.ca/rzach/blog/2014/11/lectures-on-epsilon-calculus.html
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"> <p>Back in 2009, I taught a short course on the epsilon calculus at the Vienna University of Technology. I wrote up some of the material, intending to turn them into something longer. I haven't had time to do that, but someone might find what I did helpful. So I put it up on arXiv:</p>
<p><a href="http://arxiv.org/abs/1411.3629">http://arxiv.org/abs/1411.3629</a></p>
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</ul>Fri, 14 Nov 2014 16:36:08 +0000Richard Zach658 at http://www.ucalgary.ca/rzachhttp://www.ucalgary.ca/rzach/blog/2014/11/lectures-on-epsilon-calculus.html#comments