Whole and Parts

Charles Sanders Peirce

[This material can be found in Peirce's Collected Papers, Volume 6, paragraphs 381-383.]

381. The old definition is: "Totum est quod constat plurium rerum unione." Psychologically, whatever is treated as a single object, though capable of treatment as two or more objects (parts of the whole): by "treated" meaning "thought of," "attended to," or otherwise "acted upon."

382. We may say that a whole is an ens rationis whose being consists in the copulate being of certain other things, either not entia rationis or not so much so as the whole; so that a whole is analogous to a collection, which is, in fact, a special kind of whole. There can be no doubt that the word whole always brings before the mind the image of a collection, and that we interpret the word whole by analogy with collection. The idea of a collection is itself, however, by no means an easy one to analyze. It is an ens rationis, abstraction, or fictitious subject (but the adjective must be understood in a broad sense, to be considered below), which is individual, and by means of which we are enabled to transform universal propositions into singular propositions. Thus, the proposition "all men are mortal," with a new subject and new predicate, appears as "The collection of men is a collection of mortals"; just as, for other purposes, and by means of other abstractions, we transform the same proposition into "The character of mortality is possessed by every man"; and the members of the collection are regarded as less fictitious than the collection. It very often happens that an object given indirect perception as an individual is, on closer scrutiny, seen to be identifiable with a collection of parts. But it does not seem to be strictly accurate to say that the larger object of perception is identical with that abstraction, the collection of the smaller objects. It is rather something perceived which agrees in its relations with the abstraction so well that, for convenience, it is regarded as the same thing. No doubt the parts of a perceived object are virtually objects of consciousness in the first percept; but it is useless to try to extend logical relations to the sort of thought which antecedes the completion of the percept. By the time we conceive an object as a collection, we conceive that the first reality belongs to the members of the collection and that the collection itself is a mere intellectual aspect , or way of regarding these members, justified, in ordinary cases, by certain facts. We may, therefore, define a collection as a fictitious (thought) individual, whose being consists in the being of certain less fictitious individuals.

383. Many adjectives are used to distinguish different kinds of wholes. Certain of the phrases may be defined.

• Actual whole: any whole which cannot exist without the existence of its parts. Usually identified with the Constitute whole. Monboddo's definition (Ancient Met., i. 479) is not quite accurate.

• Collective whole, or aggregate whole: defined by Chauvin as "that which has material parts separate and accidentally thrown together into one, as an army," etc. But the example shows that organization does not disqualify a whole from being called collective, although the term totum per aggregationem will no longer be applied to it, in that case. In so far as a whole is collective, any other relation between its parts is put out of view.

• Composite whole: a term of Burgersdicius, who (Inst. Met., I. xxii. §7) defines it as "quod ex duabus partibus constat quarum una est in potentia ad alterum et altera vice versa actus est alterius." It includes the whole by information and the whole by inherence.

• Comprehensive whole: a whole of logical comprehension.

• Constituent whole: a whole which is essential to its parts.

• Constitute whole: a whole whose parts are essential to it. See Actual whole (above).

• Continuous whole: a continuum regarded as a whole. In order to define it, it would first be necessary to define continuity. Now we have, perhaps, not yet succeeded in analyzing the conception of continuity; for what the mathematicians call by that name, such as the relations of all real quantities capable of being designated to an indefinite degree of approximation by means of a whole number and a decimal, does not answer the requisites of the problem.

• Copulative whole: a whole consisting of a sign which is essentially applicable to whatever certain signs, called its parts, are all applicable, but is essentially inapplicable to anything to which any one of these signs is inapplicable.

• Definite whole: a whole constituted by genus and difference.

• Definitive whole: see Definite whole (above).

• Discrete whole: the same as a Collective whole (above).

• Disjunctive whole: a whole consisting of a sign which is essentially applicable to whatever any one of certain signs, called its parts, is applicable, but is essentially inapplicable to anything to which none of these parts is applicable.

• Dissimilar whole: same as Heterogeneous whole (below).

• Essential whole: great confusion exists in the use of this very common expression. Aquinas (Summa Theol., Pt. I. lxxvi. 8) uses it in a broad sense which would make it about equivalent to Burgersdicius' composite whole, or perhaps broader. On the other hand, it is sometimes restricted to the whole per informationem, and this is perhaps the best settled use. But others make it include the physical and the metaphysical whole as its two species.

• Extensive whole: a whole of logical extension, usually called a subjective or logical whole.

• Formal whole: a comprehensive whole, especially of essential comprehension. See Actual whole (above).

• Heterogeneous whole: a term of Aquinas; a whole whose parts are dissimilar from the whole.

• Homogeneous whole: a term of Aquinas; a whole whose parts are similar to the whole, as the parts of a whole of water are.

• Integral whole (a term in common use since Abélard's time): Blundevile (1599) says, "Whole integral is that which consisteth of integral parts, which though they cleave together, yet they are distinct and severall in number, as man's body, consisting of head, brest, belly, legs, etc." The usual definition is "quod habet partem extra partem," which restricts it to space. Burgersdicius, however, says that parts which differ in their ordinal places are partes extra partes.

• Integrate whole: a pedantic variant of Integral whole (above).

• Logical whole: same as Universal whole (below).

• Mathematical whole: same as Integral whole (above).

• Metaphysical whole: a whole in that respect in which a species is the whole of its genus and difference. See Formal whole (above).

• Natural whole: a term proposed by Hamilton to replace Comprehensive or Metaphysical whole; as if that were not sufficiently provided with aliases under which to hide itself.

• Negative whole: a unit regarded as a whole, as in the phrases "deus totus est ubique," and "anima est tota in toto corpore."

• Physical whole: a whole compounded of substance and accident; but some say of matter and form; and some that both come to the same thing. In the peripatetic view, however, substance is form, not matter.

• Positive whole: a whole consisting of parts. See Negative whole (above).

• Potential whole: same as Universal whole (below); so called because the genus does not actually, but only potentially, contain the species, etc.

• Potestative whole: a term of Aquinas; equivalent to Potential whole (above).

• Predicative whole: a whole of logical depth.

• Quantitative whole: same as Integral whole (above).

• Similar whole: see Homogeneous whole (above).

• Subject whole: same as Subjective whole (below).

• Subjective whole: a very venerable name for Universal whole (below).

• Substantial whole: a whole of logical breadth.

• Universal whole: see Universal.

• Whole by accident: such a whole as neither essentially belongs to the parts nor the parts to it.

• CrossWhole by aggregation or aggregative whole: same as Collective whole (above) in an exclusive sense.

• Whole by information: a compound of act and power in the same kind, such as man, according to the Aristotelian theory of the soul.

• Whole by inherence: same as Physical whole (above).

• Whole by itself or per se: a whole which essentially belongs to its parts or its parts to it.