<!DOCTYPE html><HTML lang="en"> <head><meta charset="utf-8"> <title>Butterfield (Jeremy) - On the Persistence of Particles (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_00/PaperSummary_258.htm">On the Persistence of Particles</A></th></tr> <tr><th><A HREF = "../../Authors/B/Author_Butterfield (Jeremy).htm">Butterfield (Jeremy)</a></th></tr> <tr><th>Source: Website</th></tr> <tr><th>Paper - Abstract</th></tr> </TABLE> </CENTER> <P><CENTER><TABLE class = "Bridge" WIDTH=600><tr><td><A HREF = "../../PaperSummaries/PaperSummary_00/PaperSummary_258.htm">Paper Summary</A></td><td><A HREF = "../../PaperSummaries/PaperSummary_00/PapersToNotes_258.htm">Notes Citing this Paper</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"><ul type="disc"><li>This paper is about the metaphysical debate whether objects persist over time by the selfsame object existing at different times (nowadays called  endurance by metaphysicians), or by different temporal parts, or stages, existing at different times (called  perdurance ). </li><li>I aim to illuminate the debate by using some elementary kinematics and real analysis: resources which metaphysicians have, surprisingly, not availed themselves of. There are two main results, which are of interest to both <a name="1"></a><A HREF="../../Notes/Notes_7/Notes_760.htm">endurantists</A><SUP>1</SUP> and perdurantists. <BR><ol type="1"><li>I describe a precise formal equivalence between the way that the two metaphysical positions represent the motion of the objects of classical mechanics (both point-particles and continua). </li><li>I make precise, and prove a result about, the idea that the persistence of objects moving in a void is to be analysed in terms of tracking the continuous curves in spacetime that connect points occupied by matter. The result is entirely elementary: it is a corollary of the Heine-Borel theorem.</li></ol> </li></ul> </FONT><hr><FONT COLOR = "0000FF"><B>Comment: </B><BR><BR>See <a name="W250W"></a><A HREF = "http://trin-hosts.trin.cam.ac.uk/fellows/butterfield/Papers/PerseParticles.pdf" TARGET = "_top">Link</A>.<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="2018-08-02T05:30" pubdate>02/08/2018 05:30:30</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>