Content
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”.
See also
|
|
References
- 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.