<!DOCTYPE html><HTML lang="en"> <head><meta charset="utf-8"> <title>MacBride (Fraser) - What constitutes the numerical diversity of mathematical objects? (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_05/PaperSummary_5777.htm">What constitutes the numerical diversity of mathematical objects?</A></th></tr> <tr><th><A HREF = "../../Authors/M/Author_MacBride (Fraser).htm">MacBride (Fraser)</a></th></tr> <tr><th>Source: Analysis 66, January 2006, pp. 63-69(7)</th></tr> <tr><th>Paper - Abstract</th></tr> </TABLE> </CENTER> <P><CENTER><TABLE class = "Bridge" WIDTH=200><tr><td><A HREF = "../../PaperSummaries/PaperSummary_05/PaperSummary_5777.htm">Paper Summary</A></td></tr></TABLE></CENTER></P> <hr><P><FONT COLOR = "0000FF"><U>Author's Abstract</U><FONT COLOR = "800080"><ol type="1">The article focuses on the composition of different versions of structuralism in mathematical objects. According to the article, different versions of structuralism correspond to different interpretations of the relevant notion of form implicit in mathematical practice. The idea of structuralism states that mathematical objects are positions in structural <a name="1"></a><A HREF="../../Notes/Notes_10/Notes_1008.htm">universals</A><SUP>1</SUP>, constituted by the relations they bear to the other positions in the structures to which they belong. </ol></FONT><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="2018-08-02T06:37" pubdate>02/08/2018 06:37:18</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>