4.7 TRANSLATING ORDINARY LANGUAGE STATEMENTS INTO CATEGORICAL FORM

4 Categorical Propositions

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.

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…

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)

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

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

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

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

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)

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

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)

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)

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