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>
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Inquiry Into Inquiry<p><strong>Interpreter and Interpretant • Selection 10</strong></p><p><strong>Transfer</strong></p><p>Returning to the scene of Dewey’s “Sign of Rain” example, let’s continue examining how the transfer of knowledge through the analogy of experience works in that case.</p><p>By way of a recap, we began by considering a fragment of the reasoner’s knowledge base which is logically equivalent to a conjunction of two rules.</p><p></p><p> may be thought of as a piece of knowledge or item of information allowing for the possibility of certain conditions, expressed in the form of a logical constraint on the present universe of discourse.</p><p>Next we found it convenient to express all logical statements in terms of their models, that is, in terms of the primitive circumstances or elements of experience over which they hold true.</p><ul><li>Let be the chosen set of experiences, or the circumstances in mind under “past experience”.</li><li>Let be the collective set of experiences, or the prospective total of possible circumstances.</li><li>Let be the current experience, or the circumstances immediately present to the reasoner.</li></ul><p>If we think of the knowledge base as referring to the “regime of experience” over which it is valid, then the sets of models involved in the analogy may be ordered according to the relationships of set inclusion or logical implication existing among them.</p><p>Figure 4 shows the subsumption relations involved in the analogy of experience.</p><p><a href="https://inquiryintoinquiry.com/wp-content/uploads/2025/02/analogy-of-experience.png" rel="nofollow noopener noreferrer" target="_blank"></a> <br> </p><p>In logical terms, the analogy of experience proceeds by inducing a Rule about the validity of a current knowledge base and then by deducing a Fact, the applicability of that knowledge base to a current experience.</p><ul><li>Step 1 is Inductive, abstracting a Rule from a Case and a Fact.</li></ul><p></p><ul><li>Step 2 is Deductive, admitting a Case to a Rule and arriving at a Fact.</li></ul><p></p><p><strong>References</strong></p><ul><li>Awbrey, J.L., and Awbrey, S.M. (1995), “Interpretation as Action : The Risk of Inquiry”, <i>Inquiry : Critical Thinking Across the Disciplines</i> 15(1), 40–52. <a href="https://web.archive.org/web/20001210162300/http://chss.montclair.edu/inquiry/fall95/awbrey.html" rel="nofollow noopener noreferrer" target="_blank">Archive</a>. <a href="https://www.pdcnet.org/inquiryct/content/inquiryct_1995_0015_0001_0040_0052" rel="nofollow noopener noreferrer" target="_blank">Journal</a>. Online <a href="https://www.academia.edu/1266493/Interpretation_as_Action_The_Risk_of_Inquiry" rel="nofollow noopener noreferrer" target="_blank">(doc)</a> <a href="https://www.academia.edu/57812482/Interpretation_as_Action_The_Risk_of_Inquiry" rel="nofollow noopener noreferrer" target="_blank">(pdf)</a>.</li><li>Dewey, J. (1910), <i>How We Think</i>, D.C. Heath, Boston, MA. Reprinted (1991), Prometheus Books, Buffalo, NY. <a href="https://www.gutenberg.org/files/37423/37423-h/37423-h.htm" rel="nofollow noopener noreferrer" target="_blank">Online</a>.</li></ul><p><strong>Resources</strong></p><ul><li><a href="https://inquiryintoinquiry.com/2024/02/27/survey-of-abduction-deduction-induction-analogy-inquiry-4/" rel="nofollow noopener noreferrer" target="_blank">Survey of Abduction, Deduction, Induction, Analogy, Inquiry</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/5A3x6N" rel="nofollow noopener noreferrer" target="_blank">Academia.edu</a> • <a href="https://bsky.app/profile/inquiryintoinquiry.bsky.social/post/3lhyet3gfzk2c" rel="nofollow noopener noreferrer" target="_blank">BlueSky</a> • <a href="https://groups.io/g/lawsofform/topic/interpreter_and_interpretant/110470218" rel="nofollow noopener noreferrer" target="_blank">Laws of Form</a> • <a href="https://mathstodon.xyz/@Inquiry/113997487486895796" rel="nofollow noopener noreferrer" target="_blank">Mathstodon</a> • <a href="https://www.researchgate.net/post/Interpreter_and_Interpretant" 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/QBC7IVRQLQLYO5AMBYSDEMMD27YB3MQZ/" rel="nofollow noopener noreferrer" target="_blank">Conceptual Graphs</a> • <a href="https://groups.google.com/g/cybcom/c/8uSMJbKyFLk" rel="nofollow noopener noreferrer" target="_blank">Cybernetics</a> • <a href="https://groups.google.com/g/structural-modeling/c/2McAWX_3nrE" rel="nofollow noopener noreferrer" target="_blank">Structural Modeling</a> • <a href="https://groups.google.com/g/syssciwg/c/Q_DYjr85UyU" 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/hermeneutics/" target="_blank">#Hermeneutics</a> <a rel="nofollow noopener noreferrer" class="hashtag u-tag u-category" href="https://inquiryintoinquiry.com/tag/interpretation/" target="_blank">#Interpretation</a> <a rel="nofollow noopener noreferrer" class="hashtag u-tag u-category" href="https://inquiryintoinquiry.com/tag/interpretive-frameworks/" target="_blank">#InterpretiveFrameworks</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/logical-graphs/" target="_blank">#LogicalGraphs</a> <a rel="nofollow noopener noreferrer" class="hashtag u-tag u-category" href="https://inquiryintoinquiry.com/tag/objective-frameworks/" target="_blank">#ObjectiveFrameworks</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/visualization/" target="_blank">#Visualization</a></p>
Inquiry Into Inquiry<p><strong>Interpreter and Interpretant • Selection 9</strong></p><p><strong>Transfer</strong></p><p>Let’s examine how the transfer of knowledge through the analogy of experience works in the case of Dewey’s “Sign of Rain” example.</p><p>For concreteness, consider a fragment of the reasoner’s knowledge base which is logically equivalent to a conjunction of two rules.</p><p></p><p> may be thought of as a piece of knowledge or item of information allowing for the possibility of certain conditions, expressed in the form of a logical constraint on the present universe of discourse.</p><p>It is convenient to have the option of expressing all logical statements in terms of their models, that is, in terms of the primitive circumstances or elements of experience over which they hold true.</p><ul><li>Let be the chosen set of experiences, or the circumstances in mind under “past experience”.</li><li>Let be the collective set of experiences, or the prospective total of possible circumstances.</li><li>Let be the current experience, or the circumstances immediately present to the reasoner.</li></ul><p>If we think of the knowledge base as referring to the “regime of experience” over which it is valid, then the sets of models involved in the analogy may be ordered according to the relationships of set inclusion or logical implication existing among them.</p><p>In logical terms, the analogy of experience proceeds by inducing a Rule about the validity of a current knowledge base and then by deducing a Fact, the applicability of that knowledge base to a current experience.</p><ul><li>Step 1 is Inductive, abstracting a Rule from a Case and a Fact.</li></ul><p></p><ul><li>Step 2 is Deductive, admitting a Case to a Rule and arriving at a Fact.</li></ul><p></p><p><strong>References</strong></p><ul><li>Awbrey, J.L., and Awbrey, S.M. (1995), “Interpretation as Action : The Risk of Inquiry”, <i>Inquiry : Critical Thinking Across the Disciplines</i> 15(1), 40–52. <a href="https://web.archive.org/web/20001210162300/http://chss.montclair.edu/inquiry/fall95/awbrey.html" rel="nofollow noopener noreferrer" target="_blank">Archive</a>. <a href="https://www.pdcnet.org/inquiryct/content/inquiryct_1995_0015_0001_0040_0052" rel="nofollow noopener noreferrer" target="_blank">Journal</a>. Online <a href="https://www.academia.edu/1266493/Interpretation_as_Action_The_Risk_of_Inquiry" rel="nofollow noopener noreferrer" target="_blank">(doc)</a> <a href="https://www.academia.edu/57812482/Interpretation_as_Action_The_Risk_of_Inquiry" rel="nofollow noopener noreferrer" target="_blank">(pdf)</a>.</li><li>Dewey, J. (1910), <i>How We Think</i>, D.C. Heath, Boston, MA. Reprinted (1991), Prometheus Books, Buffalo, NY. <a href="https://www.gutenberg.org/files/37423/37423-h/37423-h.htm" rel="nofollow noopener noreferrer" target="_blank">Online</a>.</li></ul><p><strong>Resources</strong></p><ul><li><a href="https://inquiryintoinquiry.com/2024/02/27/survey-of-abduction-deduction-induction-analogy-inquiry-4/" rel="nofollow noopener noreferrer" target="_blank">Survey of Abduction, Deduction, Induction, Analogy, Inquiry</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/LEJEWz" rel="nofollow noopener noreferrer" target="_blank">Academia.edu</a> • <a href="https://bsky.app/profile/inquiryintoinquiry.bsky.social/post/3lgv57fc3uk2j" rel="nofollow noopener noreferrer" target="_blank">BlueSky</a> • <a href="https://groups.io/g/lawsofform/topic/interpreter_and_interpretant/110470218" rel="nofollow noopener noreferrer" target="_blank">Laws of Form</a> • <a href="https://mathstodon.xyz/@Inquiry/113907325393048103" rel="nofollow noopener noreferrer" target="_blank">Mathstodon</a> • <a href="https://www.researchgate.net/post/Interpreter_and_Interpretant" 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/QBC7IVRQLQLYO5AMBYSDEMMD27YB3MQZ/" rel="nofollow noopener noreferrer" target="_blank">Conceptual Graphs</a> • <a href="https://groups.google.com/g/cybcom/c/8uSMJbKyFLk" rel="nofollow noopener noreferrer" target="_blank">Cybernetics</a> • <a href="https://groups.google.com/g/structural-modeling/c/2McAWX_3nrE" rel="nofollow noopener noreferrer" target="_blank">Structural Modeling</a> • <a href="https://groups.google.com/g/syssciwg/c/Q_DYjr85UyU" 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/hermeneutics/" target="_blank">#Hermeneutics</a> <a rel="nofollow noopener noreferrer" class="hashtag u-tag u-category" href="https://inquiryintoinquiry.com/tag/interpretation/" target="_blank">#Interpretation</a> <a rel="nofollow noopener noreferrer" class="hashtag u-tag u-category" href="https://inquiryintoinquiry.com/tag/interpretive-frameworks/" target="_blank">#InterpretiveFrameworks</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/logical-graphs/" target="_blank">#LogicalGraphs</a> <a rel="nofollow noopener noreferrer" class="hashtag u-tag u-category" href="https://inquiryintoinquiry.com/tag/objective-frameworks/" target="_blank">#ObjectiveFrameworks</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/visualization/" target="_blank">#Visualization</a></p>
Inquiry Into Inquiry<p><strong>Interpreter and Interpretant • Selection 8</strong></p><p><strong>Transfer</strong></p><p>What exactly gives the acquisition of a knowledge base its distinctively inductive character? It is evidently the “analogy of experience” involved in applying what we’ve learned in the past to what confronts us in the present.</p><p>Whenever we find ourselves approaching a problem with the thought, <i>If past experience is any guide …</i> we can be sure the analogy of experience has come into play. We are seeking to find analogies between past experience as a totality and present experience as a point of application.</p><p>From a statistical point of view what we mean is this — “If past experience is a fair sample of possible experience then knowledge gained from past experience may usefully apply to present experience”. It is that mechanism which allows a knowledge base to be carried across gulfs of experience which remain indifferent to the effective contents of its rules.</p><p>Next we’ll examine how the transfer of knowledge through the analogy of experience works out in the case of Dewey’s “Sign of Rain” example.</p><p><strong>References</strong></p><ul><li>Awbrey, J.L., and Awbrey, S.M. (1995), “Interpretation as Action : The Risk of Inquiry”, <i>Inquiry : Critical Thinking Across the Disciplines</i> 15(1), 40–52. <a href="https://web.archive.org/web/20001210162300/http://chss.montclair.edu/inquiry/fall95/awbrey.html" rel="nofollow noopener noreferrer" target="_blank">Archive</a>. <a href="https://www.pdcnet.org/inquiryct/content/inquiryct_1995_0015_0001_0040_0052" rel="nofollow noopener noreferrer" target="_blank">Journal</a>. Online <a href="https://www.academia.edu/1266493/Interpretation_as_Action_The_Risk_of_Inquiry" rel="nofollow noopener noreferrer" target="_blank">(doc)</a> <a href="https://www.academia.edu/57812482/Interpretation_as_Action_The_Risk_of_Inquiry" rel="nofollow noopener noreferrer" target="_blank">(pdf)</a>.</li><li>Dewey, J. (1910), <i>How We Think</i>, D.C. Heath, Boston, MA. Reprinted (1991), Prometheus Books, Buffalo, NY. <a href="https://www.gutenberg.org/files/37423/37423-h/37423-h.htm" rel="nofollow noopener noreferrer" target="_blank">Online</a>.</li></ul><p><strong>Resources</strong></p><ul><li><a href="https://inquiryintoinquiry.com/2024/02/27/survey-of-abduction-deduction-induction-analogy-inquiry-4/" rel="nofollow noopener noreferrer" target="_blank">Survey of Abduction, Deduction, Induction, Analogy, Inquiry</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/VDJqz1" rel="nofollow noopener noreferrer" target="_blank">Academia.edu</a> • <a href="https://bsky.app/profile/inquiryintoinquiry.bsky.social/post/3lglehuvjr22h" rel="nofollow noopener noreferrer" target="_blank">BlueSky</a> • <a href="https://groups.io/g/lawsofform/topic/interpreter_and_interpretant/110470218" rel="nofollow noopener noreferrer" target="_blank">Laws of Form</a> • <a href="https://mathstodon.xyz/@Inquiry/113890218212912438" rel="nofollow noopener noreferrer" target="_blank">Mathstodon</a> • <a href="https://www.researchgate.net/post/Interpreter_and_Interpretant" 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/QBC7IVRQLQLYO5AMBYSDEMMD27YB3MQZ/" rel="nofollow noopener noreferrer" target="_blank">Conceptual Graphs</a> • <a href="https://groups.google.com/g/cybcom/c/8uSMJbKyFLk" rel="nofollow noopener noreferrer" target="_blank">Cybernetics</a> • <a href="https://groups.google.com/g/structural-modeling/c/2McAWX_3nrE" rel="nofollow noopener noreferrer" target="_blank">Structural Modeling</a> • <a href="https://groups.google.com/g/syssciwg/c/Q_DYjr85UyU" 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/hermeneutics/" target="_blank">#Hermeneutics</a> <a rel="nofollow noopener noreferrer" class="hashtag u-tag u-category" href="https://inquiryintoinquiry.com/tag/interpretation/" target="_blank">#Interpretation</a> <a rel="nofollow noopener noreferrer" class="hashtag u-tag u-category" href="https://inquiryintoinquiry.com/tag/interpretive-frameworks/" target="_blank">#InterpretiveFrameworks</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/logical-graphs/" target="_blank">#LogicalGraphs</a> <a rel="nofollow noopener noreferrer" class="hashtag u-tag u-category" href="https://inquiryintoinquiry.com/tag/objective-frameworks/" target="_blank">#ObjectiveFrameworks</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/visualization/" target="_blank">#Visualization</a></p>
Inquiry Into Inquiry<p><strong>Interpreter and Interpretant • Selection 7</strong></p><p><strong>Learning</strong></p><p>Rules in a knowledge base, as far as their effective content goes, can be obtained by any mode of inference. For example, consider a proposition of the following form.</p><p></p><p>Such a proposition is usually induced from a consideration of many past events. The inductive inference may be observed to fit the following pattern.</p><p></p><p>However, the same proposition could also be abduced as an explanation of a singular occurrence or deduced as a conclusion of a prior theory.</p><p><strong>References</strong></p><ul><li>Awbrey, J.L., and Awbrey, S.M. (1995), “Interpretation as Action : The Risk of Inquiry”, <i>Inquiry : Critical Thinking Across the Disciplines</i> 15(1), 40–52. <a href="https://web.archive.org/web/20001210162300/http://chss.montclair.edu/inquiry/fall95/awbrey.html" rel="nofollow noopener noreferrer" target="_blank">Archive</a>. <a href="https://www.pdcnet.org/inquiryct/content/inquiryct_1995_0015_0001_0040_0052" rel="nofollow noopener noreferrer" target="_blank">Journal</a>. Online <a href="https://www.academia.edu/1266493/Interpretation_as_Action_The_Risk_of_Inquiry" rel="nofollow noopener noreferrer" target="_blank">(doc)</a> <a href="https://www.academia.edu/57812482/Interpretation_as_Action_The_Risk_of_Inquiry" rel="nofollow noopener noreferrer" target="_blank">(pdf)</a>.</li><li>Dewey, J. (1910), <i>How We Think</i>, D.C. Heath, Boston, MA. Reprinted (1991), Prometheus Books, Buffalo, NY. <a href="https://www.gutenberg.org/files/37423/37423-h/37423-h.htm" rel="nofollow noopener noreferrer" target="_blank">Online</a>.</li></ul><p><strong>Resources</strong></p><ul><li><a href="https://inquiryintoinquiry.com/2024/02/27/survey-of-abduction-deduction-induction-analogy-inquiry-4/" rel="nofollow noopener noreferrer" target="_blank">Survey of Abduction, Deduction, Induction, Analogy, Inquiry</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/lP1OqM" rel="nofollow noopener noreferrer" target="_blank">Academia.edu</a> • <a href="https://bsky.app/profile/inquiryintoinquiry.bsky.social/post/3lfuwyhlk7c2t" rel="nofollow noopener noreferrer" target="_blank">BlueSky</a> • <a href="https://groups.io/g/lawsofform/topic/interpreter_and_interpretant/110470218" rel="nofollow noopener noreferrer" target="_blank">Laws of Form</a> • <a href="https://mathstodon.xyz/@Inquiry/113838957860778252" rel="nofollow noopener noreferrer" target="_blank">Mathstodon</a> • <a href="https://www.researchgate.net/post/Interpreter_and_Interpretant" 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/QBC7IVRQLQLYO5AMBYSDEMMD27YB3MQZ/" rel="nofollow noopener noreferrer" target="_blank">Conceptual Graphs</a> • <a href="https://groups.google.com/g/cybcom/c/8uSMJbKyFLk" rel="nofollow noopener noreferrer" target="_blank">Cybernetics</a> • <a href="https://groups.google.com/g/structural-modeling/c/2McAWX_3nrE" rel="nofollow noopener noreferrer" target="_blank">Structural Modeling</a> • <a href="https://groups.google.com/g/syssciwg/c/Q_DYjr85UyU" 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/hermeneutics/" target="_blank">#Hermeneutics</a> <a rel="nofollow noopener noreferrer" class="hashtag u-tag u-category" href="https://inquiryintoinquiry.com/tag/interpretation/" target="_blank">#Interpretation</a> <a rel="nofollow noopener noreferrer" class="hashtag u-tag u-category" href="https://inquiryintoinquiry.com/tag/interpretive-frameworks/" target="_blank">#InterpretiveFrameworks</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/logical-graphs/" target="_blank">#LogicalGraphs</a> <a rel="nofollow noopener noreferrer" class="hashtag u-tag u-category" href="https://inquiryintoinquiry.com/tag/objective-frameworks/" target="_blank">#ObjectiveFrameworks</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/visualization/" target="_blank">#Visualization</a></p>
Inquiry Into Inquiry<p><strong>Interpreter and Interpretant • Selection 6</strong></p><p><strong>Inquiry and Induction</strong></p><p>To understand the bearing of inductive reasoning on the closing phases of inquiry there are a couple of observations we should make.</p><ul><li>Smaller inquiries are typically woven into larger inquiries, whether the whole pattern of inquiry is carried on by a single agent or by a complex community.</li><li>There are several ways particular instances of inquiry are related to ongoing inquiries at larger scales. Three modes of interaction between component inquiries and compound inquiries may be described under the headings of Learning, Transfer, and Testing of Rules.</li></ul><p>Throughout the course of inquiry the reasoner makes use of rules which have to be transported across intervals of experience, from masses of experience where they are learned to moments of experience where they are applied. Inductive reasoning is involved in the learning and transfer of those rules, both in accumulating a knowledge base and in carrying it through the times between acquisition and application.</p> Learning The main way induction contributes to an ongoing inquiry is through the learning of rules, that is, by creating each rule added to a knowledge base, or any rule used along the way. Transfer The next way induction contributes to an ongoing inquiry is through the operation of analogy, a two‑step combination of induction and deduction which serves to transfer rules from one context to another. Testing Finally, every inquiry making use of a knowledge base amounts to a “field test” of its rules. If the knowledge base fails to serve any live inquiry in a satisfactory way then there is reason to reconsider and possibly amend its rules. <p>Next time we’ll examine how the principles of learning, transfer, and testing apply to Dewey’s “Sign of Rain” example.</p><p><strong>References</strong></p><ul><li>Awbrey, J.L., and Awbrey, S.M. (1995), “Interpretation as Action : The Risk of Inquiry”, <i>Inquiry : Critical Thinking Across the Disciplines</i> 15(1), 40–52. <a href="https://web.archive.org/web/20001210162300/http://chss.montclair.edu/inquiry/fall95/awbrey.html" rel="nofollow noopener noreferrer" target="_blank">Archive</a>. <a href="https://www.pdcnet.org/inquiryct/content/inquiryct_1995_0015_0001_0040_0052" rel="nofollow noopener noreferrer" target="_blank">Journal</a>. Online <a href="https://www.academia.edu/1266493/Interpretation_as_Action_The_Risk_of_Inquiry" rel="nofollow noopener noreferrer" target="_blank">(doc)</a> <a href="https://www.academia.edu/57812482/Interpretation_as_Action_The_Risk_of_Inquiry" rel="nofollow noopener noreferrer" target="_blank">(pdf)</a>.</li><li>Dewey, J. (1910), <i>How We Think</i>, D.C. Heath, Boston, MA. Reprinted (1991), Prometheus Books, Buffalo, NY. <a href="https://www.gutenberg.org/files/37423/37423-h/37423-h.htm" rel="nofollow noopener noreferrer" target="_blank">Online</a>.</li></ul><p><strong>Resources</strong></p><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/lQ17Wn" rel="nofollow noopener noreferrer" target="_blank">Academia.edu</a> • <a href="https://bsky.app/profile/inquiryintoinquiry.bsky.social/post/3lfpnaapook2z" rel="nofollow noopener noreferrer" target="_blank">BlueSky</a> • <a href="https://groups.io/g/lawsofform/topic/interpreter_and_interpretant/110470218" rel="nofollow noopener noreferrer" target="_blank">Laws of Form</a> • <a href="https://mathstodon.xyz/@Inquiry/113827420987235404" rel="nofollow noopener noreferrer" target="_blank">Mathstodon</a> • <a href="https://www.researchgate.net/post/Interpreter_and_Interpretant" 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/QBC7IVRQLQLYO5AMBYSDEMMD27YB3MQZ/" rel="nofollow noopener noreferrer" target="_blank">Conceptual Graphs</a> • <a href="https://groups.google.com/g/cybcom/c/8uSMJbKyFLk" rel="nofollow noopener noreferrer" target="_blank">Cybernetics</a> • <a href="https://groups.google.com/g/structural-modeling/c/2McAWX_3nrE" rel="nofollow noopener noreferrer" target="_blank">Structural Modeling</a> • <a href="https://groups.google.com/g/syssciwg/c/Q_DYjr85UyU" 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/hermeneutics/" target="_blank">#Hermeneutics</a> <a rel="nofollow noopener noreferrer" class="hashtag u-tag u-category" href="https://inquiryintoinquiry.com/tag/interpretation/" target="_blank">#Interpretation</a> <a rel="nofollow noopener noreferrer" class="hashtag u-tag u-category" href="https://inquiryintoinquiry.com/tag/interpretive-frameworks/" target="_blank">#InterpretiveFrameworks</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/logical-graphs/" target="_blank">#LogicalGraphs</a> <a rel="nofollow noopener noreferrer" class="hashtag u-tag u-category" href="https://inquiryintoinquiry.com/tag/objective-frameworks/" target="_blank">#ObjectiveFrameworks</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/visualization/" target="_blank">#Visualization</a></p>
Inquiry Into Inquiry<p><strong>Interpreter and Interpretant • Selection 5</strong></p><p><strong>Inquiry and Inference</strong></p><p>If we follow Dewey’s “Sign of Rain” story far enough to consider the import of thought for action, we realize the subsequent conduct of the interpreter, progressing up through the natural conclusion of the episode — the quickening steps, the seeking of shelter in time to escape the rain — all those acts amount to a series of further interpretants for the initially recognized signs of rain and the first impressions of the actual case. Just as critical reflection develops the positive and negative signs which gather about an idea, pragmatic interpretation explores the consequential and contrasting actions which give effective and testable meaning to a person’s belief in it.</p><p>Figure 3 charts the progress of inquiry in Dewey’s narrative according to the stages of reasoning identified in Peirce’s theory of inquiry, focusing on the compound pattern of inference formed by the first two steps.</p><p><a href="https://inquiryintoinquiry.com/wp-content/uploads/2022/04/cycle-of-inquiry-grayscale.jpg" rel="nofollow noopener noreferrer" target="_blank"></a> <br> </p><ul><li>Step 1 is Abductive, abstracting a Case from the consideration of a Fact and a Rule.</li><ul><li> In the Current situation the Air is cool.</li><li> Just Before it rains, the Air is cool.</li><li> The Current situation is just Before it rains.</li></ul></ul><ul><li>Step 2 is Deductive, admitting the Case to another Rule and arriving at a novel Fact.</li><ul><li> The Current situation is just Before it rains.</li><li> Just Before it rains, a Dark cloud will appear.</li><li> In the Current situation, a Dark cloud will appear.</li></ul></ul><p>What precedes is nowhere near a complete analysis of Dewey’s example, even so far as it might be carried out within the constraints of the syllogistic framework, and it covers only the first two steps of the inquiry process, but perhaps it will do for a start.</p><p><strong>References</strong></p><ul><li>Awbrey, J.L., and Awbrey, S.M. (1995), “Interpretation as Action : The Risk of Inquiry”, <i>Inquiry : Critical Thinking Across the Disciplines</i> 15(1), 40–52. <a href="https://web.archive.org/web/20001210162300/http://chss.montclair.edu/inquiry/fall95/awbrey.html" rel="nofollow noopener noreferrer" target="_blank">Archive</a>. <a href="https://www.pdcnet.org/inquiryct/content/inquiryct_1995_0015_0001_0040_0052" rel="nofollow noopener noreferrer" target="_blank">Journal</a>. Online <a href="https://www.academia.edu/1266493/Interpretation_as_Action_The_Risk_of_Inquiry" rel="nofollow noopener noreferrer" target="_blank">(doc)</a> <a href="https://www.academia.edu/57812482/Interpretation_as_Action_The_Risk_of_Inquiry" rel="nofollow noopener noreferrer" target="_blank">(pdf)</a>.</li><li>Dewey, J. (1910), <i>How We Think</i>, D.C. Heath, Boston, MA. Reprinted (1991), Prometheus Books, Buffalo, NY. <a href="https://www.gutenberg.org/files/37423/37423-h/37423-h.htm" rel="nofollow noopener noreferrer" target="_blank">Online</a>.</li></ul><p><strong>Resources</strong></p><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/5467KX" rel="nofollow noopener noreferrer" target="_blank">Academia.edu</a> • <a href="https://bsky.app/profile/inquiryintoinquiry.bsky.social/post/3lfkqyghpe22a" rel="nofollow noopener noreferrer" target="_blank">BlueSky</a> • <a href="https://groups.io/g/lawsofform/topic/interpreter_and_interpretant/110470218" rel="nofollow noopener noreferrer" target="_blank">Laws of Form</a> • <a href="https://mathstodon.xyz/@Inquiry/113815931184804068" rel="nofollow noopener noreferrer" target="_blank">Mathstodon</a> • <a href="https://www.researchgate.net/post/Interpreter_and_Interpretant" 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/QBC7IVRQLQLYO5AMBYSDEMMD27YB3MQZ/" rel="nofollow noopener noreferrer" target="_blank">Conceptual Graphs</a> • <a href="https://groups.google.com/g/cybcom/c/8uSMJbKyFLk" rel="nofollow noopener noreferrer" target="_blank">Cybernetics</a> • <a href="https://groups.google.com/g/structural-modeling/c/2McAWX_3nrE" rel="nofollow noopener noreferrer" target="_blank">Structural Modeling</a> • <a href="https://groups.google.com/g/syssciwg/c/Q_DYjr85UyU" 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/hermeneutics/" target="_blank">#Hermeneutics</a> <a rel="nofollow noopener noreferrer" class="hashtag u-tag u-category" href="https://inquiryintoinquiry.com/tag/interpretation/" target="_blank">#Interpretation</a> <a rel="nofollow noopener noreferrer" class="hashtag u-tag u-category" href="https://inquiryintoinquiry.com/tag/interpretive-frameworks/" target="_blank">#InterpretiveFrameworks</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/logical-graphs/" target="_blank">#LogicalGraphs</a> <a rel="nofollow noopener noreferrer" class="hashtag u-tag u-category" href="https://inquiryintoinquiry.com/tag/objective-frameworks/" target="_blank">#ObjectiveFrameworks</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/visualization/" target="_blank">#Visualization</a></p>
Inquiry Into Inquiry<p><strong>Interpreter and Interpretant • Selection 4</strong></p><p><strong>Interpretation and Inquiry</strong></p><p>To illustrate the role of sign relations in inquiry we begin with Dewey’s elegant and simple example of reflective thinking in everyday life.</p> <p>A man is walking on a warm day. The sky was clear the last time he observed it; but presently he notes, while occupied primarily with other things, that the air is cooler. It occurs to him that it is probably going to rain; looking up, he sees a dark cloud between him and the sun, and he then quickens his steps. What, if anything, in such a situation can be called thought? Neither the act of walking nor the noting of the cold is a thought. Walking is one direction of activity; looking and noting are other modes of activity. The likelihood that it will rain is, however, something <i>suggested</i>. The pedestrian <i>feels</i> the cold; he <i>thinks of</i> clouds and a coming shower.</p><p>(John Dewey, <i>How We Think</i>, 6–7)</p> <p>In Dewey’s narrative we can identify the characters of the sign relation as follows. <i>Coolness</i> is a Sign of the Object <i>rain</i>, and the Interpretant is <i>the thought of the rain’s likelihood</i>. In his description of reflective thinking Dewey distinguishes two phases, “a state of perplexity, hesitation, doubt” and “an act of search or investigation” (p. 9), comprehensive stages which are further refined in his later model of inquiry.</p><p>Reflection is the action the interpreter takes to establish a fund of connections between the sensory shock of coolness and the objective danger of rain by way of the impression rain is likely. But reflection is more than irresponsible speculation. In reflection the interpreter acts to charge or defuse the thought of rain by seeking other signs the thought implies and evaluating the thought according to the results of that search.</p><p>Figure 2 shows the semiotic relationships involved in Dewey’s story, tracing the structure and function of the sign relation as it informs the activity of inquiry, including both the movements of surprise explanation and intentional action. The labels on the outer edges of the sign‑relational triple suggest the <i>significance</i> of signs for eventual occurrences and the <i>correspondence</i> of ideas with external orientations. But there is nothing essential about the dyadic role distinctions they imply, as it is only in special or degenerate cases that such projections preserve enough information to determine the original sign relation.</p><p><a href="https://inquiryintoinquiry.com/wp-content/uploads/2022/04/deweys-sign-of-rain-example.jpg" rel="nofollow noopener noreferrer" target="_blank"></a> <br> </p><p><strong>References</strong></p><ul><li>Awbrey, J.L., and Awbrey, S.M. (1995), “Interpretation as Action : The Risk of Inquiry”, <i>Inquiry : Critical Thinking Across the Disciplines</i> 15(1), 40–52. <a href="https://web.archive.org/web/20001210162300/http://chss.montclair.edu/inquiry/fall95/awbrey.html" rel="nofollow noopener noreferrer" target="_blank">Archive</a>. <a href="https://www.pdcnet.org/inquiryct/content/inquiryct_1995_0015_0001_0040_0052" rel="nofollow noopener noreferrer" target="_blank">Journal</a>. Online <a href="https://www.academia.edu/1266493/Interpretation_as_Action_The_Risk_of_Inquiry" rel="nofollow noopener noreferrer" target="_blank">(doc)</a> <a href="https://www.academia.edu/57812482/Interpretation_as_Action_The_Risk_of_Inquiry" rel="nofollow noopener noreferrer" target="_blank">(pdf)</a>.</li><li>Dewey, J. (1910), <i>How We Think</i>, D.C. Heath, Boston, MA. Reprinted (1991), Prometheus Books, Buffalo, NY. <a href="https://www.gutenberg.org/files/37423/37423-h/37423-h.htm" rel="nofollow noopener noreferrer" target="_blank">Online</a>.</li></ul><p><strong>Resources</strong></p><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/lQ1xBG" rel="nofollow noopener noreferrer" target="_blank">Academia.edu</a> • <a href="https://bsky.app/profile/inquiryintoinquiry.bsky.social/post/3lffrrojzyk2e" rel="nofollow noopener noreferrer" target="_blank">BlueSky</a> • <a href="https://groups.io/g/lawsofform/topic/interpreter_and_interpretant/110470218" rel="nofollow noopener noreferrer" target="_blank">Laws of Form</a> • <a href="https://mathstodon.xyz/@Inquiry/113804796596813483" rel="nofollow noopener noreferrer" target="_blank">Mathstodon</a> • <a href="https://www.researchgate.net/post/Interpreter_and_Interpretant" 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/QBC7IVRQLQLYO5AMBYSDEMMD27YB3MQZ/" rel="nofollow noopener noreferrer" target="_blank">Conceptual Graphs</a> • <a href="https://groups.google.com/g/cybcom/c/8uSMJbKyFLk" rel="nofollow noopener noreferrer" target="_blank">Cybernetics</a> • <a href="https://groups.google.com/g/structural-modeling/c/2McAWX_3nrE" rel="nofollow noopener noreferrer" target="_blank">Structural Modeling</a> • <a href="https://groups.google.com/g/syssciwg/c/Q_DYjr85UyU" 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/hermeneutics/" target="_blank">#Hermeneutics</a> <a rel="nofollow noopener noreferrer" class="hashtag u-tag u-category" href="https://inquiryintoinquiry.com/tag/interpretation/" target="_blank">#Interpretation</a> <a rel="nofollow noopener noreferrer" class="hashtag u-tag u-category" href="https://inquiryintoinquiry.com/tag/interpretive-frameworks/" target="_blank">#InterpretiveFrameworks</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/logical-graphs/" target="_blank">#LogicalGraphs</a> <a rel="nofollow noopener noreferrer" class="hashtag u-tag u-category" href="https://inquiryintoinquiry.com/tag/objective-frameworks/" target="_blank">#ObjectiveFrameworks</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/visualization/" target="_blank">#Visualization</a></p>
Inquiry Into Inquiry<p><strong>Interpreter and Interpretant • Selection 3</strong></p><p>The following selection from Peirce’s “Lowell Lectures on the Logic of Science” (1866) lays out in detail his “metaphorical argument” for the relationship between interpreters and interpretant signs.</p> <p>I think we need to reflect upon the circumstance that every word implies some proposition or, what is the same thing, every word, concept, symbol has an equivalent term — or one which has become identified with it, — in short, has an <i>interpretant</i>.</p><p>Consider, what a word or symbol is; it is a sort of representation. Now a representation is something which stands for something. I will not undertake to analyze, this evening, this conception of <i>standing for</i> something — but, it is sufficiently plain that it involves the standing <i>to</i> something <i>for</i> something. A thing cannot stand for something without standing <i>to</i> something <i>for</i> that something. Now, what is this that a word stands <i>to</i>? Is it a person?</p><p>We usually say that the word <i>homme</i> stands to a Frenchman for <i>man</i>. It would be a little more precise to say that it stands <i>to</i> the Frenchman’s mind — to his memory. It is still more accurate to say that it addresses a particular remembrance or image in that memory. And what <i>image</i>, what remembrance? Plainly, the one which is the mental equivalent of the word <i>homme</i> — in short, its interpretant. Whatever a word addresses then or <i>stands to</i>, is its interpretant or identified symbol. […]</p><p>The interpretant of a term, then, and that which it stands to are identical. Hence, since it is of the very essence of a symbol that it should stand <i>to</i> something, every symbol — every word and every <i>conception</i> — must have an interpretant — or what is the same thing, must have information or implication. (Peirce 1866, <i>Chronological Edition 1</i>, pp. 466–467).</p> <p><strong>Reference</strong></p><ul><li>Peirce, C.S. (1866), “The Logic of Science, or, Induction and Hypothesis”, Lowell Lectures of 1866, pp. 357–504 in <i>Writings of Charles S. Peirce : A Chronological Edition, Volume 1, 1857–1866</i>, Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.</li></ul><p><strong>Resources</strong></p><ul><li><a href="https://inquiryintoinquiry.com/2008/08/08/hypostatic-abstraction/" rel="nofollow noopener noreferrer" target="_blank">Hypostatic Abstraction</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/LxkveR" rel="nofollow noopener noreferrer" target="_blank">Academia.edu</a> • <a href="https://bsky.app/profile/inquiryintoinquiry.bsky.social/post/3lffbuu2jds2e" rel="nofollow noopener noreferrer" target="_blank">BlueSky</a> • <a href="https://groups.io/g/lawsofform/topic/interpreter_and_interpretant/110470218" rel="nofollow noopener noreferrer" target="_blank">Laws of Form</a> • <a href="https://mathstodon.xyz/@Inquiry/113798283942375335" rel="nofollow noopener noreferrer" target="_blank">Mathstodon</a> • <a href="https://www.researchgate.net/post/Interpreter_and_Interpretant" 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/QBC7IVRQLQLYO5AMBYSDEMMD27YB3MQZ/" rel="nofollow noopener noreferrer" target="_blank">Conceptual Graphs</a> • <a href="https://groups.google.com/g/cybcom/c/8uSMJbKyFLk" rel="nofollow noopener noreferrer" target="_blank">Cybernetics</a> • <a href="https://groups.google.com/g/structural-modeling/c/2McAWX_3nrE" rel="nofollow noopener noreferrer" target="_blank">Structural Modeling</a> • <a href="https://groups.google.com/g/syssciwg/c/Q_DYjr85UyU" 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/hermeneutics/" target="_blank">#Hermeneutics</a> <a rel="nofollow noopener noreferrer" class="hashtag u-tag u-category" href="https://inquiryintoinquiry.com/tag/interpretation/" target="_blank">#Interpretation</a> <a rel="nofollow noopener noreferrer" class="hashtag u-tag u-category" href="https://inquiryintoinquiry.com/tag/interpretive-frameworks/" target="_blank">#InterpretiveFrameworks</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/logical-graphs/" target="_blank">#LogicalGraphs</a> <a rel="nofollow noopener noreferrer" class="hashtag u-tag u-category" href="https://inquiryintoinquiry.com/tag/objective-frameworks/" target="_blank">#ObjectiveFrameworks</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/visualization/" target="_blank">#Visualization</a></p>
Inquiry Into Inquiry<p><strong>Interpreter and Interpretant • Selection 2</strong></p><p>A idea of what Peirce means by an Interpretant and the part it plays in a triadic sign relation is given by the following passage.</p><p>It is clearly indispensable to start with an accurate and broad analysis of the nature of a Sign. I define a Sign as anything which is so determined by something else, called its Object, and so determines an effect upon a person, which effect I call its Interpretant, that the latter is thereby mediately determined by the former. My insertion of “upon a person” is a sop to Cerberus, because I despair of making my own broader conception understood. (Peirce 1908, <i>Selected Writings</i>, p. 404).</p><p>According to his custom of clarifying ideas in terms of their effects, Peirce tells us what a sign is in terms of what it does, the effect it brings to bear on a “person”. That effect he calls the interpretant of the sign. And what of that person? Peirce finesses that question for the moment, resorting to a “Sop to Cerberus”, in other words, a rhetorical gambit used to side‑step a persistent difficulty of exposition. In doing so, Peirce invokes the hypostatic abstraction of a “person” who conducts the movement of signs and embodies the ongoing process of semiosis.</p><p><strong>Reference</strong></p><ul><li>Peirce, C.S. (1908), “Letters to Lady Welby”, Chapter 24, pp. 380–432 in <i>Charles S. Peirce : Selected Writings (Values in a Universe of Chance)</i>, Edited with Introduction and Notes by Philip P. Wiener, Dover Publications, New York, NY, 1966.</li></ul><p><strong>Resources</strong></p><ul><li><a href="https://inquiryintoinquiry.com/2008/08/08/hypostatic-abstraction/" rel="nofollow noopener noreferrer" target="_blank">Hypostatic Abstraction</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/VvWYm7" rel="nofollow noopener noreferrer" target="_blank">Academia.edu</a> • <a href="https://bsky.app/profile/inquiryintoinquiry.bsky.social/post/3lfcmb4lmc22x" rel="nofollow noopener noreferrer" target="_blank">BlueSky</a> • <a href="https://groups.io/g/lawsofform/topic/interpreter_and_interpretant/110470218" rel="nofollow noopener noreferrer" target="_blank">Laws of Form</a> • <a href="https://mathstodon.xyz/@Inquiry/113793235820695548" rel="nofollow noopener noreferrer" target="_blank">Mathstodon</a> • <a href="https://www.researchgate.net/post/Interpreter_and_Interpretant" 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/QBC7IVRQLQLYO5AMBYSDEMMD27YB3MQZ/" rel="nofollow noopener noreferrer" target="_blank">Conceptual Graphs</a> • <a href="https://groups.google.com/g/cybcom/c/8uSMJbKyFLk" rel="nofollow noopener noreferrer" target="_blank">Cybernetics</a> • <a href="https://groups.google.com/g/structural-modeling/c/2McAWX_3nrE" rel="nofollow noopener noreferrer" target="_blank">Structural Modeling</a> • <a href="https://groups.google.com/g/syssciwg/c/Q_DYjr85UyU" 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/hermeneutics/" target="_blank">#Hermeneutics</a> <a rel="nofollow noopener noreferrer" class="hashtag u-tag u-category" href="https://inquiryintoinquiry.com/tag/interpretation/" target="_blank">#Interpretation</a> <a rel="nofollow noopener noreferrer" class="hashtag u-tag u-category" href="https://inquiryintoinquiry.com/tag/interpretive-frameworks/" target="_blank">#InterpretiveFrameworks</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/logical-graphs/" target="_blank">#LogicalGraphs</a> <a rel="nofollow noopener noreferrer" class="hashtag u-tag u-category" href="https://inquiryintoinquiry.com/tag/objective-frameworks/" target="_blank">#ObjectiveFrameworks</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/visualization/" target="_blank">#Visualization</a></p>
Inquiry Into Inquiry<p><strong>Interpreter and Interpretant • Selection 1</strong></p><p>Questions about the relationship between “interpreters” and “interpretants” in Peircean semiotics have broken out again. To put the matter as pointedly as possible — because I know someone or other is bound to — “In a theory of three‑place relations among objects, signs, and interpretant signs, where indeed is there any place for the interpretive agent?”</p><p>By way of getting my feet on the ground with the issue I’ll do what has always helped me before and review a small set of basic texts. Here is the first.</p><p><a href="https://inquiryintoinquiry.com/wp-content/uploads/2022/04/awbrey-awbrey-1995-e280a2-figure-1.png" rel="nofollow noopener noreferrer" target="_blank"></a> <br> </p><p>Words spoken are symbols or signs (<i>symbola</i>) of affections or impressions (<i>pathemata</i>) of the soul (<i>psyche</i>); written words are the signs of words spoken. As writing, so also is speech not the same for all races of men. But the mental affections themselves, of which these words are primarily signs (<i>semeia</i>), are the same for the whole of mankind, as are also the objects (<i>pragmata</i>) of which those affections are representations or likenesses, images, copies (<i>homoiomata</i>). (Aristotle, <i>De Interp.</i> i. 16a4).</p><p><strong>References</strong></p><ul><li>Aristotle, “On Interpretation” (<i>De Interp.</i>), Harold P. Cooke (trans.), pp. 111–179 in <i>Aristotle, Volume 1</i>, Loeb Classical Library, William Heinemann, London, UK, 1938.</li><li>Awbrey, J.L., and Awbrey, S.M. (1995), “Interpretation as Action : The Risk of Inquiry”, <i>Inquiry : Critical Thinking Across the Disciplines</i> 15(1), 40–52. <a href="https://web.archive.org/web/20001210162300/http://chss.montclair.edu/inquiry/fall95/awbrey.html" rel="nofollow noopener noreferrer" target="_blank">Archive</a>. <a href="https://www.pdcnet.org/inquiryct/content/inquiryct_1995_0015_0001_0040_0052" rel="nofollow noopener noreferrer" target="_blank">Journal</a>. Online <a href="https://www.academia.edu/1266493/Interpretation_as_Action_The_Risk_of_Inquiry" rel="nofollow noopener noreferrer" target="_blank">(doc)</a> <a href="https://www.academia.edu/57812482/Interpretation_as_Action_The_Risk_of_Inquiry" rel="nofollow noopener noreferrer" target="_blank">(pdf)</a>.</li></ul><p><strong>Resources</strong></p><ul><li><a href="https://inquiryintoinquiry.com/2024/03/01/survey-of-pragmatic-semiotic-information-8/" rel="nofollow noopener noreferrer" target="_blank">Survey of Pragmatic Semiotic Information</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/V3KqzD" rel="nofollow noopener noreferrer" target="_blank">Academia.edu</a> • <a href="https://bsky.app/profile/inquiryintoinquiry.bsky.social/post/3lf3k3enyo22n" rel="nofollow noopener noreferrer" target="_blank">BlueSky</a> • <a href="https://groups.io/g/lawsofform/topic/interpreter_and_interpretant/110470218" rel="nofollow noopener noreferrer" target="_blank">Laws of Form</a> • <a href="https://mathstodon.xyz/@Inquiry/113782401178953510" rel="nofollow noopener noreferrer" target="_blank">Mathstodon</a> • <a href="https://www.researchgate.net/post/Interpreter_and_Interpretant" 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/QBC7IVRQLQLYO5AMBYSDEMMD27YB3MQZ/" rel="nofollow noopener noreferrer" target="_blank">Conceptual Graphs</a> • <a href="https://groups.google.com/g/cybcom/c/8uSMJbKyFLk" rel="nofollow noopener noreferrer" target="_blank">Cybernetics</a> • <a href="https://groups.google.com/g/structural-modeling/c/2McAWX_3nrE" rel="nofollow noopener noreferrer" target="_blank">Structural Modeling</a> • <a href="https://groups.google.com/g/syssciwg/c/Q_DYjr85UyU" 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/hermeneutics/" target="_blank">#Hermeneutics</a> <a rel="nofollow noopener noreferrer" class="hashtag u-tag u-category" href="https://inquiryintoinquiry.com/tag/interpretation/" target="_blank">#Interpretation</a> <a rel="nofollow noopener noreferrer" class="hashtag u-tag u-category" href="https://inquiryintoinquiry.com/tag/interpretive-frameworks/" target="_blank">#InterpretiveFrameworks</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/logical-graphs/" target="_blank">#LogicalGraphs</a> <a rel="nofollow noopener noreferrer" class="hashtag u-tag u-category" href="https://inquiryintoinquiry.com/tag/objective-frameworks/" target="_blank">#ObjectiveFrameworks</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/visualization/" target="_blank">#Visualization</a></p>
Jon Awbrey<p>Peircean Semiotics and Triadic Sign Relations • 3<br />• <a href="https://inquiryintoinquiry.com/2024/08/23/peircean-semiotics-and-triadic-sign-relations-3-a/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2024/08</span><span class="invisible">/23/peircean-semiotics-and-triadic-sign-relations-3-a/</span></a></p><p>Having labored mightily to bring out a new edition of my primer on sign relations, including material on the pivotal concept of semiotic equivalence relations, I thought it worth the candle to post a notice of the new version here.</p><p>Sign Relations<br />• <a href="https://oeis.org/wiki/Sign_relation" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="">oeis.org/wiki/Sign_relation</span><span class="invisible"></span></a></p><p>Semiotic Equivalence Relations<br />• <a href="https://oeis.org/wiki/Sign_relation#Semiotic_equivalence_relations" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/Sign_relation#Se</span><span class="invisible">miotic_equivalence_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/LogicOfRelatives" class="mention hashtag" rel="tag">#<span>LogicOfRelatives</span></a> <a href="https://mathstodon.xyz/tags/RelationTheory" class="mention hashtag" rel="tag">#<span>RelationTheory</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/Semiosis" class="mention hashtag" rel="tag">#<span>Semiosis</span></a> <a href="https://mathstodon.xyz/tags/SignRelations" class="mention hashtag" rel="tag">#<span>SignRelations</span></a> <a href="https://mathstodon.xyz/tags/TriadicRelations" class="mention hashtag" rel="tag">#<span>TriadicRelations</span></a></p>
Jon Awbrey<p>Peircean Semiotics and Triadic Sign Relations • 2<br />• <a href="https://inquiryintoinquiry.com/2024/08/22/peircean-semiotics-and-triadic-sign-relations-2-a/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2024/08</span><span class="invisible">/22/peircean-semiotics-and-triadic-sign-relations-2-a/</span></a></p><p>When I returned to graduate school for the third time around, this time in systems engineering, I had in mind integrating my long‑standing projects investigating the dynamics of information, inquiry, learning, and reasoning, viewing each as a process whose trajectory evolves over time through the medium which gives it concrete embodiment, namely, a triadic sign relation.</p><p>Up until that time I don't believe I'd ever given much thought to sign relations that had anything smaller than infinite domains of objects, signs, and interpretant signs. Countably infinite domains are what come natural in logic, since that is the norm for the formal languages it uses. Continuous domains come first to mind when turning to physical systems, despite the fact that systems with a discrete or quantized character often enter the fray.</p><p>So it came as a bit of a novelty to me when my advisor, following the motto of engineers the world over to “Keep It Simple, Stupid!” — affectionately known by the acronym KISS — asked me to construct the simplest non‑trivial finite example of a sign relation I could possibly come up with. The outcome of that exercise I wrote up in the following primer on sign relations.</p><p>Inquiry Driven Systems • Sign Relations : A Primer<br />• <a href="https://oeis.org/wiki/Inquiry_Driven_Systems_%E2%80%A2_Part_1#Sign_Relations_:_A_Primer" 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_1#Sign_Relations_:_A_Primer</span></a></p><p>Inquiry Driven Systems • Semiotic Equivalence Relations<br />• <a href="https://oeis.org/wiki/Inquiry_Driven_Systems_%E2%80%A2_Part_1#Semiotic_Equivalence_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_1#Semiotic_Equivalence_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/LogicOfRelatives" class="mention hashtag" rel="tag">#<span>LogicOfRelatives</span></a> <a href="https://mathstodon.xyz/tags/RelationTheory" class="mention hashtag" rel="tag">#<span>RelationTheory</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/Semiosis" class="mention hashtag" rel="tag">#<span>Semiosis</span></a> <a href="https://mathstodon.xyz/tags/SignRelations" class="mention hashtag" rel="tag">#<span>SignRelations</span></a> <a href="https://mathstodon.xyz/tags/TriadicRelations" class="mention hashtag" rel="tag">#<span>TriadicRelations</span></a></p>
Jon Awbrey<p>Peircean Semiotics and Triadic Sign Relations • 1<br />• <a href="https://inquiryintoinquiry.com/2024/08/20/peircean-semiotics-and-triadic-sign-relations-1-a/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2024/08</span><span class="invisible">/20/peircean-semiotics-and-triadic-sign-relations-1-a/</span></a></p><p>As a “guide for the perplexed”, at least when it comes to semiotics, I'll use this thread to collect a budget of resources I think have served to clarify the topic in the past.</p><p>By way of a first offering, let me recommend the following most excellent paper, which I can say with all due modesty in light of the fact all its excellence is due to my most excellent co‑author.</p><p>Awbrey, J.L., and Awbrey, S.M. (1995), “Interpretation as Action : The Risk of Inquiry”, Inquiry : Critical Thinking Across the Disciplines 15(1), pp. 40–52.<br />• <a href="https://web.archive.org/web/20001210162300/http://chss.montclair.edu/inquiry/fall95/awbrey.html" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">web.archive.org/web/2000121016</span><span class="invisible">2300/http://chss.montclair.edu/inquiry/fall95/awbrey.html</span></a><br />• <a href="https://www.pdcnet.org/inquiryct/content/inquiryct_1995_0015_0001_0040_0052" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://www.</span><span class="ellipsis">pdcnet.org/inquiryct/content/i</span><span class="invisible">nquiryct_1995_0015_0001_0040_0052</span></a><br />• <a href="https://www.academia.edu/1266493/Interpretation_as_Action_The_Risk_of_Inquiry" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://www.</span><span class="ellipsis">academia.edu/1266493/Interpret</span><span class="invisible">ation_as_Action_The_Risk_of_Inquiry</span></a><br />• <a href="https://www.academia.edu/57812482/Interpretation_as_Action_The_Risk_of_Inquiry" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://www.</span><span class="ellipsis">academia.edu/57812482/Interpre</span><span class="invisible">tation_as_Action_The_Risk_of_Inquiry</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/LogicOfRelatives" class="mention hashtag" rel="tag">#<span>LogicOfRelatives</span></a> <a href="https://mathstodon.xyz/tags/RelationTheory" class="mention hashtag" rel="tag">#<span>RelationTheory</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/Semiosis" class="mention hashtag" rel="tag">#<span>Semiosis</span></a> <a href="https://mathstodon.xyz/tags/SignRelations" class="mention hashtag" rel="tag">#<span>SignRelations</span></a> <a href="https://mathstodon.xyz/tags/TriadicRelations" class="mention hashtag" rel="tag">#<span>TriadicRelations</span></a></p>
Jon Awbrey<p>Logic of Relatives <br />• <a href="https://inquiryintoinquiry.com/2024/08/05/logic-of-relatives-a/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2024/08</span><span class="invisible">/05/logic-of-relatives-a/</span></a></p><p>Relations Via Relative Terms —</p><p>The logic of relatives is the study of relations as represented in symbolic forms known as rhemes, rhemata, or relative terms.</p><p>Introduction —</p><p>The logic of relatives, more precisely, the logic of relative terms, is the study of relations as represented in symbolic forms called rhemes, rhemata, or relative terms. The treatment of relations by way of their corresponding relative terms affords a distinctive perspective on the subject, even though all angles of approach must ultimately converge on the same formal subject matter.</p><p>The consideration of relative terms has its roots in antiquity but it entered a radically new phase of development with the work of Charles Sanders Peirce, beginning with his paper “Description of a Notation for the Logic of Relatives, Resulting from an Amplification of the Conceptions of Boole's Calculus of Logic” (1870).</p><p>References —</p><p>• Peirce, C.S., “Description of a Notation for the Logic of Relatives, Resulting from an Amplification of the Conceptions of Boole's Calculus of Logic”, Memoirs of the American Academy of Arts and Sciences 9, 317–378, 1870. Reprinted, Collected Papers CP 3.45–149. Reprinted, Chronological Edition CE 2, 359–429.<br />• <a href="https://www.jstor.org/stable/25058006" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://www.</span><span class="">jstor.org/stable/25058006</span><span class="invisible"></span></a><br />• <a href="https://archive.org/details/jstor-25058006" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">archive.org/details/jstor-2505</span><span class="invisible">8006</span></a><br />• <a href="https://books.google.com/books?id=fFnWmf5oLaoC" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">books.google.com/books?id=fFnW</span><span class="invisible">mf5oLaoC</span></a></p><p>Resources —</p><p>Charles Sanders Peirce<br />• <a href="https://mywikibiz.com/Charles_Sanders_Peirce" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">mywikibiz.com/Charles_Sanders_</span><span class="invisible">Peirce</span></a></p><p>Relation Theory<br />• <a href="https://oeis.org/wiki/Relation_theory" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="">oeis.org/wiki/Relation_theory</span><span class="invisible"></span></a></p><p>Survey of Relation Theory<br />• <a href="https://inquiryintoinquiry.com/2024/03/23/survey-of-relation-theory-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">/23/survey-of-relation-theory-8/</span></a></p><p>Peirce's 1870 Logic of Relatives <br />• <a href="https://inquiryintoinquiry.com/2019/09/24/peirces-1870-logic-of-relatives-overview/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2019/09</span><span class="invisible">/24/peirces-1870-logic-of-relatives-overview/</span></a><br />• <a href="https://oeis.org/wiki/Peirce%27s_1870_Logic_Of_Relatives_%E2%80%A2_Overview" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/Peirce%27s_1870_</span><span class="invisible">Logic_Of_Relatives_%E2%80%A2_Overview</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/Logic" class="mention hashtag" rel="tag">#<span>Logic</span></a> <a href="https://mathstodon.xyz/tags/LogicOfRelatives" class="mention hashtag" rel="tag">#<span>LogicOfRelatives</span></a> <a href="https://mathstodon.xyz/tags/MathematicalLogic" class="mention hashtag" rel="tag">#<span>MathematicalLogic</span></a> <br /><a href="https://mathstodon.xyz/tags/Mathematics" class="mention hashtag" rel="tag">#<span>Mathematics</span></a> <a href="https://mathstodon.xyz/tags/RelationTheory" class="mention hashtag" rel="tag">#<span>RelationTheory</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></p>
Jon Awbrey<p>Pragmatic Truth • 4.2<br />• <a href="https://inquiryintoinquiry.com/2024/07/13/pragmatic-truth-4/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2024/07</span><span class="invisible">/13/pragmatic-truth-4/</span></a></p><p>Truth Theories —</p><p>There are practical considerations we need to keep in mind when contemplating such radically simple schemes of classification. Real‑world practice seldom presents us with pure cases and ideal types. There are many settings where it is useful to speak of a truth theory as “almost” k‑adic or to say it “would be” k‑adic if certain details are abstracted away and neglected in a particular context of discussion. That said, given the generic division of truth predicates according to their dimensionality, further species may be differentiated within each genus according to a number of more refined features.</p><p>The truth predicate in a correspondence theory of truth tells of a relation between representations and objective states of affairs and is therefore expressed by a dyadic predicate. In general terms, one says a representation is true of an objective situation, more briefly, a sign is true of an object. The nature of the correspondence may vary from theory to theory in this family. The correspondence can be fairly arbitrary or it can take on the character of an “analogy”, an “icon”, or a “morphism”, where a representation is rendered true of its object by the existence of corresponding elements and a similar structure.</p><p>Resources —</p><p>Logic Syllabus<br />• <a href="https://inquiryintoinquiry.com/logic-syllabus/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/logic-s</span><span class="invisible">yllabus/</span></a></p><p>Pragmatic Maxim<br />• <a href="https://inquiryintoinquiry.com/2023/08/07/pragmatic-maxim-a/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2023/08</span><span class="invisible">/07/pragmatic-maxim-a/</span></a></p><p>Truth Theory<br />• <a href="https://oeis.org/wiki/Truth_theory" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="">oeis.org/wiki/Truth_theory</span><span class="invisible"></span></a></p><p>Pragmatic Theory Of Truth • Document History<br />• <a href="https://oeis.org/wiki/Pragmatic_Theory_Of_Truth" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/Pragmatic_Theory</span><span class="invisible">_Of_Truth</span></a> <br />• <a href="https://oeis.org/wiki/Pragmatic_Theory_Of_Truth#Document_history" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/Pragmatic_Theory</span><span class="invisible">_Of_Truth#Document_history</span></a> </p><p>Correspondence Theory Of Truth<br />• <a href="https://oeis.org/wiki/Correspondence_Theory_Of_Truth" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/Correspondence_T</span><span class="invisible">heory_Of_Truth</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/Logic" class="mention hashtag" rel="tag">#<span>Logic</span></a> <a href="https://mathstodon.xyz/tags/Inquiry" class="mention hashtag" rel="tag">#<span>Inquiry</span></a> <a href="https://mathstodon.xyz/tags/Truth" class="mention hashtag" rel="tag">#<span>Truth</span></a> <a href="https://mathstodon.xyz/tags/PragmaticTruth" class="mention hashtag" rel="tag">#<span>PragmaticTruth</span></a> <a href="https://mathstodon.xyz/tags/TruthTheory" class="mention hashtag" rel="tag">#<span>TruthTheory</span></a> <br /><a href="https://mathstodon.xyz/tags/RelationTheory" class="mention hashtag" rel="tag">#<span>RelationTheory</span></a> <a href="https://mathstodon.xyz/tags/TriadicRelations" class="mention hashtag" rel="tag">#<span>TriadicRelations</span></a> <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></p>
Jon Awbrey<p>Pragmatic Truth • 4.1<br />• <a href="https://inquiryintoinquiry.com/2024/07/13/pragmatic-truth-4/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2024/07</span><span class="invisible">/13/pragmatic-truth-4/</span></a></p><p>Truth Theories —</p><p>Theories of truth may be described according to several dimensions of description affecting the character of the predicate “true”. The truth predicates used in different theories may be classified according to the number of things which have to be taken into account in order to evaluate the truth of a sign, counting the sign itself as the first thing. The number of dimensions is sometimes called the “arity” or “adicity” of the truth predicate.</p><p>• A truth predicate is “monadic” if it applies to its main subject, typically a concrete representation or its abstract content, independently of reference to anything else. In that case one may think of a truth bearer as being true in and of itself.</p><p>• A truth predicate is “dyadic” if it applies to its main subject only in reference to something else, a second subject. Most commonly, the ancillary subject is either an “object”, an “interpreter”, or a “language” to which the representation bears a specified relation.</p><p>• A truth predicate is “triadic” if it applies to its main subject only in reference to a second and a third subject. For example, in a pragmatic theory of truth one has to specify both the “object” of the sign and either its interpreter or another sign called its “interpretant”. In that case, one says the sign is true “of” its object “to” its interpreting agent or sign.</p><p>Resources —</p><p>Truth Theory<br />• <a href="https://oeis.org/wiki/Truth_theory" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="">oeis.org/wiki/Truth_theory</span><span class="invisible"></span></a></p><p>Pragmatic Theory Of Truth<br />• <a href="https://oeis.org/wiki/Pragmatic_Theory_Of_Truth" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/Pragmatic_Theory</span><span class="invisible">_Of_Truth</span></a> </p><p>Correspondence Theory Of Truth<br />• <a href="https://oeis.org/wiki/Correspondence_Theory_Of_Truth" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/Correspondence_T</span><span class="invisible">heory_Of_Truth</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/Logic" class="mention hashtag" rel="tag">#<span>Logic</span></a> <a href="https://mathstodon.xyz/tags/Inquiry" class="mention hashtag" rel="tag">#<span>Inquiry</span></a> <a href="https://mathstodon.xyz/tags/Truth" class="mention hashtag" rel="tag">#<span>Truth</span></a> <a href="https://mathstodon.xyz/tags/PragmaticTruth" class="mention hashtag" rel="tag">#<span>PragmaticTruth</span></a> <a href="https://mathstodon.xyz/tags/TruthTheory" class="mention hashtag" rel="tag">#<span>TruthTheory</span></a> <br /><a href="https://mathstodon.xyz/tags/RelationTheory" class="mention hashtag" rel="tag">#<span>RelationTheory</span></a> <a href="https://mathstodon.xyz/tags/TriadicRelations" class="mention hashtag" rel="tag">#<span>TriadicRelations</span></a> <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></p>
Jon Awbrey<p>Precursors Of Category Theory • 3<br />• <a href="https://inquiryintoinquiry.com/2024/05/27/precursors-of-category-theory-3-a/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2024/05</span><span class="invisible">/27/precursors-of-category-theory-3-a/</span></a></p><p>❝Act only according to that maxim by which you can at the same time will that it should become a universal law.❞</p><p>— Immanuel Kant (1785)</p><p>C.S. Peirce • “On a New List of Categories” (1867)</p><p>❝§1. This paper is based upon the theory already established, that the function of conceptions is to reduce the manifold of sensuous impressions to unity, and that the validity of a conception consists in the impossibility of reducing the content of consciousness to unity without the introduction of it.❞ (CP 1.545).</p><p>❝§2. This theory gives rise to a conception of gradation among those conceptions which are universal. For one such conception may unite the manifold of sense and yet another may be required to unite the conception and the manifold to which it is applied; and so on.❞ (CP 1.546).</p><p>Cued by Kant's idea regarding the function of concepts in general, Peirce locates his categories on the highest levels of abstraction able to provide a meaningful measure of traction in practice. Whether successive grades of conceptions converge to an absolute unity or not is a question to be pursued as inquiry progresses and need not be answered in order to begin.</p><p>Resources —</p><p>Precursors Of Category Theory<br />• <a href="https://oeis.org/wiki/Precursors_Of_Category_Theory" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/Precursors_Of_Ca</span><span class="invisible">tegory_Theory</span></a></p><p>Propositions As Types Analogy<br />• <a href="https://oeis.org/wiki/Propositions_As_Types_Analogy" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/Propositions_As_</span><span class="invisible">Types_Analogy</span></a></p><p>Survey of Precursors Of Category Theory<br />• <a href="https://inquiryintoinquiry.com/2024/05/24/survey-of-precursors-of-category-theory-5/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2024/05</span><span class="invisible">/24/survey-of-precursors-of-category-theory-5/</span></a></p><p><a href="https://mathstodon.xyz/tags/Aristotle" class="mention hashtag" rel="tag">#<span>Aristotle</span></a> <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/Carnap" class="mention hashtag" rel="tag">#<span>Carnap</span></a> <a href="https://mathstodon.xyz/tags/Hilbert" class="mention hashtag" rel="tag">#<span>Hilbert</span></a> <a href="https://mathstodon.xyz/tags/Ackermann" class="mention hashtag" rel="tag">#<span>Ackermann</span></a> <a href="https://mathstodon.xyz/tags/SaundersMacLane" class="mention hashtag" rel="tag">#<span>SaundersMacLane</span></a> <br /><a href="https://mathstodon.xyz/tags/Abstraction" class="mention hashtag" rel="tag">#<span>Abstraction</span></a> <a href="https://mathstodon.xyz/tags/Analogy" class="mention hashtag" rel="tag">#<span>Analogy</span></a> <a href="https://mathstodon.xyz/tags/CategoryTheory" class="mention hashtag" rel="tag">#<span>CategoryTheory</span></a> <a href="https://mathstodon.xyz/tags/Diagrams" class="mention hashtag" rel="tag">#<span>Diagrams</span></a> <a href="https://mathstodon.xyz/tags/FoundationsOfMathematics" class="mention hashtag" rel="tag">#<span>FoundationsOfMathematics</span></a> <br /><a href="https://mathstodon.xyz/tags/FunctionalLogic" class="mention hashtag" rel="tag">#<span>FunctionalLogic</span></a> <a href="https://mathstodon.xyz/tags/RelationTheory" class="mention hashtag" rel="tag">#<span>RelationTheory</span></a> <a href="https://mathstodon.xyz/tags/ContinuousPredicate" class="mention hashtag" rel="tag">#<span>ContinuousPredicate</span></a> <a href="https://mathstodon.xyz/tags/HypostaticAbstraction" class="mention hashtag" rel="tag">#<span>HypostaticAbstraction</span></a> <br /><a href="https://mathstodon.xyz/tags/CategoryTheory" class="mention hashtag" rel="tag">#<span>CategoryTheory</span></a> <a href="https://mathstodon.xyz/tags/PeircesCategories" class="mention hashtag" rel="tag">#<span>PeircesCategories</span></a> <a href="https://mathstodon.xyz/tags/PropositionsAsTypes" class="mention hashtag" rel="tag">#<span>PropositionsAsTypes</span></a> <a href="https://mathstodon.xyz/tags/TypeTheory" class="mention hashtag" rel="tag">#<span>TypeTheory</span></a> <a href="https://mathstodon.xyz/tags/Universals" class="mention hashtag" rel="tag">#<span>Universals</span></a></p>
Jon Awbrey<p>Precursors Of Category Theory • 2.3<br />• <a href="https://inquiryintoinquiry.com/2024/05/26/precursors-of-category-theory-2-a/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2024/05</span><span class="invisible">/26/precursors-of-category-theory-2-a/</span></a></p><p>In the logic of Aristotle categories are adjuncts to reasoning whose function is to resolve ambiguities and thus to prepare equivocal signs, otherwise recalcitrant to being ruled by logic, for the application of logical laws. The example of ζωον illustrates the fact that we don't need categories to “make” generalizations so much as to “control” generalizations, to reign in abstractions and analogies which have been stretched too far.</p><p>References —</p><p>• Aristotle, “The Categories”, Harold P. Cooke (trans.), pp. 1–109 in Aristotle, Volume 1, Loeb Classical Library, William Heinemann, London, UK, 1938.</p><p>• Karpeles, Eric (2008), Paintings in Proust, Thames and Hudson, London, UK.</p><p>Resources —</p><p>Precursors Of Category Theory<br />• <a href="https://oeis.org/wiki/Precursors_Of_Category_Theory" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/Precursors_Of_Ca</span><span class="invisible">tegory_Theory</span></a></p><p>Propositions As Types Analogy<br />• <a href="https://oeis.org/wiki/Propositions_As_Types_Analogy" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/Propositions_As_</span><span class="invisible">Types_Analogy</span></a></p><p>Survey of Precursors Of Category Theory<br />• <a href="https://inquiryintoinquiry.com/2024/05/24/survey-of-precursors-of-category-theory-5/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2024/05</span><span class="invisible">/24/survey-of-precursors-of-category-theory-5/</span></a></p><p><a href="https://mathstodon.xyz/tags/Aristotle" class="mention hashtag" rel="tag">#<span>Aristotle</span></a> <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/Carnap" class="mention hashtag" rel="tag">#<span>Carnap</span></a> <a href="https://mathstodon.xyz/tags/Hilbert" class="mention hashtag" rel="tag">#<span>Hilbert</span></a> <a href="https://mathstodon.xyz/tags/Ackermann" class="mention hashtag" rel="tag">#<span>Ackermann</span></a> <a href="https://mathstodon.xyz/tags/SaundersMacLane" class="mention hashtag" rel="tag">#<span>SaundersMacLane</span></a> <br /><a href="https://mathstodon.xyz/tags/Abstraction" class="mention hashtag" rel="tag">#<span>Abstraction</span></a> <a href="https://mathstodon.xyz/tags/Analogy" class="mention hashtag" rel="tag">#<span>Analogy</span></a> <a href="https://mathstodon.xyz/tags/CategoryTheory" class="mention hashtag" rel="tag">#<span>CategoryTheory</span></a> <a href="https://mathstodon.xyz/tags/Diagrams" class="mention hashtag" rel="tag">#<span>Diagrams</span></a> <a href="https://mathstodon.xyz/tags/FoundationsOfMathematics" class="mention hashtag" rel="tag">#<span>FoundationsOfMathematics</span></a> <br /><a href="https://mathstodon.xyz/tags/FunctionalLogic" class="mention hashtag" rel="tag">#<span>FunctionalLogic</span></a> <a href="https://mathstodon.xyz/tags/RelationTheory" class="mention hashtag" rel="tag">#<span>RelationTheory</span></a> <a href="https://mathstodon.xyz/tags/ContinuousPredicate" class="mention hashtag" rel="tag">#<span>ContinuousPredicate</span></a> <a href="https://mathstodon.xyz/tags/HypostaticAbstraction" class="mention hashtag" rel="tag">#<span>HypostaticAbstraction</span></a> <br /><a href="https://mathstodon.xyz/tags/CategoryTheory" class="mention hashtag" rel="tag">#<span>CategoryTheory</span></a> <a href="https://mathstodon.xyz/tags/PeircesCategories" class="mention hashtag" rel="tag">#<span>PeircesCategories</span></a> <a href="https://mathstodon.xyz/tags/PropositionsAsTypes" class="mention hashtag" rel="tag">#<span>PropositionsAsTypes</span></a> <a href="https://mathstodon.xyz/tags/TypeTheory" class="mention hashtag" rel="tag">#<span>TypeTheory</span></a> <a href="https://mathstodon.xyz/tags/Universals" class="mention hashtag" rel="tag">#<span>Universals</span></a></p>
Jon Awbrey<p>Precursors Of Category Theory • 2.2<br />• <a href="https://inquiryintoinquiry.com/2024/05/26/precursors-of-category-theory-2-a/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2024/05</span><span class="invisible">/26/precursors-of-category-theory-2-a/</span></a></p><p>Aristotle —</p><p>❝Things are equivocally named, when they have the name only in common, the definition (or statement of essence) corresponding with the name being different. For instance, while a man and a portrait can properly both be called animals (ζωον), these are equivocally named. For they have the name only in common, the definitions (or statements of essence) corresponding with the name being different. For if you are asked to define what the being an animal means in the case of the man and the portrait, you give in either case a definition appropriate to that case alone.</p><p>❝Things are univocally named, when not only they bear the same name but the name means the same in each case — has the same definition corresponding. Thus a man and an ox are called animals. The name is the same in both cases; so also the statement of essence. For if you are asked what is meant by their both of them being called animals, you give that particular name in both cases the same definition.❞ (Aristotle, Categories, 1.1a1–12).</p><p>Translator's Note. ❝Ζωον in Greek had two meanings, that is to say, living creature, and, secondly, a figure or image in painting, embroidery, sculpture. We have no ambiguous noun. However, we use the word ‘living’ of portraits to mean ‘true to life’.❞</p><p><a href="https://mathstodon.xyz/tags/Aristotle" class="mention hashtag" rel="tag">#<span>Aristotle</span></a> <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/Carnap" class="mention hashtag" rel="tag">#<span>Carnap</span></a> <a href="https://mathstodon.xyz/tags/Hilbert" class="mention hashtag" rel="tag">#<span>Hilbert</span></a> <a href="https://mathstodon.xyz/tags/Ackermann" class="mention hashtag" rel="tag">#<span>Ackermann</span></a> <a href="https://mathstodon.xyz/tags/SaundersMacLane" class="mention hashtag" rel="tag">#<span>SaundersMacLane</span></a> <br /><a href="https://mathstodon.xyz/tags/Abstraction" class="mention hashtag" rel="tag">#<span>Abstraction</span></a> <a href="https://mathstodon.xyz/tags/Analogy" class="mention hashtag" rel="tag">#<span>Analogy</span></a> <a href="https://mathstodon.xyz/tags/CategoryTheory" class="mention hashtag" rel="tag">#<span>CategoryTheory</span></a> <a href="https://mathstodon.xyz/tags/Diagrams" class="mention hashtag" rel="tag">#<span>Diagrams</span></a> <a href="https://mathstodon.xyz/tags/FoundationsOfMathematics" class="mention hashtag" rel="tag">#<span>FoundationsOfMathematics</span></a> <br /><a href="https://mathstodon.xyz/tags/FunctionalLogic" class="mention hashtag" rel="tag">#<span>FunctionalLogic</span></a> <a href="https://mathstodon.xyz/tags/RelationTheory" class="mention hashtag" rel="tag">#<span>RelationTheory</span></a> <a href="https://mathstodon.xyz/tags/ContinuousPredicate" class="mention hashtag" rel="tag">#<span>ContinuousPredicate</span></a> <a href="https://mathstodon.xyz/tags/HypostaticAbstraction" class="mention hashtag" rel="tag">#<span>HypostaticAbstraction</span></a> <br /><a href="https://mathstodon.xyz/tags/CategoryTheory" class="mention hashtag" rel="tag">#<span>CategoryTheory</span></a> <a href="https://mathstodon.xyz/tags/PeircesCategories" class="mention hashtag" rel="tag">#<span>PeircesCategories</span></a> <a href="https://mathstodon.xyz/tags/PropositionsAsTypes" class="mention hashtag" rel="tag">#<span>PropositionsAsTypes</span></a> <a href="https://mathstodon.xyz/tags/TypeTheory" class="mention hashtag" rel="tag">#<span>TypeTheory</span></a> <a href="https://mathstodon.xyz/tags/Universals" class="mention hashtag" rel="tag">#<span>Universals</span></a></p>
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