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6. Practice with Quality, Quantity, and Distribution The four types…
6. Practice with Quality, Quantity, and Distribution
The four types of categorical propositions are designated with the letters A, E, I, and O. The attributes of categorical propositions include quantity and quality. Distribution is a property of the terms within a categorical proposition. Within a categorical proposition, the subject term is either distributed or undistributed, and the predicate term is either distributed or undistributed.
For each categorical proposition, identify the letter designation, quantity, and quality. Also indicate whether the subject and predicate terms are distributed or undistributed.
Given Categorical Proposition: All charcoal drawing sticks are art supplies.
Letter name:
Quantity
Quality:
Subject term:
Predicate term:
Given Categorical Proposition: Some freshwater aquarium plants are not Red Tiger Lotuses.
Letter name:
Quantity
Quality:
Subject term:
Predicate term:
Given Categorical Proposition: No R-rated movies are movies that are recommended for minors.
Letter name:
Quantity
Quality:
Subject term:
Predicate term:
Given Categorical Proposition: Some heavenly bodies that orbit the sun are not true planets.
Letter name:
Quantity
Quality:
Subject term:
Predicate term:
Given Categorical Proposition: Some modern chess pieces are not game pieces that are shaped like a horse.
Letter name:
Quantity
Quality:
Subject term:
Predicate term:
Given Categorical Proposition: Some philosophical theories are theories with false assumptions.
Letter name:
Quantity
Quality:
Subject term:
Predicate term:
7. Changing Quantity
You should learn to convert categorical propositions from one type to another, which is achieved by changing their quantity and/or quality. Learning to perform this task is useful for learning the operations of conversion, obversion, and contraposition in a later section.
Change the quantity, but not the quality, of each of the following categorical propositions. Also identify the letter designations for the given proposition’s form and for the resulting proposition’s form. (Note: You should not assume that the resulting statement will necessarily be true.)
Example 1
All scientific breakthroughs are milestones of human progress.
This categorical proposition is an proposition.
If you change the quantity, but not the quality, of the given categorical proposition, what will the resulting statement be?
Some scientific breakthroughs are milestones of human progress.
No scientific breakthroughs are milestones of human progress.
Some scientific breakthroughs are not milestones of human progress.
The resulting statement is an proposition.
Example 2
No people who knit are people without scarves.
This categorical proposition is an proposition.
If you change the quantity, but not the quality, of the given categorical proposition, what will the resulting statement be?
Some people who knit are people without scarves.
All people who knit are people without scarves.
Some people who knit are not people without scarves.
The resulting statement is an proposition.
Example 3
Some French philosophers are poststructuralists.
This categorical proposition is an proposition.
If you change the quantity, but not the quality, of the given categorical proposition, what will the resulting statement be?
All French philosophers are poststructuralists.
No French philosophers are poststructuralists.
Some French philosophers are not poststructuralists.
The resulting statement is an proposition.
Example 4
Some lively fandangos are not square dances.
This categorical proposition is an proposition.
If you change the quantity, but not the quality, of the given categorical proposition, what will the resulting statement be?
No lively fandangos are square dances.
Some lively fandangos are square dances.
All lively fandangos are square dances.
The resulting statement is an proposition.
Example 5
Some board games are not games that require dice.
This categorical proposition is an proposition.
If you change the quantity, but not the quality, of the given categorical proposition, what will the resulting statement be?
No board games are games that require dice.
Some board games are games that require dice.
All board games are games that require dice.
The resulting statement is an proposition.
Example 6
No citizens of ancient Rome are currently living humans.
This categorical proposition is an proposition.
If you change the quantity, but not the quality, of the given categorical proposition, what will the resulting statement be?
Some citizens of ancient Rome are not currently living humans.
All citizens of ancient Rome are currently living humans.
Some citizens of ancient Rome are currently living humans.
The resulting statement is an proposition.
9. Changing Quantity and Quality
You should learn how to convert categorical propositions from one type to another, which is achieved by changing their quantity and/or quality. Understanding how to perform this task is useful for learning the operations of conversion, obversion, and contraposition in a later section.
Change both the quantity and the quality of each of the following categorical propositions. Also identify the letter designation for the given proposition’s form and the letter designation for the resulting proposition’s form. (Note: You should not assume that the resulting statement will necessarily be true.)
Example 1
Some computer codes are ASCII codes.
This categorical proposition is an proposition.
If you change both the quantity and the quality of the given categorical proposition, what will the resulting statement be?
All computer codes are ASCII codes.
No computer codes are ASCII codes.
Some computer codes are not ASCII codes.
The resulting statement is an proposition.
Example 2
Some board games are not games that require dice.
This categorical proposition is an proposition.
If you change both the quantity and the quality of the given categorical proposition, what will the resulting statement be?
All board games are games that require dice.
No board games are games that require dice.
Some board games are games that require dice.
The resulting statement is an proposition.
Example 3
All reduction-oxidation reactions are chemical reactions in which atoms have their oxidation state changed.
This categorical proposition is an proposition.
If you change both the quantity and the quality of the given categorical proposition, what will the resulting statement be?
Some reduction-oxidation reactions are chemical reactions in which atoms have their oxidation state changed.
Some reduction-oxidation reactions are not chemical reactions in which atoms have their oxidation state changed.
No reduction-oxidation reactions are chemical reactions in which atoms have their oxidation state changed.
The resulting statement is an proposition.
Example 4
All scientific breakthroughs are milestones of human progress.
This categorical proposition is an proposition.
If you change both the quantity and the quality of the given categorical proposition, what will the resulting statement be?
No scientific breakthroughs are milestones of human progress.
Some scientific breakthroughs are not milestones of human progress.
Some scientific breakthroughs are milestones of human progress.
The resulting statement is an proposition.
Example 5
No citizens of ancient Rome are currently living humans.
This categorical proposition is an proposition.
If you change both the quantity and the quality of the given categorical proposition, what will the resulting statement be?
All citizens of ancient Rome are currently living humans.
Some citizens of ancient Rome are currently living humans.
Some citizens of ancient Rome are not currently living humans.
The resulting statement is an proposition.
Example 6
All banana slugs are terrestrial molluscs.
This categorical proposition is an proposition.
If you change both the quantity and the quality of the given categorical proposition, what will the resulting statement be?
Some banana slugs are terrestrial molluscs.
Some banana slugs are not terrestrial molluscs.
No banana slugs are terrestrial molluscs.
The resulting statement is an proposition.
