Composition and Division

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

The label argumentation by division is sometimes used to refer to case-by-case argumentation, S. Case-by-Case.

1. Grammar of composition and division

Composition and division involve the conjunction and that 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 + V2)
(4) Peter smoked and Peter prayed.     (N + V1) and (N1 + V2)

In Aristotelian logical-grammatical terminology:

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

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 types.

Peter got married and Mary got married.
≠ Peter and Mary 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 an 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 statement produces a paraphrase of this statement. At other time, the same operation applied to another statement having apparently the same structure as the first one produces a statement that has no meaning, or whose meaning and truth conditions entirely differ from those of the original statement.

2. Aristotelian logic of composition and division

The study of paraphrastic systems is a classical object of syntactic theory. Aristotelian logic considers composition and division as a problem in logic. As Hintikka (1987) has repeatedly pointed out, the Aristotelian notion of fallacy is dialogical, S. Fallacy (I). The fallacious maneuver throws the interlocutor into confusion, and this is precisely 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 that very funny (Plato, Euth., XXIV, 298a-299d, pp. 141-142). S. 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 issue extends to a variety of discursive phenomena, under what conditions can judgments made on the basis of isolated statements be “composed” into a discourse of connected statements? The discussion is illustrated by several examples showing the full scope of the interpretation issues that are raised, even if their wording may seem contrived.

(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 at the same time write and not write” (ibid.), in the sense of: “one can (write and not write)”. The composition is misleading and absurd.
— Interpretation 2 divides the meaning; when one does not write one still retains the capacity to write, meaning: “one can know how to write, while not writing”, which is correct. Under certain circumstances, a person who can write cannot physically do so, for example if one’s hands are tied. The modal power is ambiguous between “having the capacity to” and “having the possibility to exercise that capacity”.

 (ii) The following example also uses the modal can, this time in its relation to time. 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 cabinet)

Therefore, by composition of the two statements into one:

(2) I can carry (the table along with the cabinet)

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 meaning, that is, it decomposes the utterance into two coordinated propositions, which is both absurd and fallacious:

(Five is equal to three) and (five is equal to 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 the relevance of the issue for 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 appreciative 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 killed her husband, Agamemnon. Then their son Orestes kills his mother to avenge his father. Was Orestes morally and legally entitled to do this?

“‘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 did, arguing that his two actions can be composed. His accuser rejects the composition.

This technique of decomposing a doubtful action into a series of commendable, or at least innocent, acts is arguably very productive. Stealing is just taking the bag that is there, taking it somewhere else, and failing to put it back in the same place. The division blocks the overall assessment.

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)

Abstainers start from an agreement upon the fact that “having a lot of drinks makes you sick”, and divide: “so having a drink makes you sick”. Permissive people follow the other line: “having a drink is good for health”, and proceed by composition. Abstainers argue by division, and this is considered to be fallacious by permissive individuals. Permissive individuals argue by composition, and this is considered to be fallacious by abstainers.

3. Whole and parts argument

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

3.1 Whole to parts and division

The argument based on the whole assigns to each of its parts a property evidenced on the whole:

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

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

The problem faced by whole to parts arguments mirrors that of the argument by division: 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 emerging properties

Accidental or Mechanical wholes are composed of a set of disconnected objects in a relation of neighborhood. Essential or complex wholes are made up of the conjunction of the parts plus some emerging extra properties, which 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 referred to as a composition effect. The case of the superiority of the group over the individual alleged by Aristotle is an example of such an effect, S. Ad populum.

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