<!DOCTYPE html><HTML lang="en"> <head><meta charset="utf-8"> <title>Cook (Roy T.) & Ebert (Philip A.) - Abstraction and Identity (Theo Todman's Book Collection - Paper Abstracts) </title> <link href="../../TheosStyle.css" rel="stylesheet" type="text/css"><link rel="shortcut icon" href="../../TT_ICO.png" /></head> <BODY> <CENTER> <div id="header"><HR><h1>Theo Todman's Web Page - Paper Abstracts</h1><HR></div><A name="Top"></A> <TABLE class = "Bridge" WIDTH=950> <tr><th><A HREF = "../../PaperSummaries/PaperSummary_06/PaperSummary_6175.htm">Abstraction and Identity</A></th></tr> <tr><th><A HREF = "../../Authors/C/Author_Cook (Roy T.).htm">Cook (Roy T.)</a> & <A HREF = "../../Authors/E/Author_Ebert (Philip A.).htm">Ebert (Philip A.)</a></th></tr> <tr><th>Source: Dialectica 59:2 (2005), pp. 121 139</th></tr> <tr><th>Paper - Abstract</th></tr> </TABLE> </CENTER> <P><CENTER><TABLE class = "Bridge" WIDTH=400><tr><td><A HREF = "../../PaperSummaries/PaperSummary_06/PaperSummary_6175.htm">Paper Summary</A></td><td><A HREF="#ColourConventions">Text Colour-Conventions</a></td></tr></TABLE></CENTER></P> <hr><P><FONT COLOR = "0000FF"><U>Author s Abstract</U><FONT COLOR = "800080"><ol type="1">In this paper we outline and discuss various solutions to a restricted, but we think, more interesting version of the infamous <I>Caesar Problem</I>. This restricted version, labelled the <I>C-R Problem</I>, occurs in contexts where we have two distinct abstraction principles: [ & snip & ] and want to settle <a name="1"></a><A HREF="../../Notes/Notes_0/Notes_10.htm">cross-sortal</A><SUP>1</SUP> identity claims of the form: [ & snip & ]. Both abstraction principles, however, are silent with regard to this identity  a special instance of the <I>Caesar Problem</I>. In what follows, we outline two distinct strategies to resolve the <I>C-R problem</I>. The first strategy decides such cross-abstraction identities in terms of whether or not the equivalence relations appearing on the right hand side of the abstraction principles are identical, while the second strategy settles such identities by appeal to the relevant equivalence classes. We then focus our discussion on the latter approach and offer three ways of implementing this strategy. Ultimately, we argue that this strategy fails, as each attempt to appeal to equivalence classes faces unsurmountable difficulties.</ol> </FONT><hr><FONT COLOR = "0000FF"><B>Comment: </B><BR><BR>See <a name="W402W"></a><A HREF = "https://www.st-andrews.ac.uk/~pae1/abstract_identity_final.pdf" TARGET = "_top">Link</A> (Defunct).<BR><FONT COLOR = "0000FF"><HR></P><a name="ColourConventions"></a><p><b>Text Colour Conventions (see <A HREF="../../Notes/Notes_10/Notes_1025.htm">disclaimer</a>)</b></p><OL TYPE="1"><LI><FONT COLOR = "0000FF">Blue</FONT>: Text by me; &copy; Theo Todman, 2018</li><LI><FONT COLOR = "800080">Mauve</FONT>: Text by correspondent(s) or other author(s); &copy; the author(s)</li></OL> <BR><HR><BR><CENTER> <TABLE class = "Bridge" WIDTH=950> <TR><TD WIDTH="30%">&copy; Theo Todman, June 2007 - August 2018.</TD> <TD WIDTH="40%">Please address any comments on this page to <A HREF="mailto:theo@theotodman.com">theo@theotodman.com</A>.</TD> <TD WIDTH="30%">File output: <time datetime="2018-08-02T06:42" pubdate>02/08/2018 06:42:57</time> <br><A HREF="../../Notes/Notes_10/Notes_1010.htm">Website Maintenance Dashboard</A></TD></TR> <TD WIDTH="30%"><A HREF="#Top">Return to Top of this Page</A></TD> <TD WIDTH="40%"><A HREF="../../Notes/Notes_11/Notes_1140.htm">Return to Theo Todman's Philosophy Page</A></TD> <TD WIDTH="30%"><A HREF="../../index.htm">Return to Theo Todman's Home Page</A></TD> </TR></TABLE></CENTER><HR> </BODY> </HTML>