Edward T. Dean Ph.D. student, Pure and Applied Logic, Carnegie Mellon University Advisors: Jeremy Avigad and James Cummings 5000 Forbes Ave. Baker Hall 135 Pittsburgh, PA 15213 e(my_last_name) AT andrew.cmu.edu A group blog: unwanted capture

Background

• Born in Birmingham, AL, USA.
  
  
• B.A. Philosophy and Mathematics, Harvard University.
  Thesis Advisor: Peter Koellner
  Committee: Warren Goldfarb and Gerald Sacks
  
  
• M.S. Logic, Computation and Methodology, Carnegie Mellon University.
  Thesis Advisor: Jeremy Avigad
  Committee: Wilfried Sieg
  
  
• M.S. Mathematics, Carnegie Mellon University.

Publications and Preprints

• Dedekind's treatment of Galois theory in the Vorlesungen
  DRAFT.
  

  We present a translation of a portion of Dedekind's Supplement XI to Dirichlet's Vorlesungen über Zahlentheorie which contains an investigation of the subfields of the complex numbers. In particular, Dedekind explores the lattice structure of these subfields, by studying isomorphisms between them. He also indicates how his ideas apply to Galois theory.

  After a brief introduction, we summarize the translated excerpt, emphasizing its Galois-theoretic highlights. We then take issue with Kiernan's characterization of Dedekind's work in his extensive survey article on the history of Galois theory; Dedekind has a nearly complete realization of the modern "fundamental theorem of Galois theory" (for subfields of the complex numbers), in stark contrast to the picture presented by Kiernan.

  We intend a sequel to this article of an historical and philosophical nature. With that in mind, we have sought to make Dedekind's text accessible to as wide an audience as possible. Thus we include a fair amount of background and exposition.

  @techreport{dean:dedekind_09,
    title = "{D}edekind's treatment of {G}alois theory in the \emph{{V}orlesungen}",
    author = "Edward T. Dean",
    institution = "Carnegie Mellon University",
    year = "2009"
  }
  		

  [abstract] [pdf] [original]
  
  
  
• A formal system for Euclid's Elements
  with J. Avigad and J. Mumma, to appear in Review of Symbolic Logic.
  

  We present a formal system, E, which provides a faithful model of the proofs in Euclid's Elements, including the use of diagrammatic reasoning.

  @article{ADM:euclid09,
    title = "A formal system for {E}uclid's \emph{{E}lements}",
    author = "Jeremy Avigad and Edward Dean and John Mumma",
    journal = "Review of Symbolic Logic",
    year = "2009"
  }
  		

  [abstract] [bib] [arXiv]
  
  
  
• On the dependence of the properties of space upon those of time
  translation, to appear in Collected Works of Rudolf Carnap, Vol. I.
  

  @incollection{carnap:1925a,
    title = "On the Dependence of the Properties of Space upon Those of Time",
    author = "Rudolf Carnap",
    booktitle = "Collected Works of Rudolf Carnap",
    volume = "I",
    publisher = "Open Court",
    editor = "A. W. Carus and Michael Friedman and Wolfgang Kienzler and Sven Schlotter",
    year = "2009",
    pages = "?--?",
    note = "Translated by Edward T. Dean"
  }
  		

  [bib] [Open Court]
  
  
  
• Physical concept formation
  translation (with A. W. Richardson), to appear in Collected Works of Rudolf Carnap, Vol. I.
  

  @incollection{carnap:1926a,
    title = "Physical Concept Formation",
    author = "Rudolf Carnap",
    booktitle = "Collected Works of Rudolf Carnap",
    volume = "I",
    publisher = "Open Court",
    editor = "A. W. Carus and Michael Friedman and Wolfgang Kienzler and Sven Schlotter",
    year = "2009",
    pages = "?--?",
    note = "Translated by Edward T. Dean and Alan W. Richardson"
  }
  		

  [bib] [Open Court]
  
  
  

Miscellania

Items that are unintended for publication, but which might have value to some.

• Pathak's "computational" Lebesgue differentiation theorem in context
  

  These are working notes on placing Pathak's computability-flavored version of the Lebesgue differentiation theorem into the framework developed by Hoyrup and Rojas for working with algorithmic randomness in "computable metric spaces."

  [abstract] [pdf]
  
  
  

Teaching

• 80-210: Logic and Proofs, Summer 2008
• 80-210: Logic and Proofs, Fall 2007
• 80-210: Logic and Proofs, Summer 2007
• Summer School in Logic and Formal Epistemology, 2006.
• 80-100: What Philosophy Is (TA), Spring 2006

Invited Talks

• In Defense of Euclidean Proof
  Mathematical Logic Seminar, CMU, April 2008.
  
  
• Neighborhood semantics for modal logic
  GSCL 7, University of Wisconsin, April 2006.