<!DOCTYPE html><HTML lang="en"> <head><meta charset="utf-8"> <title>Keranen (Jukka) - The Identity Problem for Realist Structuralism II: A Reply to Shapiro (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_07/PaperSummary_7166.htm">The Identity Problem for Realist Structuralism II: A Reply to Shapiro</A></th></tr> <tr><th><A HREF = "../../Authors/K/Author_Keranen (Jukka).htm">Keranen (Jukka)</a></th></tr> <tr><th>Source: MacBride - Identity and Modality, 2006, Chapter 6</th></tr> <tr><th>Paper - Abstract</th></tr> </TABLE> </CENTER> <P><CENTER><TABLE class = "Bridge" WIDTH=600><tr><td><A HREF = "../../PaperSummaries/PaperSummary_07/PaperSummary_7166.htm">Paper Summary</A></td><td><A HREF = "../../PaperSummaries/PaperSummary_07/PaperCitings_7166.htm">Books / Papers Citing this Paper</A></td><td><A HREF="#ColourConventions">Text Colour-Conventions</a></td></tr></TABLE></CENTER></P> <hr><P><FONT COLOR = "0000FF"><u>Editor s <U><A HREF="#On-Page_Link_P7166_1">Introduction</A></U><SUB>1</SUB><a name="On-Page_Return_P7166_1"></A></u><FONT COLOR = "800080"><ol type="1"><li>In 'The Identity Problem for Realist Stucturalism II: A Reply to Shapiro' Jukka Keranen argues that <U><A HREF="#On-Page_Link_P7166_2">Shapiro</A></U><SUB>2</SUB><a name="On-Page_Return_P7166_2"></A> nevertheless fails to provide an adequate account of the identity of numbers conceived as places in structures. </li><li>According to Keranen, it is an adequacy constraint upon the introduction of a type of object that some account be given of the kinds of fact that metaphysically underwrite the sameness and difference of objects of this type. More specifically, Keranen favours the view that facts about the sameness and difference of objects must be underwritten by facts about the properties they possess or relations they stand in. </li><li>He holds up set theory as an exemplar of a theory that meets this adequacy constraint, grounding the identity of sets  via the Axiom of Extensionality  in facts about their members. </li><li>Keranen doubts, however, whether <em>ante rem</em> structuralism can meet this adequacy constraint because there are no structural properties or relations that can be used to distinguish between (e.g.) the structurally indiscernible points in a Euclidean plane. </li><li>Of course, the structuralist can meet the constraint by <em>force majeure</em>, positing a supply of haecceitistic properties to distinguish between structurally indiscernible objects. But, as Keranen reflects, the positing of haecceities opens up the possibility of indiscernible structures that differ only haecceitisticallv. </li><li>Since mathematical discourse lacks the descriptive resources to distinguish between these structures, this manoeuvre on the part of the structuralist threatens to render reference to mathematical objects deeply inscrutable. </li><li>Keranen concludes that the particular difficulties encountered by <em>ante rem</em> structuralism in particular reflect deep difficulties for ontological realism in general. </li></ol></FONT> <BR><u>Sections</u><FONT COLOR = "800080"><ol type="1"><li>Identity and <a name="1"></a><A HREF="../../Notes/Notes_0/Notes_77.htm">Individuation</A><SUP>3</SUP></li><li>The Trivializing Objection</li><li>The Leibniz Principle</li><li>The  Trivial Accounts of Identity</li><li>Realist Structuralism Reconsidered</li><li>Conclusion: The Identity Problem for Realism</li></ol></FONT><BR><HR><BR><U><B>In-Page Footnotes</U></B><a name="On-Page_Link_P7166_1"></A><BR><BR><U><A HREF="#On-Page_Return_P7166_1"><B>Footnote 1</B></A></U>: <ul type="disc"><li>From <a name="2"></a>"<A HREF = "../../Abstracts/Abstract_07/Abstract_7161.htm">MacBride (Fraser) - Identity and Modality: Introduction</A>", </li><li>Bullet numbering is mine. </li></ul><a name="On-Page_Link_P7166_2"></A><U><A HREF="#On-Page_Return_P7166_2"><B>Footnote 2</B></A></U>: In <a name="3"></a>"<A HREF = "../../Abstracts/Abstract_07/Abstract_7165.htm">Shapiro (Stewart) - Structure and Identity</A>". <BR><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="2018-08-02T06:55" pubdate>02/08/2018 06:55:34</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>