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<p class="MsoNormal"><span style="mso-fareast-language:EN-US">The absurdity of absurd doesn’t only show up in the propositions-as-types explanation. Even purely logical the bottom elimination rule has the same counterintuitive property: ex falso quod libet,
from false follows everything. The issue is rather linguistic in nature there isn’t really a counterpart to False in natural language. In my logic course I explained that False should be translated as “pigs can fly”. This also explains the definition of “not
P” as “P -> False”. I used the following example: if a girl wants to say “I am not going to marry you”, she could say “If I am going to marry you then pigs can fly”. It means no.
</span><span style="font-family:"Apple Color Emoji";mso-fareast-language:EN-US">😊</span><span style="mso-fareast-language:EN-US"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="mso-fareast-language:EN-US">Thorsten <o:p></o:p></span></p>
<p class="MsoNormal"><span style="mso-fareast-language:EN-US"><o:p> </o:p></span></p>
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<p class="MsoNormal" style="margin-left:36.0pt"><b><span style="font-size:12.0pt;color:black">From:
</span></b><span style="font-size:12.0pt;color:black">Agda <agda-bounces@lists.chalmers.se> on behalf of David Banas <capn.freako@gmail.com><br>
<b>Date: </b>Friday, 28 August 2020 at 14:12<br>
<b>To: </b>Agda mailing list <agda@lists.chalmers.se><br>
<b>Subject: </b>[Agda] A philosophical question on absurd.<o:p></o:p></span></p>
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<p class="MsoNormal" style="margin-left:36.0pt"><o:p> </o:p></p>
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<p class="MsoNormal" style="margin-left:36.0pt">Hi all,<o:p></o:p></p>
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<p class="MsoNormal" style="margin-left:36.0pt"><o:p> </o:p></p>
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<p class="MsoNormal" style="margin-left:36.0pt">I'm brand new to Agda and the Curry-Howard isomorphism (and really loving this new exploration of both!), and I have a
<i>philosophical</i> objection to how the <b><span style="font-family:"Courier New"">absurd</span></b> function is used to generate whatever we need to complete a proof.<o:p></o:p></p>
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<p class="MsoNormal" style="margin-left:36.0pt"><o:p> </o:p></p>
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<p class="MsoNormal" style="margin-left:36.0pt">I understand how we are able to satisfy the Agda compiler with the definition of
<b><span style="font-family:"Courier New"">absurd</span></b>; my objection isn't mechanical/technical.<o:p></o:p></p>
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<p class="MsoNormal" style="margin-left:36.0pt"><o:p> </o:p></p>
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<p class="MsoNormal" style="margin-left:36.0pt">What bothers me is a feeling that I'm "cheating" when I use this function that can never be called, in order to "produce" that which I need to complete my proof.<o:p></o:p></p>
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<p class="MsoNormal" style="margin-left:36.0pt"><o:p> </o:p></p>
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<p class="MsoNormal" style="margin-left:36.0pt">I wonder if someone could offer a different perspective on this, for consideration.<o:p></o:p></p>
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<p class="MsoNormal" style="margin-left:36.0pt"><o:p> </o:p></p>
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<p class="MsoNormal" style="margin-left:36.0pt">Thanks!<o:p></o:p></p>
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<p class="MsoNormal" style="margin-left:36.0pt">-db<o:p></o:p></p>
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<p class="MsoNormal" style="margin-left:36.0pt"><o:p> </o:p></p>
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