Traditional Logic Chapters 6 and 7

In the following chart, indicate, as in Figure 7-2, which two pairs of statements are contradictory which two are contrary, which two staements are subcontrary, and which two statements are subalternate:

A E I O A and E- contrary A and I- subalternate E and O- subalternate I and O- subcontrary A and O- contradictory I and E-contradictory

In the following chart, indicate, as in Figure 6-2, which two pairs of statements are contradictory and which two statements are contrary: A E I O

A E I O A and E-contrary A and O-contradictory E and I- contradictory

Which pair of statements comply with the Second Law of Opposition?

A and E statements comply with the Second Law of Opposition.

Which pairs of statements comply with the Fourth Law of Opposition?

A and I statements and E and O statements comply with the Fourth Law of Opposition.

Which two pairs of statements are affected by the First Law of Opposition?

A and O and E and I statements are affected by the First Law of Opposition.

Contradictory or not: Some animals are amphibians and No animals are amphibians.

Contradictory

Contradictory or not: Some logic problems are difficult and No logic problems are difficult.

Contradictory

Contradictory or not: Some logic problems are not difficult and All logic problems are difficult.

Contradictory

Contradictory or not: Some men are not white and All men are white.

Contradictory

Contradictory or not: Some men are white and No men are white.

Contradictory

Contradictory or not: Some omelets are tasty and No omelets are tasty.

Contradictory

Contradictory or not: Some soldiers are not brave and All soldiers are brave.

Contradictory

Contradictory or not: Some tomatoes are not red and All tomatoes are red.

Contradictory

Contrary or not: All logic problems are difficult and No logic problems are difficult.

Contrary

Contrary or not: All men are white and No men are white.

Contrary

Contrary or not: All wars are bloody and No wars are bloody.

Contrary

Contrary or not: Michael Jordan is a good basketball player and Michael Jordan is not a good basketball player.

Contrary

Contrary or not: No cars are fast and All cars are fast.

Contrary

Contrary or not: No houses are well-built and All houses are well-built.

Contrary

Contrary or not: No logic problems are difficult and All logic problems are difficult.

Contrary

Contrary or not: No men are white and All men are white.

Contrary

True or false: The statement "Just do it" and the statement "All men are mortal" are subcontrary.

False, "Just do it" is not a proposition so it cannot be subcontrary.

True or false: The statement "Just do it" and the statement "All men are mortal" are contradictory.

False, "Just do it" is not a proposition.

True or false: Contrary statements cannot at the same time be false, but they can both be true.

False, Contrary statements cannot at the same time be true, but they can both be false.

True or false: Subalternate statements cannot at the same time be false, but they can both be true.

False, subalternate statements can both be false at the same time, or they can both be true at the same time.

True or false: The A statement and the I statement differ in quality and quantity.

False, the A statement and the I statement differ in quantity but are the same in quality.

True or false: The quality of the statement "All S is P" is universal.

False, the quantity of the statement "All S is P" is universal.

True or false: The statements "All S is P" and "No S is P" can both be true at the same time.

False, the statements "All S is P" and "No S is P" cannot both be true at the same time.

True or false: Two statements are contradictory if they differ from each other in quality but are the same in quantity.

False, two statements are contradictory if they differ in both quality and quantity.

Write five pairs of contradictory statements that are not in the book.

Five pairs of contradictory statements that are not in the book are: -All cats are black and Some cats are not black -No cats are black and Some cats are black -All dogs are brown and Some dogs are not brown -No dogs are brown and Some dogs are brown -All birds are red and Some birds are not red

Write five pairs of contrary statements that are not in the book.

Five pairs of contrary statements that are not in the book are: -All cats are black and No cats are black -All dogs are brown and No dogs are brown -All birds are red and No birds are red -All pens are pink and No pens are pink -All pencils are yellow and No pencils are yellow

Write five pairs of subalternate statements that are not in the book.

Five pairs of subalternate statements that are not in the book are: -All dogs are black and Some dogs are black -No dogs are black and Some dogs are not black -All rings are gold and Some rings are not gold -No rings are gold and Some rings are not gold -All birds are red and Some birds are red

Write five pairs of subcontrary statements that are not in the book.

Five pairs of subcontrary statements that are not in the book are: -Some dogs are black and Some dogs are not black -Some rings are gold and Some rings are not gold -Some birds are red and Some birds are not red -Some cats are white and Some cats are not white -Some fish are orange and Some fish are not orange

Which pair of statements complies with the Third Law of Opposition?

I and O statements comply with the Third Law of Opposition.

What do we mean in logic when we speak of 'opposition'?

In logic when we speak of 'opposition' we mean that the relationship which we call 'opposite'. If we say something is the opposite of another thing, we are saying the two things have a relationship of opposition.

Can both A and E statements be true at the same time?

No, both A and E statements cannot be true at the same time.

Can both A and O statements be false at the same time?

No, both A and O statements cannot be false at the same time.

Can both A and O statements be true at the same time?

No, both A and O statements cannot be true at the same time.

Can both E and I statements be false at the same time?

No, both E and I statements cannot be false at the same time.

Can both E and I statements be true at the same time?

No, both E and I statements cannot be false at the same time.

Can both E and I statements be true at the same time?

No, both E and I statements cannot be true at the same time.

Can both I and O statements be false at the same time?

No, both I and O statements cannot both be false at the same time.

Are there any other pairs of statements that are contrary to one another? If so, indicate which they are.

No, there is no other pairs of statements that are contrary to one another.

Contradictory or not: All logic problems are difficult and No logic problems are difficult.

Not

Contradictory or not: All logic problems are difficult and Some logic problems are difficult.

Not

Contradictory or not: All machines are loud and Some machines are loud.

Not

Contradictory or not: All men are white and No men are white.

Not

Contradictory or not: All men are white and Some men are white.

Not

Contradictory or not: All storms are violent and Some storms are violent.

Not

Contradictory or not: All wars are bloody and No wars are bloody.

Not

Contradictory or not: Michael Jordan is a good basketball player and Michael Jordan is not a good basketball player.

Not

Contradictory or not: No cars are fast and All cars are fast.

Not

Contradictory or not: No guns are loud and Some guns are not loud.

Not

Contradictory or not: No houses are well-built and All houses are well-built.

Not

Contradictory or not: No logic problems are difficult and Some logic problems are not difficult.

Not

Contradictory or not: No men are saved and Some men are not saved.

Not

Contradictory or not: No men are white and All men are white.

Not

Contradictory or not: No men are white and Some men are not white.

Not

Contradictory or not: Some logic problems are difficult and Some logic problems are not difficult.

Not

Contradictory or not: Some men are sinners and Some men are not sinners.

Not

Contradictory or not: Some men are white and Some men are not white.

Not

Contradictory or not: Some rocks are crystals and Some rocks are not crystals.

Not

Contradictory or not:No logic problems are difficult and All logic problems are difficult.

Not

Contrary or not: All logic problems are difficult and Some logic problems are difficult.

Not

Contrary or not: All machines are loud and Some machines are loud.

Not

Contrary or not: All storms are violent and Some storms are violent.

Not

Contrary or not: No guns are loud and Some guns are not loud.

Not

Contrary or not: No logic problems are difficult and Some logic problems are not difficult.

Not

Contrary or not: No men are saved and Some men are not saved.

Not

Contrary or not: No men are white and Some men are not white.

Not

Contrary or not: Some animals are amphibians and No animals are amphibians.

Not

Contrary or not: Some logic problems are difficult and No logic problems are difficult.

Not

Contrary or not: Some logic problems are difficult and Some logic problems are not difficult.

Not

Contrary or not: Some logic problems are not difficult and All logic problems are difficult.

Not

Contrary or not: Some men are not white and All men are white.

Not

Contrary or not: Some men are sinners and Some men are not sinners.

Not

Contrary or not: Some men are white and No men are white.

Not

Contrary or not: Some men are white and Some men are not white.

Not

Contrary or not: Some omelets are tasty and No omelets are tasty.

Not

Contrary or not: Some rocks are crystals and Some rocks are not crystals.

Not

Contrary or not: Some soldiers are not brave and All soldiers are brave.

Not

Contrary or not: Some tomatoes are not red and All tomatoes are red.

Not

Contrary or not: men are white and Some men are white.

Not

Subalternate or not: All logic problems are difficult and No logic problems are difficult.

Not

Subalternate or not: All men are white and No men are white.

Not

Subalternate or not: All wars are bloody and No wars are bloody.

Not

Subalternate or not: Michael Jordan is a good basketball player and Michael Jordan is not a good basketball player.

Not

Subalternate or not: No houses are well-built and All houses are well-built.

Not

Subalternate or not: Some animals are amphibian and No animals are amphibian.

Not

Subalternate or not: Some logic problems are difficult and No logic problems are difficult.

Not

Subalternate or not: Some logic problems are difficult and Some logic problems are not difficult.

Not

Subalternate or not: Some logic problems are not difficult and All logic problems are difficult.

Not

Subalternate or not: Some men are sinners and Some men are not sinners.

Not

Subalternate or not: Some men are white and No men are white.

Not

Subalternate or not: Some men are white and Some men are not white.

Not

Subalternate or not: Some omelets are tasty and No omelets are tasty.

Not

Subalternate or not: Some soldiers are not brave and All soldiers are brave.

Not

Subalternate or not: Some tomatoes are red and All tomatoes are red.

Not

Subalternate or not:No cars are fast and All cars are fast.

Not

Subalternate or not:No logic problems are difficult and All logic problems are difficult.

Not

Subalternate or not:No men are white and All men are white.

Not

Subalternate or not:Some men are not white and All men are white.

Not

Subalternate or not:Some rocks are crystals and Some rocks are not crystals.

Not

Subcontrary or not: All logic problems are difficult and No logic problems are difficult.

Not

Subcontrary or not: All logic problems are difficult and Some logic problems are difficult.

Not

Subcontrary or not: All machines are loud and Some machines are loud.

Not

Subcontrary or not: All men are white and No men are white.

Not

Subcontrary or not: All men are white and Some men are white.

Not

Subcontrary or not: All storms are violent and Some storms are violent.

Not

Subcontrary or not: All wars are bloody and No wars are bloody.

Not

Subcontrary or not: No cars are fast and All cars are fast.

Not

Subcontrary or not: No guns are loud and Some guns are not loud.

Not

Subcontrary or not: No houses are well-built and All houses are well-built.

Not

Subcontrary or not: No logic problems are difficult and All logic problems are difficult.

Not

Subcontrary or not: No logic problems are difficult and Some logic problems are not difficult.

Not

Subcontrary or not: No men are white and All men are white.

Not

Subcontrary or not: No men are white and Some men are not white.

Not

Subcontrary or not: Some animals are amphibian and No animals are amphibian.

Not

Subcontrary or not: Some logic problems are difficult and No logic problems are difficult.

Not

Subcontrary or not: Some logic problems are not difficult and All logic problems are difficult.

Not

Subcontrary or not: Some men are not white and All men are white.

Not

Subcontrary or not: Some men are white and No men are white.

Not

Subcontrary or not: Some omelets are tasty and No omelets are tasty.

Not

Subcontrary or not: Some tomatoes are not red and All tomatoes are red.

Not

Subcontrary or not: Tim Couch is a good quarterback and Tim Couch is not a good quarterback.

Not

Subcontrary or not:No men are saved and Some men are not saved.

Not

Subcontrary or not:Some soldiers are not brave and All soldiers are brave.

Not

Tell the quality and quantity of the O statement.

Quality- negative Quantity- particular

Tell the quality and quantity of the I statement.

Quality-affirmative Quantity- particular

Tell the quality and quantity of the A statement.

Quality-affirmative Quantity- universal

Tell the quality and quantity of the A statement.

Quality-affirmative Quantity-universal

Tell the quality and quantity of the O statement.

Quality-negative Quantity-particular

Tell the quality and quantity of the E statement.

Quality-negative Quantity-universal

Fill out the following chart: Affirmative Negative Universal Particular

Quantity Quality Affirmative Negative Universal A I Particular E O

Are statements in which the subject-term is the name of a certain individual universal or particular? Explain.

Statements in which the subject-term is the name of a certain individual is universal because it applies to all of the subject-class which is the one person.

Subalternate or not: All logic problems are difficult and Some logic problems are difficult.

Subalternate

Subalternate or not: All men are white and Some men are white.

Subalternate

Subalternate or not: No guns are loud and Some guns are not loud.

Subalternate

Subalternate or not: No logic problems are difficult and Some logic problems are not difficult.

Subalternate

Subalternate or not: No men are saved and Some men are not saved.

Subalternate

Subalternate or not: No men are white and Some men are not white.

Subalternate

Subalternate or not:All machines are loud and Some machines are loud.

Subalternate

Subalternate or not:All storms are violent and Some storms are violent.

Subalternate

Subcontrary or not: Some logic problems are difficult and Some logic problems are not difficult.

Subcontrary

Subcontrary or not: Some men are sinners and Some men are not sinners.

Subcontrary

Subcontrary or not: Some men are white and Some men are not white.

Subcontrary

Subcontrary or not: Some rocks are crystals and Some rocks are not crystals.

Subcontrary

Explain why the A statement "All S is P" and the E statement "No S is P" are not contradictory.

The A statement "All S is P" and the E statement "No S is P" are not contradictory because even though they differ in quality, they are both universal.

Explain why the A statement "All S is P" and the E statement "No S is P" are not subalternate.

The A statement "All S is P" and the E statement "No S is P" are not subalternate because they differ in quality but are the same in quantity and for two statements to be subalternate they must have the same quality, but differ in quantity.

Explain why the A statement "All S is P" and the E statement "No S is P" are not subcontrary.

The A statement "All S is P" and the E statement "No S is P" are not subcontrary because subcontrary statements have to be particular and A and E statements are universal.

Explain why the A statement "All S is P" and the O statement "Some S is not P" are not contrary.

The A statement "All S is P" and the O statement "Some S is not P" are not contrary because they differ in quality and quantity.

Which other pair of statements is contradictory to one another?

The E and I statements are contradictory to one another.

What is the First Law of Opposition?

The First Law of Opposition is Contradictory statements cannot at the same time be true nor at the same time be false.

What is the First Law of Opposition?

The First Law of Opposition is contradictories cannot at the same time be true nor at the same time be false.

What is the Fourth Law of Opposition?

The Fourth Law of Opposition is subalterns may both be true or both be false.If the particular is false, the universal is false;if the universal is true,then the particular is true;otherwise, their status is indeterminate.

Explain why the I statement "Some S is P" and the E statement "No S is P" are not contrary.

The I statement "Some S is P" and the E statement "No S is P" are not contrary because they differ in quality and quantity.

Explain why the I statement "Some S is P" and the O statement "Some S is not P" are not subalternate.

The I statement "Some S is P" and the O statement "Some S is not P" are not subalternate because they differ in quality but are the same in quantity and for two statements to be subalternate they must have the same quality, but differ in quantity.

Is the I statement subcontrary to the O statement? If so, explain why; if not, explain why not.

The I statement is subcontrary to the O statement because they are both particular but differ in quality.

Express the Rule of Contradiction.

The Rule of Contradiction is contradictory statements are statements that differ in both in quality and quantity.

Express the Rule of Contraries.

The Rule of Contraries is two statements are contrary to one another if they are both universal but differ in quality.

Express the Rule of Subalterns.

The Rule of Subalterns is two statements are subalternate if they have the same quality but differ in quantity.

Express the Rule of Subcontraries.

The Rule of Subcontraries is two statements are subcontrary if they are both particular statements that differ in quality.

What is the Second Law of Opposition?

The Second Law of Opposition is Contraries cannot at the same time both be true, but can at the same time both be false.

What is the Second Law of Opposition?

The Second Law of Opposition is contraries cannot at the same time both be true, but can at the same time both be false.

What is the Third Law of Opposition?

The Third Law of Opposition is subcontraries may at the same time both be true but cannot at the same time both be false.

What are the four ways A, I, E, and O statements can be related to one another in opposition?

The four ways A, I, E,and O statements can be related to one another in opposition is contradictory, contrary, subcontrary, and subalternate.

What are the four ways A, I, E, and O statements can be related to one another in opposition?

The four ways that A, I, E, and O statements can be related to one another in opposition are to be contradictory, contrary, subcontrary, and subalternate.

True or false: The A statement and the E statement are not contradictory because, although they differ in quality, they do not differ in quantity.

True

True or false: The A statement and the E statement are not subcontrary because, although they differ in quality, they are both universal.

True

True or false: The A statement and the O statement differ in both quality and quantity.

True

True or false: The quantity of the statement "Some S is P" is particular.

True

True or false: The statements "All S is P" and "No S is P" can both be false at the same time.

True

True or false: The statements "All S is P" and "Some S is P" can both be false at the same time.

True

True or false: The statements "All S is P" and "Some S is P" can both be true at the same time.

True

True or false: The statements "All football players are big" and "No football players are big" are contrary.

True

True or false: The statements "All football players are big" and "Some football players are big" are subalternate.

True

True or false: Two statements are subcontrary if they differ from each other in quality and are both particular.

True

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 and quantity.

Is the A statement contrary to the E statement?

Yes, the A statement is contrary to the E statement because even though they differ in quality, they are both universal.

Is the A statement subalternate to the I statement? If so, explain why; if not, explain why not.

Yes, the A statement is subalternate to the I statement because they have the same quality (affirmative) but differ in quantity(A-universal,I-particular).

Are there any other pairs of statements that are subalternate to one another? If so, indicate which they are.

Yes, there is one other pair of statements that are subalternate to one another and they are the E and O statements.

How do you determine whether a proposition is in logical form?

You determine whether a propositon is in logical form by checking it has a subject-term, a predicate-term, a copula, and a quantifier.

Fill out the following chart: affirmative negative universal particular

quality affirmative negative universal A E quantity particular I O

Tell the quality and quantity of the I statement.

quality-affirmative quantity-particular

Tell the quality and quantity of the A statement.

quality-affirmative quantity-universal

Can both E and O statements be false at the same time?

Yes, both E and O statements can be false at the same time.

Can both E and O statements be true at the same time?

Yes, both E and O statements can be true at the same time.

Can both I and O statements be true at the same time?

Yes, both I and O statements can both be true at the same time.

What kinds of relationships statements can have to one another?

The two relationships statements can have to one another are opposition and equivalence.

What do we call the verbal expression of a judgment?

The verbal expression of a judgment is the proposition.

With which two of these is this chapter concerned?

This chapter is concerned with subcontrary and subalternate statements.

What are we doing when we oppose propositions?

When we oppose propositions, we are saying the two things affirm and deny the same subject and predicate but differ in quality and quantity.

Can both A and E statements be false at the same time?

Yes, both A and E statements can be false at the same time.

Can both A and I statements be false at the same time?

Yes, both A and I statements can be false at the same time.

Can both A and I statements be true at the same time?

Yes, both A and I statements can be true at the same time.