<html> <head> <meta http-equiv="Content-Type" content="text/html; charset=unicode"> <title>Chapter 3</title> <style> <!-- p { margin-top: 0px; margin-bottom: 1px } td { border-color: black } td.table1column1 { padding-left: 0in; padding-right: 0in } td.table1column2 { padding-left: 0in; padding-right: 0in } --> </style> </head> <body> <p><font face="Times New Roman"><span style="font-size: 14pt; font-weight:bold">James T. Smith</span></font></p> <font face="Times New Roman"> <br> </font> <p><font face="Times New Roman"><span style="font-size: 12pt">&#160;</span></font></p> <font face="Times New Roman"> <br> </font> <p style="text-align: center"><i><span style="font-weight: bold"> <font size="6" face="Times New Roman">The Legacy of Mario Pieri</font></span></i></p> <p style="text-align: center"><i><span style="font-weight: bold"> <font size="6" face="Times New Roman">&nbsp;in Foundations and Philosophy of Mathematics</font></span></i></p> <font face="Times New Roman"> <br> </font> <p style="text-align: center"><font face="Times New Roman"><span style="font-size: 12pt">&#160;</span></font></p> <font face="Times New Roman"> <br> </font> <p style="text-align: center"><font face="Times New Roman"> <span style="font-size: 24pt; font-weight:bold">Chapter 3</span></font></p> <font face="Times New Roman"> <br> </font> <p style="text-align: center"><font face="Times New Roman"> <span style="font-size: 24pt; font-weight:bold">Two Paths to Logical </span></font><span style="font-weight: 700"> <font face="Times New Roman" size="6">Consequence:</font></span></p> <p style="text-align: center"><span style="font-weight: 700"> <font face="Times New Roman" size="6">Pieri and the Peano School</font></span><font face="Times New Roman"><br> </font></p> <p style="text-align: center"><font face="Times New Roman"><span style="font-size: 12pt">&#160;</span></font></p> <font face="Times New Roman"> <br> </font> <p style="margin-left: 0.2in; margin-right: 0.2in">&nbsp;</p> <font face="Times New Roman"> <br> </font> <p><font face="CentSchbook BT"><span style="font-size: 18pt; font-weight:bold">Contents and Hyperlinks</span></font></p> <br> <br> <div align="left"> <table width="100%" cellpadding="6" style="border-collapse: collapse; border-spacing: 0pt; empty-cells: show; font-family: 'CentSchbook BT', serif; font-size: 12pt; font-weight: normal; font-style: normal; border-color: black" id="table1"> <tr> <td class="table1column1" width="7%" align="left"> &nbsp;</td> <td class="table1column1" width="74%"> &nbsp;</td> <td class="table1column1" width="5%" align="center"> <i>pages</i></td> <td class="table1column2" width="15%" align="right"> &nbsp;</td> </tr> <tr> <td class="table1column1" width="7%" align="left"> <font size="5">3.0</font></td> <td class="table1column1" width="74%" align="left"> <span style="font-size: 18pt; "> <a href="03_00/03_00.pdf">Chapter Introduction</a></span><span style="color: #000000"><font size="5"> </font> </span><font size="5"></font> </font> </td> <td class="table1column1" width="5%" align="center"> 1</td> <td class="table1column2" width="15%" align="right"> <span style="font-size:18pt"><a href="03_00/03_00comments.pdf">comments</a></span><span style="color: #000000; font-size:18pt"> </span> </td> </tr> <tr> <td class="table1column1" width="7%" align="left"> <font size="5">3.1</font></td> <td class="table1column1" width="74%" align="left"> <font size="5"><a href="03_01/03_01.pdf">Tarski&#39;s Definition of Consequence</a></font></td> <td class="table1column1" width="5%" valign="middle" align="center">4</td> <td class="table1column2" width="15%" align="right"> <span style="font-size: 18pt; "> <a href="03_01/03_01comments.pdf">comments</a></span><span style="color: #000000"><font size="5"> </font> </span></font> </td> </tr> <tr> <td class="table1column1" width="7%" align="left"> <font size="5">3.2</font></td> <td class="table1column1" width="74%" align="left"> <font size="5"><a href="03_02/03_02.pdf">Aristotle&#39;s Counterexample Method</a></font></td> <td class="table1column1" width="5%" valign="middle" align="center">3</td> <td class="table1column2" width="15%" align="right"> <span style="font-size: 18pt; "> <a href="03_02/03_02comments.pdf">comments</a></span><span style="color: #000000"><font size="5"> </font> </span></font> </td> </tr> <tr> <td class="table1column1" width="7%" align="left"> <font size="5">3.3</font></td> <td class="table1column1" width="74%" align="left"> <font size="5"><a href="03_03/03_03.pdf">Independence of the Parallel Postulate</a></font><span style="font-size:18pt; "> </span> </td> <td class="table1column1" width="5%" valign="middle" align="center">4</td> <td class="table1column2" width="15%" align="right"> <span style="font-size: 18pt; "> <a href="03_03/03_03comments.pdf">comments</a></span></td> </tr> <tr> <td class="table1column1" width="7%" align="left"> <font size="5">3.4</font></td> <td class="table1column1" width="74%" align="left"> <font size="5"><a href="03_04/03_04.pdf">Logical Consequence in a Model-Theoretic Context:&nbsp; The Peano School</a></font></td> <td class="table1column1" width="5%" valign="middle" align="center">9</td> <td class="table1column2" width="15%" align="right"> <span style="font-size: 18pt; "> <a href="03_04/03_04comments.pdf">comments</a></span></td> </tr> <tr> <td class="table1column1" width="7%" align="left"> &nbsp;</td> <td class="table1column1" width="74%" align="left"> <font size="5">3.4.1&nbsp; Peano</font></td> <td class="table1column1" width="5%" valign="middle" align="center">&nbsp;</td> <td class="table1column2" width="15%" align="right"> &nbsp;</td> </tr> <tr> <td class="table1column1" width="7%" align="left"> &nbsp;</td> <td class="table1column1" width="74%" align="left"> <font size="5">3.4.2&nbsp; Pieri</font></td> <td class="table1column1" width="5%" valign="middle" align="center">&nbsp;</td> <td class="table1column2" width="15%" align="right"> &nbsp;</td> </tr> <tr> <td class="table1column1" width="7%" align="left"> &nbsp;</td> <td class="table1column1" width="74%" align="left"> <font size="5">3.4.3&nbsp; Padoa</font></td> <td class="table1column1" width="5%" valign="middle" align="center">&nbsp;</td> <td class="table1column2" width="15%" align="right"> &nbsp;</td> </tr> <tr> <td class="table1column1" width="7%" align="left"> &nbsp;</td> <td class="table1column1" width="74%" align="right"> <i>total</i></td> <td class="table1column1" width="5%" valign="middle" align="center"> 21</td> <td class="table1column2" width="15%" align="right">&nbsp;</td> </tr> </table> </div> <br> &nbsp;</body></html>