Postdoc position in Logic at Utrecht University, the Netherlands. The postdoc is embedded in the research project “Optimal Proofs” funded by the Netherlands Organization for Scientific Research led by Dr. Rosalie Iemhoff, Department of Philosophy and Religious Studies, Utrecht University. The project in mathematical and philosophical logic is concerned with formalization in general and proof … Continue reading PhD, Postdoc with Rosalie Iemhoff
Author: rzach
Proof by legerdemain
Peli Grietzer shared a blog post by David Auerbach on Twitter yesterday containing the following lovely quote about Smullyan and Carnap: I particularly delighted in playing tricks on the philosopher Rudolf Carnap; he was the perfect audience! (Most scientists and mathematicians are; they are so honest themselves 'that they have great difficulty in seeing through … Continue reading Proof by legerdemain
Rumfitt on truth-grounds, negation, and vagueness
Zach, Richard. 2018. “Rumfitt on Truth-Grounds, Negation, and Vagueness.” Philosophical Studies 175 (8): 2079–89. https://doi.org/10.1007/s11098-018-1114-7. In The Boundary Stones of Thought (2015), Rumfitt defends classical logic against challenges from intuitionistic mathematics and vagueness, using a semantics of pre-topologies on possibilities, and a topological semantics on predicates, respectively. These semantics are suggestive but the characterizations of … Continue reading Rumfitt on truth-grounds, negation, and vagueness
Why φ?
Yesterday, @gravbeast asked on Twitter, Does anyone know why we traditionally use Greek phi and psi for metasyntactic variables representing arbitrary logic formulas? Is it just because 'formula' begins with an 'f' sound? And chi was being used for other things? Although Whitehead and Russell already used φ and ψ for propositional functions, the convention … Continue reading Why φ?
Postdoc in Formalism, Formalization, Intuition and Understanding in Mathematics
Archives Poincaré (Nancy) and IHPST Paris are advertising for a 20-month postdoc fellowship.
Logic Colloquium, Udine
The European Summer Meeting of the Association of Symbolic Logic will be in Udine, just north of Venice, July 23-28. Abstracts for contributed talks are due on April 27. Student members of the ASL are eligible for travel grants! lc18.uniud.it
The Significance of Philosophy to Mathematics
If you wanted to explain how philosophy has been important to mathematics, and why it can and should continue to be, it would be hard to do it better than Jeremy Avigad. In this beautiful plea for a mathematically relevant philosophy of mathematics disguised as a book review he writes: Throughout the centuries, there has … Continue reading The Significance of Philosophy to Mathematics
Ptolemaic Astronomy
Working on the chapters on counterfactual conditionals for the Open Logic Project, I needed some illustrations for David Lewis's sphere models, which he jokingly called "Ptolemaic astronomy." Since Franz Berto joked that this should just require \usepackage{ptolemaicastronomy}, I wrote some LaTeX macros to make this easier using TikZ. You can download ptolemaicastronomy.sty (it should work … Continue reading Ptolemaic Astronomy
A New University of Calgary LaTeX Thesis Class based on Memoir
The University of Calgary provides a LaTeX thesis class on its website. That class is based on the original thesis class, modified over the years to keep up with changes to the thesis guidelines of the Faculty of Graduate studies. It produces atrocious results. Chapter headings are not aligned properly. Margins are set to 1 … Continue reading A New University of Calgary LaTeX Thesis Class based on Memoir
Modal Logic! Propositional Logic! Tableaux!
content/normal-modal-logic
and cover relational models for normal modal logics, frame correspondence, derivations, canonical models, and filtrations. So that’s one big exciting addition.
Since the OLP didn’t cover propositional logic separately, I just now added that part as well so I can include it as review chapters. There’s a short chapter on truth-value semantics in propositional-logic/syntax-and-semantics
. However, all the proof systems and completeness for them are covered as well. I didn’t write anything new for those, but rather made the respective sections for first-order logic flexible. OLP now has an FOL
“tag”: if FOL
is set to true, and you compile the chapter on the sequent calculus, say, you get the full first-order version with soundness proved relative to first-order structures. If FOL
is set to false, the rules for the quantifiers and identity are omitted, and soundness is proved relative to propositional valuations. The same goes for the completeness theorem: with FOL
set to false, it leaves out the Henkin construction and constructs a valuation from a complete consistent set rather than a term model from a saturated complete consistent set. This works fine if you need only one or the other; if you want both, you’ll currently get a lot of repetition. I hope to add code so that you can first compile without FOL
then with, and the second pass will refer to the text produced by the first pass rather than do everything from scratch. You can compare the two versions in the complete PDF.
Proofs systems for modal logics are tricky; and many systems don’t have nice, say, natural deduction systems. The tableau method, however, works very nicely and uniformly. The OLP didn’t have a chapter on tableaux, so this motivated me to add that as well. Tableaux are also often covered in intro logic courses (often called “truth trees”), so having them as a proof system included has the added advantage of tying in better with introductory logic material. I opted for prefixed tableaux (true and false are explicitly labelled, rather than implicit in negated and unnegated formulas), since that lends itself more easily to a comparison with the sequent calculus, but also because it extends directly to many-valued logics. The material on tableaux lives in first-order-logic/tableaux
.
Thanks to Clea Rees for the the prooftrees
package, which made it much easier to typeset the tableaux, and to Alex Kocurek for his tips on doing modal diagrams in Tikz. Making an Accessible Open Logic Textbook (for Dyslexics)
- larger type size
- shorter lines
- increased line spacing
- increased character spacing, i.e., “tracking” (although see Bigelow’s post for conflicting evidence)
- avoid ALL CAPS and italics
- avoid word hyphenation and right justified margins
- avoid centered text
ISSOTL 2017 Presentation of Student-Oriented Logic Course
Logic Courseware?
Kit Fine asked me for suggestions of online logic materials that have some interactive component, i.e., ways for students to build truth-tables, evaluate arguments, translate sentences, build models, and do derivations; ideally it would not just provide feedback to the student but also grade problems and tests. There is of course Barwise & Etchemendy's Language, … Continue reading Logic Courseware?
Graphing Survey Responses
As I reported last year, we've been running surveys in our classes that use open logic textbooks. We now have another year of data, and I've figured out R well enough to plot the results. Perhaps someone else is in a similar situation, so I've written down all the steps. Results aren't perfect yet. All the … Continue reading Graphing Survey Responses
Citations in your CV
I drank the Koolaid and set up my CV so it's generated automatically from a YAML file with a Pandoc template. The basic functionality is copied from bmschmidt/CV-pandoc-healy. My version generates the bibliography from a BibTeX file however, using biblatex. The biblatex code is tweaked to include links to PhilPapers and Google Scholar citation counts. … Continue reading Citations in your CV
Illuminated Manuscript of Aristotle, Averroes, and Ramon Llull Charging the Tower of Falsehood
Jonathan Greig (LMU Munich) posted the picture above to Twitter the other day, crediting Laura Castelli with finding it. It's from a 14th Century illuminated manuscript by Thomas Le Myésier, Breviculum ex artibus Raimundi Lulli electum, and depicts Aristotle, Averroes, and Ramon Llull leading an army charging the Tower of Falsehood. I put a full … Continue reading Illuminated Manuscript of Aristotle, Averroes, and Ramon Llull Charging the Tower of Falsehood
New in Print: forall x (Summer 2017 edition), and Incompleteness and Computability
Links to Amazon: US UK Canada Germany
The print version of Incompleteness and Computability incorporates a number of corrections and improvements suggested by my Logic III students. Compared to the version announced earlier, it also includes the two new chapters on Models of Arithmetic and on Second-order Logic. It, too, is still available free in both PDF and source code.Aldo Antonelli’s last paper
Aldo Antonelli's last paper, "Completeness and Decidability of General First-Order Logic (with a Detour Through the Guarded Fragment)" is now out in the most recent issue of the Journal of Philosophical Logic. This paper investigates the “general” semantics for first-order logic introduced to Antonelli (Review of Symbolic Logic 6(4), 637–58, 2013): a sound and complete … Continue reading Aldo Antonelli’s last paper
Association for Symbolic Logic at the Pacific APA
The ASL Spring Meeting will take place on Wednesday and Thursday at the Pacific APA in Seattle! Note that the ASL Reception will take place on Thursday, April 13, 5:00–7:00 p.m. There will be snacks and wine! Here's the program: WEDNESDAY MORNING, APRIL 12, 9:00 A.M.–12:00 P.M. Invited Speaker Session: MODALITY AND MODAL LOGIC Chair: … Continue reading Association for Symbolic Logic at the Pacific APA
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.