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

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
    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

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