Jon Awbrey<p><span class="h-card" translate="no"><a href="https://mathstodon.xyz/@JordiGH" class="u-url mention">@<span>JordiGH</span></a></span> </p><p>in a related story …</p><p><a href="https://mathstodon.xyz/tags/SignRelationalManifolds" class="mention hashtag" rel="tag">#<span>SignRelationalManifolds</span></a><br />• <a href="https://mathstodon.xyz/@Inquiry/109297055879472783" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">mathstodon.xyz/@Inquiry/109297</span><span class="invisible">055879472783</span></a></p>
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#SignRelationalManifolds
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Jon Awbrey<p><a href="https://mathstodon.xyz/tags/SignRelationalManifolds" class="mention hashtag" rel="tag">#<span>SignRelationalManifolds</span></a> • Discussion 2<br /><a href="https://inquiryintoinquiry.com/2022/11/07/sign-relational-manifolds-discussion-2/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2022/11</span><span class="invisible">/07/sign-relational-manifolds-discussion-2/</span></a></p><p>Alex Shkotin asks, “Hypothesis. Any material something can be a sign. Is it possible to give an example of something material that cannot be a sign?” I reply —</p><p>Sign relations are mathematical relations able to model discourse or thought. If a relation relates 1 thing, material or not, to a 2nd thing so that both refer to a 3rd thing and the whole relation works to model discourse or thought — then it qualifies as a sign relation.</p>
Jon Awbrey<p><a href="https://mathstodon.xyz/tags/SignRelationalManifolds" class="mention hashtag" rel="tag">#<span>SignRelationalManifolds</span></a> • Discussion 1</p><p>• <a href="https://inquiryintoinquiry.com/2022/11/07/sign-relational-manifolds-discussion-1-2/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2022/11</span><span class="invisible">/07/sign-relational-manifolds-discussion-1-2/</span></a></p><p>Torkild Thellefsen asks on <a href="https://mathstodon.xyz/tags/Facebook" class="mention hashtag" rel="tag">#<span>Facebook</span></a>, “What's at the End of a Chain of Interpretants?”</p><p>It is a <a href="https://mathstodon.xyz/tags/RecurringQuestion" class="mention hashtag" rel="tag">#<span>RecurringQuestion</span></a> — I answered as I often do.</p><p><a href="https://mathstodon.xyz/tags/SemioticManifolds" class="mention hashtag" rel="tag">#<span>SemioticManifolds</span></a>, like physical & mathematical manifolds, may be finite & bounded or infinite & unbounded but they may also be finite & unbounded, having no boundary in the topological sense. Thus <a href="https://mathstodon.xyz/tags/UnboundedSemiosis" class="mention hashtag" rel="tag">#<span>UnboundedSemiosis</span></a> does not imply <a href="https://mathstodon.xyz/tags/InfiniteSemiosis" class="mention hashtag" rel="tag">#<span>InfiniteSemiosis</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/Semiotics" class="mention hashtag" rel="tag">#<span>Semiotics</span></a> <a href="https://mathstodon.xyz/tags/Manifolds" class="mention hashtag" rel="tag">#<span>Manifolds</span></a></p>
Jon Awbrey<p><a href="https://mathstodon.xyz/tags/SignRelationalManifolds" class="mention hashtag" rel="tag">#<span>SignRelationalManifolds</span></a> • 5</p><p>• <a href="https://inquiryintoinquiry.com/2022/11/06/sign-relational-manifolds-5-2/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2022/11</span><span class="invisible">/06/sign-relational-manifolds-5-2/</span></a></p><p>Let me try to say in intuitive terms what I think is really going on here.</p><p>The problem is as old as those about <a href="https://mathstodon.xyz/tags/OtherMinds" class="mention hashtag" rel="tag">#<span>OtherMinds</span></a>, <a href="https://mathstodon.xyz/tags/Intersubjectivity" class="mention hashtag" rel="tag">#<span>Intersubjectivity</span></a>, or <a href="https://mathstodon.xyz/tags/Commensurability" class="mention hashtag" rel="tag">#<span>Commensurability</span></a> and it involves a whole slew of other old problems — <a href="https://mathstodon.xyz/tags/RealityVsAppearance" class="mention hashtag" rel="tag">#<span>RealityVsAppearance</span></a> or <a href="https://mathstodon.xyz/tags/RealityVsRepresentation" class="mention hashtag" rel="tag">#<span>RealityVsRepresentation</span></a>, not to mention <a href="https://mathstodon.xyz/tags/TheOneAndTheMany" class="mention hashtag" rel="tag">#<span>TheOneAndTheMany</span></a>. One way to sum up the question might be “conditions on the possibility of a <a href="https://mathstodon.xyz/tags/MutuallyObjectiveWorld" class="mention hashtag" rel="tag">#<span>MutuallyObjectiveWorld</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/Semiotics" class="mention hashtag" rel="tag">#<span>Semiotics</span></a> <a href="https://mathstodon.xyz/tags/Manifolds" class="mention hashtag" rel="tag">#<span>Manifolds</span></a></p>
Jon Awbrey<p><a href="https://mathstodon.xyz/tags/SignRelationalManifolds" class="mention hashtag" rel="tag">#<span>SignRelationalManifolds</span></a> • 4<br />• <a href="http://inquiryintoinquiry.com/2022/11/05/sign-relational-manifolds-4-2/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">http://</span><span class="ellipsis">inquiryintoinquiry.com/2022/11</span><span class="invisible">/05/sign-relational-manifolds-4-2/</span></a></p><p>Another set of notes I found on this theme strikes me as getting to the point more quickly and though they read a little rough in places I think it may be worth the effort to fill out their general line of approach.</p><p><a href="https://mathstodon.xyz/tags/RepresentationInvariantOntology" class="mention hashtag" rel="tag">#<span>RepresentationInvariantOntology</span></a></p><p>• <a href="https://web.archive.org/web/20150302021003/http://stderr.org/pipermail/inquiry/2003-April/thread.html#439" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">web.archive.org/web/2015030202</span><span class="invisible">1003/http://stderr.org/pipermail/inquiry/2003-April/thread.html#439</span></a></p><p>• <a href="https://web.archive.org/web/20141220180218/http://stderr.org/pipermail/inquiry/2003-April/000439.html" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">web.archive.org/web/2014122018</span><span class="invisible">0218/http://stderr.org/pipermail/inquiry/2003-April/000439.html</span></a></p><p>• <a href="https://web.archive.org/web/20141220180220/http://stderr.org/pipermail/inquiry/2003-April/000440.html" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">web.archive.org/web/2014122018</span><span class="invisible">0220/http://stderr.org/pipermail/inquiry/2003-April/000440.html</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/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><br /><a href="https://mathstodon.xyz/tags/Riemann" class="mention hashtag" rel="tag">#<span>Riemann</span></a> <a href="https://mathstodon.xyz/tags/SergeLang" class="mention hashtag" rel="tag">#<span>SergeLang</span></a> <a href="https://mathstodon.xyz/tags/Manifolds" class="mention hashtag" rel="tag">#<span>Manifolds</span></a> <br /><a href="https://mathstodon.xyz/tags/DifferentialGeometry" class="mention hashtag" rel="tag">#<span>DifferentialGeometry</span></a> <a href="https://mathstodon.xyz/tags/DifferentialLogic" class="mention hashtag" rel="tag">#<span>DifferentialLogic</span></a></p>
Jon Awbrey<p><a href="https://mathstodon.xyz/tags/SignRelationalManifolds" class="mention hashtag" rel="tag">#<span>SignRelationalManifolds</span></a> • 3<br />• <a href="http://inquiryintoinquiry.com/2022/11/03/sign-relational-manifolds-3-2/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">http://</span><span class="ellipsis">inquiryintoinquiry.com/2022/11</span><span class="invisible">/03/sign-relational-manifolds-3-2/</span></a></p><p>I'm not sure when it was I first noticed the relationship between <a href="https://mathstodon.xyz/tags/manifolds" class="mention hashtag" rel="tag">#<span>manifolds</span></a> and <a href="https://mathstodon.xyz/tags/semiotics" class="mention hashtag" rel="tag">#<span>semiotics</span></a> but I distinctly recall the passage in Serge Lang's Differential and Riemannian Manifolds (1995) which brought the triadic character of tangent vectors into high relief.</p><p>Excerpts from Lang's DARM</p><p>Chapter 2. Manifolds<br />2.1. <a href="https://mathstodon.xyz/tags/Atlases" class="mention hashtag" rel="tag">#<span>Atlases</span></a>, <a href="https://mathstodon.xyz/tags/Charts" class="mention hashtag" rel="tag">#<span>Charts</span></a>, <a href="https://mathstodon.xyz/tags/Morphisms" class="mention hashtag" rel="tag">#<span>Morphisms</span></a><br />• <a href="https://web.archive.org/web/20150302021003/http://stderr.org/pipermail/inquiry/2003-April/thread.html#442" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">web.archive.org/web/2015030202</span><span class="invisible">1003/http://stderr.org/pipermail/inquiry/2003-April/thread.html#442</span></a><br />2.2. <a href="https://mathstodon.xyz/tags/Submanifolds" class="mention hashtag" rel="tag">#<span>Submanifolds</span></a>, <a href="https://mathstodon.xyz/tags/Immersions" class="mention hashtag" rel="tag">#<span>Immersions</span></a>, <a href="https://mathstodon.xyz/tags/Submersions" class="mention hashtag" rel="tag">#<span>Submersions</span></a><br />• <a href="https://web.archive.org/web/20141220174800/http://stderr.org/pipermail/inquiry/2003-May/thread.html#448" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">web.archive.org/web/2014122017</span><span class="invisible">4800/http://stderr.org/pipermail/inquiry/2003-May/thread.html#448</span></a></p>
Jon Awbrey<p><span class="h-card" translate="no"><a href="https://mathstodon.xyz/@yog" class="u-url mention">@<span>yog</span></a></span> </p><p>Funny I thought I replied already, must have got lost in the 0zone.</p><p>At any rate, I'm just now in the middle of reworking some old work of mine somewhat along the lines you mention.</p><p><a href="https://mathstodon.xyz/tags/SignRelationalManifolds" class="mention hashtag" rel="tag">#<span>SignRelationalManifolds</span></a> <br />• <a href="https://inquiryintoinquiry.com/tag/sign-relational-manifolds/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/tag/sig</span><span class="invisible">n-relational-manifolds/</span></a></p><p>I keep getting some kind of server error ...</p>
Jon Awbrey<p><span class="h-card" translate="no"><a href="https://mathstodon.xyz/@yog" class="u-url mention">@<span>yog</span></a></span></p><p>Funny I thought I replied already, must have got lost in the 0zone.</p><p>At any rate, I'm just now in the middle of reworking some old work of mine somewhat along the lines you mention.</p><p><a href="https://mathstodon.xyz/tags/SignRelationalManifolds" class="mention hashtag" rel="tag">#<span>SignRelationalManifolds</span></a> <br />• <a href="https://inquiryintoinquiry.com/tag/sign-relational-manifolds/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/tag/sig</span><span class="invisible">n-relational-manifolds/</span></a></p><p>I keep getting some kind of server error ...</p>
Jon Awbrey<p><a href="https://mathstodon.xyz/tags/SignRelationalManifolds" class="mention hashtag" rel="tag">#<span>SignRelationalManifolds</span></a> • 2<br />• <a href="https://inquiryintoinquiry.com/2022/11/01/sign-relational-manifolds-2-2/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2022/11</span><span class="invisible">/01/sign-relational-manifolds-2-2/</span></a></p><p>Applications of <a href="https://mathstodon.xyz/tags/Manifolds" class="mention hashtag" rel="tag">#<span>Manifolds</span></a> are illustrated by the following excerpts from Doolin & Martin's Introduction to <a href="https://mathstodon.xyz/tags/DifferentialGeometry" class="mention hashtag" rel="tag">#<span>DifferentialGeometry</span></a> for Engineers.</p><p><a href="https://web.archive.org/web/20110612002240/http://suo.ieee.org/ontology/thrd28.html#04056" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">web.archive.org/web/2011061200</span><span class="invisible">2240/http://suo.ieee.org/ontology/thrd28.html#04056</span></a></p><p>Manifolds arose in connection with <a href="https://mathstodon.xyz/tags/Ontology" class="mention hashtag" rel="tag">#<span>Ontology</span></a> & <a href="https://mathstodon.xyz/tags/Semiotics" class="mention hashtag" rel="tag">#<span>Semiotics</span></a> due to the issues of <a href="https://mathstodon.xyz/tags/Perspectivity" class="mention hashtag" rel="tag">#<span>Perspectivity</span></a>, <a href="https://mathstodon.xyz/tags/OntologicalRelativity" class="mention hashtag" rel="tag">#<span>OntologicalRelativity</span></a>, & <a href="https://mathstodon.xyz/tags/Interoperability" class="mention hashtag" rel="tag">#<span>Interoperability</span></a> among multiple ontologies. As I see it, those are the very sorts of issues manifolds were invented to handle.</p><p><a href="https://mathstodon.xyz/tags/Peirce" class="mention hashtag" rel="tag">#<span>Peirce</span></a> <a href="https://mathstodon.xyz/tags/Kant" class="mention hashtag" rel="tag">#<span>Kant</span></a> <a href="https://mathstodon.xyz/tags/Riemann" class="mention hashtag" rel="tag">#<span>Riemann</span></a></p>
Jon Awbrey<p><a href="https://mathstodon.xyz/tags/SignRelationalManifolds" class="mention hashtag" rel="tag">#<span>SignRelationalManifolds</span></a> • 1<br />• <a href="https://inquiryintoinquiry.com/2022/10/31/sign-relational-manifolds-1-2/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2022/10</span><span class="invisible">/31/sign-relational-manifolds-1-2/</span></a></p><p>Riemann’s concept of a manifold, especially as later developed, bears a close relationship to Peirce’s concept of a sign relation.</p><p>Here is a set of excerpts from Murray G. Murphey (1961), The Development of Peirce’s Philosophy, discussing Peirce’s reception of Riemann’s philosophy of geometry.</p><p>Manifolds of Signs<br />• <a href="https://web.archive.org/web/20150302021003/http://stderr.org/pipermail/inquiry/2003-April/thread.html#313" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">web.archive.org/web/2015030202</span><span class="invisible">1003/http://stderr.org/pipermail/inquiry/2003-April/thread.html#313</span></a></p><p><a href="https://mathstodon.xyz/tags/SignRelations" class="mention hashtag" rel="tag">#<span>SignRelations</span></a> <a href="https://mathstodon.xyz/tags/Semiotics" class="mention hashtag" rel="tag">#<span>Semiotics</span></a><br /><a href="https://mathstodon.xyz/tags/DifferentialManifolds" class="mention hashtag" rel="tag">#<span>DifferentialManifolds</span></a><br /><a href="https://mathstodon.xyz/tags/DifferentialGeometry" class="mention hashtag" rel="tag">#<span>DifferentialGeometry</span></a><br /><a href="https://mathstodon.xyz/tags/DifferentialLogic" class="mention hashtag" rel="tag">#<span>DifferentialLogic</span></a></p>
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