ONT Hypostatic And Prescisive Abstraction
HAPA. Note 1
| When we have analyzed a proposition so as to throw into the subject everything
| that can be removed from the predicate, all that it remains for the predicate to
| represent is the form of connection between the different subjects as expressed in
| the propositional 'form'. What I mean by "everything that can be removed from the
| predicate" is best explained by giving an example of something not so removable.
| But first take something removable. "Cain kills Abel." Here the predicate
| appears as "--- kills ---." But we can remove killing from the predicate
| and make the latter "--- stands in the relation --- to ---." Suppose we
| attempt to remove more from the predicate and put the last into the form
| "--- exercises the function of relate of the relation --- to ---" and then
| putting "the function of relate to the relation" into a another subject leave
| as predicate "--- exercises --- in respect to --- to ---." But this "exercises"
| expresses "exercises the function". Nay more, it expresses "exercises the function
| of relate", so that we find that though we may put this into a separate subject, it
| continues in the predicate just the same. Stating this in another form, to say that
| "A is in the relation R to B" is to say that A is in a certain relation to R. Let
| us separate this out thus: "A is in the relation R^1 (where R^1 is the relation
| of a relate to the relation of which it is the relate) to R to B". But A is
| here said to be in a certain relation to the relation R^1. So that we can
| expresss the same fact by saying, "A is in the relation R^1 to the relation
| R^1 to the relation R to B", and so on 'ad infinitum'. A predicate which
| can thus be analyzed into parts all homogeneous with the whole I call
| a 'continuous predicate'. It is very important in logical analysis,
| because a continuous predicate obviously cannot be a 'compound'
| except of continuous predicates, and thus when we have carried
| analysis so far as to leave only a continuous predicate, we
| have carried it to its ultimate elements.
| Peirce, "Letters to Lady Welby", 14 Dec 1908, 'Selected Writings', pp. 396-397.
| Charles S. Peirce, "Letters to Lady Welby", pp. 380-432 in:
|'Charles S. Peirce: Selected Writings (Values in a Universe
| of Chance)', Edited with an Introduction and Notes by
| Philip P. Wiener, Dover, New York, NY, 1966.