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#logicalaxiom

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Jon Awbrey<p><a href="https://mathstodon.xyz/tags/LogicalGraphs" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>LogicalGraphs</span></a> • 16<br>• <a href="https://oeis.org/w/index.php?title=Logical_Graphs&amp;stable=0&amp;redirect=no#Duality" rel="nofollow noopener noreferrer" target="_blank"><span class="invisible">https://</span><span class="ellipsis">oeis.org/w/index.php?title=Log</span><span class="invisible">ical_Graphs&amp;stable=0&amp;redirect=no#Duality</span></a></p><p><a href="https://mathstodon.xyz/tags/Duality" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Duality</span></a> • Logical and Topological</p><p>Turning to the <a href="https://mathstodon.xyz/tags/InitialEquation" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>InitialEquation</span></a> or <a href="https://mathstodon.xyz/tags/LogicalAxiom" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>LogicalAxiom</span></a> whose text expression is \(``\texttt{(}~\texttt{)(}~\texttt{)}=\texttt{(}~\texttt{)}",\) Figure 8 shows the planar maps and their corresponding <a href="https://mathstodon.xyz/tags/DualGraphs" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>DualGraphs</span></a> superimposed.</p><p>Figure 8<br>• <a href="https://oeis.org/w/images/0/09/Logical_Graph_Figure_8_Visible_Frame.jpg" rel="nofollow noopener noreferrer" target="_blank"><span class="invisible">https://</span><span class="ellipsis">oeis.org/w/images/0/09/Logical</span><span class="invisible">_Graph_Figure_8_Visible_Frame.jpg</span></a></p><p><a href="https://mathstodon.xyz/tags/Logic" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Logic</span></a> <a href="https://mathstodon.xyz/tags/Peirce" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Peirce</span></a> <a href="https://mathstodon.xyz/tags/SpencerBrown" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>SpencerBrown</span></a> <a href="https://mathstodon.xyz/tags/LawsOfForm" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>LawsOfForm</span></a><br><a href="https://mathstodon.xyz/tags/PropositionalCalculus" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>PropositionalCalculus</span></a> <a href="https://mathstodon.xyz/tags/BooleanFunctions" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>BooleanFunctions</span></a><br><a href="https://mathstodon.xyz/tags/GraphTheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>GraphTheory</span></a> <a href="https://mathstodon.xyz/tags/ModelTheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>ModelTheory</span></a> <a href="https://mathstodon.xyz/tags/ProofTheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>ProofTheory</span></a></p>
Jon Awbrey<p><a href="https://mathstodon.xyz/tags/LogicalGraphs" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>LogicalGraphs</span></a> • 15<br>• <a href="https://oeis.org/w/index.php?title=Logical_Graphs&amp;stable=0&amp;redirect=no#Duality" rel="nofollow noopener noreferrer" target="_blank"><span class="invisible">https://</span><span class="ellipsis">oeis.org/w/index.php?title=Log</span><span class="invisible">ical_Graphs&amp;stable=0&amp;redirect=no#Duality</span></a></p><p>We have treated in some detail various forms of the <a href="https://mathstodon.xyz/tags/InitialEquation" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>InitialEquation</span></a> or <a href="https://mathstodon.xyz/tags/LogicalAxiom" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>LogicalAxiom</span></a> whose text expression is \(``\texttt{((}~\texttt{))}~=~".\) For comparison, let's record the plane-embedded and <a href="https://mathstodon.xyz/tags/TopologicalDual" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>TopologicalDual</span></a> forms of the axiom whose text expression is \(``\texttt{(}~\texttt{)(}~\texttt{)}=\texttt{(}~\texttt{)}".\)</p><p>Figure 7 reproduces the planar form of the equation we first saw in Figure 1.</p><p>Figure 7<br>• <a href="https://oeis.org/w/images/b/b4/Logical_Graph_Figure_7_Visible_Frame.jpg" rel="nofollow noopener noreferrer" target="_blank"><span class="invisible">https://</span><span class="ellipsis">oeis.org/w/images/b/b4/Logical</span><span class="invisible">_Graph_Figure_7_Visible_Frame.jpg</span></a></p><p><a href="https://mathstodon.xyz/tags/Logic" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Logic</span></a> <a href="https://mathstodon.xyz/tags/Peirce" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Peirce</span></a></p>
Jon Awbrey<p><a href="https://mathstodon.xyz/tags/AllLiarNoParadox" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>AllLiarNoParadox</span></a> <br>• <a href="https://inquiryintoinquiry.com/2015/08/01/all-liar-no-paradox/" rel="nofollow noopener noreferrer" target="_blank"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2015/08</span><span class="invisible">/01/all-liar-no-paradox/</span></a></p><p>A statement \(S_0\) asserts that a statement \(S_1\) is a statement that \(S_1\) is false.</p><p>The statement \(S_0\) violates an <a href="https://mathstodon.xyz/tags/Axiom" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Axiom</span></a> of <a href="https://mathstodon.xyz/tags/Logic" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Logic</span></a>, so it doesn’t really matter whether the <a href="https://mathstodon.xyz/tags/OstensibleStatement" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>OstensibleStatement</span></a> \(S_1,\) the so-called <a href="https://mathstodon.xyz/tags/Liar" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Liar</span></a>, really is a statement or has a <a href="https://mathstodon.xyz/tags/TruthValue" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>TruthValue</span></a>.</p><p><a href="https://mathstodon.xyz/tags/LogicalAxiom" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>LogicalAxiom</span></a> <a href="https://mathstodon.xyz/tags/LawOfLogic" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>LawOfLogic</span></a> <a href="https://mathstodon.xyz/tags/LogicalGraph" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>LogicalGraph</span></a><br><a href="https://mathstodon.xyz/tags/LiarParadox" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>LiarParadox</span></a> <a href="https://mathstodon.xyz/tags/Epimenides" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Epimenides</span></a> <a href="https://mathstodon.xyz/tags/EpimenidesParadox" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>EpimenidesParadox</span></a><br><a href="https://mathstodon.xyz/tags/Peirce" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Peirce</span></a> <a href="https://mathstodon.xyz/tags/Semiotics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Semiotics</span></a> <a href="https://mathstodon.xyz/tags/Semeiotics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Semeiotics</span></a> <a href="https://mathstodon.xyz/tags/SignRelations" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>SignRelations</span></a></p>
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