Difference between revisions of "Hypostatic abstraction"

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'''Hypostatic abstraction''', also known as '''hypostasis''' or '''subjectal abstraction''', is a formal operation that takes an element of information,  such as might be expressed in a proposition of the form ''X is Y'', and conceives its information to consist in the relation between a subject and another subject, such as expressed in a proposition of the form ''X has Y-ness''.  The existence of the latter subject, here ''Y-ness'', consists solely in the truth of those propositions that have the corresponding concrete term, here ''Y'', as the predicate.  The object of discussion or thought thus introduced may also be called 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]].
  
The above definition is adapted from the one given by [[Charles Sanders Peirce]] (CP 4.235, "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]]''.
  
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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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).
  
For example, a typical case of hypostatic abstraction occurs in the transformation from "honey is sweet" to "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.
  
<pre>
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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:
o-----------------------------------------------------------o
 
|                                                          |
 
|                Hypostasis                                |
 
| Sweet(honey) ---------------> Possesses(honey, sweetness) |
 
|                                                          |
 
o-----------------------------------------------------------o
 
|                                                          |
 
|        S(h)  ------------>  P(h , s)                    |
 
|                                                          |
 
o-----------------------------------------------------------o
 
|                                                          |
 
|          S                  P                          |
 
|          o  ------------>  o                          |
 
|          |                  |                          |
 
|          o                  o                          |
 
|          h                <h , s>                        |
 
|                                                          |
 
o-----------------------------------------------------------o
 
|                                                          |
 
|                              ^                          |
 
|          [S]  ------------>  /P\                          |
 
|          |                o---o                        |
 
|          |                |  |                        |
 
|          o                o  o                        |
 
|          h                h  s                        |
 
|                                                          |
 
o-----------------------------------------------------------o
 
</pre>
 
  
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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<br>
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<p>[[Image:Hypostatic Abstraction Figure 1.png|center]]</p><br>
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<p>[[Image:Hypostatic Abstraction Figure 2.png|center]]</p><br>
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<p>[[Image:Hypostatic Abstraction Figure 3.png|center]]</p><br>
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<p>[[Image:Hypostatic Abstraction Figure 4.png|center]]</p><br>
  
==References==
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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;.
  
* [[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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==See also==
  
==See also==
 
{|
 
| valign=top |
 
* [[Abstraction]]
 
* [[Abstraction (computer science)|Abstraction in computing]]
 
* [[Abstraction (mathematics)|Abstraction in mathematics]]
 
* [[Analogy]]
 
* [[Category theory]]
 
| valign=top |
 
* [[Continuous predicate]]
 
 
* [[Hypostatic object]]
 
* [[Hypostatic object]]
 
* [[Prescisive abstraction]]
 
* [[Prescisive abstraction]]
* [[Reification]]
 
* [[E-prime]]
 
|}
 
  
==External links==
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==References==
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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.
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==Resources==
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* [http://vectors.usc.edu/thoughtmesh/publish/146.php Hypostatic Abstraction &rarr; ThoughtMesh]
  
 
* [http://web.clas.ufl.edu/users/jzeman/peirce_on_abstraction.htm J. Jay Zeman, ''Peirce on Abstraction'']
 
* [http://web.clas.ufl.edu/users/jzeman/peirce_on_abstraction.htm J. Jay Zeman, ''Peirce on Abstraction'']
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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/Hypostatic_abstraction Hypostatic Abstraction @ InterSciWiki]
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* [http://mywikibiz.com/Hypostatic_abstraction Hypostatic Abstraction @ MyWikiBiz]
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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]
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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]]
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* [[Hypostatic abstraction]]
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* [[Logic of relatives]]
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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}}
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* [[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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===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]
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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}}
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==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.
 +
 +
* [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]
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* [http://planetmath.org/HypostaticAbstraction Hypostatic Abstraction], [http://planetmath.org/ PlanetMath]
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* [http://vectors.usc.edu/thoughtmesh/publish/146.php Hypostatic Abstraction], [http://vectors.usc.edu/thoughtmesh/ ThoughtMesh]
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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://en.wikiversity.org/wiki/Hypostatic_abstraction Hypostatic Abstraction], [http://en.wikiversity.org/ Wikiversity]
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* [http://beta.wikiversity.org/wiki/Hypostatic_abstraction Hypostatic Abstraction], [http://beta.wikiversity.org/ Wikiversity Beta]
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* [http://en.wikipedia.org/w/index.php?title=Hypostatic_abstraction&oldid=69736615 Hypostatic Abstraction], [http://en.wikipedia.org/ Wikipedia]
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[[Category:Charles Sanders Peirce]]
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[[Category:Inquiry]]
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[[Category:Logic]]
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[[Category:Mathematics]]
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[[Category:Ontology]]
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[[Category:Philosophy]]
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[[Category:Pragmatism]]
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[[Category:Semiotics]]

Latest revision as of 18:58, 10 November 2015

This page belongs to resource collections on Logic and Inquiry.

Hypostatic abstraction is a formal operation that takes an element of information, as expressed in a proposition \(X ~\text{is}~ Y,\!\) and conceives its information to consist in the relation between that subject and another subject, as expressed in the proposition \(X ~\text{has}~ Y\!\text{-ness}.\!\)  The existence of the abstract subject \(Y\!\text{-ness}\!\) consists solely in the truth of those propositions that contain the concrete predicate \(Y.\!\)  Hypostatic abstraction is known by many names, for example, hypostasis, objectification, reification, and subjectal abstraction.  The object of discussion or thought thus introduced is termed a hypostatic object.

The above definition is adapted from the one given by introduced Charles Sanders Peirce (CP 4.235, “The Simplest Mathematics” (1902), in Collected Papers, CP 4.227–323).

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.

For example, a typical case of hypostatic abstraction occurs in the transformation from “honey is sweet” to “honey possesses sweetness”, which transformation can be viewed in the following variety of ways:


Hypostatic Abstraction Figure 1.png


Hypostatic Abstraction Figure 2.png


Hypostatic Abstraction Figure 3.png


Hypostatic Abstraction Figure 4.png


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”.

See also

References

  • 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.

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.