Opposition Of Categorical Proposition Flashcards
are quantified categorical propositions
that have the same subject and
predicate but differing in both
QUALITY and QUANTITY
Examples:
Every river is a national territory—- therefore some river is not a national territory
CONTRADICTIONS
- is the opposition between universal
propositions that differ in QUALITY
are pair of propositions so
related to one another that they
cannot be simultaneously true but can
be simultaneously false.
Examples:
All carpenters are skilled workers —— therefore No carpenter is a skilled worker
CONTRARIETY
is the opposition between two
particular propositions that differ
in quality of the copula
Examples:
Some laymen are active church goers ———–
Some laymen are not active church goers
SUBCONTRARIETY
is the relation between universal and
particular propositions having the
same quality of the copula.
Examples:
Some S are P ——– Every S is a P
Some S are not P ——– No S is a P
SUBALTERNATION
CONTRADICTORIES LAWS: [A-O; E-I]
a. if the one is true, the other is false
b. if the one is false, the other is true
e.g. No horses are monkeys = T
Therefore some horses are monkeys = F
CONTRARIES [A - E] LAWS
a. if the one is true, the other is false
b. if the one is false, the other is doubtful
e.g. All waters are in the mountains = F
Therefore No waters are in the mountains = ?
SUBCONTRARIES [ I–O ] LAWS
a. if the one is true, the other is doubtful
b. if the one is false, the other is true
e.g. Some students are diligent = T
Therefore some students are not diligent = ?
SUBALTERNS [A-I; E-O]
a. if the universal is true, the particular
is true; but if the universal is false,
the particular is doubtful
b. if the particular is true, the universal
is doubtful; but if the particular is
false, the universal is false
❖is exemplified in EDUCATION, the formulation of a
new proposition by the interchange of the subject
& predicate of an original proposition and/or by the
use or removal of negatives.
Equivalence of Proposition
Equivalence of Proposition 4 variations
- Conversion
- Obversion
- Contraposition
- Inversion
Education is a different ways of stating a fact, like uses negative, interchange subject or predicate or leaves them as they are.
KF
The steps are:
a. interchange subject and predicate
b. do not change the quality
c. do not extend any term
Conversion
Conversion may be
a. simple conversion
b. partial conversion
[is from I to I and E to E]
e.g. I to I = Some S is P
therefore some P is S
Some fashion models are Orientals
therefore some Orientals are fashion models
e.g. E to E = No S is P
therefore No P is S
No pine tree is a weed
therefore No weed is a pine tree
Simple Conversion
[✓is from A to I and E to O]
e.g. A to I = Every S is P
therefore some P is S
Every daisy is a flower.
therefore some flower is a daisy
e.g. E to O = No S is P
therefore some P is not S
No stone is an animate being.
therefore some animate being is not a stone
Partial Conversion
= is invalid coz’ it involves extension of terms
= it is valid only if it is a definition and
S and P are interchangeable terms
e.g. Marcel is the author of Homo Viator
therefore the author of Homo Viator is Marcel.
A to A conversion
= is invalid coz’ it involves extension of terms
e.g. Some people are not Chinese
therefore some Chinese are not people
O to O conversion
The steps are:
a. retain the subject and its quantity
b. change the quality
c. put the contradictory or contrary
of the original predicate
The ff. are:
1] A to E 2] E to A
3] I to O 4] O to I
Obversion
Every S is P
therefore No S is non-P
Every man is mortal
therefore No man is immortal
A to E (Observation)
No S is P
therefore Every S is non-P
No man is unembodied.
therefore every man is embodied
E to A (Observation)
Some S is P
therefore Some S is not non-P
Some geniuses are mathematicians.
therefore Some geniuses are not non-mathematicians.
I to O (Observations)
Some S is not P
therefore Some S is non-P
Some drugs are not habit forming.
therefore Some drugs are non-habit forming.
O to I (observations)
✓is a combination of conversion and
obversion.
The steps are:
a. interchange subject and predicate
like conversion
b. it presents contradictories of
terms like obversion
➢ It has two types:
a. simple
b. complete
Contraposition
- the subject: use the contradictory of the
original predicate - Copula : change
- Predicate : use the original subject
Simple (Contraposition)
- the subject : use the contradictory of the
original predicate - Copula : do not change
- Predicate : use the contradictory of the original
subject
Complete (Contraposition)
A to E : Every S is P;
therefore No non-P is an S
Every star is a heavenly body
therefore No non-heavenly body is a star
E to I : No S is P;
therefore Some non-P is an S
No swan is a duck
therefore Some non-duck is a swan
O to I : Some S is not a P;
therefore Some non-P is an S
Some orator is not a politician
therefore Some non-politician is an orator
Simple (Contraposition)
A to A : Every S is P;
therefore Every non-P is non-S
Every star is a heavenly body
therefore Every non-heavenly body is a non-star
E to O : No S is a P;
therefore Some non-P is not non-S
No swan is a duck
therefore Some non-duck is not a non-swan
O to O : Some S is not a P;
therefore Some non-P is not a non-S
Some orator is not a politician
therefore Some non-politician is not a non-orator
Complete (Contraposition)
✓ Like contraposition, it has two types
a. simple
b. complete
✓ It goes through a series of
obversions and conversions
Inversion
- the subject: use the contradictory or immediately
opposed contrary term of the
original subject - Copula : change
- Predicate : use the original predicate
Simple (Inversion)
- the subject : use the contradictory or immediately
opposed contrary term of the
original subject - Copula : do not change
- Predicate : use the contradictory or immediately
opposed contrary term of the
original predicate
Complete (Inversion)
A to I : Every S is P;
therefore Some non-S is non-P
Every dog is irrational
therefore some non-dog is
rational
E to O : No S is P;
therefore Some non-S is not non-P
No mouse is a duck
therefore Some non-mouse is not a
non-duck
Complete (Inversion)
A to O : Every S is P;
therefore Some non-S is not P
Every man is a being for death
therefore some non-man is not a being for death
E to I : No S is P;
therefore Some non-S is a P
No man is an island
therefore Some non-man is an island
Simple (Inversion)
