Chapter 4 Categorical Propositions

Question 1

What is a proposition?

Answer 1

A sentence that is used to make a claim about how things are; true or false.

Proposition used interchaneably with Statement

Question 2

What is a categorical proposition?

Answer 2

A proposition that relates two classes of things; claims that a certain number of the members of one class are included in or exluded from another class.

Question 3

What is a term?

Answer 3

A word or phrase that can serve as the subject of a proposition. Inlude proper names, common names, and descriptive phrases.

Question 4

How many terms in a Categorical Proposition?

Answer 4

2; a subject term and a predicate term.

Question 5

What is a subject term?

Answer 5

Denotes the class whose members are claimed to be included in or exluded from a class of things by the categorical proposition.

Question 6

What is a predicate term?

Answer 6

Denotes the class of things that members of the subject class are claimed to be included in or excluded from.

Question 7

What are the 4 types of Standard Categorical Propositions?

Answer 7

1. A Propositions: All S are P : Propositions which claim all members of the subject class are included in the predicate class. (Universal and Positive)
2. ** E Propositions: No S are P** : Propositions which claim that all members of the subject class are excluded from the predicate class. (Universal and Negative)
3. I Propositions: Some S are P : Propositions which claim that some members of the subject class are included in the predicate class. (Particular and Positive)
4. O Propositions: Some S are not P : Propositions which claim that some members of the subject class are exluded from the predicate class. (Particular and Negative)

Question 8

What is a quantifier?

Answer 8

Expression which specifies how many members of the subject class are claimed to be included in or excluded from the predicate class.

3 types of Quantifiers in Standard Categorical Propositions: All, no, some.

Question 9

What is a copula?

Answer 9

Expression which links the subject term with the predicate term.

2 types of Copulas in Standard Cateforical Propositions: are, are not

Question 10

What are 2 important features of categorical propositions?

Answer 10

Quality: A matter of whether a categorical proposition affirms or denies class membership.

Quantity: Depends on whether a categorical proposition makes a claim about every cmember of the class denoted by the subject term or just some members of that class.

Question 11

What are positive propositions?

Answer 11

Claim that members of the subject class fall within the predicate class.

e.g. some donkeys are cooperative pack animals

Question 12

What are Negative Propositions?

Answer 12

Claim that members of the subject class are excluded from the predicate class.

e.g. no stained shirts are appropriate fine dining garments.

Question 13

What are universal propositions?

Answer 13

Make claims about every member of the subject class.

e.g. No stained shirts are appropriate fine dining garments.

Question 14

What are particular propositions?

Answer 14

Make claims about one or more, but not all, members of the subject class.

e.g. some donkeys are cooperative pack animals

Question 15

What are the Venn Diagram Conventions?

Answer 15

• Layout Circles like image below.
• Shading a region means that it is empty.
• Placing an x in a region means it contains at least one thing.

Question 16

What are statements with the quantifier “few” translated as.

Answer 16

I Propositions: Some S are P

A few AC/DC albums are records in my collection —> Some AC/DC albums are records in my collection.

Question 17

What are statements with the quantifier “not all” translated as?

Answer 17

O Propositions: Some S are not P

Not all novelists are destined for disappointment —> Some novelists are not destined for disappointment.

Question 18

How to translate statements that lack a quantifier?

Answer 18

You need to decide whether the quantity is more plausible being universal or particular.

Question 19

How do you translate statements that combine the quantifier “All” with the Copular “Are not”?

e.g. All cats are not canines; All professors are not hard graders

Answer 19

Translate as either E or O statements depending on Plausibiity.

No Cats are P; Some professors are not hard graders.

Question 20

How to translate statements that contain terms that denote individual people, places, or things rather than classes?

Answer 20

Use “people identical to”, “places identical to”, “things identical to”.

Question 21

How to translate statements that contain spatial and temporal adverbs?

Spatial: where, wherever, anywhere, everywhere, nowhere
Temporal: when, whenever, anytime, always, never

Answer 21

Take the subject and predicate terms to denote classes of places and times instead of nouns.

Question 22

Given that:

P = the antecedent
Q = the consequent

How to translate statements in the form “if P then Q”.

Answer 22

Turn P into the Subject Term
Turn Q into the Predicate Term
Translate as A statements.

Question 23

How to translate statments that contain the expressions “only” or “the only”?

Also how do you tell which is the subject and predicate term?

Answer 23

Translate as A statements.

Subject Term - Expression that immediately follows “the only”

Predicate Term - Expression that follows “only” by itself.

Question 24

How do you do a Transformation (a)?

Make sure to take whole subject and predicate.

Answer 24

Switch the subject and predicate terms.

Question 25

How do you do a transformation (b)?

Some iguanas are not excellent singers

Answer 25

Change the quality of the Proposition.

A&E - Change Quantifier
I&O - Change Copula

Some iguanas are excellent singers

Question 26

What is a Complement?

Answer 26

An expression which denotes the class whose members consist of everything that falls outside the class denoted by the original term.

Initial Term: iguanans
Complement: “non iguanas” or “things that are not iguanas”

Question 27

How do you do a transformation (c)?

Some iguanas are excellent singers

Answer 27

Replace one more terms with their complements.

[PREDICATE ONLY] Some iguanas are things that are not excellent singers.

Question 28

What is conversion?

All macadamia nuts are items banned in the classroom

Answer 28

Subjecting initial proposition to transformation (a).

all items banned in the classroom are macadamia nuts.

Question 29

What is Obversion?

All Macadamia nuts are items banned in the classroom.

Answer 29

Subjecting intial proposition to Transformation (b) + Transformation (c)[Predicate]

No Macadamia buts are items permitted in the classroom.

Question 30

What is Contraposition?

All macadamia nuts are items banned in the classroom.

Answer 30

Subjecting initial proposition to transformation (a) + transformation (c) [Subject and Predicate]

All items permitted in the classroom are things that are not macadamia nuts.

Question 31

Explain all the equivalences.

Answer 31