<!DOCTYPE html><HTML lang="en"> <head><meta charset="utf-8"> <title>Parsons (Terence) - Conditional Disputations (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_06/PaperSummary_6240.htm">Conditional Disputations</A></th></tr> <tr><th><A HREF = "../../Authors/P/Author_Parsons (Terence).htm">Parsons (Terence)</a></th></tr> <tr><th>Source: Parsons - Indeterminate Identity, 2000, Chapter 6</th></tr> <tr><th>Paper - Abstract</th></tr> </TABLE> </CENTER> <P><CENTER><TABLE class = "Bridge" WIDTH=400><tr><td><A HREF = "../../PaperSummaries/PaperSummary_06/PaperSummary_6240.htm">Paper Summary</A></td><td><A HREF="#ColourConventions">Text Colour-Conventions</a></td></tr></TABLE></CENTER></P> <hr><P><FONT COLOR = "0000FF"><U>Analytic <U><A HREF="#On-Page_Link_P6240_1">TOC</A></U><SUB>1</SUB><a name="On-Page_Return_P6240_1"></A></U><FONT COLOR = "800080"><ol type="1"><li>Truth-conditions for conditionals are discussed, and the Lukasiewicz conditional '&rArr;' is adopted; such a conditional is false when the antecedent is true and the consequent false, and true if the truth-value status of the consequent is at least as high as that of the antecedent (counting lack of truth-value as a status intermediate between truth and falsity). </li><li>A conditional 'If A then B' is to be read either with this conditional ('A &rArr; B') or given the "if-true" reading ('!A &rArr; B'). </li><li>The Lukasiewicz conditional satisfies <em>modus ponens</em>, <em>modus tollens</em>, hypothetical syllogism, and contraposition, but only a restricted form of conditional proof: taking 'A' as a premiss and deriving 'B' allows you to conditionalize and infer '!A &rArr; B' but not 'A &rArr; B'. (No non-bivalent truth-status-functional conditional satisfies all of <em>modus ponens</em>, <em>modus tollens</em>, and conditional proof, so one can do no better.) </li><li>If one wishes to state <a name="1"></a><A HREF="../../Notes/Notes_0/Notes_81.htm">Leibniz's Law</A><SUP>2</SUP> as a conditional, the bare Lukasiewicz conditional form is incorrect, but the "if-true" version is correct: '!a = b &rArr; (&phi;a &rArr; &phi;b)'. </li><li><a name="3"></a><A HREF = "../../Authors/B/Author_Broome (John).htm">John Broome</A> gives a different version, which is logically equivalent to this one. Johnson criticizes these versions, but gives a conditionalized-conditional version that is also equivalent. </li><li>A second argument of Williamson is considered which defends bivalent versions of the Tarski biconditionals; it is held that his rationales for the biconditionals are subject to interpretation, and that interpretations that do not make them beg the question rationalize only non-bivalent versions. </li></ol> </FONT><BR><HR><BR><U><B>In-Page Footnotes</U></B><a name="On-Page_Link_P6240_1"></A><BR><BR><U><A HREF="#On-Page_Return_P6240_1"><B>Footnote 1</B></A></U>: Taken from <a name="2"></a>"<A HREF = "../../Abstracts/Abstract_06/Abstract_6234.htm">Parsons (Terence) - Indeterminate Identity: Analytical Table of Contents</A>". <BR><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="2018-08-02T06:43" pubdate>02/08/2018 06:43:56</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>