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Terms Without Nouns
- Must add plural nouns
- Ex. Some roses are red -> Some roses are red flowers
- Only are and are not are allowed in standard form.
- Ex. Trespassers will be prosecuted -> All trespassers are people who will be prosecuted
- A proposition that makes an assertion about a specific person, place, thing or time.
- Ex. The moon is full tonight -> All things identical to the moon are things that are full tonight OR All times identical to tonight are times the moon is full
- Describe where something happens.
- Eg. wherever, everywhere, anywhere, somewhere, nowhere, upstairs, and underground
- Ex. Wherever there is smoke, there is a fire -> All places that have smoke are places that have fire
- Describe when something happens
- Eg. Whenever, never, always, anytime, yesterday, and tomorrow.
- Ex. She never brings her lunch to school -> No times she goes to school are times she brings her lunch
- Describe an unspecified person or persons.
- Eg. whoever, anyone, anybody, everyone, no one, and someone
- Ex. Whoever took my journal is in big trouble -> All people who took my journal are people in big trouble
- Describe an unspecified thing or things
- Eg. what, whatever, anything, something, and everything
- Ex. What goes around comes around -> All things that go around are things that come around
- Ordinary language statements have implied quantifiers.
- Ex. Sharks are predators -> All sharks are predators
- Ex2. Children live next door -> Some children are people who live next door
- Some ordinary language statements contain quantifiers that are non standard because they are not "all" or "some"
- Ex. Not every investment banker is a crook -> Some investment bankers are not crooks.
Quantifier "all" is combined with "are not"
- Depending on the meaning, these statements should either be translated as "No S are P" or "Some S are not P"
- Ex. All prisoners are not violent -> Some prisoners are not violent people
Statements that begin with "few" "a few" "almost all" "not quite all"
- Must be translated as a compound arrangement of an I and O Proposition
- Ex. Few sailors entered the regatta -> Some sailors are people who entered the regatta and some sailors are not people who entered the regatta.
Are always translated as universals. This involves "if", "then" or "only if"
Conditional Statements with IF
- The language following the actual or implied "if" goes in the subject term
- Ex. If a salesperson calls on the phone, then I just hang up -> All calls from salespersons are calls where I hang up
Conditional Statements with "then" and "only if"
- Are statements that go in the predicate term
Unless = If not
- Translate statements containing "unless" as categorical propositions having negated subject terms.
- Ex. Tomatoes are edible unless they are spoiled -> All unspoiled tomatoes are edible tomatoes
- Propositions include "only", "none but" "none except" "no...except" go into the predicate term
- Ex. Only persons wearing wristbands can enter the festival -> All persons who can enter the festival are persons wearing wristabands
Statements that begin with "The Only"
- Are translated differently than "only" and terms that follow "the only" go into the subject term
- Ex. Android phones are the only phones imported by her company -> All phones imported by her company are android phones
- "All except S are P" and "All but S are P" and they require conjoined categorical propositions.
- Ex. All except those under 21 are allowed to gamble in Las Vegas -> No under 21 persons are persons allowed to gamble in Las Vegas, and all non under 21 persons are persons allowed to gamble in Las Vegas
All S are P
A prop. shaded S circle
No S are P
E prop. Shaded middle circle
Some S are P
I prop. X in middle circle
Some S are not P
O prop. X in S circle
When you go from a Universal statement to a Particular statement you make the existential fallacy
It is false that some A are B
It is the contradictory proposition that is created so. All A are B is an A prop with Shaded A circle and the contradictory is Some A are not B which is an X in the A circle
Propositions that start with "all" "no" or "some"
- Can be affirmative and negative
- Affirmative: All S are P and Some S are P
- Negative: No S are P and Some S are not P
A statement Distribution
Distributes the Subject
E statement distributes
I statement distributes
O statement distributes