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	<title>rattus rattus' blog &#187; logic</title>
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	<link>http://blog.rats.at</link>
	<description>where lies keep rotting away</description>
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		<title>Logicians&#8217; warm-up</title>
		<link>http://blog.rats.at/494/logicians-warm-up</link>
		<comments>http://blog.rats.at/494/logicians-warm-up#comments</comments>
		<pubDate>Tue, 30 Jun 2009 09:13:08 +0000</pubDate>
		<dc:creator>rattus</dc:creator>
				<category><![CDATA[Quotes]]></category>
		<category><![CDATA[Riddles]]></category>
		<category><![CDATA[logic]]></category>
		<category><![CDATA[The Fallacy Files]]></category>

		<guid isPermaLink="false">http://blog.rats.at/?p=494</guid>
		<description><![CDATA[No example of the liar&#8217;s paradox but a good warm-up is The Puzzle of the Masked Men (found at Fallacy Files) During a bank robbery, one of the masked robbers shot a bank guard. The police caught all four robbers and interrogated them in an attempt to determine which was the shooter. Each was questioned [...]]]></description>
			<content:encoded><![CDATA[<p>No example of the liar&#8217;s paradox but a good warm-up is</p>
<blockquote><p><a title="The Puzzle of the Masked Men by Fallacy Files" href="http://www.fallacyfiles.org/archive062009.html#06282009" target="_blank">The Puzzle of the Masked Men</a> (found at <a title="Fallacy Files" href="http://www.fallacyfiles.org" target="_blank">Fallacy Files</a>)</p>
<p>During a bank robbery, one of the masked robbers shot a bank guard. The police caught all four robbers and interrogated them in an attempt to determine which was the shooter. Each was questioned while attached to a lie detector machine and &#8230; (read on at <a title="The Puzzle of the Masked Men by Fallacy Files" href="http://www.fallacyfiles.org/archive062009.html#06282009" target="_blank">Fallacy Files</a>)</p></blockquote>
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		<title>Proving a true statement</title>
		<link>http://blog.rats.at/38/proving-a-true-statement</link>
		<comments>http://blog.rats.at/38/proving-a-true-statement#comments</comments>
		<pubDate>Thu, 16 Feb 2006 08:40:56 +0000</pubDate>
		<dc:creator>rattus</dc:creator>
				<category><![CDATA[I am a liar]]></category>
		<category><![CDATA[coffee]]></category>
		<category><![CDATA[indirect proof]]></category>
		<category><![CDATA[logic]]></category>
		<category><![CDATA[paradoxes]]></category>
		<category><![CDATA[prove]]></category>
		<category><![CDATA[truth]]></category>

		<guid isPermaLink="false">http://blog.rats.at/38/proving-a-true-statement</guid>
		<description><![CDATA[Have you ever tried to prove something indirectly? I am pretty sure you are doing it all day long. According to Wikipedia, see Wikipedia: Indirect Proof, it is as simple as the following: If you have no water, you can&#8217;t make coffee. This seems to be undoubtedly true to me, at least since adolescence. And [...]]]></description>
			<content:encoded><![CDATA[<p>Have you ever tried to prove something indirectly? I am pretty sure you are doing it all day long. According to Wikipedia, see <a target="_blank" title="Wikipedia on " href="http://en.wikipedia.org/wiki/Indirect_proof">Wikipedia: Indirect Proof</a>, it is as simple as the following:</p>
<blockquote><p>If you have no water, you can&#8217;t make coffee.</p></blockquote>
<p>This seems to be undoubtedly true to me, at least since adolescence. And it is because water is one of the <a title="rattus rattus about making good coffee" href="/15/cooking-coffee" target="_self">essential ingredients for coffee</a>.<br />
Let us apply the nice rules of Indirect Proving to another statement that is true.</p>
<blockquote><p>First the statement itself:<br />
<strong>This statement is true.</strong></p>
<p>Now, we assume that it is wrong (meaning &#8220;we have no water&#8221;). Then we will see if this leads to a contradiction (or something as unbearable as &#8220;being unable to make more coffee&#8221;).</p>
<p>If the statement is wrong, that is<br />
<strong>&#8220;This statement is true&#8221; is wrong.</strong><br />
it follows that <strong>This statement is wrong</strong>. Because of this, saying the statement is wrong, it follows that <strong>The statement is true</strong>. But this contradicts our assumption.</p></blockquote>
<p>Witty readers probably see that the proof did not precisely lead to a contradiction but to a paradox. Let me suggest that for a moment, we adopt this paradoxical situation here as being as futile as a contradiction.</p>
<p>Well, here is another example of an often heard, and certainly true statement right for you to try out what we have just learned:</p>
<blockquote><p>I am saying the truth.</p></blockquote>
<p>. . .</p>
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