Transcript 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)
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 sportsinclined 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