Michael Piotrowski<p><a href="https://mastodon.acm.org/tags/PhD" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>PhD</span></a> job in the Dept. of Language and Information Sciences at the University of Lausanne: my colleague Davide Picca has an open PhD position starting on October 1, 2025 in an SNSF-funded project focused on the computational analysis of Charles S. <a href="https://mastodon.acm.org/tags/Peirce" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Peirce</span></a>’s manuscripts.</p><p>Deadline for application: May 19, 2025</p><p><a href="https://career5.successfactors.eu/career?company=universitdP&career_job_req_id=22226&career_ns=job_listing&navBarLevel=JOB_SEARCH" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">career5.successfactors.eu/care</span><span class="invisible">er?company=universitdP&career_job_req_id=22226&career_ns=job_listing&navBarLevel=JOB_SEARCH</span></a></p><p><a href="https://mastodon.acm.org/tags/PhDposition" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>PhDposition</span></a> <a href="https://mastodon.acm.org/tags/AcademicJob" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>AcademicJob</span></a> <a href="https://mastodon.acm.org/tags/DigitalHumanities" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>DigitalHumanities</span></a> <a href="https://mastodon.acm.org/tags/ComputationalHumanities" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>ComputationalHumanities</span></a> <a href="https://mastodon.acm.org/tags/NLProc" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>NLProc</span></a> <a href="https://mastodon.acm.org/tags/CulturalHeritage" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>CulturalHeritage</span></a></p>
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#peirce
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Jon Awbrey<p>C.S. Peirce • Logic of Number (MS 229)<br>• <a href="https://inquiryintoinquiry.com/2012/09/01/c-s-peirce-logic-of-number-ms-229/" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2012/09</span><span class="invisible">/01/c-s-peirce-logic-of-number-ms-229/</span></a></p><p>❝All other sciences without exception depend upon the principles of mathematics; and mathematics borrows nothing from them but hints.❞</p><p>— C.S. Peirce </p><p><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/Inquiry" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Inquiry</span></a> <a href="https://mathstodon.xyz/tags/Mathematics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Mathematics</span></a> <a href="https://mathstodon.xyz/tags/Science" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Science</span></a> <br><a href="https://mathstodon.xyz/tags/FoundationsOfMathematics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>FoundationsOfMathematics</span></a> <a href="https://mathstodon.xyz/tags/Pragmatism" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Pragmatism</span></a></p>
jan“…read superficially, Darwin’s ideas can indeed tip into a vision of “mindless, purposeless algorithmic” selection—a view popularized by several late-twentieth-century biologists and philosophers (eg, Dennett, Dawkins). … Yet Darwin’s own texts, especially when read in the context of thinkers like Whitehead or Peirce, open onto the possibility that teleology is not an external imposition but a creative principle intrinsic to living organisms…”<br>—Matthew Segall, Hans Jonas' "The Phenomenon of Life”: A dialogue with Timothy Jackson about Jonas' treatment of Darwinism<br><a class="hashtag" href="https://pleroma.microblog.se/tag/darwin" rel="nofollow noopener noreferrer" target="_blank">#darwin</a> <a class="hashtag" href="https://pleroma.microblog.se/tag/dennet" rel="nofollow noopener noreferrer" target="_blank">#dennet</a> <a class="hashtag" href="https://pleroma.microblog.se/tag/dawkins" rel="nofollow noopener noreferrer" target="_blank">#dawkins</a> <a class="hashtag" href="https://pleroma.microblog.se/tag/whitehead" rel="nofollow noopener noreferrer" target="_blank">#whitehead</a> <a class="hashtag" href="https://pleroma.microblog.se/tag/peirce" rel="nofollow noopener noreferrer" target="_blank">#peirce</a>
jan“Tim…suggested that, if one generalizes Darwin’s principle in line with thinkers like Charles Sanders Peirce or Alfred North Whitehead, natural selection can be extended beyond biology to show how constraint and self-organization interact with selection-like processes even in physics and chemistry. Understood in this broader way, variation and selection become part of a generative schema of immanent form-production, not just a set of blind mechanics that weed out unfit mutations.”<br>—Matthew Segall, Hans Jonas' "The Phenomenon of Life: A dialogue with Timothy Jackson about Jonas' treatment of Darwinism”<br><a href="https://footnotes2plato.substack.com/p/hans-jonas-the-phenomenon-of-life" rel="nofollow noopener noreferrer" target="_blank">https://footnotes2plato.substack.com/p/hans-jonas-the-phenomenon-of-life</a><br><a class="hashtag" href="https://pleroma.microblog.se/tag/darwin" rel="nofollow noopener noreferrer" target="_blank">#darwin</a> <a class="hashtag" href="https://pleroma.microblog.se/tag/peirce" rel="nofollow noopener noreferrer" target="_blank">#peirce</a> <a class="hashtag" href="https://pleroma.microblog.se/tag/whitehead" rel="nofollow noopener noreferrer" target="_blank">#whitehead</a>
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/" rel="nofollow noopener noreferrer" translate="no" target="_blank"><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/" rel="nofollow noopener noreferrer" translate="no" target="_blank"><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/" rel="nofollow noopener noreferrer" translate="no" target="_blank"><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" rel="nofollow noopener noreferrer" translate="no" target="_blank"><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" rel="nofollow noopener noreferrer" translate="no" target="_blank"><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" rel="nofollow noopener noreferrer" translate="no" target="_blank"><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/" rel="nofollow noopener noreferrer" translate="no" target="_blank"><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/" rel="nofollow noopener noreferrer" translate="no" target="_blank"><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="nofollow noopener noreferrer" target="_blank">#<span>Peirce</span></a> <a href="https://mathstodon.xyz/tags/Inquiry" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Inquiry</span></a> <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/Mathematics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Mathematics</span></a> <a href="https://mathstodon.xyz/tags/Reflection" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Reflection</span></a> <br><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/SignRelations" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>SignRelations</span></a> <a href="https://mathstodon.xyz/tags/HigherOrderSignRelations" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>HigherOrderSignRelations</span></a> <br><a href="https://mathstodon.xyz/tags/InquiryDrivenSystems" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>InquiryDrivenSystems</span></a> <a href="https://mathstodon.xyz/tags/ReflectiveInterpretiveFrameworks" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>ReflectiveInterpretiveFrameworks</span></a> <br><a href="https://mathstodon.xyz/tags/Arithmetization" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Arithmetization</span></a> <a href="https://mathstodon.xyz/tags/G%C3%B6delNumbers" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>GödelNumbers</span></a> <a href="https://mathstodon.xyz/tags/Quotation" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Quotation</span></a> <a href="https://mathstodon.xyz/tags/UseAndMention" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>UseAndMention</span></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/" rel="nofollow noopener noreferrer" translate="no" target="_blank"><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" rel="nofollow noopener noreferrer" translate="no" target="_blank"><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" rel="nofollow noopener noreferrer" translate="no" target="_blank"><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" rel="nofollow noopener noreferrer" translate="no" target="_blank"><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/" rel="nofollow noopener noreferrer" translate="no" target="_blank"><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/" rel="nofollow noopener noreferrer" translate="no" target="_blank"><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="nofollow noopener noreferrer" target="_blank">#<span>Peirce</span></a> <a href="https://mathstodon.xyz/tags/Inquiry" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Inquiry</span></a> <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/Mathematics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Mathematics</span></a> <a href="https://mathstodon.xyz/tags/Reflection" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Reflection</span></a> <br><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/SignRelations" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>SignRelations</span></a> <a href="https://mathstodon.xyz/tags/HigherOrderSignRelations" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>HigherOrderSignRelations</span></a> <br><a href="https://mathstodon.xyz/tags/InquiryDrivenSystems" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>InquiryDrivenSystems</span></a> <a href="https://mathstodon.xyz/tags/ReflectiveInterpretiveFrameworks" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>ReflectiveInterpretiveFrameworks</span></a></p>
Jon Awbrey<p>Signs Of Signs • 4<br>• <a href="https://inquiryintoinquiry.com/2025/03/20/signs-of-signs-4-a/" rel="nofollow noopener noreferrer" translate="no" target="_blank"><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" rel="nofollow noopener noreferrer" translate="no" target="_blank"><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" rel="nofollow noopener noreferrer" translate="no" target="_blank"><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" rel="nofollow noopener noreferrer" translate="no" target="_blank"><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="nofollow noopener noreferrer" target="_blank">#<span>Peirce</span></a> <a href="https://mathstodon.xyz/tags/Inquiry" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Inquiry</span></a> <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/Mathematics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Mathematics</span></a> <a href="https://mathstodon.xyz/tags/Reflection" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Reflection</span></a> <br><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/SignRelations" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>SignRelations</span></a> <a href="https://mathstodon.xyz/tags/HigherOrderSignRelations" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<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/" rel="nofollow noopener noreferrer" translate="no" target="_blank"><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" rel="nofollow noopener noreferrer" translate="no" target="_blank"><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" rel="nofollow noopener noreferrer" translate="no" target="_blank"><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/" rel="nofollow noopener noreferrer" translate="no" target="_blank"><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/" rel="nofollow noopener noreferrer" translate="no" target="_blank"><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="nofollow noopener noreferrer" target="_blank">#<span>Peirce</span></a> <a href="https://mathstodon.xyz/tags/Inquiry" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Inquiry</span></a> <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/Mathematics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Mathematics</span></a> <a href="https://mathstodon.xyz/tags/Reflection" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Reflection</span></a> <br><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/SignRelations" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>SignRelations</span></a> <a href="https://mathstodon.xyz/tags/HigherOrderSignRelations" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<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/" rel="nofollow noopener noreferrer" translate="no" target="_blank"><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" rel="nofollow noopener noreferrer" translate="no" target="_blank"><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" rel="nofollow noopener noreferrer" translate="no" target="_blank"><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/" rel="nofollow noopener noreferrer" translate="no" target="_blank"><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/" rel="nofollow noopener noreferrer" translate="no" target="_blank"><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="nofollow noopener noreferrer" target="_blank">#<span>Peirce</span></a> <a href="https://mathstodon.xyz/tags/Inquiry" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Inquiry</span></a> <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/Mathematics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Mathematics</span></a> <a href="https://mathstodon.xyz/tags/Reflection" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Reflection</span></a> <br><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/SignRelations" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>SignRelations</span></a> <a href="https://mathstodon.xyz/tags/HigherOrderSignRelations" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<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/" rel="nofollow noopener noreferrer" translate="no" target="_blank"><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/" rel="nofollow noopener noreferrer" translate="no" target="_blank"><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" rel="nofollow noopener noreferrer" translate="no" target="_blank"><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/" rel="nofollow noopener noreferrer" translate="no" target="_blank"><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/" rel="nofollow noopener noreferrer" translate="no" target="_blank"><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" rel="nofollow noopener noreferrer" translate="no" target="_blank"><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" rel="nofollow noopener noreferrer" translate="no" target="_blank"><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="nofollow noopener noreferrer" target="_blank">#<span>Peirce</span></a> <a href="https://mathstodon.xyz/tags/Inquiry" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Inquiry</span></a> <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/Mathematics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Mathematics</span></a> <a href="https://mathstodon.xyz/tags/Reflection" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Reflection</span></a> <br><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/SignRelations" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>SignRelations</span></a> <a href="https://mathstodon.xyz/tags/HigherOrderSignRelations" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>HigherOrderSignRelations</span></a></p>
Jon Awbrey<p>The object of reasoning is to find out …<br>• <a href="https://inquiryintoinquiry.com/2024/01/23/the-object-of-reasoning-is-to-find-out-a/" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2024/01</span><span class="invisible">/23/the-object-of-reasoning-is-to-find-out-a/</span></a></p><p>❝No longer wondered what I would do in life but defined my object.❞</p><p>— C.S. Peirce (1861), “My Life, written for the Class-Book”, (CE 1, 3)</p><p>❝The object of reasoning is to find out, from the consideration of what we already know, something else which we do not know.❞</p><p>— C.S. Peirce (1877), “The Fixation of Belief”, (CP 5.365)</p><p>If the object of an investigation is to find out something we do not know then the clues we discover along the way are the signs which determine that object.</p><p>People will continue to be confused about determination so long as they can think of no other forms but analytic-behaviorist-causal-dyadic-temporal, object-as-stimulus, sign-as-response varieties. It’s true ordinary language biases us toward billiard‑ball styles of dyadic determination but there are triadic forms of constraint, determination, and interaction not captured by S‑R chains of that order.</p><p>Pragmatic objects of signs and concepts are anything we talk or think about and semiosis does not conduct its transactions within the bounds of object as cue, sign as cue ball, and interpretants as solids, stripes, and pockets.</p><p>References —</p><p>• Peirce, C.S. (1859–1861), “My Life, written for the Class-Book”, pp. 1–3 in Writings of Charles S. Peirce : A Chronological Edition, Volume 1, 1857–1866, Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.</p><p>• Peirce, C.S. (1877), “The Fixation Of Belief”, Popular Science Monthly 12 (Nov 1877), pp. 1–15. Reprinted in Collected Papers, CP 5.358–387.<br>• <a href="https://www.cspeirce.com/menu/library/bycsp/fixation/fx-frame.htm" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://www.</span><span class="ellipsis">cspeirce.com/menu/library/bycs</span><span class="invisible">p/fixation/fx-frame.htm</span></a> </p><p><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/Logic" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Logic</span></a> <a href="https://mathstodon.xyz/tags/Inquiry" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Inquiry</span></a> <a href="https://mathstodon.xyz/tags/Reasoning" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Reasoning</span></a> <a href="https://mathstodon.xyz/tags/Pragmata" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Pragmata</span></a> <a href="https://mathstodon.xyz/tags/FixationOfBelief" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>FixationOfBelief</span></a></p>
Jon Awbrey<p>Cactus Language • Overview 3.2<br>• <a href="https://inquiryintoinquiry.com/2025/03/07/cactus-language-overview-3/" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2025/03</span><span class="invisible">/07/cactus-language-overview-3/</span></a></p><p>Given a body of conceivable propositions we need a way to follow the threads of their indications from their object domain to their values for the mind and a way to follow those same threads back again. Moreover, we need to implement both ways of proceeding in computational form. Thus we need programs for tracing the clues sentences provide from the universe of their objects to the signs of their values and, in turn, from signs to objects. Ultimately, we need to render propositions so functional as indicators of sets and so essential for examining the equality of sets as to give a rule for the practical conceivability of sets. Tackling that task requires us to introduce a number of new definitions and a collection of additional notational devices, to which we now turn.</p><p>Resources —</p><p>Cactus Language • Overview<br>• <a href="https://oeis.org/wiki/Cactus_Language_%E2%80%A2_Overview" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/Cactus_Language_</span><span class="invisible">%E2%80%A2_Overview</span></a></p><p>Survey of Animated Logical Graphs<br>• <a href="https://inquiryintoinquiry.com/2024/03/18/survey-of-animated-logical-graphs-7/" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2024/03</span><span class="invisible">/18/survey-of-animated-logical-graphs-7/</span></a></p><p>Survey of Theme One Program<br>• <a href="https://inquiryintoinquiry.com/2024/02/26/survey-of-theme-one-program-6/" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2024/02</span><span class="invisible">/26/survey-of-theme-one-program-6/</span></a></p><p><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/Logic" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Logic</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/LogicalGraphs" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>LogicalGraphs</span></a> <a href="https://mathstodon.xyz/tags/DifferentialLogic" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>DifferentialLogic</span></a> <br><a href="https://mathstodon.xyz/tags/AutomataTheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>AutomataTheory</span></a> <a href="https://mathstodon.xyz/tags/FormalLanguages" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>FormalLanguages</span></a> <a href="https://mathstodon.xyz/tags/FormalGrammars" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>FormalGrammars</span></a> <a href="https://mathstodon.xyz/tags/GraphTheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>GraphTheory</span></a></p>
Jon Awbrey<p>Cactus Language • Overview 3.1<br>• <a href="https://inquiryintoinquiry.com/2025/03/07/cactus-language-overview-3/" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2025/03</span><span class="invisible">/07/cactus-language-overview-3/</span></a></p><p>In the development of Cactus Language to date the following two species of graphs have been instrumental.</p><p>• Painted And Rooted Cacti (PARCAI).<br>• Painted And Rooted Conifers (PARCOI).</p><p>It suffices to begin with the first class of data structures, developing their properties and uses in full, leaving discussion of the latter class to a part of the project where their distinctive features are key to developments at that stage. Partly because the two species are so closely related and partly for the sake of brevity, we'll always use the genus name “PARC” to denote the corresponding cacti.</p><p>To provide a computational middle ground between sentences seen as syntactic strings and propositions seen as indicator functions the language designer must not only supply a medium for the expression of propositions but also link the assertion of sentences to a means for inverting the indicator functions, that is, for computing the “fibers” or “inverse images” of the propositions.</p><p><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/Logic" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Logic</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/LogicalGraphs" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>LogicalGraphs</span></a> <a href="https://mathstodon.xyz/tags/DifferentialLogic" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>DifferentialLogic</span></a> <br><a href="https://mathstodon.xyz/tags/AutomataTheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>AutomataTheory</span></a> <a href="https://mathstodon.xyz/tags/FormalLanguages" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>FormalLanguages</span></a> <a href="https://mathstodon.xyz/tags/FormalGrammars" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>FormalGrammars</span></a> <a href="https://mathstodon.xyz/tags/GraphTheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>GraphTheory</span></a></p>
Jon Awbrey<p>Cactus Language • Overview 2<br>• <a href="https://inquiryintoinquiry.com/2025/03/06/cactus-language-overview-2/" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2025/03</span><span class="invisible">/06/cactus-language-overview-2/</span></a></p><p>In order to facilitate the use of propositions as indicator functions it helps to acquire a flexible notation for referring to propositions in that light, for interpreting sentences in a corresponding role, and for negotiating the requirements of mutual sense between the two domains. If none of the formalisms readily available or in common use meet all the design requirements coming to mind then it is necessary to contemplate the design of a new language especially tailored to the purpose.</p><p>In the present application, there is a pressing need to devise a general calculus for composing propositions, computing their values on particular arguments, and inverting their indications to arrive at the sets of things in the universe which are indicated by them. </p><p>For computational purposes it is convenient to have a middle ground or an intermediate language for negotiating between the “koine” of sentences regarded as strings of literal characters and the realm of propositions regarded as objects of logical value, even if that makes it necessary to introduce an artificial medium of exchange between the two domains.</p><p>If the necessary computations are to be carried out in an organized fashion, and ultimately or partially by familiar classes of machines, then the strings expressing logical propositions are likely to find themselves parsed into tree‑like data structures at some stage of the game. As far as their abstract structures as graphs are concerned, there are several species of graph‑theoretic data structures fitting the task in a reasonably effective and efficient way.</p><p><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/Logic" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Logic</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/LogicalGraphs" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>LogicalGraphs</span></a> <a href="https://mathstodon.xyz/tags/DifferentialLogic" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>DifferentialLogic</span></a> <br><a href="https://mathstodon.xyz/tags/FormalLanguages" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>FormalLanguages</span></a></p>
Jon Awbrey<p>Cactus Language • Overview 1.2<br>• <a href="https://inquiryintoinquiry.com/2025/03/01/cactus-language-overview-1/" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2025/03</span><span class="invisible">/01/cactus-language-overview-1/</span></a></p><p>Resource —</p><p>For readers interested and intrepid enough to read ahead, here’s an outline of my work in progress on the OEIS Wiki, which I’ll be revising and serializing to my Inquiry blog.</p><p>Part 1<br>• <a href="https://oeis.org/wiki/Cactus_Language_%E2%80%A2_Part_1" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/Cactus_Language_</span><span class="invisible">%E2%80%A2_Part_1</span></a></p><p>Cactus Language • Syntax<br>• <a href="https://oeis.org/wiki/Cactus_Language_%E2%80%A2_Part_1#Syntax" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/Cactus_Language_</span><span class="invisible">%E2%80%A2_Part_1#Syntax</span></a></p><p>Part 2<br>• <a href="https://oeis.org/wiki/Cactus_Language_%E2%80%A2_Part_2" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/Cactus_Language_</span><span class="invisible">%E2%80%A2_Part_2</span></a></p><p>Generalities About Formal Grammars<br>• <a href="https://oeis.org/wiki/Cactus_Language_%E2%80%A2_Part_2#Generalities" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/Cactus_Language_</span><span class="invisible">%E2%80%A2_Part_2#Generalities</span></a></p><p>Part 3<br>• <a href="https://oeis.org/wiki/Cactus_Language_%E2%80%A2_Part_3" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/Cactus_Language_</span><span class="invisible">%E2%80%A2_Part_3</span></a></p><p>Cactus Language • Stylistics<br>• <a href="https://oeis.org/wiki/Cactus_Language_%E2%80%A2_Part_3#Stylistics" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/Cactus_Language_</span><span class="invisible">%E2%80%A2_Part_3#Stylistics</span></a></p><p>Cactus Language • Mechanics<br>• <a href="https://oeis.org/wiki/Cactus_Language_%E2%80%A2_Part_3#Mechanics" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/Cactus_Language_</span><span class="invisible">%E2%80%A2_Part_3#Mechanics</span></a></p><p>Cactus Language • Semantics<br>• <a href="https://oeis.org/wiki/Cactus_Language_%E2%80%A2_Part_3#Semantics" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/Cactus_Language_</span><span class="invisible">%E2%80%A2_Part_3#Semantics</span></a></p><p>Stretching Exercises<br>• <a href="https://oeis.org/wiki/Cactus_Language_%E2%80%A2_Part_3#Stretching_Exercises" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/Cactus_Language_</span><span class="invisible">%E2%80%A2_Part_3#Stretching_Exercises</span></a></p><p>References<br>• <a href="https://oeis.org/wiki/Cactus_Language_%E2%80%A2_References" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/Cactus_Language_</span><span class="invisible">%E2%80%A2_References</span></a></p><p>Document History <br>• <a href="https://oeis.org/wiki/Cactus_Language_%E2%80%A2_Document_History" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/Cactus_Language_</span><span class="invisible">%E2%80%A2_Document_History</span></a></p><p><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/Logic" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Logic</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/LogicalGraphs" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>LogicalGraphs</span></a> <a href="https://mathstodon.xyz/tags/DifferentialLogic" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>DifferentialLogic</span></a> <br><a href="https://mathstodon.xyz/tags/Automata" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Automata</span></a> <a href="https://mathstodon.xyz/tags/FormalLanguages" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>FormalLanguages</span></a> <a href="https://mathstodon.xyz/tags/FormalGrammars" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>FormalGrammars</span></a> <a href="https://mathstodon.xyz/tags/GraphTheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>GraphTheory</span></a></p>
Jon Awbrey<p>Cactus Language • Overview 1.1<br>• <a href="https://inquiryintoinquiry.com/2025/03/01/cactus-language-overview-1/" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2025/03</span><span class="invisible">/01/cactus-language-overview-1/</span></a></p><p>❝Thus, what looks to us like a sphere of scientific knowledge more accurately should be represented as the inside of a highly irregular and spiky object, like a pincushion or porcupine, with very sharp extensions in certain directions, and virtually no knowledge in immediately adjacent areas. If our intellectual gaze could shift slightly, it would alter each quill’s direction, and suddenly our entire reality would change.❞</p><p>— Herbert J. Bernstein • “Idols of Modern Science”</p><p>The following report describes a calculus for representing propositions as sentences, that is, as syntactically defined sequences of signs, and for working with those sentences in light of their semantically defined contents as logical propositions. In their computational representation the expressions of the calculus parse into a class of graph‑theoretic data structures whose underlying graphs are called “painted cacti”.</p><p>Painted cacti are a specialization of what graph‑theorists refer to as “cacti”, which are in turn a generalization of what they call “trees”. The data structures corresponding to painted cacti have especially nice properties, not only useful in computational terms but interesting from a theoretical standpoint. The remainder of the present Overview is devoted to motivating the development of the indicated family of formal languages, going under the generic name of Cactus Language.</p><p><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/Logic" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Logic</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/LogicalGraphs" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>LogicalGraphs</span></a> <a href="https://mathstodon.xyz/tags/DifferentialLogic" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>DifferentialLogic</span></a> <br><a href="https://mathstodon.xyz/tags/Automata" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Automata</span></a> <a href="https://mathstodon.xyz/tags/FormalLanguages" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>FormalLanguages</span></a> <a href="https://mathstodon.xyz/tags/FormalGrammars" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>FormalGrammars</span></a> <a href="https://mathstodon.xyz/tags/GraphTheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>GraphTheory</span></a></p>
Jon Awbrey<p>Ouch❢<br>• <a href="https://inquiryintoinquiry.com/2025/02/27/ouch%e2%9d%a2-a/" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2025/02</span><span class="invisible">/27/ouch%e2%9d%a2-a/</span></a></p><p>❝A child hears it said that the stove is hot. But it is not, he says; and, indeed, that central body is not touching it, and only what that touches is hot or cold. But he touches it, and finds the testimony confirmed in a striking way. Thus, he becomes aware of ignorance, and it is necessary to suppose a self in which this ignorance can inhere. …</p><p>❝In short, error appears, and it can be explained only by supposing a self which is fallible.</p><p>❝Ignorance and error are all that distinguish our private selves from the absolute ego of pure apperception.❞</p><p>🙞 C.S. Peirce • “Questions Concerning Certain Faculties Claimed For Man”<br>• <a href="https://www.cspeirce.com/menu/library/bycsp/question/qu-frame.htm" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://www.</span><span class="ellipsis">cspeirce.com/menu/library/bycs</span><span class="invisible">p/question/qu-frame.htm</span></a></p><p>Resource —</p><p>Survey of Cybernetics<br>• <a href="https://inquiryintoinquiry.com/2024/01/25/survey-of-cybernetics-4/" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2024/01</span><span class="invisible">/25/survey-of-cybernetics-4/</span></a></p><p><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/Ego" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Ego</span></a> <a href="https://mathstodon.xyz/tags/Error" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Error</span></a> <a href="https://mathstodon.xyz/tags/Ignorance" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Ignorance</span></a> <a href="https://mathstodon.xyz/tags/Inquiry" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Inquiry</span></a> <a href="https://mathstodon.xyz/tags/Selfhood" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Selfhood</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/Cybernetics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Cybernetics</span></a></p>
Jon Awbrey<p>Theory and Therapy of Representations • 5<br>• <a href="https://inquiryintoinquiry.com/2025/02/25/theory-and-therapy-of-representations-5-b/" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2025/02</span><span class="invisible">/25/theory-and-therapy-of-representations-5-b/</span></a></p><p>Re: R.J. Lipton and K.W. Regan • Legal Complexity<br>• <a href="https://rjlipton.com/2022/09/04/legal-complexity/" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">rjlipton.com/2022/09/04/legal-</span><span class="invisible">complexity/</span></a></p><p>❝I do not pretend to understand the moral universe;<br> the arc is a long one, my eye reaches but little ways;<br> I cannot calculate the curve and complete the figure by<br> the experience of sight; I can divine it by conscience.<br> And from what I see I am sure it bends towards justice.❞ </p><p>🙞 Theodore Parker<br>• <a href="https://web.archive.org/web/20200302045624/https://books.google.com/books?id=eHgYAAAAYAAJ&pg=PA48#v=onepage&q&f=false" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">web.archive.org/web/2020030204</span><span class="invisible">5624/https://books.google.com/books?id=eHgYAAAAYAAJ&pg=PA48#v=onepage&q&f=false</span></a></p><p>The arc of the moral universe may bend toward justice — there's hope it will.<br>For the logic of laws to converge on justice may take some doing on our part.</p><p>Resources —</p><p>Survey of Cybernetics<br>• <a href="https://inquiryintoinquiry.com/2024/01/25/survey-of-cybernetics-4/" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2024/01</span><span class="invisible">/25/survey-of-cybernetics-4/</span></a></p><p>Survey of Differential Logic<br>• <a href="https://inquiryintoinquiry.com/2024/02/25/survey-of-differential-logic-7/" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2024/02</span><span class="invisible">/25/survey-of-differential-logic-7/</span></a></p><p>Survey of Inquiry Driven Systems<br>• <a href="https://inquiryintoinquiry.com/2024/02/28/survey-of-inquiry-driven-systems-6/" rel="nofollow noopener noreferrer" translate="no" target="_blank"><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><a href="https://mathstodon.xyz/tags/AdaptiveSystems" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>AdaptiveSystems</span></a> <a href="https://mathstodon.xyz/tags/Cybernetics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Cybernetics</span></a> <a href="https://mathstodon.xyz/tags/SystemsTheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>SystemsTheory</span></a> <a href="https://mathstodon.xyz/tags/Governance" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Governance</span></a> <a href="https://mathstodon.xyz/tags/Democracy" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Democracy</span></a> <br><a href="https://mathstodon.xyz/tags/Plato" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Plato</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/MaxWeber" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>MaxWeber</span></a> <a href="https://mathstodon.xyz/tags/Accountability" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Accountability</span></a> <a href="https://mathstodon.xyz/tags/Representation" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Representation</span></a> <a href="https://mathstodon.xyz/tags/Statistics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Statistics</span></a> <br><a href="https://mathstodon.xyz/tags/Inquiry" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Inquiry</span></a> <a href="https://mathstodon.xyz/tags/InquiryDrivenSystems" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>InquiryDrivenSystems</span></a> <a href="https://mathstodon.xyz/tags/Observation" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Observation</span></a> <a href="https://mathstodon.xyz/tags/Expectation" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Expectation</span></a> <a href="https://mathstodon.xyz/tags/Intention" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Intention</span></a></p>
Jon Awbrey<p>Theory and Therapy of Representations • 4<br>• <a href="https://inquiryintoinquiry.com/2025/02/24/theory-and-therapy-of-representations-4-b/" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2025/02</span><span class="invisible">/24/theory-and-therapy-of-representations-4-b/</span></a></p><p>Re: Ontolog Forum • Paola Di Maio<br>• <a href="https://groups.google.com/g/ontolog-forum/c/Ek_7cCCyFkQ/m/qI0kQv4UAgAJ" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">groups.google.com/g/ontolog-fo</span><span class="invisible">rum/c/Ek_7cCCyFkQ/m/qI0kQv4UAgAJ</span></a></p><p>JA: What are the forces distorting our representations of what's observed, what's expected, and what's intended?</p><p>PDM: The short answer is — the force behind all distortions is our own unenlightened mind, and all the shortfalls this comes with. </p><p>I think that's true, we have to keep reflecting on the state of our personal enlightenments. If we can do that without losing our heads and our systems thinking caps, there will be much we can do to promote the general Enlightenment of the State.</p><p>On both personal and general grounds we have a stake in the projects of self‑governing systems — whether it is possible for them to exist and what it takes for them to thrive in given environments. Systems on that order have of course been studied from many points of view and at many levels of organization. Whether we address them under the names of adaptive, cybernetic, error-correcting, intelligent, or optimal control systems they all must be capable to some degree of learning, reasoning, and self‑guidance.</p><p>Resources —</p><p>Survey of Cybernetics<br>• <a href="https://inquiryintoinquiry.com/2024/01/25/survey-of-cybernetics-4/" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2024/01</span><span class="invisible">/25/survey-of-cybernetics-4/</span></a></p><p>Survey of Differential Logic<br>• <a href="https://inquiryintoinquiry.com/2024/02/25/survey-of-differential-logic-7/" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2024/02</span><span class="invisible">/25/survey-of-differential-logic-7/</span></a></p><p>Survey of Inquiry Driven Systems<br>• <a href="https://inquiryintoinquiry.com/2024/02/28/survey-of-inquiry-driven-systems-6/" rel="nofollow noopener noreferrer" translate="no" target="_blank"><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><a href="https://mathstodon.xyz/tags/AdaptiveSystems" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>AdaptiveSystems</span></a> <a href="https://mathstodon.xyz/tags/Cybernetics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Cybernetics</span></a> <a href="https://mathstodon.xyz/tags/SystemsTheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>SystemsTheory</span></a> <a href="https://mathstodon.xyz/tags/Governance" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Governance</span></a> <a href="https://mathstodon.xyz/tags/Democracy" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Democracy</span></a> <br><a href="https://mathstodon.xyz/tags/Plato" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Plato</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/MaxWeber" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>MaxWeber</span></a> <a href="https://mathstodon.xyz/tags/Accountability" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Accountability</span></a> <a href="https://mathstodon.xyz/tags/Representation" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Representation</span></a> <a href="https://mathstodon.xyz/tags/Statistics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Statistics</span></a> <br><a href="https://mathstodon.xyz/tags/Inquiry" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Inquiry</span></a> <a href="https://mathstodon.xyz/tags/InquiryDrivenSystems" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>InquiryDrivenSystems</span></a> <a href="https://mathstodon.xyz/tags/Observation" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Observation</span></a> <a href="https://mathstodon.xyz/tags/Expectation" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Expectation</span></a> <a href="https://mathstodon.xyz/tags/Intention" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Intention</span></a></p>
Jon Awbrey<p>Theory and Therapy of Representations • 3.2<br>• <a href="https://inquiryintoinquiry.com/2025/02/23/theory-and-therapy-of-representations-3-b/" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2025/02</span><span class="invisible">/23/theory-and-therapy-of-representations-3-b/</span></a></p><p>Scene 2. Theory and Therapy of Representations • 1<br>• <a href="https://inquiryintoinquiry.com/2025/02/21/theory-and-therapy-of-representations-1-b/" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2025/02</span><span class="invisible">/21/theory-and-therapy-of-representations-1-b/</span></a></p><p>Statistics were originally the data a ship of state needed for stationkeeping and staying on course. The Founders of the United States, like the Cybernauts of the Enlightenment they were, engineered a ship of state with checks and balances and error-controlled feedbacks for the sake of representing both reality and the will of the people. In that connection Max Weber saw how a state's accounting systems are intended as representations of realities its crew and passengers must observe or perish.</p><p>That brings us to Question 2 —</p><p>• What are the forces distorting our representations of what's observed, what's expected, and what's intended?</p><p>Resources ─</p><p>Survey of Cybernetics<br>• <a href="https://inquiryintoinquiry.com/2024/01/25/survey-of-cybernetics-4/" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2024/01</span><span class="invisible">/25/survey-of-cybernetics-4/</span></a></p><p>Pragmatic Theory Of Truth<br>• <a href="https://oeis.org/wiki/Pragmatic_Theory_Of_Truth" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/Pragmatic_Theory</span><span class="invisible">_Of_Truth</span></a></p><p><a href="https://mathstodon.xyz/tags/AdaptiveSystems" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>AdaptiveSystems</span></a> <a href="https://mathstodon.xyz/tags/Cybernetics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Cybernetics</span></a> <a href="https://mathstodon.xyz/tags/SystemsTheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>SystemsTheory</span></a> <a href="https://mathstodon.xyz/tags/Governance" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Governance</span></a> <a href="https://mathstodon.xyz/tags/Democracy" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Democracy</span></a> <br><a href="https://mathstodon.xyz/tags/Plato" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Plato</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/MaxWeber" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>MaxWeber</span></a> <a href="https://mathstodon.xyz/tags/Accountability" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Accountability</span></a> <a href="https://mathstodon.xyz/tags/Representation" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Representation</span></a> <a href="https://mathstodon.xyz/tags/Statistics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Statistics</span></a> <br><a href="https://mathstodon.xyz/tags/Inquiry" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Inquiry</span></a> <a href="https://mathstodon.xyz/tags/InquiryDrivenSystems" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>InquiryDrivenSystems</span></a> <a href="https://mathstodon.xyz/tags/Observation" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Observation</span></a> <a href="https://mathstodon.xyz/tags/Expectation" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Expectation</span></a> <a href="https://mathstodon.xyz/tags/Intention" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Intention</span></a></p>
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