COMPOSITION AND DIVISION
WHOLE AND PARTS argument

Aristotle considers composition or “combination of words” and division to be verbal fallacies, that is fallacies of words, as opposed to fallacies of things or method, see Fallacies 2. They are discussed in the Sophistical Refutations (RS 4) and in the Rhetoric (II, 24, 1401a20 – 1402b5; RR p. 128).

The term argumentation by division is sometimes used to refer to case-by-case argumentation.

1. Grammar of composition and division

Composition and division involve the conjunction and, which can coordinate:

— Phrases:

(1) Peter and Paul came.                   (No and N1) + Verb
(2) Peter smoked and prayed.            No + (V1 and V2)

— Statements:

(3) Peter came and Paul came.            (N + V1) and (N1 + V1)
(4) Peter smoked and Peter smoked     (N + V1) and (N1 + V2)

In Aristotelian logical-grammatical terminology:

(3) and (4) are obtained by division from (1) and (2) respectively
(1) and (2) are obtained by composition from (3) and (4) respectively

The compound and divided statements are sometimes semantically equivalent and sometimes not.

(i) Equivalent — (1) and (3) on the one hand, (2) and (4) on the other hand are roughly equivalent, although it seems that (1), not (3), implies that Peter and Paul came together. In this case, composition and division are possible, and the coordination is used simply to avoid repetition.

(ii) Not equivalent — sometimes phrase coordination (composed statement) is not equivalent to sentence coordination (divided statement). The semantic phenomena involved are of very different kinds.

Peter got married and Mary got married.
≠ Peter and Mary got married.

If Peter and Mary are brother and sister, the custom being what it is, the composition is unambiguous. Without such information, the composition introduces ambiguity.

The operation of division can produce a meaningless discourse:

The flag is red and black.
* The flag is red and the flag is black.

B is between A and C.
* B is between A and B is between C.

Sometimes a syntactic operation applied to a proposition produces a paraphrase of that proposition. At other times, the same operation applied to another proposition having apparently the same structure as the first one produces a proposition that has no meaning, or whose meaning and truth conditions are completely different from those of the original proposition.

2. Aristotelian logic of composition and division

The study of paraphrase systems is a classical object of syntactic theory. Aristotelian logic regards composition and division as a problem of logic. As Hintikka (1987) has repeatedly pointed out, the Aristotelian notion of fallacy is dialogical, see Fallacy (I). The fallacious maneuver confuses the interlocutor, and this is exactly what happens with composition and division. The following case is one of the oldest and most famous illustrations of the fallacy of composition:

This dog is your dog (is yours); and this dog is a father (of several puppies).
So this dog is your father and you are the brother of the puppies.

The interlocutor is disoriented, and everyone finds it very funny (Plato, Euth., XXIV, 298a-299d, pp. 141-142). see Sophism.

Aristotle analyzes this kind of sophistical and sophisticated problem in the Sophistical Refutations and in the Rhetoric under the heading of “Paralogism of composition and division”. He shows that the question extends to a variety of discursive phenomena, under what conditions can judgments made on the basis of isolated statements be “composed” into a discourse in which the statements are connected? The discussion is illustrated by several examples , which, although their formulation may seem contrived, show the full scope of the interpretative issues that are raised

(i) Consider the statement: “It is possible to write while not writing” (RS, 4); it can be interpreted in two ways:

— Interpretation 1 composes the meaning: “one can write and not write at the same time” (ibid.), in the sense of: “one can (write and not write)”. This construction is misleading and absurd.
— Interpretation 2 divides the meaning; if one does not write one still retains the ability to write, viz: « one can know how to write while not writing », which is correct. Under certain circumstances, a person who can write cannot physically do so, e.g., if his hands are tied. The modal force is ambiguous between “having the ability to” and “having the possibility of exercising that ability”.

 (ii) The following example also uses the modal can, this time in its relation to time and circumstances. Consider the statement “if you can carry one thing, you can carry several” (RS, 4, 166a30: 11):

(1) (I can carry the table) and (I can carry the cupboard)

Therefore, by composition of the two statements into one:

(2) I can carry (the table together with the cupboard).

Which is not necessarily the case.

(iii) The fallacy of division is illustrated by the example “five is equal to three and two” (after RS, 4, 166a30, p.12):

— Interpretation (1) divides the meaning, i.e., it divides the utterance into two coordinated propositions, which is both absurd and fallacious:

(five equals three) and (five equals two).

— Interpretation (2) composes the meaning, which is correct:

Five is equal to (three and two)

In the Rhetoric, the notion of composition is discussed with several examples that clearly show its relevance to argumentation. The argument by composition and division “[asserts] of the whole what is true of the parts, or of the parts what is true of the whole” (Rhet, II, 24, 1401a20-30; RR, pp. 381), which makes it possible to present things from quite different angles. This technique of argumentation involves statements constructed around evaluative and modal predicates such as:

— is good; — is just; — is able to —; — can —;
— knows —; — said.

The following example is taken from Sophocles play, Electra. Clytemnestra has killed her husband, Agamemnon. Then their son Orestes kills his mother to avenge his father. Was Orestes morally and legally justified in doing so?

“‘T’is right that she who slays her lord should die’; ‘it is right too, that the son should avenge his father’. Very good: these two things are what Orestes has done.” Still, perhaps the two things, once they are put together, do not form a right act. (Rhet., II. 24, 1401a35-b5, RR, 383).

Orestes justifies what he has done by arguing that his two actions can be composed. His accuser denies the composition.

This technique of decomposing a dubious action into a series of praiseworthy, or at least innocent action, is arguably very productive. Stealing is simply taking the bag that is there, taking it somewhere else, and not putting it back in the same place. The division blocks the overall evaluation.

A second example clearly shows that fallacy and argument are two sides of the same coin:

If a double portion of a certain thing is harmful to health, then a single portion must not be called wholesome, since it is absurd that two good things should make one bad thing. Put thus, the enthymeme is refutative; put as follows, demonstrative “for one good thing cannot be made up of two bad things”. The whole line of argument is fallacious. (Rhet., Ii. 24, 1401a30, RR p.381-383)

The teetotallers begin by an agreeing that “drinking a lot makes you sick”, and they divide: “so having one drink makes you sick”. Permissive people follow the other line: “having a drink is good for your health”, and proceed by composition. Abstainers argue by division, and this is considered to be fallacious by permissive people. Permissive people argue by composition, and this is considered to be fallacious by abstainers.

3. Whole and part argument

The two labels “composition and division” and “part and whole” are considered equivalent in practice (van Eemeren & Garssen, 2009).

3.1 Whole to parts and division

The whole argument assigns to each of its parts a property that is proved on the whole:

If the whole is P, then each of its parts must be P.

If the country is rich, then each of its regions (inhabitants …) must be rich.
The Americans are rich, so this one must be rich; let’s ransom him!

The problem faced by the whole-to-parts argument is the same as that of the division argument: can the property evidenced on the whole be transferred to each of its parts?

3.2 Parts to whole and composition

The argument based on the parts assigns to the whole they make up the properties evidenced on each of its parts:

If every part of a whole is P, then the whole is P.
If every player is good, then the team is good (?).

The problem faced by parts to whole arguments mirrors that of the argument by composition: is the property evidenced by each part also evidenced by the whole?

4. Complex wholes and emergent properties

Accidental or mechanical wholes are composed of a set of unrelated objects in a neighborhood relation. Essential or complex wholes consist of the conjunction of the parts plus some emergent additional properties, that distinguishes them from an inert juxtaposition of components. The degree of complexity of the whole is superior to the simple arithmetical addition of its parts. This process is called the composition effect. Aristotle’s case of the superiority of the group over the individual alleged by is an example of such an effect, see Ad populum.

This issue is also found in rhetoric, where a distinction is made between metonymy and synecdoche, the former focusing upon neighborhood relations and the latter on relations between a complex whole and its parts.