Aristotle and the Square of Opposition

OPPOSITION OF PROPOSITION:

The doctrine of opposition of proposition may be considered from two points of view. Firstly, we may considered it as  expressing relations between proposition in the traditional schedule :       (A, E, I, O) (Proposition) secondary we may considered it as a process of inference.

The term opposition is used for the relation between the two proposition having the same subject and the same predicate but differing either inequality, are in quality or in both. The traditional logicians applied the doctrine of proposition to the four kinds of categorical proposition.

Taking a ‘A’, ‘E’,’I’,’O’ proposition in pairs, four kinds of proposition are possible, there are  contradiction, contrarily, sub – contrarily and sub – alteration. These four forms of opposition are represented by diagram called the square of proposition.

1)     Contradictory opposition (or Contradiction):

Contradictory opposition is the relation between two proposition having the same subject and same predicate which refer both in quantity and quality. It is the relation between A & O proposition, and between E & I proposition. Thus, the proposition, “All honest men are not happy” are contradictory.

Similarly, the propositions. “All politicians are unselfish & some politician are selfish” are contradictory.

2)     Contrary opposition (or contrariety) :

Contrary opposition is the relation between two universal propositions deferring in quality. It is the relation between ‘A’ & ‘E’ proposition. Thus, the propositions. “All ministers are corrupt & no ministers are corrupt” are contraries.

3)     Sub – contrary opposition (or Sub – contrariety):

Sub – contrary opposition is the relation between two particular propositions deferring in quality. It is the relation between ‘I’ & ‘O’ propositions. Thus “some dishonest men are not rich” are sub – contrary.

4)     Sub – alter opposition (or sub – alternation)

Sub – alter opposition is the relation between two proposition having the same quantity. A and I proposition, as well as E & O proposition are sub alters.

                  Eg.:      “All painter are artist”

                              “some painter are artist” are sub - alter.

Similarly, no saints are immoral & some saints are not immoral are sub – alter.

In this kind of opposition, the universal is called sub – alternant and the particular is called sub- alternate. 

The Four Aristotelian Propositions
Universal affirmative	A	Omne S est P	Every S is P	All S is P
Universal negative	E	Nullum S est P	No S is P	All S is not P
Particular affirmative	I	Quoddam S est P	Some S is P	Some S is P
Particular negative	O	Quoddam S non est P	Some S is not P	Some S is not P

RELATION TABLE FOR THE SECOND PROPOSITION TO THE FIRST PROPOSITION

1) CONTRADICTORY OPPOSITION ( OR CONTRADICTION )

It is a relation between A and O proposition and between E and I proposition

2) CONTRARY OPPOSITION ( OR CONTRARIETY )

It is the relation between A and E proposition

3) SUBCONTRARY OPPOSITION ( OR SUBCONTRARIETY )

It is the relation between I and O proposition

4) SUBALTERN OPPOSITION ( OR SUBALTERNATION )

It is the relation between A and I proposition as well as E and O proposition 

OPPOSITION	PROPOSITION		RELATION
CONTRADICTORY OPPOSIOTION ( OR CONTRADICTION )	1ST PROPOSITION	ALL S IS P	A
	2ND PROPOSITION	SOME S IS NOT P	O
	1ST PROPOSITION	NO S IS P	E
	2ND PROPOSITION	SOME S IS P	I
CONTRARY OPPOSITION (OR CONTRARIETY)	1ST PROPOSITION	ALL S IS P	A
	2ND PROPOSITION	NO S IS P	E
SUBCONTRARY OPPOSITION (OR SUBCONTRARIETY)	1ST PROPOSITION	SOME S IS P	I
	2ND PROPOSITION	SOME S IS NOT P	O
SUBCONTRARY OPPOSITION (OR SUBCONTRARIETY)	1ST PROPOSITION	ALL S IS P	A
	2ND PROPOSITION	SOME S IS P	I
	1ST PROPOSITION	NO S IS P	E
	2ND PROPOSITION	SOME S IS NOT P	O

PRACTICE  & SOLVE : 

(BASED ON THE PATTERN OF QUESTION PAPER OF UNIVERSITY)

Point out the relation of the second proposition to the first proposition in the following pairs of propositions :

i)          Some physicists are mathematicians.

All mathematicians are physicists. 

ii)         All criminals are to be punished

            Some criminals are not be punished . 

iii)         Some students are lazy

Some students are not lazy 

iv)        No saints are pious.

All saints are pious . 

v)         China is not a democratic country.

China is democratic country . 

vi)        Some vegetarians are those who enjoy good health.

No vegetarian are those who enjoy good health.