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

No identical twins are fraternal twins.

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 identical twins are fraternal twins.

Some identical twins are not fraternal twins.

All identical twins are fraternal twins.

The resulting statement is an proposition.

Example 2

All reduction-oxidation reactions are chemical reactions in which atoms have their oxidation state changed.

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 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.

Some reduction-oxidation reactions are chemical reactions in which atoms have their oxidation state changed.

The resulting statement is an proposition.

Example 3

Some pleasant walks in the park are occasions for being mugged.

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 pleasant walks in the park are occasions for being mugged.

Some pleasant walks in the park are not occasions for being mugged.

All pleasant walks in the park are occasions for being mugged.

The resulting statement is an proposition.

Example 4

Some people who jog in the morning are not people who wake up before dawn.

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 jog in the morning are people who wake up before dawn.

All people who jog in the morning are people who wake up before dawn.

No people who jog in the morning are people who wake up before dawn.

The resulting statement is an proposition.

Example 5

All fractions of two integers are rational numbers.

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 fractions of two integers are not rational numbers.

Some fractions of two integers are rational numbers.

No fractions of two integers are rational numbers.

The resulting statement is an proposition.

Example 6

No fictional starship captains are timid commanders.

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 fictional starship captains are not timid commanders.

All fictional starship captains are timid commanders.

Some fictional starship captains are timid commanders.

The resulting statement is an proposition.

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8. Changing 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 the quality, but not the quantity, 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

All fractions of two integers are rational numbers.

This categorical proposition is an proposition.

If you change the quality, but not the quantity, of the given categorical proposition, what will the resulting statement be?

Some fractions of two integers are not rational numbers.

Some fractions of two integers are rational numbers.

No fractions of two integers are rational numbers.

The resulting statement is an proposition.

Example 2

Some friendly ghosts are not poltergeists.

This categorical proposition is an proposition.

If you change the quality, but not the quantity, of the given categorical proposition, what will the resulting statement be?

All friendly ghosts are poltergeists.

Some friendly ghosts are poltergeists.

No friendly ghosts are poltergeists.

The resulting statement is an proposition.

Example 3

Some French philosophers are poststructuralists.

This categorical proposition is an proposition.

If you change the quality, but not the quantity, of the given categorical proposition, what will the resulting statement be?

No French philosophers are poststructuralists.

Some French philosophers are not poststructuralists.

All French philosophers are poststructuralists.

The resulting statement is an proposition.

Example 4

Some plastic dolls are dolls that walk and talk.

This categorical proposition is an proposition.

If you change the quality, but not the quantity, of the given categorical proposition, what will the resulting statement be?

All plastic dolls are dolls that walk and talk.

No plastic dolls are dolls that walk and talk.

Some plastic dolls are not dolls that walk and talk.

The resulting statement is an proposition.

Example 5

Some New World vultures are not California condors.

This categorical proposition is an proposition.

If you change the quality, but not the quantity, of the given categorical proposition, what will the resulting statement be?

All New World vultures are California condors.

Some New World vultures are California condors.

No New World vultures are California condors.

The resulting statement is an proposition.

Example 6

No Shakespearean plays are plays by Christopher Marlowe.

This categorical proposition is an proposition.

If you change the quality, but not the quantity, of the given categorical proposition, what will the resulting statement be?

Some Shakespearean plays are plays by Christopher Marlowe.

Some Shakespearean plays are not plays by Christopher Marlowe.

All Shakespearean plays are plays by Christopher Marlowe.

The resulting statement is an proposition.