<!DOCTYPE html><HTML lang="en"> <head><meta charset="utf-8"> <title>Shapiro (Stewart) - Modality and Ontology (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_373.htm">Modality and Ontology</A></th></tr> <tr><th><A HREF = "../../Authors/S/Author_Shapiro (Stewart).htm">Shapiro (Stewart)</a></th></tr> <tr><th>Source: Mind 102.407, July 1993, pp. 455-481</th></tr> <tr><th>Paper - Abstract</th></tr> </TABLE> </CENTER> <P><CENTER><TABLE class = "Bridge" WIDTH=400><tr><td><A HREF = "../../PaperSummaries/PaperSummary_00/PaperSummary_373.htm">Paper Summary</A></td><td><A HREF="#ColourConventions">Text Colour-Conventions</a></td></tr></TABLE></CENTER></P> <hr><P><FONT COLOR = "0000FF"><U>Philosophers Index Abstract</U><FONT COLOR = "800080"><ol type="1">This paper concerns the relationship between ideology and ontology. The starting point is a series of recent programs whose strategy is to reduce ontology in mathematics by invoking some ideology, typically a <a name="1"></a><A HREF="../../Notes/Notes_1/Notes_121.htm">modal</A><SUP>1</SUP> operator. In each case, there are straightforward, often trivial, translations from the set-theoretic language of the realist to the proposed language with added ideology, and vice-versa. The contention is that, because of these translations, neither system can claim a major epistemological advantage over the other. The prima facie intractability of knowledge of abstract objects indicates an intractability concerning knowledge of the "new" notions. The prevailing criterion of ontological commitment, due to Quine, is that the ontology of a theory is the range of its bound variables; but recall that Quine insists on a fixed, and very austere ideology. It is proposed here that, when this constraint is relaxed, the Quinean criterion is flawed, and an alternative, in structuralist terms, is developed.</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="2018-08-03T00:13" pubdate>03/08/2018 00:13:33</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>