Hypostatic abstraction

{{Short description|Formal operation in mathematical logic}} {{See also|Reification (fallacy)}} {{more footnotes|date=June 2022}}

'''Hypostatic abstraction''' in philosophy and mathematical logic, also known as '''hypostasis''' or '''subjectal abstraction''', is a formal operation that transforms a predicate into a relation; for example "Honey ''is'' sweet" is transformed into "Honey ''has'' sweetness". The relation is created between the original subject and a new term that represents the property expressed by the original predicate.

== Description ==

=== Technical definition === Hypostasis changes a propositional formula of the form ''X is Y'' to another one of the form ''X has the property of being Y'' or ''X has Y-ness''. The logical functioning of the second object ''Y-ness'' consists solely in the truth-values of those propositions that have the corresponding abstract property ''Y'' as the predicate. The object of thought introduced in this way may be called a ''hypostatic object'' and in some senses an ''abstract object'' and a '''''formal object'''''.

The above definition is adapted from the one given by Charles Sanders Peirce.<ref>CP 4.235, "The Simplest Mathematics" (1902), in ''Collected Papers'', CP 4.227–323</ref> As Peirce describes it, the main point about the formal operation of hypostatic abstraction, insofar as it operates on formal linguistic expressions, is that it converts a predicative adjective or predicate into an extra subject, thus increasing by one the number of "subject" slots—called the ''arity'' or ''adicity''—of the main predicate.

The distinction between particular objects and a ''formal object'' is noted by Anthony Kenny:<ref>Kenny, A. (1963), ''Action, Emotion and Will'', London, New York: Routledge and Kegan Paul; Humanities Press</ref> we might identify any object as having a certain property to which we respond, but the formal object of that response is the property which we implicitly ascribe to the particular object by virtue of us having that response: thus if a certain red rose is "lovely", the rose has the property of loveliness, and this loveliness is the formal object of our aesthetic appreciation of the rose.<ref>Scarantino, A. and de Sousa, R., [https://plato.stanford.edu/archives/sum2021/entries/emotion/ "Emotion"], ''The Stanford Encyclopedia of Philosophy'' (Summer 2021 Edition), Edward N. Zalta (ed.), accessed on 4 December 2024</ref>

=== Application === thumb|upright=1.2|The transformation of "honey is sweet" into "honey possesses sweetness" can be viewed in several ways.

The grammatical trace of this hypostatic transformation is a process that extracts the adjective "sweet" from the predicate "is sweet", replacing it by a new, increased-arity predicate "possesses", and as a by-product of the reaction, as it were, precipitating out the substantive "sweetness" as a second subject of the new predicate.

The abstraction of hypostasis takes the concrete physical sense of "taste" found in "honey is sweet" and ascribes to it the formal metaphysical characteristics in "honey has sweetness".

==References== {{reflist}}

=== Sources === {{refbegin}} * {{Cite book |last=Peirce |first=C.S. |author-link=Charles Sanders Peirce |title=Collected Papers of Charles Sanders Peirce, vols. 1–6 (1931–1935) |title-link=Charles Sanders Peirce bibliography#CP |editor1-first=Charles |editor1-last=Hartshorne |editor1-link=Charles Hartshorne |editor2-link=Paul Weiss (philosopher) |editor2-first=Paul |editor2-last=Weiss |location=Cambridge, Massachusetts |publisher=Harvard University Press}} * {{Cite book |last=Peirce |first=C.S. |author-link=Charles Sanders Peirce |title=Collected Papers of Charles Sanders Peirce, vols. 7–8 (1958) |title-link=Charles Sanders Peirce bibliography#CP |editor1-link=Arthur Burks |editor1-first=Arthur W. |editor1-last=Burks |location=Cambridge, Massachusetts |publisher=Harvard University Press}} * {{Cite journal |last=Zeman |first=J. Jay |title=Peirce on Abstraction |year=1982 |url=http://users.clas.ufl.edu/jzeman/peirce_on_abstraction.htm |url-status=dead |archive-url=https://web.archive.org/web/20201101010626/http://users.clas.ufl.edu/jzeman/peirce_on_abstraction.htm |archive-date=1 November 2020 |journal=The Monist |volume=65 |issue=2 |pages=211–229 |via=University of Florida |doi=10.5840/monist198265210|url-access=subscription }} {{refend}}

Category:Abstraction Category:Mathematical analysis Category:Mathematical logic Category:Mathematical relations Category:Concepts in metaphysics Category:Charles Sanders Peirce