<!DOCTYPE html><HTML lang="en"> <head><meta charset="utf-8"> <title>Sider (Ted) - Another Look at Armstrong's Combinatorialism (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_19/PaperSummary_19832.htm">Another Look at Armstrong's Combinatorialism</A></th></tr> <tr><th><A HREF = "../../Authors/S/Author_Sider (Ted).htm">Sider (Ted)</a></th></tr> <tr><th>Source: Nos 39 (2005): 680 696</th></tr> <tr><th>Paper - Abstract</th></tr> </TABLE> </CENTER> <P><CENTER><TABLE class = "Bridge" WIDTH=400><tr><td><A HREF = "../../PaperSummaries/PaperSummary_19/PaperSummary_19832.htm">Paper Summary</A></td><td><A HREF="#ColourConventions">Text Colour-Conventions</a></td></tr></TABLE></CENTER></P> <hr><P><FONT COLOR = "0000FF"><u>Author s Introduction</u><FONT COLOR = "800080"><ol type="1"><li>The core idea of David Armstrong s combinatorial theory of possibility is attractive. <em>Rearrangement</em> is the key to <a name="1"></a><A HREF="../../Notes/Notes_1/Notes_121.htm">modality</A><SUP>1</SUP>; possible worlds result from scrambling bits and pieces of other possible worlds. Yet I encounter great difficulty when trying to formulate the theory rigorously, and my best attempts are vulnerable to counterexamples. </li><li>The Leibnizian biconditionals relate <em>possibility</em> and <em>necessity</em> to possible world and <em>true in</em>: <ul type="disc"><li>p is possible iff p is true in some possible world </li><li>p is necessary iff p is true in all possible worlds </li></ul>Given an account of the latter notions, one can reduce the former via the biconditionals. In <em>A Combinatorial Theory of Possibility</em>, and then again in <em>A World of States of Affairs</em>, Armstrong characterizes possible worlds as rearrangements of elements of the actual world. But he says comparatively little about <em>true in</em>. This omission figures prominently in what follows. </li><li>Section 1 of this paper reconstructs Armstrong s theory, section 2 defends it from criticisms due to Fraser MacBride and Holly Gail Thomas, and section 3 gives a number of objections to that theory. Section 4 develops yet another objection, building on work by David Lewis.</li></ol> </FONT><hr><FONT COLOR = "0000FF"><B>Comment: </B><BR><BR>See <a name="W1014W"></a><A HREF = "http://www.tedsider.org/papers/armstrong.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="2018-08-03T00:13" pubdate>03/08/2018 00:13:35</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>