Difference between revisions of "Continuous predicate"

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A '''continuous predicate''', as described by [[Charles Sanders Peirce]], is a special type of [[relation (mathematics)|relation]]al [[predicate]] that arises as the [[limit (mathematics)|limit]] of an iterated process of [[hypostatic abstraction]].
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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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A '''continuous predicate''', as described by Charles Sanders Peirce, is a special type of [[relation (mathematics)|relational predicate]] that arises as the limit of an iterated process of [[hypostatic abstraction]].
  
 
Here is one of Peirce's definitive discussions of the concept:
 
Here is one of Peirce's definitive discussions of the concept:
  
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<blockquote>
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<div style="margin-left:5em; margin-right:20em">
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<p>When we have analyzed a proposition so as to throw into the subject everything that can be removed from the predicate, all that it remains for the predicate to represent is the form of connection between the different subjects as expressed in the propositional ''form''. What I mean by "everything that can be removed from the predicate" is best explained by giving an example of something not so removable.</p>
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When we have analyzed a proposition so as to throw into the subject everything that can be removed from the predicate, all that it remains for the predicate to represent is the form of connection between the different subjects as expressed in the propositional ''form''.&nbsp; What I mean by &ldquo;everything that can be removed from the predicate&rdquo; is best explained by giving an example of something not so removable.
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But first take something removable.&nbsp; &ldquo;Cain kills Abel.&rdquo;&nbsp; Here the predicate appears as &ldquo;&mdash; kills &mdash;.&rdquo;&nbsp; But&nbsp;we can remove killing from the predicate and make the latter &ldquo;&mdash; stands in the relation &mdash; to &mdash;.&rdquo;&nbsp; Suppose we attempt to remove more from the predicate and put the last into the form &ldquo;&mdash; exercises the function of relate of the relation &mdash; to &mdash;&rdquo; and then putting &ldquo;the function of relate to the relation&rdquo; into another subject leave as predicate &ldquo;&mdash; exercises &mdash; in respect to &mdash; to &mdash;.&rdquo;&nbsp; But&nbsp;this &ldquo;exercises&rdquo; expresses &ldquo;exercises the function&rdquo;.&nbsp; Nay more, it expresses &ldquo;exercises the function of relate&rdquo;, so that we find that though we may put this into a separate subject, it continues in the predicate just the same.
  
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<p>But first take something removable.  "Cain kills Abel."  Here the predicate appears as "— kills —."  But we can remove killing from the predicate and make the latter "— stands in the relation — to —."  Suppose we attempt to remove more from the predicate and put the last into the form "— exercises the function of relate of the relation — to —" and then putting "the function of relate to the relation" into another subject leave as predicate "— exercises — in respect to — to —."  But this "exercises" expresses "exercises the function". Nay more, it expresses "exercises the function of relate", so that we find that though we may put this into a separate subject, it continues in the predicate just the same.</p>
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Stating this in another form, to say that &ldquo;A is in the relation R to B&rdquo; is to say that A is in a certain relation to R.&nbsp; Let us separate this out thus:&nbsp; &ldquo;A is in the relation R<sup>1</sup> (where R<sup>1</sup> is the relation of a relate to the relation of which it is the relate) to R to B&rdquo;.&nbsp; But&nbsp;A is here said to be in a certain relation to the relation R<sup>1</sup>.&nbsp; So that we can express the same fact by saying, &ldquo;A is in the relation R<sup>1</sup> to the relation R<sup>1</sup> to the relation R to B&rdquo;, and so on ''ad&nbsp;infinitum''.
  
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<p>Stating this in another form, to say that "A is in the relation R to B" is to say that A is in a certain relation to R. Let us separate this out thus:  "A is in the relation R¹ (where R¹ is the relation of a relate to the relation of which it is the relate) to R to B".  But A is here said to be in a certain relation to the relation R¹.  So that we can express the same fact by saying, "A is in the relation R¹ to the relation R¹ to the relation R to B", and so on ''ad infinitum''.</p>
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A predicate which can thus be analyzed into parts all homogeneous with the whole I call a ''continuous predicate''.&nbsp; It is very important in logical analysis, because a continuous predicate obviously cannot be a ''compound'' except of continuous predicates, and thus when we have carried analysis so far as to leave only a continuous predicate, we have carried it to its ultimate elements.
  
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<p>A predicate which can thus be analyzed into parts all homogeneous with the whole I call a ''continuous predicate''.  It is very important in logical analysis, because a continuous predicate obviously cannot be a ''compound'' except of continuous predicates, and thus when we have carried analysis so far as to leave only a continuous predicate, we have carried it to its ultimate elements.  (C.S. Peirce, "Letters to Lady Welby" (14 December 1908), ''Selected Writings'', pp. 396–397).</p>
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(C.S. Peirce, &ldquo;Letters to Lady Welby&rdquo; (14 December 1908), ''Selected Writings'', pp.&nbsp;396&ndash;397).
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</blockquote>
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</div>
  
 
==References==
 
==References==
  
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* [[Charles Sanders Peirce|Peirce, C.S.]], "Letters to Lady Welby", pp. 380–432 in ''Charles S. Peirce : Selected Writings (Values in a Universe of Chance)'', [[Philip P. Wiener]] (ed.), Dover, New York, NY, 1966.
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* [[Charles Sanders Peirce|Peirce, C.S.]], &ldquo;Letters to Lady Welby&rdquo;, pp.&nbsp;380&ndash;432 in ''Charles S. Peirce : Selected Writings (Values in a Universe of Chance)'', Philip P. Wiener (ed.), Dover&nbsp;Publications, New&nbsp;York, NY, 1966.
  
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==Related topics==
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==Resources==
  
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* [http://vectors.usc.edu/thoughtmesh/publish/147.php Continuous Predicate &rarr; ThoughtMesh]
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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/Continuous_predicate Continuous Predicate @ InterSciWiki]
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* [http://mywikibiz.com/Continuous_predicate Continuous Predicate @ MyWikiBiz]
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* [http://ref.subwiki.org/wiki/Continuous_predicate Continuous Predicate @ Subject Wikis]
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* [http://en.wikiversity.org/wiki/Continuous_predicate Continuous Predicate @ Wikiversity]
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* [http://beta.wikiversity.org/wiki/Continuous_predicate Continuous Predicate @ 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]]
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{{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]]
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* [[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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===Relational concepts===
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{{col-begin}}
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{{col-break}}
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* [[Continuous predicate]]
 
* [[Hypostatic abstraction]]
 
* [[Hypostatic abstraction]]
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* [[Hypostatic object]]
 
 
* [[Logic of relatives]]
 
* [[Logic of relatives]]
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* [[Prescisive abstraction]]
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* [[Logical matrix]]
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{{col-break}}
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* [[Relation (mathematics)|Relation]]
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* [[Relation composition]]
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* [[Relation construction]]
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* [[Relation reduction]]
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{{col-break}}
 
* [[Relation theory]]
 
* [[Relation theory]]
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* [[Relative term]]
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* [[Sign relation]]
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* [[Triadic relation]]
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{{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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==Resources==
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===Related articles===
  
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* [http://vectors.usc.edu/thoughtmesh/publish/147.php Continuous Predicate → ThoughtMesh]
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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]
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{{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]
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{{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]
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* [http://intersci.ss.uci.edu/wiki/index.php/Inquiry_Driven_Systems Inquiry Driven Systems : Inquiry Into Inquiry]
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{{col-end}}
  
 
==Document history==
 
==Document history==
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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.
 
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.
  
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{{col-begin}}
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* [http://intersci.ss.uci.edu/wiki/index.php/Continuous_predicate Continuous Predicate], [http://intersci.ss.uci.edu/ InterSciWiki]
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{{col-break}}
 
 
* [http://mywikibiz.com/Continuous_predicate Continuous Predicate], [http://mywikibiz.com/ MyWikiBiz]
 
* [http://mywikibiz.com/Continuous_predicate Continuous Predicate], [http://mywikibiz.com/ MyWikiBiz]
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* [http://beta.wikiversity.org/wiki/Continuous_predicate Continuous Predicate], [http://beta.wikiversity.org/ Beta Wikiversity]
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* [http://planetmath.org/ContinuousPredicate Continuous Predicate], [http://planetmath.org/ PlanetMath]
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* [http://www.netknowledge.org/wiki/Continuous_predicate Continuous Predicate], [http://www.netknowledge.org/ NetKnowledge]
 
 
* [http://semanticweb.org/wiki/Continuous_predicate Continuous Predicate], [http://semanticweb.org/ SemanticWeb]
 
* [http://semanticweb.org/wiki/Continuous_predicate Continuous Predicate], [http://semanticweb.org/ SemanticWeb]
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* [http://planetmath.org/encyclopedia/ContinuousPredicate.html Continuous Predicate], [http://planetmath.org/ PlanetMath]
 
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{{col-break}}
 
 
* [http://vectors.usc.edu/thoughtmesh/publish/147.php Continuous Predicate], [http://vectors.usc.edu/thoughtmesh/ ThoughtMesh]
 
* [http://vectors.usc.edu/thoughtmesh/publish/147.php Continuous Predicate], [http://vectors.usc.edu/thoughtmesh/ ThoughtMesh]
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* [http://www.getwiki.net/-Continuous_Predicate Continuous Predicate], [http://www.getwiki.net/ GetWiki]
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* [http://wikinfo.org/w/index.php?title=Continuous_predicate Continuous Predicate], [http://wikinfo.org/w/ Wikinfo]
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* [http://www.wikinfo.org/index.php?title=Continuous_predicate Continuous Predicate], [http://www.wikinfo.org/ Wikinfo]
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* [http://en.wikiversity.org/wiki/Continuous_predicate Continuous Predicate], [http://en.wikiversity.org/ Wikiversity]
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* [http://www.textop.org/wiki/index.php?title=Continuous_predicate Continuous Predicate], [http://www.textop.org/wiki/ Textop Wiki]
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* [http://beta.wikiversity.org/wiki/Continuous_predicate Continuous Predicate], [http://beta.wikiversity.org/ Wikiversity Beta]
 
* [http://en.wikipedia.org/w/index.php?title=Continuous_predicate&oldid=96870273 Continuous Predicate], [http://en.wikipedia.org/ Wikipedia]
 
* [http://en.wikipedia.org/w/index.php?title=Continuous_predicate&oldid=96870273 Continuous Predicate], [http://en.wikipedia.org/ Wikipedia]
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[[Category:Computer Science]]
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[[Category:Charles Sanders Peirce]]
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[[Category:Linguistics]]
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[[Category:Inquiry]]
 
[[Category:Logic]]
 
[[Category:Logic]]
 
[[Category:Mathematics]]
 
[[Category:Mathematics]]
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[[Category:Ontology]]
 
[[Category:Philosophy]]
 
[[Category:Philosophy]]
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[[Category:Pragmatism]]
 
[[Category:Semiotics]]
 
[[Category:Semiotics]]

Latest revision as of 04:08, 10 November 2015

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

A continuous predicate, as described by Charles Sanders Peirce, is a special type of relational predicate that arises as the limit of an iterated process of hypostatic abstraction.

Here is one of Peirce's definitive discussions of the concept:

When we have analyzed a proposition so as to throw into the subject everything that can be removed from the predicate, all that it remains for the predicate to represent is the form of connection between the different subjects as expressed in the propositional form.  What I mean by “everything that can be removed from the predicate” is best explained by giving an example of something not so removable.

But first take something removable.  “Cain kills Abel.”  Here the predicate appears as “— kills —.”  But we can remove killing from the predicate and make the latter “— stands in the relation — to —.”  Suppose we attempt to remove more from the predicate and put the last into the form “— exercises the function of relate of the relation — to —” and then putting “the function of relate to the relation” into another subject leave as predicate “— exercises — in respect to — to —.”  But this “exercises” expresses “exercises the function”.  Nay more, it expresses “exercises the function of relate”, so that we find that though we may put this into a separate subject, it continues in the predicate just the same.

Stating this in another form, to say that “A is in the relation R to B” is to say that A is in a certain relation to R.  Let us separate this out thus:  “A is in the relation R1 (where R1 is the relation of a relate to the relation of which it is the relate) to R to B”.  But A is here said to be in a certain relation to the relation R1.  So that we can express the same fact by saying, “A is in the relation R1 to the relation R1 to the relation R to B”, and so on ad infinitum.

A predicate which can thus be analyzed into parts all homogeneous with the whole I call a continuous predicate.  It is very important in logical analysis, because a continuous predicate obviously cannot be a compound except of continuous predicates, and thus when we have carried analysis so far as to leave only a continuous predicate, we have carried it to its ultimate elements.

(C.S. Peirce, “Letters to Lady Welby” (14 December 1908), Selected Writings, pp. 396–397).

References

  • Peirce, C.S., “Letters to Lady Welby”, pp. 380–432 in Charles S. Peirce : Selected Writings (Values in a Universe of Chance), Philip P. Wiener (ed.), Dover Publications, New York, NY, 1966.

Resources

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=Continuous_predicate&oldid=466865"