Continuous predicate is a term coined by Charles Sanders Peirce (1839-1914) to describe a special type of relational predicate that results in the limitation of a recursive process of hypostatic abstraction .
Here is one of Peirce’s definitive discussions of the concept:
When we Analyzed-have a proposal so as to throw into the subject Everything That Can Be removed from the predicate, All That Remains it for the predicate is to Represent the form of connection entre les different subjects as Expressed in the propositional form . What I mean by “all 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 it from the predicate and make the latter “- stands in the relation – to -.” The role of the relationship between the relationship and the relationship of the relationship to the relationship ” exercises – in respect to – to -. ” But this “exercises” expresses “exercises the function”. Nay more, it expresses “exercises the function of narrative”, so that we find that, although it is 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 R¹ (where R¹ is the relationship of a report to the relationship of which it is the story) to R to B “. A goal is a certain relationship to the relation R¹. So we can express the same fact by saying, “A is in the relation R¹ to the relationship R¹ to the relation R to B”, and so on ad infinitum .
I call a continuous predicate . It is very significant in logical analysis, Because a continuous Obviously predicate can not be a compound except of continuous predicates, and THUS When We-have the carried analysis so far as to leave only a continuous predicate, we-have the carried it to icts ultimate items. (CS Peirce, “Letters to Lady Welby” (December 14, 1908), Selected Writings , pp. 396-397).
- Peirce, CS , “Letters to Lady Welby,” pp. 380-432 in Charles S. Peirce: Selected Writings (Values in a Universe of Chance) , Philip P. Wiener (ed.), Dover, New York, NY, 1966.