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Hypostatic abstraction in
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
mathematical logic
Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of forma ...
, also known as hypostasis or subjectal abstraction, is a formal operation that transforms a predicate
Predicate or predication may refer to:
* Predicate (grammar), in linguistics
* Predication (philosophy)
* several closely related uses in mathematics and formal logic:
**Predicate (mathematical logic)
**Propositional function
**Finitary relation, o ...
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
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, r ...
expressed by the original predicate.
Description
Technical definition
Hypostasis changes apropositional formula
In propositional logic, a propositional formula is a type of syntactic formula which is well formed and has a truth value. If the values of all variables in a propositional formula are given, it determines a unique truth value. A propositional for ...
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 metaphysics, the distinction between abstract and concrete refers to a divide between two types of entities. Many philosophers hold that this difference has fundamental metaphysical significance. Examples of concrete objects include plants, h ...
'' 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 philosopher, logician, mathematician and scientist who is sometimes known as "the father of pragmatism".
Educated as a chemist and employed as a scientist for ...
.CP 4.235, "The Simplest Mathematics" (1902), in ''Collected Papers'', CP 4.227–323 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 of a certain type of ...
or predicate into an extra subject, thus increasing by one the number of "subject" slots—called the ''arity
Arity () is the number of arguments or operands taken by a function, operation or relation in logic, mathematics, and computer science. In mathematics, arity may also be named ''rank'', but this word can have many other meanings in mathematics. ...
'' or ''adicity''—of the main predicate.
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 studies the fundamental nature of reality, the first principles of being, identity and change, space and time, causality, necessity, and possibility. It includes questions about the nature of conscio ...
characteristics in "honey has sweetness". This is the fallacy of reification.
See also
References
Sources
* * * {{Metaphysics Abstraction Mathematical analysis Mathematical logic Mathematical relations Metaphysics Charles Sanders Peirce