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| \textbf{Hypostatic abstraction}, also known as \textbf{hypostasis} or \textbf{subjectal abstraction}, is a formal operation that takes an element of information, such as might be expressed in a proposition of the form \textit{X is Y}, and conceives its information to consist in the relation between a subject and another subject, such as expressed in a proposition of the form \textit{X has Y-ness}. The existence of the latter subject, here \textit{Y-ness}, consists solely in the truth of those propositions that have the corresponding concrete term, here \textit{Y}, as the predicate. The object of discussion or thought thus introduced may also be called a \textit{hypostatic object}. |
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| The above definition is adapted from one given by Charles Sanders Peirce (CP 4.235). 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 an adjective or some part of a predicate into an extra subject, upping the arity of the main predicate in the process. |
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| For example, a typical case of hypostatic abstraction occurs in the transformation from ``honey is sweet" to ``honey possesses sweetness", which transformation can be viewed in the following variety of ways: |
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| \begin{quote}\begin{verbatim} |
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| o-----------------------------------------------------------o |
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| | . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | |
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| | . . . . . . . . Hypostasis. . . . . . . . . . . . . . . . | |
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| | Sweet(honey) ---------------> Possesses(honey, sweetness) | |
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| | . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | |
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| o-----------------------------------------------------------o |
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| | . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | |
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| | . . . . S(h). ------------> . P(h , s). . . . . . . . . . | |
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| | . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | |
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| o-----------------------------------------------------------o |
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| | . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | |
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| | . . . . . S . . . . . . . . . P . . . . . . . . . . . . . | |
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| | . . . . . o . ------------> . o . . . . . . . . . . . . . | |
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| | . . . . . | . . . . . . . . . | . . . . . . . . . . . . . | |
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| | . . . . . o . . . . . . . . . o . . . . . . . . . . . . . | |
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| | . . . . . h . . . . . . . .<h , s>. . . . . . . . . . . . | |
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| o-----------------------------------------------------------o |
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| | . . . . . . . . . . . . . . . ^ . . . . . . . . . . . . . | |
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| | . . . . .[S]. ------------> ./P\. . . . . . . . . . . . . | |
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| | . . . . . | . . . . . . . . o---o . . . . . . . . . . . . | |
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| | . . . . . | . . . . . . . . | . | . . . . . . . . . . . . | |
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| | . . . . . o . . . . . . . . o . o . . . . . . . . . . . . | |
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| | . . . . . h . . . . . . . . h . s . . . . . . . . . . . . | |
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| o-----------------------------------------------------------o |
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| \end{verbatim}\end{quote} |
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| The grammatical trace of this hypostatic transformation tells of 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 new second subject of the new predicate, ``possesses". |
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| \section{References} |
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| \begin{itemize} |
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| \item |
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| Peirce, Charles Sanders (1902), ``The Simplest Mathematics", CP 4.227--323 in \textit{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. |
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| \end{itemize} |
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