continuous predicate

continuous predicate

A

continuous predicate

, as described by Charles Sanders Peirce, is a special type of relational (

http://planetmath.org/RelationTheory

)

predicate

that arises as the limit of an iterated process of

hypostatic abstraction

.

The following is an extended exposition of the

concept

in Peirce’s own words:

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 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 express 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 1908/1966, pp. 396–397).

1

References

•

Peirce, Charles Sanders (1908/1966), Letter of 14 December 1908, “Letters to Lady Welby”, pp. 380–432 in

Charles S. Peirce : Selected Writings (Values in a

Universe

of Chance)

, Philip P. Wiener (ed.), Dover Publications, New York, NY, 1966.

Title

continuous predicate

Canonical

name

ContinuousPredicate

Date of creation

2013-11-16 13:45:43

Last modified on

2013-11-16 13:45:43

Owner

Jon Awbrey (15246)

Last modified by

Jon Awbrey (15246)

Numerical id

7

Author

Jon Awbrey (15246)

Entry type

Definition

Classification

msc 03B30

Classification

msc 03B22

Classification

msc 03B15

Classification

msc 03A05

Classification

msc 00A30

Classification

msc 03B42

Synonym

continuous relation

Related topic

HypostaticAbstraction

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