5 found
Order:
Disambiguations
Nathaniel Miller [4]Nathaniel S. Miller [1]
  1.  4
    Euclid and His Twentieth Century Rivals: Diagrams in the Logic of Euclidean Geometry.Nathaniel Miller - 2007 - Center for the Study of Language and Inf.
    Twentieth-century developments in logic and mathematics have led many people to view Euclid’s proofs as inherently informal, especially due to the use of diagrams in proofs. In _Euclid and His Twentieth-Century Rivals_, Nathaniel Miller discusses the history of diagrams in Euclidean Geometry, develops a formal system for working with them, and concludes that they can indeed be used rigorously. Miller also introduces a diagrammatic computer proof system, based on this formal system. This volume will be of interest to mathematicians, computer (...)
    Direct download  
     
    Export citation  
     
    Bookmark   16 citations  
  2.  18
    The Time of Our Lives: Life Span Development of Timing and Event Tracking.J. Devin McAuley, Mari Riess Jones, Shayla Holub, Heather M. Johnston & Nathaniel S. Miller - 2006 - Journal of Experimental Psychology: General 135 (3):348-367.
  3.  30
    On the Inconsistency of Mumma's Eu.Nathaniel Miller - 2012 - Notre Dame Journal of Formal Logic 53 (1):27-52.
    In several articles, Mumma has presented a formal diagrammatic system Eu meant to give an account of one way in which Euclid's use of diagrams in the Elements could be formalized. However, largely because of the way in which it tries to limit case analysis, this system ends up being inconsistent, as shown here. Eu also suffers from several other problems: it is unable to prove several wide classes of correct geometric claims and contains a construction rule that is probably (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   6 citations  
  4.  51
    A Brief Proof of the Full Completeness of Shin’s Venn Diagram Proof System.Nathaniel Miller - 2006 - Journal of Philosophical Logic 35 (3):289 - 291.
    In an article in the Journal of Philosophical Logic in 1996, "Towards a Model Theory of Venn Diagrams," (Vol. 25, No. 5, pp. 463-482), Hammer and Danner proved the full completeness of Shin's formal system for reasoning with Venn Diagrams. Their proof is eight pages long. This note gives a brief five line proof of this same result, using connections between diagrammatic and sentential representations.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
  5.  10
    A Brief Proof of the Full Completeness of Shin’s Venn Diagram Proof System.Nathaniel Miller - 2006 - Journal of Philosophical Logic 35 (3):289-291.
    In an article in the Journal of Philosophical Logic in 1996, "Towards a Model Theory of Venn Diagrams,", Hammer and Danner proved the full completeness of Shin's formal system for reasoning with Venn Diagrams. Their proof is eight pages long. This note gives a brief five line proof of this same result, using connections between diagrammatic and sentential representations.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark