<!DOCTYPE html><HTML lang="en"> <head><meta charset="utf-8"> <title>Parsons (Terence) - The Evans Argument, Properties and Ddiff (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_6238.htm">The Evans Argument, Properties and Ddiff</A></th></tr> <tr><th><A HREF = "../../Authors/P/Author_Parsons (Terence).htm">Parsons (Terence)</a></th></tr> <tr><th>Source: Parsons - Indeterminate Identity, 2000, Chapter 4</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_6238.htm">Paper Summary</A></td><td><A HREF="#ColourConventions">Text Colour-Conventions</a></td></tr></TABLE></CENTER></P> <hr><P><FONT COLOR = "0000FF"><U>Analytic <U><A HREF="#On-Page_Link_P6238_1">TOC</A></U><SUB>1</SUB><a name="On-Page_Return_P6238_1"></A></U><FONT COLOR = "800080"><ol type="1"><li>Gareth Evans's 1978 argument disproving the existence of indeterminate identity is discussed. On a simple analysis it appeals to the (invalid) contrapositive version of <a name="1"></a><A HREF="../../Notes/Notes_0/Notes_81.htm">Leibniz's Law</A><SUP>2</SUP>; on a deeper analysis it presumes incorrectly that the formula '&nabla;(x = a)' expresses a property (the property of <em>being indeterminately identical with a</em>).</li><li>The proof is an RAA of the hypothesis that that formula expresses a property. This fact is not due to non-extensionality or to anything like the semantic paradoxes; instead it is akin to the "paradoxes" of naive set theory, due to the fact that identity is defined in terms of global quantification over all (worldly) properties. </li><li>A test for whether a formula '&phi;x' expresses a worldly property is whether it satisfies the principle that joint (determinate) satisfaction and (determinate) dissatisfaction of the formula makes a "Definite Difference" in the identity of the objects in question; that is, that there are no objects x and y such that '&phi;x' & '! &phi;y' are both true, along with '&nabla;x = y'. </li><li>If a formula satisfies this principle, then an abstract, '&lambda;x&phi;x', constructed from it stands for a worldly property; otherwise we can either say that it does not stand for a property, or that it stands for a non-worldly "conceptual" property. </li></ol> </FONT><BR><HR><BR><U><B>In-Page Footnotes</U></B><a name="On-Page_Link_P6238_1"></A><BR><BR><U><A HREF="#On-Page_Return_P6238_1"><B>Footnote 1</B></A></U>: Taken from <a name="2"></a>"<A HREF = "../../Abstracts/Abstract_06/Abstract_6234.htm">Parsons (Terence) - Indeterminate Identity: Analytical Table of Contents</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="2018-08-02T06:43" pubdate>02/08/2018 06:43:54</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>