Hypostatic abstraction in

philosophy Philosophy ('love of wisdom' in Ancient Greek) is a systematic study of general and fundamental questions concerning topics like existence, reason, knowledge, Value (ethics and social sciences), value, mind, and language. It is a rational an ...

and

mathematical logic Mathematical logic is the study of Logic#Formal logic, formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory). Research in mathematical logic com ...

, also known as hypostasis or subjectal abstraction, is a formal operation that transforms a predicate into a

relation Relation or relations may refer to: General uses * International relations, the study of interconnection of politics, economics, and law on a global level * Interpersonal relationship, association or acquaintance between two or more people * ...

; 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 Property is a system of rights that gives people legal control of valuable things, and also refers to the valuable things themselves. Depending on the nature of the property, an owner of property may have the right to consume, alter, share, re ...

expressed by the original predicate.

Description

Technical definition

Hypostasis changes a

propositional formula In propositional logic, a propositional formula is a type of syntactic formula which is well formed. If the values of all variables in a propositional formula are given, it determines a unique truth value. A propositional formula may also be call ...

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 In philosophy and the arts, a fundamental distinction exists between abstract and concrete entities. While there is no universally accepted definition, common examples illustrate the difference: numbers, sets, and ideas are typically classif ...

'' and a ''formal object''. The above definition is adapted from the one given by

Charles Sanders Peirce Charles Sanders Peirce ( ; September 10, 1839 – April 19, 1914) was an American scientist, mathematician, logician, and philosopher who is sometimes known as "the father of pragmatism". According to philosopher Paul Weiss (philosopher), Paul ...

. 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 A predicative expression (or just predicative) is part of a clause predicate, and is an expression that typically follows a copula or linking verb, e.g. ''be'', ''seem'', ''appear'', or that appears as a second complement (object complement) of ...

or predicate into an extra subject, thus increasing by one the number of "subject" slots—called the ''

arity In logic, mathematics, and computer science, arity () is the number of arguments or operands taken by a function, operation or relation. In mathematics, arity may also be called rank, but this word can have many other meanings. In logic and ...

'' or ''adicity''—of the main predicate. The distinction between particular objects and a ''formal object'' is noted by Anthony Kenny: 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.Scarantino, A. and de Sousa, R.
"Emotion"
''The Stanford Encyclopedia of Philosophy'' (Summer 2021 Edition), Edward N. Zalta (ed.), accessed on 4 December 2024

Application

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 Metaphysics is the branch of philosophy that examines the basic structure of reality. It is traditionally seen as the study of mind-independent features of the world, but some theorists view it as an inquiry into the conceptual framework of h ...

characteristics in "honey has sweetness".

References

Sources

* * * {{Metaphysics Abstraction Mathematical analysis Mathematical logic Mathematical relations Concepts in metaphysics Charles Sanders Peirce

Description

Technical definition

Application

See also

References

Sources