SUO: Re: Lifecycle Integration Schema :> Abstractions & Their Deciduation Problems
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LIS. Discussion Note 110
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I think that it would be useful at this time to run back through
one of Peirce's best descriptions of the two kinds of abstraction,
and try to tackle it line by line.
The first and simpler type of abstraction is "prescisive abstraction" --
where here I have taken something like the running average of several
different spellings of the term -- that merely extracts or selectively
attends to a feature or a property of a more concrete object. In this
case one passes from an object to one of its properties, very analogous
to the sort of mathematical operation that is usually called "projection".
Here, one speaks of "prescinding" the property in question from the object,
and thus prescisive abstraction has the alternative name of "prescission".
The second, more substantial type of abstraction is "hypostatic abstraction".
This is the operation that we think of a bringing the abstract object proper
into being, or into the sphere of human thought, or at least into the frame
of a particular discussion. In this case one passes from a concrete object
or situation, via a selection of properties, to end with an abstract object.
| Look through the modern logical treatises, and you will find that they
| almost all fall into one or other of two errors, as I hold them to be;
| that of setting aside the doctrine of abstraction (in the sense in
| which an abstract noun marks an abstraction) as a grammatical topic
| with which the logician need not particularly concern himself; and
| that of confounding abstraction, in this sense, with that operation
| of the mind by which we pay attention to one feature of a percept to
| the disregard of others. The two things are entirely disconnected.
Here Peirce gives a first description of the two types of abstraction
and emphasizes the importance of distinguishing them from one another.
| The most ordinary fact of perception, such as "it is light",
| involves 'precisive' abstraction, or 'prescission'.
In other words, all attention is selective to some degree,
so any perception, such as that which we typically express
by means of the sentence "It is light" involves prescission,
a trimming of the whole experience to crop an observed fact.
| But 'hypostatic' abstraction, the abstraction which transforms
| "it is light" into "there is light here", which is the sense
| which I shall commonly attach to the word abstraction (since
| 'prescission' will do for precisive abstraction) is a very
| special mode of thought.
In the transformation from "It is light" to "There is light here",
the spelling "light" is transformed from an adjective into a noun.
This is the typical grammatical clue that an underlying operation
of "hypostatic" or "subjectal" abstraction has been accomplished.
| It consists in taking a feature of a percept or percepts (after it has
| already been prescinded from the other elements of the percept), so as
| to take propositional form in a judgment (indeed, it may operate upon
| any judgment whatsoever), and in conceiving this fact to consist in the
| relation between the subject of that judgment and another subject, which
| has a mode of being that merely consists in the truth of propositions of
| which the corresponding concrete term is the predicate.
This is very significant. It marks not just a grammatical
transformation that happens to be taking place in a given
example of hypostatic abstraction, but describes the very
form of a certain transformation that took place all along
the frontiers of thought in the formal sciences beginning
toward the middle of the Nineteenth Century, a development
in which C.S. Peirce was a major force and prime expositor.
But I'll need to save the rest of that story for tomorrow.
Jon Awbrey
| Reference:
|
| C.S. Peirce, CP 4.235, "The Simplest Mathematics",
| Chapter 3 of the "Minute Logic", Jan-Feb 1902.
|
| http://suo.ieee.org/ontology/msg05091.html
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