Difference between revisions of "Logic of relatives"

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The '''logic of relatives''', short for the '''logic of relative terms''', is the study of [[relation (mathematics)|relation]]s as represented in symbolic forms known as ''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.
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<font size="3">&#9758;</font> This page belongs to resource collections on [[Logic Live|Logic]] and [[Inquiry Live|Inquiry]].
  
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The consideration of ''[[relative term]]s'' 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 [[Logic of Relatives (1870)|"Description of a Notation for the Logic of Relatives, Resulting from an Amplification of the Conceptions of Boole's Calculus of Logic" (1870)]].
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The '''logic of relatives''', more precisely, the '''logic of relative terms''', is the study of [[relation (mathematics)|relation]]s as represented in symbolic forms known as ''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.
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The consideration of ''[[relative term]]s'' has its roots in antiquity, but it entered a radically new phase of development with the work of [[Charles Sanders Peirce]], beginning with his 1870 paper &ldquo;[[Logic of Relatives (1870)|Description of a Notation for the Logic of Relatives, Resulting from an Amplification of the Conceptions of Boole's Calculus of Logic]]&rdquo;.
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==See also==
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* [[Logic of Relatives (1870)]]
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* [[Logic of Relatives (1883)]]
  
 
==References==
 
==References==
  
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* [[Charles Sanders Peirce|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, ''Chronological Edition'' CE 2, 359–429.
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* [[Charles Sanders Peirce|Peirce, C.S.]], &ldquo;Description of a Notation for the Logic of Relatives, Resulting from an Amplification of the Conceptions of Boole's Calculus of Logic&rdquo;, ''Memoirs of the American Academy of Arts and Sciences'' 9, 317&ndash;378, 1870.  Reprinted, ''Collected Papers'' CP&nbsp;3.45&ndash;149, ''Chronological Edition'' CE&nbsp;2, 359&ndash;429.
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* [http://intersci.ss.uci.edu/wiki/index.php/Peirce%27s_1870_Logic_Of_Relatives Awbrey, J.L., &ldquo;Peirce's 1870 Logic of Relatives&rdquo;]
  
 
==Bibliography==
 
==Bibliography==
  
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* [[Aristotle]], "[[The Categories]]", [[Harold P. Cooke]] (trans.), pp. 1–109 in ''Aristotle, Vol. 1'', [[Loeb Classical Library]], [[William Heinemann]], London, UK, 1938.
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* Aristotle, &ldquo;The Categories&rdquo;, Harold P. Cooke (trans.), pp.&nbsp;1&ndash;109 in ''Aristotle, Volume&nbsp;1'', Loeb Classical Library, William Heinemann, London, UK, 1938.
  
−
* Aristotle, "[[On Interpretation]]", [[Harold P. Cooke]] (trans.), pp. 111–179 in ''Aristotle, Vol. 1'', [[Loeb Classical Library]], [[William Heinemann]], London, UK, 1938.
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* Aristotle, &ldquo;On Interpretation&rdquo;, Harold P. Cooke (trans.), pp.&nbsp;111&ndash;179 in ''Aristotle, Volume&nbsp;1'', Loeb Classical Library, William Heinemann, London, UK, 1938.
  
−
* Aristotle, "[[Prior Analytics]]", [[Hugh Tredennick]] (trans.), pp. 181–531 in ''Aristotle, Vol. 1'', [[Loeb Classical Library]], William Heinemann, London, UK, 1938.  
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* Aristotle, &ldquo;Prior Analytics&rdquo;, Hugh Tredennick (trans.), pp.&nbsp;181&ndash;531 in ''Aristotle, Volume&nbsp;1'', Loeb Classical Library, William Heinemann, London, UK, 1938.  
  
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* [[George Boole|Boole, George]], ''An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities'', [[Macmillan Publishers|Macmillan]], 1854.  Reprinted with corrections, [[Dover Publications]], New York, NY, 1958.
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* Boole, George, ''An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities'', Macmillan Publishers, 1854.  Reprinted with corrections, Dover Publications, New&nbsp;York, NY, 1958.
  
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* Maddux, Roger D., ''Relation Algebras'', vol. 150 in 'Studies in Logic and the Foundations of Mathematics', Elsevier Science, 2006.
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* Maddux, Roger D., ''Relation Algebras'', vol. 150 in &lsquo;Studies in Logic and the Foundations of Mathematics&rsquo;, Elsevier Science, 2006.
  
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* Peirce, C.S., ''Collected Papers of Charles Sanders Peirce'', vols. 1–6, [[Charles Hartshorne]] and [[Paul Weiss]] (eds.), vols. 7–8, [[Arthur W. Burks]] (ed.), Harvard University Press, Cambridge, MA, 1931–1935, 1958.  Cited as CP volume.paragraph.
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* Peirce, C.S., ''Collected Papers of Charles Sanders Peirce'', vols. 1&ndash;6, Charles Hartshorne and Paul Weiss (eds.), vols. 7&ndash;8, Arthur W. Burks (ed.), Harvard University Press, Cambridge, MA, 1931&ndash;1935, 1958.  Cited as CP&nbsp;volume.paragraph.
  
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* Peirce, C.S., ''Writings of Charles S. Peirce : A Chronological Edition, Volume 2, 1867–1871'', Peirce Edition Project (eds.), Indiana University Press, Bloomington, IN, 1984.  Cited as CE 2.
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* Peirce, C.S., ''Writings of Charles S. Peirce : A Chronological Edition, Volume 2, 1867&ndash;1871'', Peirce Edition Project (eds.), Indiana University Press, Bloomington, IN, 1984.  Cited as CE&nbsp;2.
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==Syllabus==
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===Focal nodes===
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* [[Inquiry Live]]
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* [[Logic Live]]
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===Peer nodes===
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* [http://intersci.ss.uci.edu/wiki/index.php/Logic_of_relatives Logic of Relatives @ InterSciWiki]
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* [http://mywikibiz.com/Logic_of_relatives Logic of Relatives @ MyWikiBiz]
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* [http://ref.subwiki.org/wiki/Logic_of_relatives Logic of Relatives @ Subject Wikis]
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* [http://en.wikiversity.org/wiki/Logic_of_relatives Logic of Relatives @ Wikiversity]
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* [http://beta.wikiversity.org/wiki/Logic_of_relatives Logic of Relatives @ Wikiversity Beta]
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===Logical operators===
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{{col-begin}}
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{{col-break}}
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* [[Exclusive disjunction]]
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* [[Logical conjunction]]
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* [[Logical disjunction]]
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* [[Logical equality]]
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{{col-break}}
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* [[Logical implication]]
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* [[Logical NAND]]
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* [[Logical NNOR]]
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* [[Logical negation|Negation]]
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{{col-end}}
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===Related topics===
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{{col-begin}}
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{{col-break}}
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* [[Ampheck]]
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* [[Boolean domain]]
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* [[Boolean function]]
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* [[Boolean-valued function]]
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* [[Differential logic]]
 +
{{col-break}}
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* [[Logical graph]]
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* [[Minimal negation operator]]
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* [[Multigrade operator]]
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* [[Parametric operator]]
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* [[Peirce's law]]
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{{col-break}}
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* [[Propositional calculus]]
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* [[Sole sufficient operator]]
 +
* [[Truth table]]
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* [[Universe of discourse]]
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* [[Zeroth order logic]]
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{{col-end}}
  
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==See also==
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===Relational concepts===
  
 
{{col-begin}}
 
{{col-begin}}
 
{{col-break}}
 
{{col-break}}
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* [[Arity]]
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* [[Continuous predicate]]
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* [[Binary relation]]
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* [[Hypostatic abstraction]]
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* [[Category theory]]
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* [[Logic of relatives]]
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* [[Database]]
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* [[Logical matrix]]
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* [[Logic of Relatives (1870)]]
 
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* [[Logic of Relatives (1883)]]
 
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* [[Operation (mathematics)|Operation]]
 
 
{{col-break}}
 
{{col-break}}
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* [[Operator]]
 
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* [[Predicate]]
 
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* [[Property (philosophy)|Property]]
 
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* [[Proposition]]
 
 
* [[Relation (mathematics)|Relation]]
 
* [[Relation (mathematics)|Relation]]
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* [[Relational algebra]]
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* [[Relation composition]]
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* [[Relational database]]
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* [[Relation construction]]
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* [[Relation reduction]]
 
{{col-break}}
 
{{col-break}}
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* [[Relational model]]
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* [[Relation theory]]
 
* [[Relative term]]
 
* [[Relative term]]
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* [[Rheme]]
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* [[Sign relation]]
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* [[Role]]
 
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* [[Relation theory]]
 
 
* [[Triadic relation]]
 
* [[Triadic relation]]
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* [[Universal algebra]]
 
 
{{col-end}}
 
{{col-end}}
  
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===Information, Inquiry===
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 +
{{col-begin}}
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{{col-break}}
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* [[Inquiry]]
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* [[Dynamics of inquiry]]
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{{col-break}}
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* [[Semeiotic]]
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* [[Logic of information]]
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{{col-break}}
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* [[Descriptive science]]
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* [[Normative science]]
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{{col-break}}
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* [[Pragmatic maxim]]
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* [[Truth theory]]
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{{col-end}}
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===Related articles===
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{{col-begin}}
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{{col-break}}
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* [http://intersci.ss.uci.edu/wiki/index.php/Cactus_Language Cactus Language]
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* [http://intersci.ss.uci.edu/wiki/index.php/Futures_Of_Logical_Graphs Futures Of Logical Graphs]
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* [http://intersci.ss.uci.edu/wiki/index.php/Propositional_Equation_Reasoning_Systems Propositional Equation Reasoning Systems]
 +
{{col-break}}
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* [http://intersci.ss.uci.edu/wiki/index.php/Differential_Logic_:_Introduction Differential Logic : Introduction]
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* [http://intersci.ss.uci.edu/wiki/index.php/Differential_Propositional_Calculus Differential Propositional Calculus]
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* [http://intersci.ss.uci.edu/wiki/index.php/Differential_Logic_and_Dynamic_Systems_2.0 Differential Logic and Dynamic Systems]
 +
{{col-break}}
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* [http://intersci.ss.uci.edu/wiki/index.php/Introduction_to_Inquiry_Driven_Systems Introduction to Inquiry Driven Systems]
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* [http://intersci.ss.uci.edu/wiki/index.php/Prospects_for_Inquiry_Driven_Systems Prospects for Inquiry Driven Systems]
 +
* [http://intersci.ss.uci.edu/wiki/index.php/Inquiry_Driven_Systems Inquiry Driven Systems : Inquiry Into Inquiry]
 +
{{col-end}}
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 +
==Document history==
 +
 +
Portions of the above article were adapted from the following sources under the [[GNU Free Documentation License]], under other applicable licenses, or by permission of the copyright holders.
 +
 +
* [http://intersci.ss.uci.edu/wiki/index.php/Logic_of_relatives Logic of Relatives], [http://intersci.ss.uci.edu/ InterSciWiki]
 +
* [http://mywikibiz.com/Logic_of_relatives Logic of Relatives], [http://mywikibiz.com/ MyWikiBiz]
 +
* [http://semanticweb.org/wiki/Logic_of_Relatives Logic of Relatives], [http://semanticweb.org/ Semantic Web]
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* [http://wikinfo.org/w/index.php/Logic_of_relatives Logic of Relatives], [http://wikinfo.org/w/ Wikinfo]
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* [http://en.wikiversity.org/wiki/Logic_of_relatives Logic of Relatives], [http://en.wikiversity.org/ Wikiversity]
 +
* [http://beta.wikiversity.org/wiki/Logic_of_relatives Logic of Relatives], [http://beta.wikiversity.org/ Wikiversity Beta]
 +
* [http://en.wikipedia.org/w/index.php?title=Logic_of_relatives&oldid=43501411 Logic of Relatives], [http://en.wikipedia.org/ Wikipedia]
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[[Category:Charles Sanders Peirce]]
 
[[Category:Formal Languages]]
 
[[Category:Formal Languages]]
 
[[Category:Formal Sciences]]
 
[[Category:Formal Sciences]]
 
[[Category:Formal Systems]]
 
[[Category:Formal Systems]]
 
[[Category:Inquiry]]
 
[[Category:Inquiry]]
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[[Category:Linguistics]]
 
 
[[Category:Logic]]
 
[[Category:Logic]]
 
[[Category:Mathematics]]
 
[[Category:Mathematics]]
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[[Category:Philosophy]]
 
[[Category:Science]]
 
[[Category:Science]]
 
[[Category:Semiotics]]
 
[[Category:Semiotics]]
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[[Category:Philosophy]]
 

Latest revision as of 22:48, 10 November 2015

☞ This page belongs to resource collections on Logic and Inquiry.

The logic of relatives, more precisely, the logic of relative terms, is the study of relations as represented in symbolic forms known as 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.

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 1870 paper “Description of a Notation for the Logic of Relatives, Resulting from an Amplification of the Conceptions of Boole's Calculus of Logic”.

See also

References

  • 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, Chronological Edition CE 2, 359–429.

Bibliography

  • Aristotle, “The Categories”, Harold P. Cooke (trans.), pp. 1–109 in Aristotle, Volume 1, Loeb Classical Library, William Heinemann, London, UK, 1938.
  • Aristotle, “On Interpretation”, Harold P. Cooke (trans.), pp. 111–179 in Aristotle, Volume 1, Loeb Classical Library, William Heinemann, London, UK, 1938.
  • Aristotle, “Prior Analytics”, Hugh Tredennick (trans.), pp. 181–531 in Aristotle, Volume 1, Loeb Classical Library, William Heinemann, London, UK, 1938.
  • Boole, George, An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities, Macmillan Publishers, 1854. Reprinted with corrections, Dover Publications, New York, NY, 1958.
  • Maddux, Roger D., Relation Algebras, vol. 150 in ‘Studies in Logic and the Foundations of Mathematics’, Elsevier Science, 2006.
  • Peirce, C.S., Collected Papers of Charles Sanders Peirce, vols. 1–6, Charles Hartshorne and Paul Weiss (eds.), vols. 7–8, Arthur W. Burks (ed.), Harvard University Press, Cambridge, MA, 1931–1935, 1958. Cited as CP volume.paragraph.
  • Peirce, C.S., Writings of Charles S. Peirce : A Chronological Edition, Volume 2, 1867–1871, Peirce Edition Project (eds.), Indiana University Press, Bloomington, IN, 1984. Cited as CE 2.

Syllabus

Focal nodes

Peer nodes

Logical operators

Template:Col-breakTemplate:Col-breakTemplate:Col-end

Related topics

Template:Col-breakTemplate:Col-breakTemplate:Col-breakTemplate:Col-end

Relational concepts

Template:Col-breakTemplate:Col-breakTemplate:Col-breakTemplate:Col-end

Information, Inquiry

Template:Col-breakTemplate:Col-breakTemplate:Col-breakTemplate:Col-breakTemplate:Col-end

Related articles

Template:Col-breakTemplate:Col-breakTemplate:Col-breakTemplate:Col-end

Document history

Portions of the above article were adapted from the following sources under the GNU Free Documentation License, under other applicable licenses, or by permission of the copyright holders.

Retrieved from "https://mywikibiz.com/index.php?title=Logic_of_relatives&oldid=466873"