<!DOCTYPE html><HTML lang="en"> <head><meta charset="utf-8"> <title>Todman (Theo) - Thesis - Probability (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_17/PaperSummary_17865.htm">Thesis - Probability</A></th></tr> <tr><th><A HREF = "../../Authors/T/Author_Todman (Theo).htm">Todman (Theo)</a></th></tr> <tr><th>Source: </th></tr> <tr><th>Paper - Abstract</th></tr> </TABLE> </CENTER> <P><CENTER><TABLE class = "Bridge" WIDTH=400><tr><td><A HREF = "../../PaperSummaries/PaperSummary_17/PaperSummary_17865.htm">Paper Summary</A></td><td><A HREF = "../../Notes/Notes_2/Notes_220.htm">Link to Latest Write-Up Note</A></td></tr></TABLE></CENTER></P> <hr><P><FONT COLOR = "0000FF"><ul type="disc"><li>This pseudo-Paper is intended as the mechanism to record time spent on the Note '<a name="1"></a><A HREF="../../Notes/Notes_2/Notes_220.htm">Probability</A><SUP>1</SUP>' during my Thesis research, as from 2011. </li><li>For the actual time recorded, click on "Paper Summary" above. </li></ul><FONT COLOR = "0000FF"><hr><br><B><u><U><A HREF="#On-Page_Link_P17865_2">Write-up</A></U><SUB>2</SUB><a name="On-Page_Return_P17865_2"></A></u> (as at 12/08/2007 10:17:46): Probability</B><BR><br><B>A requirement of great importance, therefore, is the ability to assign a probability to any statement about the world (or within a model), in accord with the likelihood of it being a true statement.</B><ol type="1"><li><a name="2"></a><A HREF="../../Notes/Notes_4/Notes_459.htm">Ideally</A><SUP>3</SUP>, we would like to assign a mathematical probability to any statement, ie. a real number in the range 0 to 1, with 0 representing impossibility & 1 representing certainty. As in the frequency theory of probability, the assigned number should represent the proportion of situations in which the statement is expected to turn out to be true.</li><li>In <a name="3"></a><A HREF="../../Notes/Notes_4/Notes_460.htm">practical</A><SUP>4</SUP> life, where it is unreasonable to assign a numerical probability to an event, we do assign non-mathematical probabilities to statements and base our actions on them.</li><li>It also makes sense to say that certain statements are more probable than others, even when they do not refer to the same <a name="4"></a><A HREF="../../Notes/Notes_4/Notes_461.htm">domain</A><SUP>5</SUP> of experience. </li><li>It would seem to be possible to assign a <a name="5"></a><A HREF="../../Notes/Notes_4/Notes_462.htm">priori</A><SUP>6</SUP> probabilities to statements about the world, the probability being assigned a priori to that particular potential experience, by reference to other actual experiences, though not a priori to all experience.</li><li>A statement with a low a priori probability may yet have a higher a posteriori probability because of the strength of actual testimony or experimental evidence. </li></ol><BR><HR><BR><U><B>In-Page Footnotes</U></B><a name="On-Page_Link_P17865_2"></A><BR><BR><U><A HREF="#On-Page_Return_P17865_2"><B>Footnote 2</A></B></U>: <ul type="disc"><li>This is the write-up as it was when this Abstract was last output, with text as at the timestamp indicated (12/08/2007 10:17:46). </li><li><A HREF = "../../Notes/Notes_2/Notes_220.htm">Link to Latest Write-Up Note</A>. </li></ul><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></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="2018-08-13T13:22" pubdate>13/08/2018 13:22:01</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>