Why Scanlon Left Logic for Political Philosophy

T. M. Scanlon is one of the foremost moral and political philosophers alive. But he started as a logician, working with Benacerraf as an undergraduate at Princeton, Dummett during a Fulbright at Oxford, and Dreben for his Ph.D. at Harvard. His first two papers were:

Here’s why he didn’t stay a logician:

So I came [to Harvard], and I was still interested in logic, so I wrote a thesis in logic with Burt Dreben. […] And then I left after three years and started teaching in Princeton. Then, gradually, I kind of shifted over into moral and political philosophy, although I published a few things in logic. Because I enjoyed the techniques, I was good enough to learn them pretty quickly, but I didn’t have any originality. I didn’t have much instinct about what was the next thing to try to prove.

Pen Maddy: Is Math Mysterious?

They ask, “Is there something mysterious about mathematics?” Among others, Pen Maddy answers. http://ideas.aeon.co/questions/is-there-something-mysterious-about-math

Eight Logicians Elected to the American Academy

The American Academy of Arts & of Sciences has announced its 2015 class of members.  The recipients of this prestigious honor include eight logicians:

  • Sanjeev Arora (Computer Science, Princeton University) works in complexity theory, and is especially known for his work on probabilistically checkable proofs. He previously won the Gödel Prize for his work on interactive proof systems.
  • László Babai (Computer Science, University of Chicago) works in computational complexity theory, graph theory, and combinatorics. He previously won the Gödel Prize for his work on interactive proof systems.
  • Joseph Y. Halpern (Computer Science, Cornell University) works on knowledge representation, epistemic and temporal modal logic, and reasoning under uncertainty. He previously won the Gödel Prize (I sense a pattern!) for his work on reasoning about distributed systems.
  • Hans Kamp (Linguistics, Universität Stuttgart) has made seminal contributions to formal semantics and modal logic. He previously won the Prix Jean Nicod.
  • John MacFarlane (Philosophy, University of California, Berkeley) works on the philosophy of logic and language.  He also wrote pandoc.
  • Tim Maudlin (Philosophy, NYU) is a philosopher of science and logic; in logic specifically, he has worked on truth and paradox.
  • Joseph Sifakis (École Polytechnique Fédérale de Lausanne and CNRS) works in formal verification and model checking. He was previously awarded the Turing Award.
  • Johan van Benthem (ILLC, Universiteit van Amsterdam and Philosophy Stanford University) is a pure and applied logic all-star, working mainly on modal logic and logic & language. In addition to a number of other honours, he was knighted in 2014.

Anita Burdman Feferman, 1927-2015

Anita Burdman Feferman, the noted biographer of Jean van Heijenoort and Alfred Tarski, died on April 9.  She was the author of Politics, Logic, and Love: The Life of Jean van Heijenoort (Jones and Bartlett, 1993, reprinted as From Trotsky to Gödel, CRC Press, 200) and the co-author of Alfred Tarski: Life and Logic (CUP, 2004).  Both are wonderful books that portray the mathematical work as well as the human side of their subjects in careful and exciting but also tactful ways.  They are meticulously researched and true scholarly achievements. Van Heijenoort and Tarski led interesting lives in turbulent times; when Anita told their stories, you couldn’t help but be engrossed.  She was a wonderfully open and warm person; and conversations with her were just as engaging as her books are.  She will be missed.

Finding Cheryl’s Birthday with DEMO

Following up on the Dynamic Epistemic Logic treatment of Cheryl’s Birthday Puzzle, Malvin Gattinger (ILLC Amsterdam) has formalized the problem in DEMO_S5, a Dynamic Epistemic Logic model checker written in Haskell by Jan van Eijck (CWI Amsterdam and ILLC). The original DEMO system was described in:

Jan van Eijck: “DEMO—a demo of epistemic modelling” In: Johan van Benthem, Dov Gabbay, and Benedikt Löwe, eds., Interactive Logic. Selected Papers from the 7th Augustus de Morgan Workshop, London. Vol. 1. Amsterdam University Press, 2007.

Go to Malvin’s page to download the source and documentation. Malvin’s original post follows, used under a Creative Commons Attribution 3.0 Unported license.

This report shows how to solve the famous riddle from Singapore (see NYTimes or SASMO on facebook) with dynamic epistemic logic and model checking in Haskell.

You can read it below or download the PDF or download the source files.

We use DEMO_S5 and a modified version of KRIPKEVIS.

module CHERYL where
import Data.List
import Data.Function
import DEMO_S5
import KRIPKEVIS

We first define the set of all possibilities:

allpos :: [(Int, String)]
allpos = [ (15,"May"), (16,"May"), (19,"May"), (17,"June"), (18,"June"),
  (14,"July"), (16,"July"), (14,"August"), (15,"August"), (17,"August") ]

This forms the set of worlds in our initial model. Moreover, also the set of actual worlds is the full set, hence allpos occurs twice in the definition below. The two elements of rels define the epistemic relations of Albert and Bernard. Instead of listing explicitly which possibilities they can distinguish we use haskell functions to say that they confuse the same day and the same month, respectively.

initCheryl :: EpistM (Int,String)
initCheryl = Mo allpos [a,b] [] rels allpos where
  rels = [ ( a, groupBy ((==) `on` snd) allpos ), ( b, groupBy ((==) `on` fst) (sortBy (compare `on` fst) allpos) ) ]

This is the initial model with all possibilities:

The formula saying that i knows Cheryl’s birthday is defined as the disjunction over all statements of the form “Agent i knows that the birthday is s”:

knWhich :: Agent -> Form (Int, [Char])
knWhich i = Disj [ Kn i (Info s) | s <- allpos ]

Now we update the model three times, using the function upd_pa for public announcements.

First with Albert: I don’t know when Cheryl’s birthday is and I know that Bernard does not know.

model2 = upd_pa initCheryl (Conj [Ng $ knWhich a, Kn a $ Ng (knWhich b)])

The second announcement by Bernard: “Now I know when Cheryl’s birthday is.”

model3 = upd_pa model2 (knWhich b)

Finally, Albert says: “Now I also know when Cheryl’s birthday is.”

model4 = upd_pa model3 (knWhich a)

Lastly, this helper function uses texModel from our modified KRIPKEVIS module to generate the drawings:

myTexModel :: EpistM (Int,String) -> String -> IO String
myTexModel (Mo states _ _ rels pointed) fn =
  texModel showState showAg showVal "" (VisModel states rels [(s,0)|s<-states] pointed) fn
  where
    showState (n,string) = (show n) ++ string
    showVal _ = ""
    showAg i = if i==a then "Albert" else "Bernard"

Mancosu on Frege and Direction

Remember the part in Frege’s Grundlagen where he starts to talk about abstraction by talking about the direction of lines?  Two lines have the same direction if and only if they are parallel; this gives an identity criterion for directions of lines.  Ever wondered why Frege starts bringing in geometry? What the historical context and possible influences were?

Paolo Mancosu has you covered:

I offer in this paper a contextual analysis of Frege’s Grundlagen, section 64. It is surprising that with so much ink spilled on that section, the sources of Frege’s discussion of definitions by abstraction have remained elusive. I hope to have filled this gap by providing textual evidence coming from, among other sources, Grassmann, Schlömilch, and the tradition of textbooks in geometry for secondary schools (including a textbook Frege had used when teaching in a Privatschule in Jena in 1882–1884). In addition, I put Frege’s considerations in the context of a widespread debate in Germany on ‘directions’ as a central notion in the theory of parallels.

Grundlagen, Section 64: Frege’s Discussion of Definitions by Abstraction in Historical Context, History and Philosophy of Logic 36 (1), 2015

Ask Your Librarian to Subscribe to PhilPapers!

PhilPapers now has almost 1.75 million entries.  Like the Stanford Encyclopedia, the project is non-profit and largely run by volunteers.  In order to be sustainable, they do need funding.  And like the Stanford Encyclopedia, they are asking for our help: so ask your library to subscribe!

The merger of Philosophy Research Index into PhilPapers has now been completed. More than half a million items have been added to the PhilPapers index, greatly improving our coverage of older publications and print publications not available online. At 1.75M items, our index is now three times the size of the nearest commercial alternative. We thank our colleagues at the Philosophy Documentation Center for their ceaseless efforts to collect relevant data.

We have also implemented new automatic classification mechanisms. Approximately 2/3 of all index entries (1.1M) now have some classification information associated with them. About half of the new entries from PRI have been automatically categorized. These results are now going through a process of manual curation by subject editors, to double-check categorization choices and more finely assign subject descriptors to published works.

The categorization of all listings in this growing database remains a work in progress. But with over one million categorized entries and 5000 bibliographies already included, PhilPapers is easily the largest bibliography of philosophical works ever created. We are grateful for the impressive work done by our 600 subject editors.

PhilPapers is more complete, more accessible, and less expensive than any commercial alternative. But we have significant costs to cover, and we need to be realistic about finances to sustain access for everyone. Our subscription program for large institutional users is progressing well. Among the institutions with the heaviest use of PhilPapers, more than half have subscribed. We much appreciate this strong support and encourage all large institutional users to participate in like manner. This will ensure the budget we need to cover costs, with maximum access and improving functionality.

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Good job, and thank you, PhilPapers and especially David Bourget and Dave Chalmers!

Logicians Yap, Kooi Explain Viral Birthday Logic Puzzle

You’ve probably seen the “birthday logic puzzle” that’s gone viral in the past few days. If you haven’t, you might want to try to solve it yourself. Here it is:

be00992c-012d-4216-9e7a-2751a79c75c4-620x372

Two dynamic epistemic logicians, Audrey Yap (UVic) and Barteld Kooi (Groningen) explained the solution (and how to get it) on facebook.  “Dynamic” here modifies “epistemic”, not “logicians:”  there is something called “dynamic epistemic logic” which is used here.  FWIW, I know that Audrey at least is very dynamic.

Audrey’s solution, posted with her kind permission:

These are all the possibilities at the start. The red lines represent Albert’s uncertainty, and the blue lines represent Bernard’s uncertainty. So there’s a red line between May 15 and May 16 because Albert would only know it’s May and not what date. And there’s a blue line between May 15 and Aug 15 because Bernard would only know it’s the 15th and not what month.

initialuncert
​Then the first important piece of information is that Albert knows that Bernard doesn’t know the date. This eliminates a lot of dates, because if Albert is certain that Bernard doesn’t know the date, we can’t be in a month where Bernard might know the date. That effectively eliminates May and June, because in both of those months, there’s a possibility Bernard could already know the date.

first
​And then the next interesting thing we learn is that, after learning that piece of information, Bernard does know the date. So here’s what it looks like with May and June eliminated and how we figure out what to do with that information. Since Bernard now knows the date, it can’t be the 14th, since then he still wouldn’t know.

second
​Then last, when we see that Albert actually learned the date from hearing the fact that Bernard does, know there’s only one date it could possibly be. So here’s what it looks like when we eliminate the 14th as a possibility.

third

Barteld Kooi’s video explanation is here on facebook and also on YouTube:

Logic without Borders: Essays in Honor of Jouko Väänänen

A Festschrift for Jouko Väänänen‘s 60th birthday is now out with de Gruyter, edited by Åsa Hirvonen, Juha Kontinen, Roman Kossak, and Andrés Villaveces:

In recent years, mathematical logic has developed in many directions, the initial unity of its subject matter giving way to a myriad of seemingly unrelated areas. The articles collected here, which range from historical scholarship to recent research in geometric model theory, squarely address this development. These articles also connect to the diverse work of Väänänen, whose ecumenical approach to logic reflects the unity of the discipline.

It’s expensive, but the table of contents features an all-star cast:

  1. Juliette Kennedy, On the “Logic without Borders” Point of View
  2. Samson Abramsky, Arrow’s Theorem by Arrow Theory
  3. John T. Baldwin, How Big Should the Monster Model Be?
  4. John P. Burgess, Modal Logic in the Modal Sense of Modality
  5. Xavier Caicedo, Lindström’s Theorem for Positive Logics, a Topological View
  6. Zoé Chatzidakis, Model Theory of Fields With Operators – a Survey
  7. Carlos Augusto Di Prisco, Some Aspects of the Ramsey Theory of Real Numbers
  8. Mirna Džamonja, The Singular World of Singular Cardinals
  9. Curtis Franks, Logical Nihilism
  10. Pietro Galliani, The Doxastic Interpretation of Team Semantics
  11. Lauri Hella and Jouko Väänänen, The Size of a Formula as a Measure of Complexity
  12. Wilfrid Hodges, Notes on the History of Scope<
  13. Jan Hubička and Jaroslav Nešetřil, Universal Structures with Forbidden Homomorphisms
  14. Tapani Hyttinen, Counting Measure and Forking in Finite Models
  15. Richard Kaye and Tin Lok Wong, The Model Theory of Generic Cuts
  16. Juha Kontinen, On Natural Deduction in Dependence Logic
  17. Steven Lindell, Henry Towsner, and Scott Weinstein, Infinitary Methods in Finite Model Theory
  18. Maryanthe Malliaris and Saharon Shelah, Saturating the Random Graph with an Independent Family of Small Range
  19. Ilkka Niiniluoto, Constructive Realism in Mathematics
  20. Jeff B. Paris and Alena Vencovská, The Twin Continua of Inductive Methods
  21. Saharon Shelah, A.E.C. with Not Too Many Models
  22. ouko Väänänen, Pursuing Logic without Borders/li>
  23. A Radio Interview with Jouko Väänänen