<!DOCTYPE html><HTML lang="en"> <head> <meta charset="utf-8"> <link href="../../TheosStyle.css" rel="stylesheet" type="text/css"><link rel="shortcut icon" href="../../TT_ICO.png" /> <title>Note: Christian Tractatus (Theo Todman's Web Page)</title> </head><body> <a name="Top"></a> <h1>Theo Todman's Web Page - Notes Pages</h1><hr><h2>Christian Tractatus</h2><p class = "Centered">(Text as at 12/08/2007 10:17:46)<hr> <P><FONT COLOR = "0000FF"><B>We must note that beliefs are not held in isolation, but form a network of interconnected beliefs commonly called a world view. </B><ol type="1"><li>Any world view must be self-consistent. That is, all its statements must be simultaneously relatively true. For a world view to be absolutely true, all its component beliefs must simultaneously be true of the world.</li><li>Any world view may be condensed into an irreducible set of propositions, none of which duplicates any of the contents of another & which collectively cover the world view. Since, however, there may be difficulty in ensuring the independence of the propositions, we may have to be satisfied with a non-disjoint covering set (as in topology). </li><li>Let us suppose that a world view is composed of a set of irreducible propositions {p<FONT FACE="Arial" SIZE=2>i</FONT><FONT FACE="Arial">} enumerated by the index set <B>I</B> and let each of these propositions have probability <B>P</B>(p<FONT FACE="Arial" SIZE=2>i</FONT><FONT FACE="Arial">). Then, the probability of the world view is (or is closely related to) the product, over I, of these probabilities, ie. <FONT FACE="Symbol" SIZE=4>P</FONT><FONT FACE="Arial" SIZE=2>i</FONT><FONT FACE="Symbol" SIZE=2>e</FONT><B><FONT FACE="Arial" SIZE=2>I</B></FONT><FONT FACE="Arial">(<B>P</B>(p<FONT FACE="Arial" SIZE=2>i<FONT FACE="Arial">)).</li><li>Naively, we can deduce two consequences from the above, given below. <ul type="disc"><li>Firstly, no sophisticated world view can have a high probability of being true in all its parts, because the number of irreducible propositions it contains will be be large while their probabilities will often be low. To take a trivial example, let us suppose our world view consists of an irreducible set of 20 propositions, each of which we take to be 90% certain; then, we have only the right to be 12% certain of the truth of our world view.</li><li>Secondly, the greater the number of irreducible propositions in a world view, the lower the probability of that world view. Hence the force and importance of Occam's Razor, of which more will be said later. </li></ul></li></ol></P> <BR><HR><BR><CENTER><TABLE class = "Bridge" WIDTH=950><TR> <TH WIDTH="25%">Note last updated</TH> <TH WIDTH="50%">Reference for this Topic</TH> <TH WIDTH="25%">Parent Topic</TH></TR> <TR><TD WIDTH="25%">12/08/2007 10:17:46</TD> <TD WIDTH="50%">222 (World Views)</TD> <TD WIDTH="25%"><A href ="../../Notes/Notes_1/Notes_174.htm">Certainty</A></TD></TR> </TABLE></center> <BR><HR><BR><h3>Summary of Note Links to this Page</h3> <CENTER> <TABLE Class = "Bridge" WIDTH=950> <TR> <td bgcolor="#ffff4d" WIDTH="20%"><A href = "../../Notes/Notes_1/Notes_174.htm#6"><span title="Medium Quality">Certainty</span></A></TD> <TD WIDTH="20%">&nbsp;</TD> <TD WIDTH="20%">&nbsp;</TD> <TD WIDTH="20%">&nbsp;</TD> <TD WIDTH="20%">&nbsp;</TD> </TR> </TABLE> </CENTER> <P class = "Centered">To access information, click on one of the links in the table above.</P> <a name="ColourConventions"></a><br><hr><br><h3 class = "Left">Text Colour Conventions</h3><OL TYPE="1"><li><FONT COLOR = "0000FF">Blue</FONT>: Text by me; &copy; Theo Todman, 2018</li></OL><BR> <center><BR><HR><BR><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="2018-08-01T03:06" pubdate>01/08/2018 03:06:49</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>