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#GödelNumbers

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Jon Awbrey<p>Higher Order Sign Relations • Discussion 1<br />• <a href="https://inquiryintoinquiry.com/2025/03/27/higher-order-sign-relations-discussion-1-a/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2025/03</span><span class="invisible">/27/higher-order-sign-relations-discussion-1-a/</span></a></p><p>Re: FB | Charles S. Peirce Society • John Corcoran<br />• <a href="https://www.facebook.com/groups/peircesociety/posts/1768975423238442/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://www.</span><span class="ellipsis">facebook.com/groups/peircesoci</span><span class="invisible">ety/posts/1768975423238442/</span></a></p><p>Questions about the proper treatment of use and mention from the standpoint of Peirce’s theory of signs came up recently in discussions on Facebook. In pragmatic semiotics the trade‑off between “signs-of-objects” and “signs-as-objects” opens up the wider space of Higher Order Sign Relations. In previous work on Inquiry Driven Systems I introduced the subject in the following way.</p><p>When interpreters reflect on their use of signs they require an appropriate technical language in which to pursue their reflections. They need signs referring to sign relations, signs referring to elements and components of sign relations, and signs referring to properties and classes of sign relations. The orders of signs developing as reflection evolves can be organized under the heading of “higher order signs” and the reflective sign relations involving them can be referred to as “higher order sign relations”.</p><p>References —</p><p>John Corcoran<br />• <a href="https://johncorcoran.academia.edu/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="">johncorcoran.academia.edu/</span><span class="invisible"></span></a></p><p>Schemata : The Concept of Schema in the History of Logic<br />• <a href="https://www.academia.edu/12691868/SCHEMATA_THE_CONCEPT_OF_SCHEMA_IN_THE_HISTORY_OF_LOGIC" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://www.</span><span class="ellipsis">academia.edu/12691868/SCHEMATA</span><span class="invisible">_THE_CONCEPT_OF_SCHEMA_IN_THE_HISTORY_OF_LOGIC</span></a></p><p>Use And Mention, Use Without Mention, Mention Without Use<br />• <a href="https://www.academia.edu/s/ea64a3484e/schemata#comment_525151" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://www.</span><span class="ellipsis">academia.edu/s/ea64a3484e/sche</span><span class="invisible">mata#comment_525151</span></a></p><p>Resources —</p><p>Higher Order Sign Relations<br />• <a href="https://oeis.org/wiki/Inquiry_Driven_Systems_%E2%80%A2_Part_12#Higher_Order_Sign_Relations" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/Inquiry_Driven_S</span><span class="invisible">ystems_%E2%80%A2_Part_12#Higher_Order_Sign_Relations</span></a> </p><p>Survey of Inquiry Driven Systems<br />• <a href="https://inquiryintoinquiry.com/2024/02/28/survey-of-inquiry-driven-systems-6/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2024/02</span><span class="invisible">/28/survey-of-inquiry-driven-systems-6/</span></a></p><p>Survey of Semiotics, Semiosis, Sign Relations<br />• <a href="https://inquiryintoinquiry.com/2024/01/26/survey-of-semiotics-semiosis-sign-relations-5/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2024/01</span><span class="invisible">/26/survey-of-semiotics-semiosis-sign-relations-5/</span></a></p><p><a href="https://mathstodon.xyz/tags/Peirce" class="mention hashtag" rel="tag">#<span>Peirce</span></a> <a href="https://mathstodon.xyz/tags/Inquiry" class="mention hashtag" rel="tag">#<span>Inquiry</span></a> <a href="https://mathstodon.xyz/tags/Logic" class="mention hashtag" rel="tag">#<span>Logic</span></a> <a href="https://mathstodon.xyz/tags/Mathematics" class="mention hashtag" rel="tag">#<span>Mathematics</span></a> <a href="https://mathstodon.xyz/tags/Reflection" class="mention hashtag" rel="tag">#<span>Reflection</span></a> <br /><a href="https://mathstodon.xyz/tags/Semiotics" class="mention hashtag" rel="tag">#<span>Semiotics</span></a> <a href="https://mathstodon.xyz/tags/SignRelations" class="mention hashtag" rel="tag">#<span>SignRelations</span></a> <a href="https://mathstodon.xyz/tags/HigherOrderSignRelations" class="mention hashtag" rel="tag">#<span>HigherOrderSignRelations</span></a> <br /><a href="https://mathstodon.xyz/tags/InquiryDrivenSystems" class="mention hashtag" rel="tag">#<span>InquiryDrivenSystems</span></a> <a href="https://mathstodon.xyz/tags/ReflectiveInterpretiveFrameworks" class="mention hashtag" rel="tag">#<span>ReflectiveInterpretiveFrameworks</span></a> <br /><a href="https://mathstodon.xyz/tags/Arithmetization" class="mention hashtag" rel="tag">#<span>Arithmetization</span></a> <a href="https://mathstodon.xyz/tags/G%C3%B6delNumbers" class="mention hashtag" rel="tag">#<span>GödelNumbers</span></a> <a href="https://mathstodon.xyz/tags/Quotation" class="mention hashtag" rel="tag">#<span>Quotation</span></a> <a href="https://mathstodon.xyz/tags/UseAndMention" class="mention hashtag" rel="tag">#<span>UseAndMention</span></a></p>
Inquiry Into Inquiry<p><strong>Higher Order Sign Relations • Discussion 1</strong></p><p>Re: <a href="https://www.facebook.com/groups/peircesociety" rel="nofollow noopener noreferrer" target="_blank">FB | Charles S. Peirce Society</a> • <a href="https://www.facebook.com/groups/peircesociety/posts/1768975423238442/" rel="nofollow noopener noreferrer" target="_blank">John Corcoran</a></p><p>Questions about the proper treatment of use and mention from the standpoint of Peirce’s theory of signs came up recently in discussions on Facebook.&nbsp; In pragmatic semiotics the trade‑off between “signs-of-objects” and “signs-as-objects” opens up the wider space of <i>higher order sign relations</i>.&nbsp; In previous work on Inquiry Driven Systems I introduced the subject in the following way.</p><p>When interpreters reflect on their use of signs they require an appropriate technical language in which to pursue their reflections.&nbsp; They need signs referring to sign relations, signs referring to elements and components of sign relations, and signs referring to properties and classes of sign&nbsp;relations.&nbsp; The orders of signs developing as reflection evolves can be organized under the heading of “higher order signs” and the reflective sign relations involving them can be referred to as “higher order sign relations”.</p><p><strong>References</strong></p><ul><li><a href="https://johncorcoran.academia.edu/" rel="nofollow noopener noreferrer" target="_blank">John Corcoran</a></li><ul><li><a href="https://www.academia.edu/12691868/SCHEMATA_THE_CONCEPT_OF_SCHEMA_IN_THE_HISTORY_OF_LOGIC" rel="nofollow noopener noreferrer" target="_blank">Schemata : The Concept of Schema in the History of Logic</a></li><li><a href="https://www.academia.edu/s/ea64a3484e/schemata#comment_525151" rel="nofollow noopener noreferrer" target="_blank">Use And Mention, Use Without Mention, Mention Without Use</a></li></ul></ul><p><strong>Resources</strong></p><ul><li><a href="https://oeis.org/wiki/Inquiry_Driven_Systems_%E2%80%A2_Overview" rel="nofollow noopener noreferrer" target="_blank">Inquiry Driven Systems</a></li><ul><li><a href="https://oeis.org/wiki/Inquiry_Driven_Systems_%E2%80%A2_Part_10#Reflective_Interpretive_Frameworks" rel="nofollow noopener noreferrer" target="_blank">Reflective Interpretive Frameworks</a></li><ul><li><a href="https://oeis.org/wiki/Inquiry_Driven_Systems_%E2%80%A2_Part_12#Higher_Order_Sign_Relations" rel="nofollow noopener noreferrer" target="_blank">Higher Order Sign Relations</a></li></ul></ul><li><a href="https://inquiryintoinquiry.com/2024/02/28/survey-of-inquiry-driven-systems-6/" rel="nofollow noopener noreferrer" target="_blank">Survey of Inquiry Driven Systems</a></li><li><a href="https://inquiryintoinquiry.com/2024/01/26/survey-of-semiotics-semiosis-sign-relations-5/" rel="nofollow noopener noreferrer" target="_blank">Survey of Semiotics, Semiosis, Sign Relations</a></li></ul><p>cc: <a href="https://www.academia.edu/community/lQq2R0" rel="nofollow noopener noreferrer" target="_blank">Academia.edu</a> • BlueSky • <a href="https://groups.io/g/lawsofform/topic/higher_order_sign_relations/111962888" rel="nofollow noopener noreferrer" target="_blank">Laws of Form</a> • <a href="https://mathstodon.xyz/@Inquiry/114241756103141345" rel="nofollow noopener noreferrer" target="_blank">Mathstodon</a> • <a href="https://www.researchgate.net/post/Higher_Order_Sign_Relations_Discussion" rel="nofollow noopener noreferrer" target="_blank">Research Gate</a><br>cc: <a href="https://lists.cs.uni-kassel.de/hyperkitty/list/cg@lists.iccs-conference.org/thread/CLSNF43X3NLU5TLBPE6VYTPAEY273T2H/" rel="nofollow noopener noreferrer" target="_blank">Conceptual Graphs</a> • <a href="https://groups.google.com/g/cybcom/c/LtEXddlFovg" rel="nofollow noopener noreferrer" target="_blank">Cybernetics</a> • <a href="https://groups.google.com/g/structural-modeling/c/9-ReYmpRH1g" rel="nofollow noopener noreferrer" target="_blank">Structural Modeling</a> • <a href="https://groups.google.com/g/syssciwg/c/Nrfvfrt48vM" rel="nofollow noopener noreferrer" target="_blank">Systems Science</a></p><p><a rel="nofollow noopener noreferrer" class="hashtag u-tag u-category" href="https://inquiryintoinquiry.com/tag/arithmetization/" target="_blank">#Arithmetization</a> <a rel="nofollow noopener noreferrer" class="hashtag u-tag u-category" href="https://inquiryintoinquiry.com/tag/c-s-peirce/" target="_blank">#CSPeirce</a> <a rel="nofollow noopener noreferrer" class="hashtag u-tag u-category" href="https://inquiryintoinquiry.com/tag/godel-numbers/" target="_blank">#GödelNumbers</a> <a rel="nofollow noopener noreferrer" class="hashtag u-tag u-category" href="https://inquiryintoinquiry.com/tag/higher-order-sign-relations/" target="_blank">#HigherOrderSignRelations</a> <a rel="nofollow noopener noreferrer" class="hashtag u-tag u-category" href="https://inquiryintoinquiry.com/tag/inquiry/" target="_blank">#Inquiry</a> <a rel="nofollow noopener noreferrer" class="hashtag u-tag u-category" href="https://inquiryintoinquiry.com/tag/inquiry-driven-systems/" target="_blank">#InquiryDrivenSystems</a> <a rel="nofollow noopener noreferrer" class="hashtag u-tag u-category" href="https://inquiryintoinquiry.com/tag/inquiry-into-inquiry/" target="_blank">#InquiryIntoInquiry</a> <a rel="nofollow noopener noreferrer" class="hashtag u-tag u-category" href="https://inquiryintoinquiry.com/tag/logic/" target="_blank">#Logic</a> <a rel="nofollow noopener noreferrer" class="hashtag u-tag u-category" href="https://inquiryintoinquiry.com/tag/mathematics/" target="_blank">#Mathematics</a> <a rel="nofollow noopener noreferrer" class="hashtag u-tag u-category" href="https://inquiryintoinquiry.com/tag/quotation/" target="_blank">#Quotation</a> <a rel="nofollow noopener noreferrer" class="hashtag u-tag u-category" href="https://inquiryintoinquiry.com/tag/reflection/" target="_blank">#Reflection</a> <a rel="nofollow noopener noreferrer" class="hashtag u-tag u-category" href="https://inquiryintoinquiry.com/tag/reflective-interpretive-frameworks/" target="_blank">#ReflectiveInterpretiveFrameworks</a> <a rel="nofollow noopener noreferrer" class="hashtag u-tag u-category" href="https://inquiryintoinquiry.com/tag/semiotics/" target="_blank">#Semiotics</a> <a rel="nofollow noopener noreferrer" class="hashtag u-tag u-category" href="https://inquiryintoinquiry.com/tag/sign-relations/" target="_blank">#SignRelations</a> <a rel="nofollow noopener noreferrer" class="hashtag u-tag u-category" href="https://inquiryintoinquiry.com/tag/triadic-relations/" target="_blank">#TriadicRelations</a> <a rel="nofollow noopener noreferrer" class="hashtag u-tag u-category" href="https://inquiryintoinquiry.com/tag/use-and-mention/" target="_blank">#UseAndMention</a> <a rel="nofollow noopener noreferrer" class="hashtag u-tag u-category" href="https://inquiryintoinquiry.com/tag/visualization/" target="_blank">#Visualization</a></p>
Jon Awbrey<p>Riffs and Rotes<br />• <a href="https://oeis.org/wiki/Riffs_and_Rotes" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="">oeis.org/wiki/Riffs_and_Rotes</span><span class="invisible"></span></a></p><p><a href="https://mathstodon.xyz/tags/RiffsAndRotes" class="mention hashtag" rel="tag">#<span>RiffsAndRotes</span></a> <a href="https://mathstodon.xyz/tags/Primes" class="mention hashtag" rel="tag">#<span>Primes</span></a><br /><a href="https://mathstodon.xyz/tags/Arithmetic" class="mention hashtag" rel="tag">#<span>Arithmetic</span></a> <a href="https://mathstodon.xyz/tags/Arithmetization" class="mention hashtag" rel="tag">#<span>Arithmetization</span></a><br /><a href="https://mathstodon.xyz/tags/GraphTheory" class="mention hashtag" rel="tag">#<span>GraphTheory</span></a> <a href="https://mathstodon.xyz/tags/NumberTheory" class="mention hashtag" rel="tag">#<span>NumberTheory</span></a><br /><a href="https://mathstodon.xyz/tags/PrimeNumbers" class="mention hashtag" rel="tag">#<span>PrimeNumbers</span></a> <a href="https://mathstodon.xyz/tags/G%C3%B6delNumbers" class="mention hashtag" rel="tag">#<span>GödelNumbers</span></a></p>
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