Test 1 Flashcards
To learn the square of opposition, along with first, second, third figure syllogisms, and converting statements.
What is a syllogism?(Aristotle’s definition)
Certain things are stated, and something besides what is stated follows necessarily
Draw the square of opposition
(Check to see if correct)
Conversion of All A is B
Some B is A
Conversion of Some A is B
Some B is A
Conversion of Some A is not B
No conversion
Conversion of No A is B
No B is A
Contrary of All A is B
If All A is B is true then No B is A must be false
Contradictory of All A is B
If All A is B is true then Some A is not B must be false; If All A is B is false then some A is not B must be true
Sub-alternation of All A is B
If All A is B is true then some A is B is also true
Sub-contrary of Some A is B
If Some A is B is false then Some A is not B is true
Contradictory of Some A is B
If some A is B is true, then No A is B must be false, If some A is B is false, then No A is B must be true
Sub-alternation of Some A is B
If Some A is B is false, then All A is B must be false also
Contrary of No A is B
If No A is B is true, then All A is B must be false
Contradictory of No A is B
If No A is B is true, then Some A is B must be false; if No A is B is false, then Some A is B must be true
Sub-alternation of No A is B
If No A is B is true, then Some A is not B is also true
Sub-contrary of Some A is not B
If Some A is not B is false then Some A is B must be true
Contradictory of Some A is not B
If some A is not B is true, then All A is B must be false; if Some A is not B is false then All A is B must be true
Sub-alternation of Some A is not B
If Some A is not B is false, then No A is B must also be false
Unknown relationships in square of opposition for contraries
If one is false, it implies nothing about the truth or falsity of the other
Unknown relationships in square of opposition for sub-contraries
The truth of one implies nothing of the truth or falsity of the other one
Unknown relationships in square of opposition for sub-alternations
The falsity of the universal implies nothing about the particular, and the truth of the particular implies nothing about the universal
All A is B is the
Universal Affirmative
represented by A
No A is B is the
Universal Negative
represented by the letter E
Some A is B is the
Particular Affirmative
represented by the letter I
Some A is not B is the
Particular Negative
represented by the letter O
Saying B belongs to all A is saying
All A is B
Saying B is predicated by all A says
All A is B
Order of first figure syllogism
B is A-Major premise
C is B-Minor premise
Therefore C is A
Order of second figure syllogism:
No N is M-Major premise
All O is M-Minor premise
Therefore No O is N
Order of third figure syllogism:
All S is P-Major premise
All S is R-Minor premise
Therefore Some R is P
In the syllogism, the conclusion is always stated in this order:
Minor term predicated Major term, I.E. A is the Major term C is the Minor term B is the middle term All B is A (Major premise) All C is B (Minor premise) Therefore All C is A(Minor then major)
First figure syllogisms that work:
AAA (All B is A, All C is B, All C is A)
EAE (No B is A, All C is B, No C is A)
AII (All B is A, Some C is B, Some C is A)
EIO(No B is A, Some C is B, Some C is not A)
Second figure syllogisms that work:
EAE (No N is M, All O is M, No O is N)
AEE (All N is M, No O is M, No O is N)
EIO (No N is M, Some O is M, Some O is not N)
AOO (All N is M, Some O is not M, Some O is not N)
Third figure syllogisms that work:
AAI (All S is P, All S is R, Some R is P)
EAO (No S is P, All S is R, Some R is not P)
IAI (Some S is P, All S is R, Some R is P)
OAO (Some S is not P, All S is R, Some R is not S)
AII (All S is P, Some S is R, Some R is P)
EIO (No S is P, Some S is R, Some R is not S)
