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TABLE OF CONTENT
WHAT WE WILL TACKLE
Today we will be discussing about a topic within logic which is conversion and its multiple
aspects and processes.
E AND I
PRINCIPLES
The Simple Conversion of e
and I principles
ACCIDENT
CONVERTION
Accident Conversion of a
Proposition
INCONVERTABILITY
OBVERSION
AA, , EE ,, I I AaNnDd OO
Inconvertibility of O
And its Process
Obversion
ObversionofofA,A,E,E,I and
I andO
principles
O Principles
SIMPLE CONVERSION OF E AND I PRINCIPLES
SIMPLE CONVERTION
OF E AND I PRINCIPLES
An E proposition converts simply to an E
proposition. There can be no danger in the over
extension in the conversion of E since all its terms are
universal.
It must be remembered that only universal
negative (E) and particular affirmative (I) proposition
can be converted through simple conversion
No angels are mortals (E)
Therefore, no mortals are
angels (E)
No cat is a dog (E)
No dog is a cat (E)
Some animals are not mammals
(i)
therefore, some mammals are
not animals (i)
SIMPLE CONVERSION OF E AND I PRINCIPLES
SIMPLE CONVERTION
OF E AND I PRINCIPLES
An E proposition converts simply to an E
proposition. There can be no danger in the over
extension in the conversion of E since all its terms are
universal.
It must be remembered that only universal
negative (E) and particular affirmative (I) proposition
can be converted through simple conversion
Some mortals are men (I)
Therefore, some men are
mortals (I)
No learned man is ignorant (E)
No one who is ignorant is
learned (E)
IN SUMMARY
Two principles
are interchangeable.
ACCIDENT CONVERSION OF A PROPOSITION
Accident Conversion
of a Proposition
When an A proposition is converted, the extension of the converse
is limited. A converts
to I. The reason for this is that A is an affirmative proposition;
consequently, its predicate is
particular. This predicate, when used as subject of the converse,
must be taken as a particular
term; otherwise, there would be an over extension of P.
All computers are gadgets (A)
Therefore, some gadgets are
computers (I)
No computers are robots (E)
Therefore, some robots are not
computers (O)
All bananas are fruits (A)
Therefore, some fruits are
bananas (I)
No human being is a monkey (E)
Therefore, some monkeys are not
human beings (O)
OBVERSION
INCONVERTIBILITY
OF O
O proposition cannot be converted without
violating either the second or third rule for
a valid conversion. If we say that "Some S is not
P, therefore, "Some P is not S," we find that there
is an over extension of S in the converse,
thereby violating the third rule. For S in the
converse to
be particular, the copula must be affirmative.
But the copula must be negative since the rule
is to
retain the quality of the copula in converting,
and O has a negative quality.
OBVERSION
We cannot, then, legitimately
proceed from "Some taxi drivers are
not honest" to "Some
honest are not taxi drivers," The
second statement may be true, but
its truth is not implied
necessarily in the given statement. It
is not a valid converse of the given
O proposition.
Some taxi drivers are not honest
Some honest are not taxi drivers
Some people are Christians
Some Christians are not
people
OBVERSION
OBVERSION
Obversion is the process whereby the given statement is
called the obverted we derive or
infer another proposition called the obverse whose subject
is the same as original subject but
whose predicate is the contradictory of the given
predicate. This second or inferred, proposition,
however, expresses the same meaning as the given
proposition. Put in another way, to obvert is
to state negatively what is given positively, or to express
positively what is given negatively.
All men are mortal (OBVERTED)
Therefore, no men are immortal
(OBVERSE)
No fish is unable to swim. (OBVERTED)
All fishes are able to swim (OBVERSE).
Some things are indestructible
(OBVERTED)
Some things are not destructible
(OBVERSE)
OBVERSION
TO GET A CORRECT OBVERSE
FOLLOW THESE RULES
Retain the subject term.
Negate the copula or change the
quality of the copula — from positive
to negative or from
negative to positive.
Contradict the predicate of the
obverted.
(The safest way to contradict is to
prefix "un" or "non." It is not always safe
to use the
prefixes "in, ir, im," because they do not
always affect a denial. Thus, while
"material" and
immaterial' are contradictories.
"Memorable" and "immemorable" are
not. While "finite" and
"infinite" are opposites, "tense" and
"intense" are not.
INCONVERTIBILITY OF O
Obversion of
A, E, I and O
We learned how to change the quality of a
proposition in section. Remember, quality refers to
whether the proposition
is “affirmative” or “negative.” For instance,
changing the quality of “All S are P”
would give us “No S are P.”
E OBVERTS TO A
No honest man is
untrustworthy
No S is Un-P
Every man is trustworthy
Every S is P
A OBVERTS TO E
Every good artist is
creative
Every S is P
No good artist is
uncreative
No S is Un-P
INCONVERTIBILITY OF O
Obversion of
A, E, I and O
Since the obverted and obverse
express the same thing, both have the
same truth value. If the obverted is trues
the obverse is also true; if false, the
obverse is also false.
I OBVERTS TO O
Some men are emotionally
insecure
Some S in In-P
Some men are not
emotionally secure
Some S is not P
O OBVERTS TO I
Some lands are not
productive
Some S is not P
Some lands are
unproductive
Some S is Un-P