<!DOCTYPE html><HTML lang="en"> <head><meta charset="utf-8"> <title>Williamson (Timothy) - Probability and Danger (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_15/PaperSummary_15965.htm">Probability and Danger</A></th></tr> <tr><th><A HREF = "../../Authors/W/Author_Williamson (Timothy).htm">Williamson (Timothy)</a></th></tr> <tr><th>Source: The Amherst Lecture in Philosophy 4 (2009): 1 35</th></tr> <tr><th>Paper - Abstract</th></tr> </TABLE> </CENTER> <P><CENTER><TABLE class = "Bridge" WIDTH=400><tr><td><A HREF = "../../PaperSummaries/PaperSummary_15/PaperSummary_15965.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 Abstract</U><FONT COLOR = "800080"><ul type="disc"><li>What is the epistemological structure of situations where many small risks amount to a large one? Lottery and preface paradoxes and puzzles about quantum-mechanical blips threaten the idea that competent deduction is a way of extending our knowledge (MPC). </li><li>Seemingly, everyday knowledge involves small risks, and competently deducing the conjunction of many such truths from them yields a conclusion too risky to constitute knowledge. </li><li>But the dilemma between scepticism and abandoning MPC is false. In extreme cases, objectively improbable truths are known. Safety is <a name="1"></a><A HREF="../../Notes/Notes_1/Notes_121.htm">modal</A><SUP>1</SUP>, not probabilistic, in structure, with closure and factiveness conditions. It is modelled using closeness of worlds. </li><li>Safety is analogous to knowledge. It suggests an interpretation of possible worlds semantics for epistemic logic. </li><li>To avoid logical omniscience, a relation of epistemic counterparthood between formulas is introduced. This supports a safety conception of knowledge and formalizes how extending knowledge by deduction depends on logical competence.</li></ul> </FONT><hr><FONT COLOR = "0000FF"><B>Comment: </B><BR><BR>See <a name="W842W"></a><A HREF = "http://www.amherstlecture.org/williamson2009/index.html" 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="2018-08-03T00:15" pubdate>03/08/2018 00:15:58</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>