<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>13</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Batens, Diderik</style></author></authors><secondary-authors><author><style face="normal" font="default" size="100%">Allo, Patrick</style></author><author><style face="normal" font="default" size="100%">Van Kerkhove, Bart</style></author></secondary-authors></contributors><titles><title><style face="normal" font="default" size="100%">The Consistency of Peano Arithmetic. A Defeasible Perspective</style></title><secondary-title><style face="normal" font="default" size="100%">Modestly Radical or Radically Modest. Festschrift for Jean Paul Van Bendegem on the Occasion of His 60th Birthday</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2014</style></year></dates><publisher><style face="normal" font="default" size="100%">College Publications</style></publisher><pages><style face="normal" font="default" size="100%">11–59</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;This paper proposes to replace \sys{PA}, Peano Arithmetic, by a theory \sys{APA} defined in terms of (i)&amp;nbsp;a set of axioms that is classically equivalent to the Peano axioms and (ii)&amp;nbsp;a defeasible logic that minimizes inconsistency, viz.\ an inconsistency-adaptive logic. If \sys{PA} is consistent, its set of theorems coincides with the set of \sys{APA}-theorems. If \sys{PA} is inconsistent, \sys{APA} is non-trivial and has the following remarkable property: there is a unique non-standard number that is its own successor and every `desirable' \sys{PA}-theorem is retained if restricted to the other numbers. The restriction can be expressed in the language of arithmetic. And there is much more.&lt;/p&gt;</style></abstract></record></records></xml>