Lesson Six

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Lesson Six

• Division
• Part I, L. 6

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Introduction

• In general, division is the distribution of
  something into its parts. It helps us to know a
  thing, because when we divide a thing into its
  parts, we can know that thing better and more
  distinctly.
• When we studied signs, we divided them into
  natural, conventional, and formal, enabling us to
  better understand what a sign is by knowing its
  parts in detail.

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• Making an outline is an example of dividing
  something in order to better understand it. If
  we can make a good outline, we can be fairly sure
  we understand the subject thoroughly. This is
  why outlining is a useful skill in studying,
  since it helps us see the logical order between
  the principal points as well as the relation
  between them and their relative importance.

4

• The purpose of division in Logic is to enable us
  to define well. It is necessary to divide in
  order to define well, because by dividing a genus
  adequately into its species, we achieve clearer
  knowledge of the species. We seek to define a
  species, or nature, as we will see shortly.

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The Rules of Division

• Division, like nearly every other sort of
  activity, can be done well or badly. To achieve
  its goal in Logic, it must obviously be done
  correctly, as it seems extremely unlikely that we
  will arrive at knowledge by mistake. We can
  summarize the requirements for good division in
  the form of rules that can be used to evaluate
  whether any division is good or bad.

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Rule 1

• The dividing parts must be inferior, that is,
  less universal, than the whole being divided.
• Obviously, if we are dividing something, each
  member of the division must be less universal
  than what is being divided. The thing divided
  should be a universal, since that is what Logic
  deals with, as opposed to a merely physical
  division such as cutting a cake into pieces.

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• Therefore, the members of a division must be less
  universal. They cannot be singulars, either,
  because we differentiate between singulars by
  counting them, not by division.
• For example, we can divide tree into its species
  oak, mahogany, maple, apple, pine, cedar, etc.
  Both the thing divided (tree) and the members of
  the division are universals.

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Rule 2

• 2. The dividing parts must exhaust the species.
• For a division to be a good one, it must
  adequately and completely divide the species.
  There must be nothing which belongs to the
  species as a whole which does not fall under one
  of the parts.

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• For example, when we divide Predicables into
  genus, species, specific difference, property,
  and accident, we have complied with this rule,
  since there are no other possible connections
  between a subject and a predicate other than
  these five. If we were to divide Predicable into
  genus and species, we would not have an
  exhaustive division, because something would have
  been left out.

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• As a consequence of this Rule, we realize that
  there must be at least two members of every
  division. Otherwise it will not be a division at
  all, as every whole must contain at least two
  parts.

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Rule 3

• The dividing parts must be formally opposed, such
  that one part excludes all others.
• It must be impossible for anything belonging to
  the species to fall under two or more dividing
  parts, for then the division will not serve to
  distinguish them. We can assure this by ensuring
  that there is opposition of some kind between the
  parts.

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• We can divide using contradictory opposition, as
  when we divide Religions into Christian and
  non-Christian. This is the easiest and surest
  way to comply with Rule 3, as there can be no
  doubt that the parts exclude each other. It is
  also exhaustive, as there are only two members of
  the division. Yet this kind of division is often
  not very useful.

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• We can divide using privative opposition, as when
  we divide human beings into sighted and blind.
• We can divide by contrary opposition, as when we
  divide numbers into odd and even. This differs
  from division using privative opposition, because
  each of the members has a positive existence in
  the same way, unlike privative opposition, where
  one has a positive existence and the other a
  negative existence (the lack of something that
  ought to be present.)

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• And we can divide using relative opposition
  between the parts in various ways, either by
  using parts which have a mutual reference to each
  other, as when we divide family into parents and
  children, or parts which differ merely formally
  within their genus, as when we divide flowers
  into roses, lilies, and daisies.

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Rule 4

• The same criterion of division must be maintained
  throughout the division.
• The criterion of a division is the basis or
  viewpoint used to make the division. For
  example, we can divide human beings according to
  nationality into French, Swedish, German,
  Spanish, Egyptian, Russian, Japanese, etc. But
  we cannot suddenly begin to divide them as
  right-handed and left-handed halfway through,
  which would be to change the criterion of
  division from nationality to handedness.

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• This Rule does not prevent us from dividing
  something exhaustively using one criterion and
  then dividing the same thing using another. This
  is called co-division. Either way of dividing
  human beings is perfectly acceptable as long as
  we dont confuse them.

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• Another legitimate procedure is known as
  sub-division, which is dividing a whole according
  to one criterion, then dividing one or more of
  the parts according to another. This is a
  division made under another division, or a
  division subordinate to the original one. For
  example, we divided things into ten Categories,
  and proceeded to divide some of the Categories
  according to other criteria.

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The Kinds of Division

• The different kinds of division result from the
  different kinds of wholes and parts.
• The first kind is the division of a universal
  whole into its subjective parts. In this type of
  division, the whole is predicable of each of its
  parts. This is the most basic type of logical
  division.

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• For example, we can divide animal into rational
  and non-rational. This is the division of a
  genus into its species using essential
  differences.

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• The second kind of division is the division of an
  integral whole into its component parts. In this
  kind of division we divide into parts which,
  taken together, constitute the whole. The parts
  do not share a common nature, but rather make up
  the whole.
• For example, we can divide families into parents,
  children, aunts and uncles, grandparents, etc.
  It is not possible to predicate the whole of the
  parts (we cannot say that the parents are a
  family).

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• Finally, we can divide accidentally in at least
  three ways.
• First, we can divide a subject according to its
  accidents, for example, as when we divide human
  beings into right-handed and left-handed, or into
  black, white, yellow, red, etc.

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• Second, we can divide an accident according to
  its subject, which is the reverse of the previous
  type. For example, we can divide the sense of
  sight according to whether it is found in human
  beings, dogs, cats, bulls, flies, etc.

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• Lastly, we can divide an accident according to
  its accidents. For example, the policeman
  divides the accident of velocity according to
  quantity, another accident, for the purpose of
  giving speeding tickets.