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'''Hypostatic abstraction''' is a 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, ''hypostasis'', ''objectification'', ''reification'', and ''subjectal abstraction''.  The object of discussion or thought thus introduced is termed a ''[[hypostatic object]]''.

'''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]]''.

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).

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).

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.

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.

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:

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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* [[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.

* [[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.

==Related topics==

==Resources==

 

 

 

 

 

 

 

 

===Logical operators===

* [[Continuous predicate]]

* [[Continuous predicate]]

* [[Hypostatic object]]

* [[Hypostatic abstraction]]

* [[Prescisive abstraction]]

* [[Relation (mathematics)|Relation]]

* [[Relation composition]]

* [[Triadic relation]]

==Resources==

===Related articles===

 

* [http://vectors.usc.edu/thoughtmesh/publish/146.php Hypostatic Abstraction &rarr; ThoughtMesh]

* [http://planetmath.org/encyclopedia/DifferentialPropositionalCalculus.html Jon Awbrey, &ldquo;Differential Propositional Calculus&rdquo;]

* [http://web.clas.ufl.edu/users/jzeman/peirce_on_abstraction.htm J. Jay Zeman, ''Peirce on Abstraction'']

* [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Differential_Logic_:_Introduction Jon Awbrey, &ldquo;Differential Logic : Introduction&rdquo;]

==Document history==

==Document history==

[[Category:Logic]]

[[Category:Logic]]

[[Category:Mathematics]]

[[Category:Mathematics]]

[[Category:Semiotics]]

[[Category:Semiotics]]