University of Calgary

# Richard Zach's blog

## CfP: 2015 Logic Colloquium in Helsinki

Submitted by Richard Zach on Sun, 01/18/2015 - 8:25am

## Logic Colloquium 2015European Summer Meeting of the Association for Symbolic Logic

Helsinki, Finland, 3-8 August 2015
http://www.helsinki.fi/lc2015

The annual European Summer Meeting of the Association for Symbolic Logic, 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, CLMPS 2015, and with the SLS Summer School in Logic

### Plenary lectures

Toshiyasu Arai (Chiba)
Sergei Artemov (New York)
Steve Awodey (Pittsburgh)
Johan van Benthem (Amsterdam and Stanford)
Artem Chernikov (Paris)
Ilias Farah (York)
Danielle Macbeth (Haverford)
Andrei Morozov (Novosibirsk)
Kobi Peterzil (Haifa)
Ralf Schindler (Münster)
Saharon Shelah (TBC) (Jerusalem and Rutgers)
Sebastiaan Terwijn (Nijmegen)

### Tutorials

Erich Grädel (Aachen)
Menachem Magidor (Jerusalem).

### Special sessions

Set Theory, organized by Heike Mildenberger (Freiburg)

Model theory, organized by Dugald Macpherson (Leeds)

Computability Theory, organized by Russell Miller (New York) and Alexandra Soskova (Sofia)

Proof Theory, organized by Benno van den Berg (Amsterdam) and Michael Rathjen (Leeds)

Philosophy of Mathematics and Logic, organized by Patricia Blanchette (Notre Dame) and Penelope Maddy (Irvine)

Logic and Quantum Foundations, organized by Samson Abramsky (Oxford)

## Travel Awards and Contributed Talks

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.

The Logic Colloquium will include contributed talks of 20 minutes' length. Abstracts on contributed talks are published in the Bulletin of Symbolic Logic.

The deadline for travel award applications and abstract submission  is Tuesday, May 3, 2015. Please see http://www.helsinki.fi/lc2015/submission.html for information about applying for travel awards and for submitting an abstract.

## John Shepherdson, 1926-2015

Submitted by Richard Zach on Fri, 01/16/2015 - 10:36am

Sad news from Philip Welch at Bristol:  John Shepherdson has died.

I deeply regret having to impart the very sad news that John Shepherdson died in Bristol on Thursday of an inoperable sarcoma.

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.

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.

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.

Philip Welch

## Brilliance and Other Causes of Academic Gender Gaps

Submitted by Richard Zach on Fri, 01/16/2015 - 8:35am

Every mathematician and philosopher should watch this video by Sarah-Jane Leslie (Philosophy, Princeton) on her study with Andrei Cimpian (Psych, Illinois). Takes just 11 minutes.

Then you can go and read the original study in Science or any of the writeups in, e.g., the Science news blog, Chronicle, Daily Nous, etc.

## Logical Operators in the SEP

Submitted by Richard Zach on Fri, 01/09/2015 - 1:54pm

The Stanford Encyclopedia of Philosophy now has entries on:

## Ivor Grattan-Guinness, 1941-2014

Submitted by Richard Zach on Wed, 01/07/2015 - 7:02am

I learned today that Ivor Grattan-Guinness, the historian of mathematics and logic, died last month.

Obituaries:

## Nerlim: a Master Bibliography Style that Allows Books to have both Authors and Editors

Submitted by Richard Zach on Mon, 12/22/2014 - 1:09pm

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

Gödel, K., 1986. Collected Works, vol. I. S. Feferman et al., eds. Oxford: Oxford University Press.

There is a wonderful package that allows you to generate new BibTeX bibliography styles based on a large number of customization options: custom-bib.  It comes with one big master bibliography style merlin.mbs from which your custom style is generated. I've produced a modified file which will also print both author and editor for a book that has both.

Merry Christmas.

## Halbach & Visser: Self-reference in arithmetic

Submitted by Richard Zach on Sun, 12/14/2014 - 7:19am

New in the Review of Symbolic Logic (part 1, part 2)

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.

## Storify'd Michael Beaney's Vienna Circle Lecture on Susan Stebbing

Submitted by Richard Zach on Sat, 12/13/2014 - 6:19am

## More on Shatunovsky, Kagan, and Yanovskaya

Submitted by Richard Zach on Sat, 12/13/2014 - 5:51am

In response to my post about "lesser known Russian/Soviet logicians", Lev Beklemishev commented:

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.

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.

A good informative article on Shatunovsky is his obituary written by Chebotarev and published, I think, in Uspekhi matematicheskih nauk [link].

By email, Mark van Atten wrote:

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 The Selected Correspondence of L.E.J. Brouwer (ed. Van Dalen, Springer 2011), pp. 290-291. 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.

The date as given by Van Dalen there is 1925. The online-edition of the correspondence at extras.springer.com, 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.

That online edition also includes a short second letter from Kagan, dated Feburay 8, 1925 (on Alexandrov and Urysohn, but without specifically scientific content).

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.'

Alas, the online edition contains no mention of Schönfinkel.

Lev responded:

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.

By the way, Kagan was the grandfather of Yakov Sinai, 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...

Mark responded to Lev's question:

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?

The interview Lev mentioned is on youtube. 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.

## Some Lesser Known (to me) Russian/Soviet Logicians

Submitted by Richard Zach on Tue, 12/09/2014 - 8:42am

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:

Samuil Osipovich Shatunovsky (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."

Ivan Vladislavovich Sleshinsky (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 The algebra of logic into Russian.

Platon Sergeevich Poretsky (1846-1907) worked on Boolean algebraic logic, teaching in Kazan. He's credited with being the first mathematician to teach logic in Russia.

Kahan was a little harder to track down, but apparently Kahan is an alternative transcription of Ка́ган:

Veniamin Fedorovich Kagan (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, Yekaterinoslav (now Dnipropetrovsk).

In the process of googling about I also happened on Sofya Aleksandrovna Yanovskaya (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 webpage of the institute have A. A. Markov as the first chair, 1959-1979.  From this biography, in addition to her teaching and research in mathematics, she was influential in other interesting ways:

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 La Géométrie, 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.

A special issue of Modern Logic 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 here.

UPDATE: Follow-up here.

## Graduate Programs in Philosophical Logic

Submitted by Richard Zach on Mon, 12/08/2014 - 7:29am

Shawn Standefer has done us all a great service by starting and populating a Wiki of PhD programs in Philosophical Logic!

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 PhilBio.net wiki.

## One person's modus ponens...

Submitted by Richard Zach on Sat, 12/06/2014 - 11:06am

...is another's modus tollens.

[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.

Julia Robinson, in: Constance Reid, The Autobiography of Julia Robinson. The College Mathematics Journal, Vol. 17, No. 1, (1986), pp. 3-21

Submitted by Richard Zach on Sat, 12/06/2014 - 9:25am

Jan Zygmunt and Robert Purdy have a paper ("Adolf Lindenbaum: Notes on his Life, with Bibliography and Selected References", open access) in the latest issue of Logica Universalis 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.

The entire issue is dedicated to Lindenbaum. Jean-Yves Beziau gives this poignant quote in the introduction:

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 tout court of a problem. He always wants to have the most ??? solutions. Most what? The easiest, the shortest, the most general, etc.
Lindenbaum was murdered by the Nazis in 1941, at age 37.

## Kennedy's Interpreting Gödel Out Now

Submitted by Richard Zach on Tue, 12/02/2014 - 7:56am

Interpreting Gödel: Critical Essays, edited by Juliette Kennedy, was just published by Cambridge. It looks extremely interesting, with an all-star cast of contributors:

1. Introduction: Gödel and analytic philosophy: how did we get here? Juliette Kennedy
Part I. Gödel on Intuition:
2. Intuitions of three kinds in Gödel's views on the continuum, John Burgess
3. Gödel on how to have your mathematics and know it too, Janet Folina
Part II. The Completeness Theorem:
4. Completeness and the ends of axiomatization, Michael Detlefsen
5. Logical completeness, form, and content: an archaeology, Curtis Franks
Part III. Computability and Analyticity:
6. Gödel's 1946 Princeton bicentennial lecture: an appreciation, Juliette Kennedy
7. Analyticity for realists, Charles Parsons
Part IV. The Set-theoretic Multiverse:
8. Gödel's program, John Steel
9. Multiverse set theory and absolutely undecidable propositions, Jouko Väänänen
Part V. The Legacy:
10. Undecidable problems: a sampler, Bjorn Poonen
11. Reflecting on logical dreams, Saharon Shelah.

## Two New(ish) Surveys on Gödel's Incompleteness Theorems

Submitted by Richard Zach on Fri, 11/28/2014 - 10:49am

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.

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 Lev Beklemishev:

Л.Д. Беклемишев (2010). Теоремы Гёделя о неполноте и границы их применимости. I., Успехи Математических Наук 65(5) 61-104. PDF.

English translation:

L. D. Beklemishev (2010). Gödel incompleteness theorems and the limits of their applicability. I., Russian Mathematical Surveys 65(5) 857-898. PDF

The second is by Bernd Buldt:

B. Buldt (2014). The scope of Gödel’s first incompleteness theorem, Logica Universalis. forthcoming. PDF preprint

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.

## Possible Postdoc on Genesis of Mathematical Knowledge

Submitted by Richard Zach on Fri, 11/28/2014 - 8:52am
Via the APMP list:
Expressions of interest are invited for a postdoc grant (financed by Junta de Andalucia) associated with the following research project:
“THE GENESIS OF MATHEMATICAL KNOWLEDGE: COGNITION, HISTORY, PRACTICES” (P12-HUM-1216). IP: Jose Ferreiros
Contact: josef@us.es
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 before start of the grant,  [update:] by 2014 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.
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.

## Kalmár's Compleness Proof

Submitted by Richard Zach on Tue, 11/18/2014 - 7:05pm

Dana Scott's proof reminded commenter "fbou" of Kalmár's 1935 completeness proof. (Original paper in German on the Hungarian Kalmár site.) Mendelsohn's Introduction to Mathematical Logic also uses this to prove completeness of propositional logic. Here it is (slightly corrected):

We need the following lemma:

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 $p_1^v, \dots, p_n^v \vdash \phi.$

This is proved by induction on complexity of $\phi$.

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 $\Gamma(v, 0) = \emptyset$.

Notes:

• 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.
• Scott's proof does not require the deduction theorem, but does require proof of substitutability of equivalents.

## Dana Scott's Favorite Completeness Proof

Submitted by Richard Zach on Sun, 11/16/2014 - 5:15pm

Last week I gave my decision problem talk at Berkeley. I briefly mentioned the 1917/18 Hilbert/Bernays completeness proof 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:

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.

1. If a formula is provable, then it is a tautology.

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.

1. If a formula is not provable, then it is not a tautology.

We need three lemmata about provable formulae. The symbols $T$ and $F$ are for true and false. We write negation here as $\lnot p$.

1. $\vdash p \rightarrow [\phi(p) \leftrightarrow \phi(T)]$.
2. $\vdash \lnot p \rightarrow [\phi(p) \leftrightarrow \phi(F) ]$.
3. If $\phi$ has no propositional variables, then either $\vdash \phi \leftrightarrow T$ or $\vdash \phi \leftrightarrow F$.

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.

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.

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

I don't know the answer. Do you?

The only thing it reminded me of was this old paper 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.

Dana's proof is a lot simpler, though. Thanks to him for allowing me to post his question here.

## Lectures on the Epsilon Calculus

Submitted by Richard Zach on Fri, 11/14/2014 - 9:36am

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:

http://arxiv.org/abs/1411.3629

## The Real Reasons Why Philosophers Shouldn't Use LaTeX

Submitted by Richard Zach on Wed, 10/29/2014 - 10:29am

Josh Parsons (Oxford) has written a widely discussed post on "The LaTeX cargo cult," explaining why he discourages philosophy students from using LaTeX.  He makes some interesting points.  But what he has left out is the overarching principle that you should simply always use the best tool for the purpose at hand - and "best" should take into account lots of things: cost (in money and time you need to invest to become proficient in the use of the tool), ease of use, functionality, and the needs of the prospective audience.

For a long time, LaTeX had the upper hand over available alternatives (i.e., Microsoft Word).  It produced high quality output (Word didn't), it was free (Word wasn't), it could do lots of things Word couldn't do (like bibliographies), it was an open format (Word wasn't).  Well, times have changed. There are more alternatives, and the alternatives now can do lots of things they didn't use to be able to. The latest Word document format is open, and based on open standards like XML. There are free, open source alternatives to Microsoft, such as LibreOffice. The alternatives have gotten better at typesetting, and you can now do most of the things in which LaTeX had the upper hand for a long time, e.g., bibliographies and reference management, through plug ins and add-ons (both non-free like Endnote, and free, open, cross-platform like Zotero or JabRef).

So while at one point "well, I use bibliographies and references a lot, and I want to have a nice-looking hardcopy" were sufficient reason to use LaTeX and spurn Word, that's no longer the case.

Given this fact, other considerations should probably play a more important role now when deciding whether to learn LaTeX and when to use it.

• LaTeX still has a steep learning curve and you can run into complex issues (and simple issues that are hard to solve).  If you have limited amounts of time - say if you're a grad student writing a dissertation - then becoming proficient at and writing everything in LaTeX will probably be a distraction.
• LaTeX on its own is very bad at revision control and commenting, but Word and LibreOffice are very good at it.  If your piece of writing requires others to read, comment on, and make revisions to it - say, if you're a grad student writing a dissertation with an advisor who doesn't use LaTeX and would like to easily comment on your drafts - then don't use LaTeX. (The same goes for writing any kind of administrative document that anyone else in your institution has to open, comment on, reformat, reuse, or revise!)
• LaTeX is very good at producing print-based output, but pretty bad at producing output that can easily be reused in other formats - say, on a web page or in a form - so if you need to use your piece of writing in settings where formatted or unformatted text is needed - say, if you're a grad student preparing funding applications via web-based forms - think twice about using LaTeX.
• LaTeX is very good at making your writing conform to a given format (e.g., a thesis or journal layout), but it can be very time consuming to make LaTeX output conform to a format for which no class or style package exists.  So if there's an Word (or PowerPoint or whatever) template for what you need but no LaTeX style file - then it'll probably be easier to just use that.  (E.g., I wouldn't dream of writing letters of recommendation in LaTeX given that there's an institutional letterhead template.)

Of course all this doesn't mean that you should never use LaTeX, and I think it also doesn't mean that we should discourage students from learning (about) it.  In fact, I think it would be a mistake to do so. There are lots of scenarios in which LaTeX is the best option.  And there are good reasons grad students should at least have a passing familiarity with LaTeX.

• Do you work in a (sub)field where LaTeX use is prevalent (logic, physics, math)? Then you should probably learn and use LaTeX. (Parsons acknowledges this! But even if all you do is TA intro to formal logic once, learning and using LaTeX can pay off immensely!)
• Does the thing you're writing need any of the powerful features that LaTeX has but, say, LibreOffice doesn't?  Use LaTeX.
• Does your advisor use LaTeX and invite you to co-author a paper with her? Learn LaTeX.

There are other reasons to use LaTeX. There are other reasons to not use LaTeX (and scenarios where other tools are better).  But don't not use or learn LaTeX because it's a cargo cult - it isn't - or because it's a proprietary format - it isn't - or because it's not a "declarative language."  It's a powerful tool that's useful in certain contexts. If you find yourself in such a context, learn it, and use it. And given that it is relatively widely used, at least learn what it is so you can make an informed decision. And perhaps encourage your students to do so, too.