4. Before going to distribution
there are some points that
should be understand first
5. A proposition that tells us about a
relationship between two classes or
categories is called categorical
proposition.
6. All cats are animals
Classes/terms
There are two classes/terms in categorical preposition
1. Subject class (cats)
2. Predicate class (animals)
7. Quantity and Quality
The quantity of a proposition is either universal or
particular. The quantity is determined by the
quantifier--'All' and 'No' indicate universal quantity,
while 'some' indicates particular.
The quality of a proposition is either affirmative or
negative.
8. There are four forms of categorical proposition
Universal affirmative: A All S are P
Universal negative: E No S are P
Particular affirmative: I Some S are p
Particular negative: O Some S are not P
To be more correct, Aand I letters came from the
Latin affirmo, and Eand O from the
Latin nego.
9. Distribution
applies to terms/class (subject and predicate) of categorical
propositions.
If the reference is to the whole of the class, then the
class is said to be distributed. A term is distributed when it
refers to all the members of the class
If the reference is only to part of the class, then the class is
said to be undistributed. A term is undistributed when it
refers to less than all the members of its class
Distribution of Terms in the Four Types of Categorical
Propositions
10. Type A propositions: All S are P (universal affirmative)
{S= Distributed, P = undistributed}
The A proposition asserts that every member of the subject
class (All S) is a member of (but not the whole of) the
predicate class.
Since reference is made to every member of the subject
class (All S…), the
subject is said to be distributed.
But Is reference being made to every member of the
predicate class?
NO.
For example, if you say:
11. All dogs (S) are animals(P):
reference is made to every member of the subject
class(All dogs).
so we can say that an A proposition distributes its
subject.
reference is not made to every member of the predicate
class(animals ) because all animals are not dogs.
So an A proposition does not distribute its predicate
class
Subject distributed predicate undistributed
12. Type E propositions: No S are P (universal negative)
{S = distributed, P = distributed}
The E proposition's quantifier (No S…) makes
reference in a negative way to every / All member of
the subject class.
E propositions also state that not a single member of
the S class is a member of the P class,
and thus the reference is to the whole of the predicate
class.
This could be only if the whole of the P class were
examined and no S were found.
Therefore, the predicate of E propositions is
distributed. For example, if you say:
13. No dogs (S) are cats (P):
Reference is being made to all the member of the subject
class it mean you have examined all members (Dogs)
Reference is being made also to all member of predicate
class
Examined all the members (cats)
Subject distributed predicate distributed
14. Type I propositions: Some S are P (particular affirmative)
{S = undistributed, P = undistributed}
The quantifier makes it clear that only some members
of the subject class are being referred to not all
members.
so the subject is undistributed.
But Is the predicate class similarly undistributed?
YES
because reference is being made to only some of the
members of that class not the whole of it. For example,
if you say:
15. Some men are wealthy
you are identifying only some members of the wealthy
class
who are members of the subject class (i.e., men).
You are not concerned with the rest of the P class (the
wealthy) who are of another kind (women who are
wealthy).
Hence, in I propositions, both the subject class and
the predicate class are undistributed,
16. Type O propositions: Some S are not P (particular negative)
{S = undistributed, P = distributed}
The quantifier "some" in type O propositions indicates
that reference is being made to only some members of
the subject class (Some S …) not to all members .
The subject term of the O propositions is therefore
undistributed.
Is the predicate class also undistributed?
NO, it is distributed,
because to say that Some S is not P, you have to know
the sum total of the P class to make this assertion.
For example, if you say:
17. Some citizens are not property owners.
you have to know the sum total of property owners to
assert that some citizens do not belong or are not found
anywhere in the class of property owners.
If you deny that something is inside a certain circle
(property owners)
you have to deny that it can be found anywhere in that
circle (you have to know the contents of the whole circle!).
You have to refer to the whole circle, not just part of it.
Hence, in type O propositions, the subject is always
undistributed and the predicate is always distributed
18. Law of distribution
It has two main points
1) All universal propositions distribute their subject
class.
2) All particular negative propositions distribute their
predicate class.
19. Conclusion
Universal affirmative (A) propositions distributes its
subject class and does not distribute its predicate class
Universal negative(E) propositions distribute its both
classes
Particular affirmative (I) propositions does not
distribute its classes
Particular negative (O) proposition does not distribute
its subject class but distributes its predicate class
