Reasoning by composition and by division: traditional - Eris

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Reasoning by composition and by division:
traditional accounts and examples
Adelino Cattani
Department of Philosophy - University of Padua
adelino.cattani@unipd.it
Abstract: Reasoning by composition and by division: traditional accounts and examples, is a presentation of the traditional
accounts and examples of reasoning by composition and by division and serves as background information
for the Finocchiaro-Woods exchange. The contribution by Adelino Cattani, is a presentation of the many
accounts of composition-division fallacy that, being by and large confused and confusing at the conceptual
level, and trivial and unreal at the illustrative-empirical level, generate the exchange between Maurice
Finocchiaro and John Woods. The debate between the two distinguished scholars exemplifies a case of
dialogue-debate, conforming to Eris’ manifesto, whose purpose is to reflect on theory of argumentation and
on practice of debate and to promote confrontation of conflicting contributions on argumentation and debate.
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«Space is nothing but a relation. For, in the first
place, any space must consists of parts: and if parts
are not spaces, the whole is not space.»
(F.H. Bradley, Appearance and Reality, Allen and
Unwin, London, 18972, p. 37)
1. Reasoning by composition and by division: traditional accounts and examples
To judge is, in the scholastic definition, to affirm or deny, to join or split, to unite
or separate, i.e. an operation of composition or division. Therefore, it is of capital
importance to know when to join and when to separate notions and parts.
The part-whole relation can generate an universal inferential «locus communis», that
is a fundamental argumentative scheme: part and whole are used as warrants, of remarkable
theoretical and empirical significance, in a argument in order to provide the inference from
premises to conclusion, from reasons to claim.
All deductive arguments presuppose the rule that what is said of all is said of each. It
works from a whole to the parts. Inductive argument is the reverse process of arriving at a
whole starting from the parts. But the part/whole relation originates other so-called «partwhole arguments» and we find it also in the rhetorical domain, in connection with some
special fallacies.
There are some interesting mistakes in reasoning having to do with parts (fragments,
individuals, persons, members) and whole (set, class, collection, body, group).
Reasoning by composition and by division: traditional accounts and examples
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Composition and division are the names of the special fallacies regarding the
combination and the separation of parts. The one is the flip side of the other. In this paper
I will focus on this kind of flaw in an argument.
Starting from the whole-parts relation, we may follow two opposite directions of
reasoning: reasoning from parts to whole or reasoning from whole to parts. That is to say,
we may proceed by:
1. Inclusion of the parts in the whole
2. Division of the whole into its parts
Naturally, the whole/parts interaction may be a physical interaction, or a logical
connection or a psychological one. This constitutes a first problem in the process of
transition from whole to parts and from parts to whole.
Furthermore, a whole is either a mere collection of elements or an organised arrangement
of parts: a pile of books or a classified library, a mass of bricks or a house. This constitutes
another problem. It is not at all simple to answer the question: «If all parts have the property
x, does the whole has x too?». As Woods and Walton, two notable scholars of fallacies, say,
for the great majority of properties and aggregates, the composibility or divisibility of the
properties with respect to the aggregate cannot be determined abstractly; one needs (1) an
interpretation of properties and of aggregate; (2) a knowledge of the world; and (3) a
tolerable nose for metaphysical taxonomy (Woods and Walton, 1989).
We need to compose/decompose at least in three situations:
1. In order to define.
2. In order to create figures of speech by means of a variety of expressions.
3. In order to organise and manipulate an argument. We will explain briefly every
point.
1. Composition and division in definition. A good definition requires a good division,
namely the setting out of all the different parts of a subject. Further, it is necessary to split
complex matters in some way if we want to analyse them. If one says «There are three things
to consider in order to analyse this matter: first is… second is … and finally…» this appears
as a natural and perfectly acceptable division. But no division is naturally given and no
division has to be accepted as inevitable. On the contrary, some cultural prospect or opinion
lies behind every division.
There are three rules of a good division. First, it should be based on the same
criterion (have a common ground or root or basis); second, it should be complete; and,
third, its parts should be mutually exclusive, that is not crossing or overlapping. If a
dichotomy is supposed to be exhaustive and exclusive when in fact it is not, this generates
a so-called “black and white” fallacy.
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2. Composition and division in rhetorical figures. Composition of parts and division of a
whole can be used as a trope. The substitution of a part for a whole generates a common
form of synecdoche, a trope in which the part stands for the whole, as in «sail » for «ship»,
or in «A hungry stomach has no ears». Decomposition is a condition for mastering our
language and a means for enriching our variety and variations of style.
3. Composition and division in argumentative inference. Composition and division, as we
will see, can be used also as an organising principle for an argument. The connection
between parts and whole is used as an argumentative tool in many ways. One can deduce
something about parts on the basis of their membership in a whole, or one can generalise
about a whole on the basis of the qualities of the parts.
Following Aristotle (Rhetoric 1401 a 25), one type of reasoning consists in combining
what was divided, and another in dividing what was united. Here are some examples offered
by Aristotle.
«One who knows the letters knows the whole word, since the word is the same
thing as the letters which compose it» (Rhetoric, 1401 a 28).
If it were so, a busy believer could conceive a convenient formula for saying his
prayer: it would suffice to recite every day in the morning the alphabet and leave to God
the task of combining the letters in order to construct the prayer.
«Two and three are five.
Two and three are even and odd.
Therefore, five is even and odd.»
(Example of division drawn from Sophistical Refutations, 116 a 33)
Aristotle deals with composition and division in two places, in Sophistical Refutations,
166 a 22-37 and in Rhetoric, 1401 a 25-35. As an example of an illegitimate reasoning,
Aristotle gives the following.
«I say that a man can walk while sitting, because that old man sitting over there can
walk.
Therefore he can both walk and sit at the same time.»
This sentence is true if it means that a sitting man is able to walk (in the divided,
potential sense). The assertion is false if it means that a man can walk while sitting (in the
combined, actual sense).
In addition, here is another similar example:
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«A man can write while not writing.»
(He maintains the power of writing even if he is not writing now.)
Chaïm Perelman and Lucie Olbrechts-Tyteca claim that the inclusion relation (the
inclusion of the parts in the whole and the division of the whole into its parts) is a quasilogical argumentative scheme, that is similar in form to mathematical or formal argument
(like the contradiction, the tautology, the argument of reciprocity, the argument by
transitivity, the argument by comparison), and therefore particularly persuasive, due to their
logical validity. They deal with this type of argument in three sections: the section § 55
entitled «Inclusion of the parts in the whole», § 56 entitled «Division of the whole into
parts», and section § 73 entitled «The group and its members». As we will see in the section
«Group/member interaction», the disreputable or worthy action of an individual member
of a group reflects on the group as a whole and vice versa.
The authors of The New Rhetoric offer the following example, taken from John Locke:
«For whatsoever is not lawful for the whole Church cannot by any ecclesiastic right
become lawful to any of its members».
William Rowe (1962, p. 92) asserts that not all inferences having the form «All parts
of T have x. Therefore, T has x» are fallacious. Sometimes they are fallacious, sometimes
are valid or sound, but there exists no formal or general way of sorting the acceptable from
the unacceptable cases.
There are properties that are universalizable: the lawn is in flower because daisies
and pansies are in flower. Other qualities of the parts are not automatically transferable to
the whole and vice versa. For example, when we are dealing with relative or cumulative
properties: light or heavy, simple or complex, precious or worthless.
Examples of these untransferable properties spring readily in mind: a cocktail is
different from its components; not all the details of a nice picture are necessarily nice; a
group of athletes may play together effectively without being outstanding individual players.
On the contrary, even fine athletes may play poorly together.
2. Part-whole general «loci»
We find two general and contrasting principles governing the whole-part relation.
1. The first affirms that what is true of the whole is true of the parts and vice versa.
In other terms, the same reason or reasoning applies to the whole and to the parts. In Latin
sentence: Eadem est ratio totius et partium.
«All the parts of this machine are made of iron. Therefore, this machine is made of
iron.»
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Nothing to object. It is a valid form of composition. The argument presupposes the
rule that whatever is predicated of every part of a whole may be predicated of the whole.
A similar, but more problematic Aristotelian instance, is:
«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.» (Rhetorica, 1401 a 29)
The underlying general «locus» is:
«It is not possible that if one is good, two are bad.» Consequently, «if two portions
are harmful, also one portion is harmful; if one portion is wholesome, two portions
cannot be harmful.»
2. The second principle takes the opposite direction and says that a whole is greater
than or different from the sum of its parts. Something might be true of the whole without
being true of the parts and vice versa. A work of art may be very different from the sum of
all its details. It is imaginable that a medley of ugly things may turn out to be very lovely. Or
a society may be a little different from the sum of its members: as the American poet and
humorist, Keith Preston, said, «we have sometimes been tempted to define democracy as
an institution in which the whole is equal to the scum of all the parts».
If we transfer this second principle to the realm of reasoning, we can say that, the
whole argument is not equal to the sum of its premises or its sub-arguments. This serves
also as a response to the classical criticism of the vacuity of syllogism.
These two principles are often misunderstood or applied when they shouldn’t. As
an instance of this misapplication, we offer the following examples:
«Every part of this aircraft is light.
Therefore, the whole aircraft is light.»
Invalid composition. But it does not seem to cause serious confusion in the
common affairs of life.
The exact reverse of the fallacy of composition is the fallacy of division, which
consists in transferring to the parts the characteristics of the whole. The fallacy of division
is committed when it is argued that because the whole has a characteristic, the parts has this
characteristic too. For division, the same considerations and principles hold.
«Water is one of the lightest substances, for it is composed of the lightest
substances, hydrogen, which is combined with oxygen.» (Sprangler, 1986, p. 130)
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If we accept this reasoning, we fall into the fallacy of division. For example:
«The machine is heavy. Therefore all the parts of he machine are heavy.»
Sorry! It’s clearly a faulty argument. That the whole item weights more than one kilo
does not implies that every individual component will weight more than one kilo.
3. All together or one at a time?
We have to distinguish between every and all taken distributively or collectively. The
difference between distributive and collective is exemplified by the notions of human nature and
of human race. Human nature is a distributive notion (it is entire in every man taken singularly);
human race, on the contrary, is a collective notion. Consider:
«A Ferrari uses more gasoline than a small car. Therefore, all Ferrari use more
gasoline than all small cars.»
It is true that singularly one Ferrari use more gasoline than a small car, but, because
there are many more utility cars than Ferrari circulating, it is obviously false that Ferrari all
together use more gasoline than all other small cars.
There are situations where a characteristic cannot be legitimately transferred from
parts to whole or vice versa. But the connection between «the soldiers of the regiment are
strong» and «the regiment is strong» is not totally ineffective. The premise seems a good
and necessary (but not sufficient) reason for the conclusion.
«Every animal is rational or irrational.
But not every animal is rational.
Therefore, every animal is irrational.»
(Peter of Spain, Summulae Logicales, 27 va 20)
Or consider the following, only a little less silly mistake:
«All of our employees get eight hours of sleep, as well work for eight hours. Therefore
we are proud of the fact that our employees can sleep and work at the same time.»
The fallacy of composition has occurred. «This fallacious combination misconstrues
the fact that two opposing things may exist in combination, but only if one is potential and
the other is actual.» (Sprangler, 1986, p. 130)
«Each brick is three inches high, thus the brick wall is three inches high.»
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«Since the life expectancy of the inhabitants is 75 years, the city can be expected to
perish after about 75 years.»
«Conventional bombs did more damage in World War II than a nuclear bombs.
Thus, a conventional bomb is more dangerous than nuclear bomb.»
(Example of faulty division, drawn from Irving Copi)
«All items in this stand cost € 9,90.»
(If «all» is used collectively, take all of them. It is an unrepeatable deal! If it is used
distributively, think twice before you buy.)
4. Group/members interaction.
Our concept of the group influences our concept of the individual belonging to the
group and vice versa. The relation between individual and group is considered analogous to
the relation existing between acts and person (Perelman e Olbrechts-Tyteca, § 73). But
«great care is called for in any argument from a part to a collective group, from one human
person to his community; and still greater care when the argument is in a reverse direction,
above all in questions of social philosophy» (Gilby, 1949, p. 76).
We know that an individual person behaves differently if he/she is alone or included
in a group: this phenomenon is testified by mob psychology researches, but well known by
instigators and demagogues too. So the questions of collective and distributive categories
are not only affairs of logic but also of sociology. As is noted by Thomas Gilby, «there is
always something about the whole that does not belong to the parts; in the composition
another entity is produced, over and above the components, of a character different, and
sometimes less admirable: the voice of the mob, the yell of the crowd, and even public
policy, these are less than human. When real and individual personality is merged into a
pack, take care» (Gilby, 1949, p. 70).
The individual and the group interact. Interaction means that a membership
influences our concept of the members and our concept of the members influences our
concept of the group to which a person belongs. A high estimation of the qualities
possessed by the group influences our opinion of the qualities possessed by its members.
Or, in order to disqualify the entire group, we may stress the errors of individual members.
Example of this simple argumentative scheme, aiming to guarantee transition from
the whole to its parts, is:
«N is member of a prestigious group. Therefore N is prestigious.»
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No reasoning of this type should obviously be accepted without close scrutiny of the
contents, in particular of the acceptability of substitution of a part for a whole. Consider the
following assertion of a child:
«My father is working at a very important corporation.»
(He is the garbage man of the corporation)
«The Logic Club of Padua is known as an intelligent association. Therefore, Leo, a
member of the Club, is intelligent»
(A silly induction to be sure. One is conferring upon an individual some of the skill
attached to the group or class that the individual belongs to). «Too stupid, again»,
you say.
In order to avoid this type of fallacy of division one should carefully examine if:
1. The composition or division are allowable, given the nature of the properties
considered: perhaps one is incorrectly transferring to the whole its members’ qualities or
the quality of whole to its members. (Unfortunately, as we have said, for this transition there
is no formal or general rule. The logical rules are not enough and we need some more
pragmatic, substantial rules of relevance concerning the extensibility of our data).
2. There is an equivocation on collective and distributive sense of words, i.e. if
something that is true only in a separate sense is taken in a combined sense or if «all» is taken
in the sense of «all together» in one occurrence and in the sense of «each individual» in
another one.
This is the reason why a committee whose members are all resolute and firmly
determined may be not at all resolute and determined in his final decision. The intuitive idea
that the collective behaviours correspond to the individual ones is denied by Bernard
Mandeville in his Fable of the Bees, about private vices and public virtues.
5. Part/whole fallacies
If we make incorrect inferences from properties of a whole to properties of its parts,
and from properties of parts to properties of the whole of which they are parts, special
forms of wrong reasoning occur, called fallacy of composition or fallacy of division. These
fallacies require naturally an analysis in terms of part-whole relation.
5.1. Verbal composition/division
Composition and division are, in the first place, forms of discursive connection and
separation, operations carried out in the act of speaking. Sometimes the fallacy originates
from the linguistic ambiguity of the term «all», meaning either «every singular part» or «the
whole taken together». In order to obviate this confusion, the rigorous languages, such as
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Latin, had a collective «tota» and a distributive «omnia», making a grammatical distinction
between the collective entity and the individuals within it. Grammatical and structural
identity is not a guarantee of soundness, since not all properties are subject to generalisation.
The risk is to slip on a banana skin of terms used with different meanings.
There is a story to the effect that, addressing a women audience, a preacher pointed
out that they were «all destined to become wives of some good man». Either he was a strong
supporter of polygamy or he meant «each» of them.
Care is needed in distinguishing between terms used in a collective or distributive
sense. A term is used distributively if it says something about each and every member of
the group; a term is used collectively in order to say something about the group as such. We
know that the whole is sometime different from the sum of its composing parts. If it were
otherwise, we could not use the salt in our food, considering that both chlorine and sodium
are poisonous. In addition, cartoons would not move on the movie screen. To assert that
the perception of a moving picture on the screen is an illusion because a film consists of
many motionless frames is an example of a wrong composition.
«All the wise men of Greece are seven.
Solon and Periander are wise men of Greece.
Therefore Solon and Periander are seven.»
A classical instance of division, an extreme example, caricature of the real ones for
sake of clearness, due to Thomas Blundeville (Blundeville, 1599, p. 191).
«The apostles are twelve.
Paul is an apostle.
Paul is twelve.»
The argument is, in its formal structure, similar to the following
«The apostles are saints.
Paul is an apostle.
Paul is saint.»
(“Twelve” refers to all-together, “saints” to each and every).
A valid and disambiguating argument, where there is no confusion and no division, could be:
«The apostles as a group are twelve in number.
Paul is one of the apostles.
Paul is one of the twelve apostles.»
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5.2. Non-verbal composition/division
The strong principle of composition asserts that what is true of each part of a whole
is also true of the whole itself.
«Each member of the team is married; therefore the team also has a wife».
«Too stupid». «Too artificial», you say.
It is hard to image that anyone would be convinced by this argument. But not all instances
of this kind of fallacy are so obvious. There are less silly and more sophisticated situations.
«No jury verdict is safe, as every juryman is liable to error.»
It is true that each and every individual juryman may err, but this does not means
that any whole jury will err (Evans e Palmer, 19862, p. 247). This quality of unreliability is
true of a group distributively but not collectively.
In order to see that the argument is invalid, it is sufficient to inspect the following
reasoning having a similar form:
«Every side of a square is a straight line. Therefore a square is a straight line.» (Black,
19522, p. 232)
«Everybody in the city pays his debt. Therefore you can be sure that the city will
pay its debts.» (Black, 19522, p. 232)
Similarly and conversely, a strong principle of division asserts that what holds true for a set
as a whole holds true for each member of the set.
«Because the brain is capable of consciousness, each neural cell in the brain must be
capable of consciousness.»
(Faulty brain process and faulty division.)
You might just as well try:
«Italy is a catholic country. Thus, each Italian is catholic.»
Here are some more examples of the fallacy, generally found in the literature.
«The brick wall is six feet tall. Thus, the bricks in the wall are six feet tall.»
«Germany is a rich country. Thus, each German is rich.»
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«This must be a good team, because each of its members is an excellent athlete.»
(An athletic team, like an orchestra, is not good because all the players are separately
good, if they are incapable to play co-operatively. Each player’s readiness to work
under a good trainer is one of the necessary conditions for the excellence of the
team.
The opposite line of reasoning consists in assuming that the parts of a whole must
have the properties of the whole.
«Since this is a good team, the members of the team must bee good players.»
One very interesting context involves the relationship between partial and total
truth. Why is a witness in court made to swear that he will tell «the whole truth and
nothing but the truth»? Because partial truth may be a total lie. As an example of
the fallacy of the half-truth, we may offer the following.
«The captain was sober today.»
It is left unsaid that he was sober yesterday too, the day before yesterday and always.
What is said is perfectly true, but what is left unsaid is essential for the representation of the
total accurate picture. «The captain was sober today» is a way for insinuating falsely
something by saying something that is true: here a partial truth is not part of the total truth
but of a falsehood. Lying while saying the truth is an art.1
5.3. Hasty generalisation
Arguing from parts to whole and arguing from individual cases to a general case is
similar to the process of generalisation. A generalisation has the following form:
«A lot of A is x. It is probable, therefore, that all A are x.»
This form of reasoning is supported by a weak principle of composition: «What is
true of most parts of a whole is also true of the whole itself» (the converse weak principle
of division affirms that what holds true for a set as a whole holds true for most members
of the set).
In general, the more the parts that are examined, the stronger the argument is.
If the sample used is not adequate or the cases examined are not enough, we commit
the fallacy of hasty generalisation. Hasty generalisation differs from composition only because
Examples of sentences that are literally true, but are used as a vehicle for falsehood are examined in Cattani,
A. (1995).
1
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the first is a prediction about individuals of a whole (from «some» to «all»), the second about
whole formed by individuals (from «all parts» to «whole»). I infer that the next swan will be
white on the basis that the swans I have seen in the past were all white. This is generalisation
that might be too hasty. It is sound and valid only if every individual swan has the property
attributed to all swans.
On the contrary, it is not necessary that every part of an organisation be democratic
in order for the whole organisation to be considered democratic. You may argue that an
organisation is undemocratic because the executive committee is appointed by different
groups rather than elected. This might be a fallacy of composition if you fail to mention
that decisions of executive committee are by majority vote (Capaldi, 19722, pp. 103-104).
5.4. False dichotomy
To present a whole as if naturally divided into two opposed alternatives, whereas
there is at least one other possibility, generates possibly a false dichotomy. A dichotomy is
false when it is supposed to be exhaustive and exclusive when in fact it is not. A dichotomy
is not false if the two alternatives cover all the possibilities and the choice of one rules out
the other. In order to verify the soundness of a statement having the form «it is either x or
y», we should ask the following questions: 1. Is it really an either-or situation (namely a
disjunction where the two things exhaust all the possibilities)? 2. Is it the only possible
division? Are the choices the only ones possible? If it is so, the argument is a sound form
of reasoning; if it is not so, the so-called bifurcation or “black and white” fallacy occurs.
5.5. The Gambler’s fallacy
We can see in the gambler’s fallacy a variation of the fallacy of division. «Perhaps the
gambler confuses the individual probability of p1 & p2…& pj (where each is equal to 0.5,
but where the probability of the entire sequence is decreased as each one pi is added) with
the conjunctive probability. Thus the probability of some individual pi is confused with the
probability of a whole sequenced of pi’s» (Woods and Walton, 1989, p. 116).
6. Conclusions
To sum up, we briefly highlight some points that we can draw from the preceding
considerations.
First. Composition and division (or decomposition), which are the converse one of
the other, are generally classified as linguistic fallacies, characterised by a semantic or
syntactic ambiguity, following Aristotle (at least the Aristotle of Sophistical Refutations), who
included them into the six fallacies depending on language. But, as Walton notes, this
practice is hard to explain, because the examples typically given are arguments that have to
do with relationships between parts and whole of physical and non-verbal aggregates: «they
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are more accurately and usefully seen as formalistic fallacies that have to do with inferences
from parts to wholes and vice versa» (Walton, 1995, pp. 64-65). The modern conception of
these fallacies is generally non-linguistic and more substantive.
On that account, we may distinguish al least three different types of erroneous and
simplistic reasoning concerning the whole-part relation.
1. The fallacy determined by the word «all» used equivocally.
2. The fallacy created by arguing directly from the properties of the component
parts to the properties of the whole itself or vice versa.
3. The fallacy committed when one assumes that the attributes of single parts, taken
distributively, hold collectively for the global whole or vice versa.
Second. It seems that these types of fallacies fit more naturally into the category of
the unintentional fallacies, that is the kind of wrong reasoning that occurs without any
deliberate intent to mislead. Certainly, forms of composition and of division such as those
we find in the literature are unusual in real life, but not absent. Usually the context makes it
clear how a term should be interpreted.
The fallacies of composition and division are connected with some other fallacies,
namely syntactical amphiboly, faulty generalisation, gambler’s fallacy, guilt by association
fallacy and accent. Further, they are sometimes connected with «category mistakes» too.
Third. Since the possibilities for argumentation depend on what each participant is
ready to concede, on the values he recognises, on the facts on which he indicates his
agreement, we can say that any argumentation is good or bad for some audience. Most of, if
not all, the traditional fallacies of informal logic may be viewed as valid arguments but with
an unacceptable major premise, and therefore as unsound arguments. In the case of
composition, the erroneous premise and the unsoundness consist in believing that what is
true of all the parts is true of the whole, without qualifications.
Fourth. We have seen that a fallacy of composition is an argument that requires the
untenable premise that if all parts of a set have some quality, then the whole set will also
have this quality. Erroneously attributing a property of a whole to its constituent parts or
vice versa is a violation of one of the «Ten Commandments» of critical discussion elaborated
by F. H. van Eemeren e R. Grootendorst, namely rule no. 8: «In his argumentation a party
may only use arguments that are logically valid or capable of being validated by making
explicit one or more unexpressed premises» (van Eemeren e Grootendorst, 1992, pp. 208209).
Violations of this rule occur if one is confusing the properties of the parts and
wholes, in two ways:
- a relative or structure-dependent property of a whole is ascribed to a part of a
whole
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- a relative or structure-dependent property of a part of a whole is ascribed to the
whole.
In daily life we find an incredible number of unacceptable arguments. Most of them
are formally valid (and therefore extremely convincing), but unsound: we have examined
some examples of unsound arguments and conclusions because the major premise
concerning the part/whole relation is unacceptable. Some of the examples given in the
literature are so stupid that it is hard to imagine they could deceive anyone. Raymond
Boudon gives more serious instances of fallacies of composition and division. There are
situations where what is locally true may result globally false. Or what is true at a given time
may become false on the long run. He offers two examples. The first concerning the socialeconomic domain: the introduction of machinery in industry may provoke strikes in some
farms and reduce the strikes at the level of the economic system as a whole. Similarly,
whereas an individual worker may get rich, workers as a whole may worsen their condition.
The second drawn from epistemology: the conceptions of two rival groups of scientists may
be both founded on subjective reasons, but this does not mean that in the future one of
them will not prevail over the other because his reason will result objectively true (Boudon,
1986, cap. 6; Boudon, 1990, pp. 225-226).
To take the words of Woods and Walton (1989, p. 117), «composition and division
are indeed fallacies of some genuine importance - easy enough to commit and mischievous
enough to avoid committing». Composition and decomposition remain interesting to
logicians; and to epistemologists and sociologists too. And mostly to economists, because
society is greater and more than just the people who live in it and vice versa. Using
Finocchiaro’s words: “With regard to the fallacy of composition, the problem of how
frequently it occurs is more striking than for the case of the other fallacies, because the
contrast is greater and starker between the scarcity of scholarly analyses and the triviality of
textbook examples on the one hand, and the widespread claims made (especially by
economists) about its prevalence and importance. Thus, the empirical search for real or
realistic examples is a relatively urgent task” (Finocchiaro, 2015, p. 36).
References
Black, M. (19522). Critical Thinking. Englewood Cliffs, N.J.: Prentice-Hall.
Blundeville, T. (1599). The Art of Logicke.
Boudon, R. (1986). L’idéologié. L’origine des idées recue. Paris: Fayard.
Boudon, R. (1990). L’art de se persuader des idées douteuses, fragiles ou fausses. Paris: Fayard.
Capaldi, N. (19722). The Art of Deception. Buffalo and New York: Prometheus Books.
Cattani, A. (1995). On implicative function of the obviousness, or “You shall not take
anything in vain”. In F. van Eemeren et al. (eds.), Proceedings of the Third ISSA
Reasoning by composition and by division: traditional accounts and examples
Adelino Cattani
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Conference on Argumentation, vol. III: Reconstruction and Application, pp. 96-101.
Amsterdam: Sic Sat.
Cattani A. (2011). 50 Discorsi ingannevoli. Padova: Edizioni GB.
Crosswhite J. (1993) Being unreasonable: Perelman and the problem of fallacies.
Argumentation, 7 (4), 385-402.
Evans, D. e Palmer, H. (19862). Understanding Arguments. Cardiff: University of Wales Press.
Finocchiaro M. A. (1981). Fallacies and the evaluation of reasoning. American Philosophical
Quarterly. 18 (1), 13-22.
Finocchiaro, M. A. (1970). The Fallacy of Composition: Guiding concepts, historical cases,
and research problems. Journal of Applied Logic, 13(2), 24–43.
Finocchiaro, M. A. (2005), Arguments about Arguments: Systematic, Critical, and Historical Essays
in Logical Theory. New York: Cambridge University Press.
Finocchiaro, M. A. (2014). Meta-argumentation: An Approach to Logic and Argumentation Theory.
London: College Publications.
Gilby, T. (1949). Barbara Celarent. A Description of Scholastic Dialectic. London: Longmans
Green.
Hamblin C. L. (1970). Fallacies. London: Methuen.
Kienpointner M. (1992). Alltagslogik. Stuttgart: Frommann-Holzboog.
Perelman C. and Olbrechts-Tyteca L. (1958). Traité de l’argumentation. La nouvelle rhétorique.
Paris: Presses Universitaires de France.
Rowe W. L. (1962). The fallacy of composition. Mind, 71, 87-92.
Sprangler, M. M. (1986). Logic. An Aristotelian Approach, Lanham-New York-London:
University Press of America.
van Eemeren, F. H. and Grootendorst, R. (1992). Argumentation, Communication, and Fallacies.
A pragma-dialectical Perspective. Hillsdale, N.J.: Lawrence Erlbaum Associates.
Walton, D. (1995). A Pragmatic Theory of Fallacy. Tuscaloosa and London: The University of
Alabama Press.
Woods J. and Walton D. (1989). Fallacies. Selected Papers 1972-1982. Dordrecht: Foris.
Woods, J. (2013). Errors of Reasoning: Naturalizing the Logic of Inference. London: College
Publications.
Reasoning by composition and by division: traditional accounts and examples
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