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>
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#HigherOrderSignRelations
2 posts · 2 participants · 0 posts today
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. 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>. 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><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>Higher Order Sign Relations • 1<br />• <a href="https://inquiryintoinquiry.com/2025/03/22/higher-order-sign-relations-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">/22/higher-order-sign-relations-1-a/</span></a></p><p>Higher Order Sign Relations • Introduction —</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>Some years ago I was formatting my old dissertation proposal on Inquiry Driven Systems for the web when the subject of “signs about signs” arose on the Peirce List. It called to mind the part of my document on Higher Order Sign Relations, on which basis Reflective Interpretive Frameworks are constructed, and the introduction to which begins as above.</p><p>Resources —</p><p>Inquiry Driven Systems<br />• <a href="https://oeis.org/wiki/Inquiry_Driven_Systems_%E2%80%A2_Overview" 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_Overview</span></a> </p><p>Reflective Interpretive Frameworks<br />• <a href="https://oeis.org/wiki/Inquiry_Driven_Systems_%E2%80%A2_Part_10#Reflective_Interpretive_Frameworks" 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_10#Reflective_Interpretive_Frameworks</span></a> </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></p>
Inquiry Into Inquiry<p><strong>Higher Order Sign Relations • 1</strong></p><p><strong>Higher Order Sign Relations • Introduction</strong></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>Some years ago I was formatting my old dissertation proposal on Inquiry Driven Systems for the web when the subject of “signs about signs” arose on the Peirce List. It called to mind the part of my document on Higher Order Sign Relations, on which basis Reflective Interpretive Frameworks are constructed, and the introduction to which begins as above.</p><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/5A3Qgj" rel="nofollow noopener noreferrer" target="_blank">Academia.edu</a> • BlueSky • <a href="https://groups.io/g/lawsofform/topic/higher_order_sign_relations/111851506" rel="nofollow noopener noreferrer" target="_blank">Laws of Form</a> • <a href="https://mathstodon.xyz/@Inquiry/114208001547886678" rel="nofollow noopener noreferrer" target="_blank">Mathstodon</a> • <a href="https://www.researchgate.net/post/Higher_Order_Sign_Relations" 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/MORIXKHB6YVUQGPF5EY2GUILGL5UNX7Y/" rel="nofollow noopener noreferrer" target="_blank">Conceptual Graphs</a> • <a href="https://groups.google.com/g/cybcom/c/8YdnwZeJ5ew" rel="nofollow noopener noreferrer" target="_blank">Cybernetics</a> • <a href="https://groups.google.com/g/structural-modeling/c/5AdnNqv1bVY" rel="nofollow noopener noreferrer" target="_blank">Structural Modeling</a> • <a href="https://groups.google.com/g/syssciwg/c/4ssNya1sI14" 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/c-s-peirce/" target="_blank">#CSPeirce</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-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/recursion/" target="_blank">#Recursion</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/relation-theory/" target="_blank">#RelationTheory</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/type-theory/" target="_blank">#TypeTheory</a></p>
Jon Awbrey<p>Signs Of Signs • 4<br />• <a href="https://inquiryintoinquiry.com/2025/03/20/signs-of-signs-4-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">/20/signs-of-signs-4-a/</span></a> </p><p>Re: Michael Harris • Language About Language<br />• <a href="https://mathematicswithoutapologies.wordpress.com/2015/05/23/language-about-language/comment-page-1/#comment-380" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">mathematicswithoutapologies.wo</span><span class="invisible">rdpress.com/2015/05/23/language-about-language/comment-page-1/#comment-380</span></a> </p><p>❝But then inevitably I find myself wondering whether a proof assistant, or even a formal system, can make the distinction between “technical” and “fundamental” questions. There seems to be no logical distinction. The formalist answer might involve algorithmic complexity, but I don't think that sheds any useful light on the question. The materialist answer (often? usually?) amounts to just‑so stories involving Darwin, and lions on the savannah, and maybe an elephant, or at least a mammoth. I don't find these very satisfying either and would prefer to find something in between, and I would feel vindicated if it could be proved (in I don't know what formal system) that the capacity to make such a distinction entails appreciation of music.❞</p><p>Peirce proposed a distinction between “corollarial” and “theorematic” reasoning in mathematics which strikes me as similar to the distinction Michael Harris seeks between “technical” and “fundamental” questions.</p><p>I can't say I have a lot of insight into how the distinction might be drawn but I recall a number of traditions pointing to the etymology of “theorem” as having to do with the observation of objects and practices whose depth of detail always escapes full accounting by any number of partial views.</p><p>On the subject of music, all I have is the following incidental —</p><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>Perhaps it takes a number theorist to appreciate it …</p><p>Resource —</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><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></p>
Jon Awbrey<p>Signs Of Signs • 3<br />• <a href="https://inquiryintoinquiry.com/2025/03/19/signs-of-signs-3-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">/19/signs-of-signs-3-a/</span></a></p><p>Re: Michael Harris • Language About Language<br />• <a href="https://mathematicswithoutapologies.wordpress.com/2015/05/23/language-about-language/comment-page-1/#comment-353" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">mathematicswithoutapologies.wo</span><span class="invisible">rdpress.com/2015/05/23/language-about-language/comment-page-1/#comment-353</span></a></p><p>❝And if we don't [keep our stories straight], who puts us away?❞</p><p>One's answer, or at least one's initial response to that question will turn on how one feels about formal realities. As I understand it, reality is that which persists in thumping us on the head until we get what it's trying to tell us. Are there formal realities, forms which drive us in that way?</p><p>Discussions like those tend to begin by supposing we can form a distinction between external and internal. That is a formal hypothesis, not yet born out as a formal reality. Are there formal realities which drive us to recognize them, to pick them out of a crowd of formal possibilities?</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 Pragmatic Semiotic Information<br />• <a href="https://inquiryintoinquiry.com/2024/03/01/survey-of-pragmatic-semiotic-information-8/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2024/03</span><span class="invisible">/01/survey-of-pragmatic-semiotic-information-8/</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></p>
Jon Awbrey<p>Signs Of Signs • 2<br />• <a href="https://inquiryintoinquiry.com/2025/03/18/signs-of-signs-2-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">/18/signs-of-signs-2-a/</span></a></p><p>Re: Michael Harris • Language About Language<br />• <a href="https://mathematicswithoutapologies.wordpress.com/2015/05/23/language-about-language/comment-page-1/#comment-346" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">mathematicswithoutapologies.wo</span><span class="invisible">rdpress.com/2015/05/23/language-about-language/comment-page-1/#comment-346</span></a> </p><p>❝I compared mathematics to a “consensual hallucination”, like virtual reality, and I continue to believe that the aim is to get (consensually) to the point where that hallucination is a second nature.❞</p><p>I think that's called “coherentism”, normally contrasted with or complementary to “objectivism”. It's the philosophy of a gang of co‑conspirators who think, “We'll get off scot‑free so long as we all keep our stories straight.”</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 Pragmatic Semiotic Information<br />• <a href="https://inquiryintoinquiry.com/2024/03/01/survey-of-pragmatic-semiotic-information-8/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2024/03</span><span class="invisible">/01/survey-of-pragmatic-semiotic-information-8/</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></p>
Jon Awbrey<p>Signs Of Signs • 1<br />• <a href="https://inquiryintoinquiry.com/2025/03/16/signs-of-signs-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">/16/signs-of-signs-1-a/</span></a></p><p>Re: Michael Harris • Language About Language <br />• <a href="https://mathematicswithoutapologies.wordpress.com/2015/05/23/language-about-language/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">mathematicswithoutapologies.wo</span><span class="invisible">rdpress.com/2015/05/23/language-about-language/</span></a></p><p>There is a language and a corresponding literature treating logic and mathematics as related species of communication and information gathering, namely, the pragmatic-semiotic tradition transmitted through the lifelong efforts of C.S. Peirce. It is by no means a dead language but it continues to fly beneath the radar of many trackers in logic and math today. Nevertheless, the resource remains for those who wish to look into it.</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 Pragmatic Semiotic Information<br />• <a href="https://inquiryintoinquiry.com/2024/03/01/survey-of-pragmatic-semiotic-information-8/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2024/03</span><span class="invisible">/01/survey-of-pragmatic-semiotic-information-8/</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://www.academia.edu/community/LpWxoO" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://www.</span><span class="">academia.edu/community/LpWxoO</span><span class="invisible"></span></a><br />• <a href="https://www.researchgate.net/post/Signs_Of_Signs" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://www.</span><span class="ellipsis">researchgate.net/post/Signs_Of</span><span class="invisible">_Signs</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></p>
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