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4 Categorical Propositions

4 Categorical Propositions. 4.7 TRANSLATING ORDINARY LANGUAGE STATEMENTS INTO CATEGORICAL FORM. 1 Terms without Nouns. Some cars are red ----> Some cars are red things (or red cars ) All clowns are happy ----> All clowns are happy people ( or happy goofballs)

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4 Categorical Propositions

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  1. 4 Categorical Propositions 4.7 TRANSLATING ORDINARY LANGUAGE STATEMENTS INTO CATEGORICAL FORM

  2. 1 Terms without Nouns Some cars are red ----> Some cars are red things (or red cars) All clowns are happy ----> All clowns are happy people (or happy goofballs) The point is, some accurate noun, but no particular noun, is required.

  3. 2 Nonstandard Verbs Other forms of “to be” beside “are” and “are not” “Will” Some book bindings will tear ---> Some book bindings are bindings that will tear (or things that will tear) “Have been” Some guys have been swimming ---> Some guys are guys that have been swimming (or people that have been swimming) Etc…

  4. 2 Nonstandard Verbs (cont) Some statements contain no form of the verb “to be”: All puppies bark ---> All puppies are demons that bark (or dogs that bark, or beasts that bark)

  5. 3 Singular Propositions Singular propositions are propositions that assert something about a particular person, place, thing, or time: Rookie is an evil dog ----> All dogs identical to rookie are evil dogs There is a sandwich on the counter ----> All places identical to the counter are places with a sandwich Or There is a sandwich on the counter ----> Some sandwiches are things on the counter

  6. 4 Adverbs and Pronouns Spatial adverbs: Where, wherever, anywhere, everywhere, nowhere (translate as places) Temporal adverbs: When, whenever, anytime, always, never (translate as times) Anywhere you go, there you are ----> All places that you go are places that you are Nowhere is where I want to be ----> No places are places I want to be Or Nowhere is where I want to be ----> All places identical to nowhere are places I want to be

  7. 4 Adverbs and Pronouns Personal pronouns: Who, whoever, anyone (translate as persons) Impersonal pronouns: What, whatever, anything (translate as things) Whoever misses class is in big trouble -----> All persons who miss class are persons in big trouble What goes up, must come down ----> All things that go up are things that come down

  8. 5 Unexpressed Quantifiers You must use your understanding of what is being said in a sentence to determine the quantifier: A dog is a potential disaster ----> All dogs are potential disasters A dog is barking at me -----> Some dogs are dogs that are barking at me

  9. 6 Nonstandard Quantifiers A few leaves have fallen ----> Some leaves are leaves that have fallen Not one leaf is green -----> No leaves are green leaves All children are not sports-inclined kids ----> Some children are not sports-inclined kids Or All children are not fully educated kids -----> No children are fully educated kids Few dog bites seriously hurt me ----> Some dog bites are bites that seriously hurt me and Some dog bites are not bites that seriously hurt me (read page 230 for an explanation of compound translations)

  10. 7 Conditional Statements “If, Then” statements are conditional statements; the part following “if” is called the antecedent (what comes before), and the part following “then” is called the consequent (what comes after). Conditional statements are translated as universal propositions: If it’s on the deck, then it’s mine ----> All things that are on the deck are my things If you want it, then you can’t have it -----> No things you want are things you can have

  11. 8 Exclusive Propositions “Only,” “None but,” “None except,” “No … except” signal exclusive propositions. The language following those ‘excluders’ goes in the predicate term. Only jerks drive off after dinging your door ----> All door dingers who drive off are jerks No teams except NFC North teams are good -----> All good teams are NFC North teams They like only KFC ----> All foods they like are KFC foods (Read 232 about some cases that require compound translations)

  12. 9 “The Only” Unlike “only” the words that follow “the only” go in the subject term position. The only good Chicago Bear is Brian Urlacher ----> All good Bears are players identical to Brian Urlacher (compare to: Only Brian Urlacher is a good Chicago Bear -----> All good Bears are players identical to Brian Urlacher)

  13. 10 Exceptive Propositions “All except S are P” or “All but S are P” are exceptive propositions and require TWO statements to capture their meaning All sandwiches except hoagies are icky hot ----> No hot hoagies are icky sandwiches and All hot non-hoagies are icky sandwiches All but Toyotas are unreliable cars ----> No Toyotas are unreliable cars and All non-Toyotas are unreliable cars

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