<div>Ordinary language allows the statement of logically absurd propositions that are grammatically and syntactically correct. Ralph references the famous "Epimenides paradox," that was in part the inspiration for mathematician and logician Bertrand Russell to develop his theory of types to construct a "language" that would avoid the logical absurdities of ordinary language. Some philosophers and logicians regard ordinary language as so flawed that is it has questionable value for technical philosophy. For example, a self referential statement such as "This sentence is false." is logically absurd. If the sentence is true, it must be false. If it is false, then it is true. Russell's theory of types addressed these sorts of self referential statements:</div>
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<div><a href="http://en.wikipedia.org/wiki/Epimenides_paradox">http://en.wikipedia.org/wiki/Epimenides_paradox</a></div>
<div>
<p>Paradoxical versions of the Epimenides problem are closely related to a class of more difficult logical problems, including the <a title="Liar paradox" href="http://en.wikipedia.org/wiki/Liar_paradox">liar paradox</a>, <a title="Russell's paradox" href="http://en.wikipedia.org/wiki/Russell%27s_paradox">Russell's paradox</a>, and the <a title="Burali-Forti paradox" href="http://en.wikipedia.org/wiki/Burali-Forti_paradox">Burali-Forti paradox</a>, all of which have self-reference in common with Epimenides. Indeed, the Epimenides paradox is usually classified as a variation on the liar paradox, and sometimes the two are not distinguished. The study of self-reference led to important developments in logic and mathematics in the twentieth century.</p>
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<div>The Epimenides paradox appears explicitly in "Mathematical Logic as Based on the Theory of Types", by <a title="Bertrand Russell" href="http://en.wikipedia.org/wiki/Bertrand_Russell">Bertrand Russell</a>, in the <i>American Journal of Mathematics</i>, volume 30, number 3 (July, 1908), pages 222-262, which opens with the following:</div>
<div>
<dl>
<dd><i>The oldest contradiction of the kind in question is the Epimenides. Epimenides the Cretan said that all Cretans were liars, and all other statements made by Cretans were certainly lies. Was this a lie?</i> </dd></dl>
<p>In that article, Russell uses the Epimenides paradox as the point of departure for discussions of other problems, including the <a title="Burali-Forti paradox" href="http://en.wikipedia.org/wiki/Burali-Forti_paradox">Burali-Forti paradox</a> and the paradox now called <a title="Russell's paradox" href="http://en.wikipedia.org/wiki/Russell%27s_paradox">Russell's paradox</a>. Since Russell, the Epimenides paradox has been referenced repeatedly in logic. Typical of these references is <i><a title="Gödel, Escher, Bach" href="http://en.wikipedia.org/wiki/G%C3%B6del,_Escher,_Bach">Gödel, Escher, Bach</a></i> by <a title="Douglas Hofstadter" href="http://en.wikipedia.org/wiki/Douglas_Hofstadter">Douglas Hofstadter</a>, which accords the paradox a prominent place in a discussion of self-reference.</p>
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<div class="printfooter">Vision2020 Post: Ted Moffett</div></div>
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<div><span class="gmail_quote">On 4/26/09, <b class="gmail_sendername">Ralph Nielsen</b> <<a href="mailto:nielsen@uidaho.edu">nielsen@uidaho.edu</a>> wrote:</span>
<blockquote class="gmail_quote" style="PADDING-LEFT: 1ex; MARGIN: 0px 0px 0px 0.8ex; BORDER-LEFT: #ccc 1px solid">
<div style="WORD-WRAP: break-word">I just happened to run across this little tidbit from something that proclaims itself as MOSCOW EDUCATION (IDAHO); <span style="FONT-SIZE: 13px; COLOR: rgb(51,51,51); FONT-FAMILY: 'Trebuchet MS'">EDUCATIONAL RESEARCH, STATISTICS, REPORTS, AND COMMENTARY FROM MOSCOW, IDAHO, by some-one who calls himself Right-Mind.</span>
<div><font face="'Trebuchet MS'" color="#333333" size="3"><span style="FONT-SIZE: 13px"><br></span></font></div>
<div><font face="'Trebuchet MS'" color="#333333" size="3"><span style="FONT-SIZE: 13px"><span style="FONT-SIZE: 14px; COLOR: rgb(0,0,0); FONT-FAMILY: Helvetica">
<p style="MARGIN: 0px 0px 12px; LINE-HEIGHT: 14px"><font style="COLOR: rgb(51,51,51)" face="Verdana" color="#333333" size="3">In the Moscow Pullman Daily News:</font></p>
<p style="MARGIN: 0px 0px 10px; LINE-HEIGHT: 20px; BACKGROUND-COLOR: rgb(232,232,232)"><font style="COLOR: rgb(51,51,51)" face="Verdana" color="#333333" size="3">There is only one absolute truth: "There is no 'absolute truth.' " Lovers of wisdom have known this for centuries.</font></p>
<p style="MARGIN: 0px 0px 10px; LINE-HEIGHT: 20px; BACKGROUND-COLOR: rgb(232,232,232)"><font style="COLOR: rgb(51,51,51)" face="Verdana" color="#333333" size="3">—<b>Ralph Nielsen, Moscow</b></font></p>
<p style="MARGIN: 0px 0px 12px; LINE-HEIGHT: 14px"><font style="COLOR: rgb(51,51,51)" face="Verdana" color="#333333" size="3">Maybe that statement is embraced by Nielsen; but he would fail 8</font><font style="COLOR: rgb(51,51,51)" face="Verdana" color="#333333" size="2"><sup>th</sup></font><font style="COLOR: rgb(51,51,51)" face="Verdana" color="#333333" size="3"> grade logic for making such an illogical statement.</font></p>
<p style="MARGIN: 0px 0px 12px; LINE-HEIGHT: 14px"><font face="Verdana" color="#333333" size="3"><span style="FONT-SIZE: 12px; LINE-HEIGHT: normal">*****************************************************************************</span></font></p>
<p style="MARGIN: 0px 0px 12px; LINE-HEIGHT: 14px"><span style="FONT-SIZE: 12px; COLOR: rgb(51,51,51); LINE-HEIGHT: normal; FONT-FAMILY: Verdana">It would seem that Mr. Right-Mind has never heard of a logical paradox. As a matter of fact, I heard this from a graduate of Gonzaga University, who said he has never forgotten this humbling fact that was taught by his philosophy professor at Gonzaga. </span></p>
<p style="MARGIN: 0px 0px 12px; LINE-HEIGHT: 14px"><font face="Verdana" color="#333333" size="3"><span style="FONT-SIZE: 12px; LINE-HEIGHT: normal">We can even find a logical paradox in the Bible, "It was one of them, their very own prophet, who said, "Cretans are always liars..." That testimony is true" (Titus 1:12). As Right-Mind would say, "<span style="FONT-SIZE: 14px; COLOR: rgb(0,0,0); LINE-HEIGHT: 14px; FONT-FAMILY: Helvetica"><font style="COLOR: rgb(51,51,51)" face="Verdana" color="#333333" size="3">Maybe that statement is embraced by Paul, in his letter to Titus; but he would fail 8</font><font style="COLOR: rgb(51,51,51)" face="Verdana" color="#333333" size="2"><sup>th</sup></font><font style="COLOR: rgb(51,51,51)" face="Verdana" color="#333333" size="3"> grade logic for making such an illogical statement."</font></span></span></font></p>
<p style="MARGIN: 0px 0px 12px; LINE-HEIGHT: 14px"><span style="FONT-SIZE: 12px; COLOR: rgb(51,51,51); LINE-HEIGHT: normal; FONT-FAMILY: Verdana">Ralph Nielsen</span></p><span class="sg">
<p style="MARGIN: 0px 0px 12px; LINE-HEIGHT: 14px"><span style="FONT-SIZE: 12px; COLOR: rgb(51,51,51); LINE-HEIGHT: normal; FONT-FAMILY: Verdana"> </span></p>
<p style="MARGIN: 0px 0px 12px; LINE-HEIGHT: 14px"><font face="Verdana" color="#333333" size="3"><span style="FONT-SIZE: 12px; LINE-HEIGHT: normal"><br></span></font></p></span></span></span></font></div></div><br>=======================================================<br>
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