Chapter 4 Categorical Propositions Flashcards
What is a proposition?
A sentence that is used to make a claim about how things are; true or false.
Proposition used interchaneably with Statement
What is a categorical proposition?
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.
What is a term?
A word or phrase that can serve as the subject of a proposition. Inlude proper names, common names, and descriptive phrases.
How many terms in a Categorical Proposition?
2; a subject term and a predicate term.
What is a subject term?
Denotes the class whose members are claimed to be included in or exluded from a class of things by the categorical proposition.
What is a predicate term?
Denotes the class of things that members of the subject class are claimed to be included in or excluded from.
What are the 4 types of Standard Categorical Propositions?
- A Propositions: All S are P : Propositions which claim all members of the subject class are included in the predicate class. (Universal and Positive)
- ** 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)
- 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)
- 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)
What is a quantifier?
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.
What is a copula?
Expression which links the subject term with the predicate term.
2 types of Copulas in Standard Cateforical Propositions: are, are not
What are 2 important features of categorical propositions?
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.
What are positive propositions?
Claim that members of the subject class fall within the predicate class.
e.g. some donkeys are cooperative pack animals
What are Negative Propositions?
Claim that members of the subject class are excluded from the predicate class.
e.g. no stained shirts are appropriate fine dining garments.
What are universal propositions?
Make claims about every member of the subject class.
e.g. No stained shirts are appropriate fine dining garments.
What are particular propositions?
Make claims about one or more, but not all, members of the subject class.
e.g. some donkeys are cooperative pack animals
What are the Venn Diagram Conventions?
- 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.
What are statements with the quantifier “few” translated as.
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.
What are statements with the quantifier “not all” translated as?
O Propositions: Some S are not P
Not all novelists are destined for disappointment —> Some novelists are not destined for disappointment.
How to translate statements that lack a quantifier?
You need to decide whether the quantity is more plausible being universal or particular.
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
Translate as either E or O statements depending on Plausibiity.
No Cats are P; Some professors are not hard graders.
How to translate statements that contain terms that denote individual people, places, or things rather than classes?
Use “people identical to”, “places identical to”, “things identical to”.
How to translate statements that contain spatial and temporal adverbs?
Spatial: where, wherever, anywhere, everywhere, nowhere
Temporal: when, whenever, anytime, always, never
Take the subject and predicate terms to denote classes of places and times instead of nouns.
Given that:
P = the antecedent
Q = the consequent
How to translate statements in the form “if P then Q”.
Turn P into the Subject Term
Turn Q into the Predicate Term
Translate as A statements.
How to translate statments that contain the expressions “only” or “the only”?
Also how do you tell which is the subject and predicate term?
Translate as A statements.
Subject Term - Expression that immediately follows “the only”
Predicate Term - Expression that follows “only” by itself.
How do you do a Transformation (a)?
Make sure to take whole subject and predicate.
Switch the subject and predicate terms.
How do you do a transformation (b)?
Some iguanas are not excellent singers
Change the quality of the Proposition.
A&E - Change Quantifier
I&O - Change Copula
Some iguanas are excellent singers
What is a Complement?
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”
How do you do a transformation (c)?
Some iguanas are excellent singers
Replace one more terms with their complements.
[PREDICATE ONLY] Some iguanas are things that are not excellent singers.
What is conversion?
All macadamia nuts are items banned in the classroom
Subjecting initial proposition to transformation (a).
all items banned in the classroom are macadamia nuts.
What is Obversion?
All Macadamia nuts are items banned in the classroom.
Subjecting intial proposition to Transformation (b) + Transformation (c)[Predicate]
No Macadamia buts are items permitted in the classroom.
What is Contraposition?
All macadamia nuts are items banned in the classroom.
Subjecting initial proposition to transformation (a) + transformation (c) [Subject and Predicate]
All items permitted in the classroom are things that are not macadamia nuts.
Explain all the equivalences.
