Hypostatic abstraction in 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.
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.[1] 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.
Applicationedit
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". This is the fallacy of reification[citation needed].
Zeman, J. Jay (1982). . The Monist. 65 (2): 211–229. doi:10.5840/monist198265210. Archived from the original on 1 November 2020 – via University of Florida.
January 01, 1970
hypostatic, abstraction, also, reification, fallacy, this, article, includes, list, general, references, lacks, sufficient, corresponding, inline, citations, please, help, improve, this, article, introducing, more, precise, citations, june, 2022, learn, when, . See also Reification fallacy This article includes a list of general references but it lacks sufficient corresponding inline citations Please help to improve this article by introducing more precise citations June 2022 Learn how and when to remove this message Hypostatic abstraction in 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 Contents 1 Description 1 1 Technical definition 1 2 Application 2 See also 3 References 3 1 SourcesDescription editTechnical definition edit 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 1 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 Application edit nbsp 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 This is the fallacy of reification citation needed See also editAbstraction Abstraction in computing Abstraction in mathematics Analogy Category theory Continuous predicate E prime Hypostasis philosophy and religion Reification Subsumptive containment hierarchyReferences edit CP 4 235 The Simplest Mathematics 1902 in Collected Papers CP 4 227 323 Sources edit Peirce C S Hartshorne Charles Weiss Paul eds Collected Papers of Charles Sanders Peirce vols 1 6 1931 1935 Cambridge Massachusetts Harvard University Press Peirce C S Burks Arthur W ed Collected Papers of Charles Sanders Peirce vols 7 8 1958 Cambridge Massachusetts Harvard University Press Zeman J Jay 1982 Peirce on Abstraction The Monist 65 2 211 229 doi 10 5840 monist198265210 Archived from the original on 1 November 2020 via University of Florida Retrieved from https en wikipedia org w index php title Hypostatic abstraction amp oldid 1196378056, wikipedia, wiki, book, books, library,
