<!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>One cannot be said to believe meaningfully in doctrines of which one is ignorant or which are as yet merely implicit consequences of initial premises.</B><ol type="1"><li>For example, the axioms of the mathematical theory of Groups, or of number theory, are very simple. However, because of our limited intelligence, their consequences are often astonishing in their depth and subtlety. We would not say we believed a theorem to be true until it had been discovered and we had worked through the proof, even though its truth had always been implicit in the axioms.</li><li>This raises the issue of the distinction between knowledge and <a name="1"></a><A HREF = "../Notes_4/Notes_463.htm">understanding</A><SUP>1</SUP>.</li><li>In any sufficiently rich model of some sub-system of the world, the <a name="2"></a><A HREF = "../Notes_4/Notes_464.htm">recursive</A><SUP>2</SUP> application of the rules of the model may take us into areas of the model that do not mirror the world. </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%">238 (Implicit Beliefs)</TD> <TD WIDTH="25%"><A href ="../../Notes/Notes_1/Notes_177.htm">Belief</A></TD></TR> </TABLE></center> <hr><h3>Summary of Note Links from this Page</h3> <CENTER> <TABLE Class = "Bridge" WIDTH=950> <TR> <td bgcolor="#ffcccc" WIDTH="20%"><A href = "../../Notes/Notes_4/Notes_463.htm"><span title="Low Quality">Implicit Beliefs - Knowledge + Understanding</span></A></TD> <td bgcolor="#ffcccc" WIDTH="20%"><A href = "../../Notes/Notes_4/Notes_464.htm"><span title="Low Quality">Implicit Beliefs - Recursion</span></A></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> <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_177.htm#5"><span title="Medium Quality">Belief</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="2018-08-01T03:07" pubdate>01/08/2018 03:07:05</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>