Chapter 6: Contradictory and Contrary Statements Flashcards
What are the two kinds of relationships statements can have to one another?
Opposition and equivalence.
What do we mean in logic when we speak of ‘opposition’?
We mean the relationship which we observe in things we call ‘opposite’
What are we doing when we oppose propositions?
We affirm or deny the same predicate of the same subject.
What are the four ways A, E, I, and O statements can be related to one another in opposition?
They can be contradictory, contrary, subcontrary, or subalternate.
Express the Rule of Contradiction.
Contradictory statements are statements that differ in both quality or quantity.
Tell the quality and quantity of the A statement.
The A statement is affirmative and universal.
Tell the quality and quantity of the O statement.
The O statement is negative and particular.
Does the A statement contradict the O statement? If so, explain why; if not explain why not.
Yes. The A statement contradicts the O statement because they differ in both quality (the A statement is affirmative, while the O statement is negative) and quantity (the A statement is universal, while the O statement is particular).
Which other pair of statements are contradictory to one another?
The E statement and the I statements are contradictory to one another, since they differ in both quality and quantity.
Are these statements contradictory to each other? All logic problems are difficult and some logic problems are difficult.
No.
Are these statements contradictory to each other? No logic problems are difficult and all logic problems are difficult.
No.
Are these statements contradictory to each other? No logic problems are difficult and some logic problems are difficult.
Yes.
Are these statements contradictory to each other? All logic problems are difficult and some logic problems are not difficult.
Yes.
Are these statements contradictory to each other? All logic problems are difficult and no logic problems are difficult.
No.
Are these statements contradictory to each other? No logic problems are difficult and some logic problems are not difficult.
No.
Are these statements contradictory to each other? Some logic problems are difficult and some logic problems are not difficult.
No.
Are these statements contradictory to each other? Some men are happy and some men are not happy.
No.
Are these statements contradictory to each other? No men are happy and some men are not happy.
No.
Are these statements contradictory to each other? No men are happy and all men are happy.
No.
Are these statements contradictory to each other? All men are happy and some men are not happy.
Yes.
Are these statements contradictory to each other? No men are happy and some men are happy.
Yes.
Are these statements contradictory to each other? No men are happy and all men are happy.
No.
Are these statements contradictory to each other? All men are happy and some men are happy.
No.
What is the first law of opposition?
Contradictories cannot at the same time be true nor at the same time be false.
Can both the A and O statements be true at the same time?
No.
Can both the A and O statements be false at the same time?
No.
Can both the E and I statements be true at the same time?
No.
Can both the E and I statements be false at the same time?
No.
Which two pairs of statements are affected by the First Law of Opposition?
The A and O statements, and the E and I statements.
Are these two statements contradictory to each other?No cars are fast and all cars are fast.
No.
Are these two statements contradictory to each other? Some omelettes are tasty and no omelettes are tasty.
Yes.
Are these two statements contradictory to each other? Some tomatoes are not red and all tomatoes are red.
Yes.
Are these two statements contradictory to each other? Michael Jordan is a good basketball player and Michael Jordan is not a good basketball player.
No.
Are these two statements contradictory to each other? No guns are loud and some guns are not loud.
No.
Are these two statements contradictory to each other? Some rocks are not crystals and some rock are crystals.
No.
Are these two statements contradictory to each other? Some men are sinners and some men are not sinners.
No.
Are these two statements contradictory to each other? No men are saved and some men are not saved.
No.
Are these two statements contradictory to each other? All wars are bloody and no wars are bloody.
No.
Are these two statements contradictory to each other? Some soldiers are not brave and all soldiers are brave.
Yes.
Are these two statements contradictory to each other? Some animals are amphibians and no animals are amphibians.
Yes.
Are these two statements contradictory to each other? No houses are well built and All houses are well built.
No.
Are these two statements contradictory to each other? All storms are violent and some storms are violent.
No.
Are these two statements contradictory to each other? All machines are loud and some machines are loud.
No.
Explain why the A statement (All S is P) is not contradictory to the E statement (No S is P) are not contradictory.
Because they must differ in both quality and quantity, but the A and E statements only differ in quality.
Express the Rule of Contraries.
Two statements are contrary to one another if they are both universal but differ in quantity.
Tell the quality and quantity of the A statement.
The A statement is affirmative and universal.
Tell the quality and quantity of the E statement.
The E statement is negative and universal.
Is the A statement contrary to the E statement? If so, explain why; if not explain why not.
Yes. The A statement is contrary to the E statement because they are both universals which differ in quality.
Are there any other pairs of contraries (other than A and E statements)? If so, what are they?
There is no other pair of statements which are contrary to one another.
Are these statement contrary to one another? All logic problems are difficult and some logic problems are difficult.
No.
Are these statement contrary to one another? No logic problems are difficult and All logic problems are difficult.
Yes.
Are these statement contrary to one another? Some logic problems are difficult and No logic problems are difficult.
No.
Are these statement contrary to one another? Some logic problems are difficult and All logic problems are difficult.
No.
Are these statement contrary to one another? All logic problems are difficult and No logic problems are difficult.
Yes.
Are these statement contrary to one another? No logic problems are difficult and Some logic problems are difficult.
No.
Are these statement contrary to one another? Some logic problems are difficult and some logic problems are difficult.
No.
Are these statement contrary to one another? Some men are happy and Some men are happy.
No.
Are these statement contrary to one another? No men are happy and Some men are happy
No.
Are these statement contrary to one another? All men are happy and No men are happy
Yes.
Are these statement contrary to one another? Some men are happy and All men are happy.
No.
Are these statement contrary to one another? Some men are happy and No men are happy.
No.
Are these statement contrary to one another? No men are happy and All men are happy.
Yes.
Are these statement contrary to one another? All men are happy and Some men are happy.
No.
