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Hypostatic abstraction (view source)

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'''Hypostatic abstraction''' is a [[is::formal operation]] that takes an element of information, as expressed in a proposition <math>X\ \operatorname{is}\ Y,</math> and conceives its information to consist in the relation between that subject and another subject, as expressed in the proposition <math>X\ \operatorname{has}\ Y\!\operatorname{-ness}.</math>  The existence of the abstract subject <math>Y\!\operatorname{-ness}</math> consists solely in the truth of those propositions that contain the concrete predicate <math>Y.\!</math>  Hypostatic abstraction is known under many names, for example, ''[[aka::hypostasis]]'', ''[[aka::objectification]]'', ''[[aka::reification]]'', and ''[[aka::subjectal abstraction]]''.  The object of discussion or thought thus introduced is termed a ''[[hypostatic object]]''.
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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 above definition is adapted from the one given by [[introduced by::Charles Sanders Peirce]] (CP 4.235, "[[introduced in::The Simplest Mathematics]]" (1902), in ''Collected Papers'', CP 4.227–323).
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'''Hypostatic abstraction''' is a formal operation that takes an element of information, as expressed in a proposition <math>X ~\text{is}~ Y,\!</math> and conceives its information to consist in the relation between that subject and another subject, as expressed in the proposition <math>X ~\text{has}~ Y\!\text{-ness}.\!</math>&nbsp; The existence of the abstract subject <math>Y\!\text{-ness}\!</math> consists solely in the truth of those propositions that contain the concrete predicate <math>Y.\!</math>&nbsp; Hypostatic abstraction is known by many names, for example, ''hypostasis'', ''objectification'', ''reification'', and ''subjectal abstraction''.&nbsp; The object of discussion or thought thus introduced is termed a ''[[hypostatic object]]''.
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The way that Peirce describes it, the main thing about the formal operation of hypostatic abstraction, insofar as it can be observed to operate on formal linguistic expressions, is that it converts an adjective or some part of a predicate into an extra [[subject]], upping the ''[[changes::arity of the main predicate|arity]]'', also called the ''[[changes::adicity]]'', of the main predicate in the process.
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The above definition is adapted from the one given by introduced [[Charles Sanders Peirce]] (CP&nbsp;4.235, &ldquo;[[The Simplest Mathematics]]&rdquo; (1902), in ''Collected Papers'', CP&nbsp;4.227&ndash;323).
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For example, a typical case of hypostatic abstraction occurs in the transformation from "honey is sweet" to "[[example::honey possesses sweetness]]", which transformation can be viewed in the following variety of ways:
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The way that Peirce describes it, the main thing about the formal operation of hypostatic abstraction, insofar as it can be observed to operate on formal linguistic expressions, is that it converts an adjective or some part of a predicate into an extra subject, upping the ''arity'', also called the ''adicity'', of the main predicate in the process.
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For example, a typical case of hypostatic abstraction occurs in the transformation from &ldquo;honey is sweet&rdquo; to &ldquo;honey possesses sweetness&rdquo;, which transformation can be viewed in the following variety of ways:
    
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<p>[[Image:Hypostatic Abstraction Figure 4.png|center]]</p><br>
 
<p>[[Image:Hypostatic Abstraction Figure 4.png|center]]</p><br>
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The grammatical trace of this hypostatic transformation tells of a process that abstracts the adjective "sweet" from the main predicate "is sweet", thus arriving at a new, increased-arity predicate "possesses", and as a by-product of the reaction, as it were, precipitating out the substantive "sweetness" as a new second subject of the new predicate, "possesses".
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The grammatical trace of this hypostatic transformation tells of a process that abstracts the adjective &ldquo;sweet&rdquo; from the main predicate &ldquo;is sweet&rdquo;, thus arriving at a new, increased-arity predicate &ldquo;possesses&rdquo;, and as a by-product of the reaction, as it were, precipitating out the substantive &ldquo;sweetness&rdquo; as a new second subject of the new predicate, &ldquo;possesses&rdquo;.
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==See also==
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* [[Hypostatic object]]
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* [[Prescisive abstraction]]
    
==References==
 
==References==
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* [[Charles Sanders Peirce|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.
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* [[Charles Sanders Peirce|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.
    
==Resources==
 
==Resources==
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===Focal nodes===
 
===Focal nodes===
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* [[Inquiry Live]]
 
* [[Inquiry Live]]
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* [[Logic Live]]
 
* [[Logic Live]]
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===Peer nodes===
 
===Peer nodes===
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* [http://beta.wikiversity.org/wiki/Hypostatic_abstraction Hypostatic Abstraction @ Beta Wikiversity]
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* [http://intersci.ss.uci.edu/wiki/index.php/Hypostatic_abstraction Hypostatic Abstraction @ InterSciWiki]
 
* [http://mywikibiz.com/Hypostatic_abstraction Hypostatic Abstraction @ MyWikiBiz]
 
* [http://mywikibiz.com/Hypostatic_abstraction Hypostatic Abstraction @ MyWikiBiz]
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* [http://www.netknowledge.org/wiki/Hypostatic_abstraction Hypostatic Abstraction @ NetKnowledge]
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* [http://ref.subwiki.org/wiki/Hypostatic_abstraction Hypostatic Abstraction @ Subject Wikis]
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* [http://en.wikiversity.org/wiki/Hypostatic_abstraction Hypostatic Abstraction @ Wikiversity]
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* [http://beta.wikiversity.org/wiki/Hypostatic_abstraction Hypostatic Abstraction @ Wikiversity Beta]
    
===Logical operators===
 
===Logical operators===
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===Related articles===
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===Information, Inquiry===
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* [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Propositional_Equation_Reasoning_Systems Jon Awbrey, &ldquo;Propositional Equation Reasoning Systems&rdquo;]
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* [[Inquiry]]
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* [[Dynamics of inquiry]]
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* [[Semeiotic]]
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* [[Logic of information]]
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* [[Descriptive science]]
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* [[Normative science]]
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* [[Pragmatic maxim]]
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* [[Truth theory]]
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* [http://planetmath.org/encyclopedia/DifferentialPropositionalCalculus.html Jon Awbrey, &ldquo;Differential Propositional Calculus&rdquo;]
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===Related articles===
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* [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Differential_Logic_:_Introduction Jon Awbrey, &ldquo;Differential Logic : Introduction&rdquo;]
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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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* [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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* [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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==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/Hypostatic_abstraction Hypostatic Abstraction], [http://intersci.ss.uci.edu/ InterSciWiki]
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* [http://mywikibiz.com/Hypostatic_abstraction Hypostatic Abstraction], [http://mywikibiz.com/ MyWikiBiz]
 
* [http://mywikibiz.com/Hypostatic_abstraction Hypostatic Abstraction], [http://mywikibiz.com/ MyWikiBiz]
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* [http://beta.wikiversity.org/wiki/Hypostatic_abstraction Hypostatic Abstraction], [http://beta.wikiversity.org/ Beta Wikiversity]
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* [http://planetmath.org/HypostaticAbstraction Hypostatic Abstraction], [http://planetmath.org/ PlanetMath]
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* [http://www.netknowledge.org/wiki/Hypostatic_abstraction Hypostatic Abstraction], [http://www.netknowledge.org/ NetKnowledge]
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* [http://planetmath.org/encyclopedia/HypostaticAbstraction.html Hypostatic Abstraction], [http://planetmath.org/ PlanetMath]
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* [http://knol.google.com/k/jon-awbrey/hypostatic-abstraction/3fkwvf69kridz/7 Hypostatic Abstraction], [http://knol.google.com/ Google Knol]
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* [http://vectors.usc.edu/thoughtmesh/publish/146.php Hypostatic Abstraction], [http://vectors.usc.edu/thoughtmesh/ ThoughtMesh]
 
* [http://vectors.usc.edu/thoughtmesh/publish/146.php Hypostatic Abstraction], [http://vectors.usc.edu/thoughtmesh/ ThoughtMesh]
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* [http://www.getwiki.net/-Hypostatic_Abstraction Hypostatic Abstraction], [http://www.getwiki.net/ GetWiki]
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* [http://wikinfo.org/w/index.php?title=Hypostatic_abstraction Hypostatic Abstraction], [http://wikinfo.org/w/ Wikinfo]
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* [http://www.wikinfo.org/index.php?title=Hypostatic_abstraction Hypostatic Abstraction], [http://www.wikinfo.org/ Wikinfo]
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* [http://en.wikiversity.org/wiki/Hypostatic_abstraction Hypostatic Abstraction], [http://en.wikiversity.org/ Wikiversity]
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* [http://www.textop.org/wiki/index.php?title=Hypostatic_abstraction Hypostatic Abstraction], [http://www.textop.org/wiki/ Textop Wiki]
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* [http://beta.wikiversity.org/wiki/Hypostatic_abstraction Hypostatic Abstraction], [http://beta.wikiversity.org/ Wikiversity Beta]
 
* [http://en.wikipedia.org/w/index.php?title=Hypostatic_abstraction&oldid=69736615 Hypostatic Abstraction], [http://en.wikipedia.org/ Wikipedia]
 
* [http://en.wikipedia.org/w/index.php?title=Hypostatic_abstraction&oldid=69736615 Hypostatic Abstraction], [http://en.wikipedia.org/ Wikipedia]
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[[Category:Philosophy]]
 
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