<html><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; ">At closer inspection I need to discard this idea:<br><div><br class="Apple-interchange-newline"><blockquote type="cite"><span class="Apple-style-span" style="border-collapse: separate; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-align: auto; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0; ">I wonder wether in the study of reasoning, iteration could be a concatenation of deductions along the same rule, while (primitive) recursion could be a concatenation of abductions along the same rule.<span class="Apple-converted-space"> </span></span></blockquote><br></div><div>Recursion - as a mode of access to some object - requires an instantiation of other objects which are accessed in the same/analogous way. Each intermediate instance is incomplete in the sense that the missing component has to be accessed as another object in this chain. However, the nature of incompleteness differs dramatically from the incomplete knowledge in abduction. In abduction (hypothesis ) it is a lack of evidence, rather than a lack of access to some object. In deduction or abduction we may keep or "burn" the intermediate premises, when we draw chains of conclusions. But in recursion we need all intermediate instances at once.</div><div>best wishes</div><div>Thomas </div><br><div> <span class="Apple-style-span" style="border-collapse: separate; border-spacing: 0px 0px; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-align: auto; -khtml-text-decorations-in-effect: none; text-indent: 0px; -apple-text-size-adjust: auto; text-transform: none; orphans: 2; white-space: normal; widows: 2; word-spacing: 0px; "><span class="Apple-style-span" style="border-collapse: separate; border-spacing: 0px 0px; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-align: auto; -khtml-text-decorations-in-effect: none; text-indent: 0px; -apple-text-size-adjust: auto; text-transform: none; orphans: 2; white-space: normal; widows: 2; word-spacing: 0px; "><div>*********************************************************</div><div>Thomas Noll</div><div><a href="http://flp.cs.tu-berlin.de/~noll">http://flp.cs.tu-berlin.de/~noll</a></div><div><a href="mailto:noll@cs.tu-berlin.de">noll@cs.tu-berlin.de</a></div><div>Escola Superior de Musica de Catalunya, Barcelona </div><div>Departament de Teoria i Composició </div><div>Tel (priv.): +34 93 268 75 19</div><div>Tel (mobil): +34 66 368 12 02</div><div><br class="khtml-block-placeholder"></div><div>*********************************************************</div><div><br class="khtml-block-placeholder"></div><div><br><br class="khtml-block-placeholder"></div><br class="Apple-interchange-newline"></span></span> </div><br></body></html>