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Terms Without Nouns
- Must add plural nouns
- Ex. Some roses are red -> Some roses are red flowers
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Nonstandard Verbs
- Only are and are not are allowed in standard form.
- Ex. Trespassers will be prosecuted -> All trespassers are people who will be prosecuted
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Singular Propositions
- 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
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Spatial adverbs
- 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
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Temporal Adverbs
- 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
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Unspecified persons
- 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
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Unspecified Things
- 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
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Unexpressed Quantifiers
- 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
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Nonstandard Quantifiers
- 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.
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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
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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.
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Conditional Statements
Are always translated as universals. This involves "if", "then" or "only if"
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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
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Conditional Statements with "then" and "only if"
- Are statements that go in the predicate term
- Ex.
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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
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Exclusive Propositions
- 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
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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
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Exceptive Propositions
- "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
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All S are P
A prop. shaded S circle
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No S are P
E prop. Shaded middle circle
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Some S are P
I prop. X in middle circle
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Some S are not P
O prop. X in S circle
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Existential Import
When you go from a Universal statement to a Particular statement you make the existential fallacy
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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
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Quantifiers
Propositions that start with "all" "no" or "some"
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Quality
- 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
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A statement Distribution
Distributes the Subject
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E statement distributes
Both
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I statement distributes
None
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O statement distributes
Predicate
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