The Care and Breeding of Abstract Objects

Hypostatic Abstraction is a formal operation on a subject–predicate form which preserves its information while introducing a new subject and upping the “arity” of its predicate.  To cite a notorious example, hypostatic abstraction turns “Opium is drowsifying” into “Opium has dormitive virtue”.

Introduction

Hypostatic abstraction is a formal operation which takes an element of information, as expressed in a proposition and conceives its information to consist in the relation between that subject and another subject, as expressed in the proposition   The existence of the abstract subject consists solely in the truth of those propositions containing the concrete predicate   Hypostatic abstraction is known under many names, for example, hypostasis, objectification, reification, and subjectal abstraction.  The object of discussion or thought thus introduced is termed a hypostatic object.

The above definition is adapted from the one given by Charles Sanders Peirce (CP 4.235, “The Simplest Mathematics” (1902), in Collected Papers, CP 4.227–323).

The way that Peirce describes it, the main thing about the formal operation of hypostatic abstraction, insofar as it can be observed to operate on formal linguistic expressions, is that it converts some part of a predicate into a number of additional subjects, at the same time creating a new predicate that tells how all of the subjects are related, at least, according to the information in the original proposition.

For example, a typical case of hypostatic abstraction occurs in the grammatical transformation which turns “honey is sweet” into “honey possesses sweetness”.  This transformation may be visualized in the following variety of ways.

The grammatical trace of the hypostatic transformation occurring in this case articulates a process that abstracts the adjective “sweet” from the main predicate “is sweet”, thus arriving at 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 2-place predicate, “possesses”.

References

• Peirce, C.S., Collected Papers of Charles Sanders Peirce, vols. 1–6, Charles Hartshorne and Paul Weiss (eds.), vols. 7–8, Arthur W. Burks (ed.), Harvard University Press, Cambridge, MA, 1931–1935, 1958.

Resources

• Charles Sanders Peirce • Bibliography
• ThoughtMesh • Hypostatic Abstraction
• J. Jay Zeman • “Peirce on Abstraction”