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 hassweetness”. The relationship is created entre les 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 the X of the form Y or X has Y-ness . The logical functioning of the second object Y-ness Consists Solely in the Truth Gains Of Those proposals That avez la Corresponding abstract property Y as the predicate. The object of thought 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 (CP 4.235, “The Simplest Mathematics” (1902), in Collected Papers , PC 4227-323). As it is described, it is important that it be used in an analogous way, and that it converts to an adjective or predicate into an extra subject, thereby increasing the number of “subject” slots. – called the arity or adicity – of the main predicate.
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 a by-product of the reaction, as it was, precipitating out the substantive “sweetness” as a second subject of the new predicate.
The abstraction of hypostasis takes the form of “taste” in “honey is sweet” and gives it formal metaphysical characteristics in “honey has sweetness”.
- Peirce, CS , Collected Papers of Charles Sanders Peirce , vols. 1-6 (1931-1935), Charles Hartshorne and Paul Weiss , eds., Vols. 7-8 (1958), Arthur W. Burks , ed., Harvard University Press, Cambridge, MA.