Standard Categorical Format

1. Standard Categorical Format – translating ordinary language statements into categorical form. While few statements in ordinary written and oral expression are categorical propositions in standard form, many of them can be translated into standard form propositions. The necessity for this translation is twofold: the first is that the operations and inference pertinent to standard form categorical propositions become applicable to these statements, and the second is that such statements, once translated are completely clear and unambiguous as to their meaning. The simple rule for this translation is to understand the meaning of the given statement and then reformulate it in a new statement that has a quantifier, subject term, copula, and predicate term.

a. terms without nouns – The subject and predicate terms of a categorical proposition must contain either a noun or noun substitute that serves to denote the class indicated by the term. Nouns and noun substitute denote classes, while adjectives connote attributes. If a term consists of only an adjective, a noun or noun substitute should be introduced to make the term genuinely denotative.

Some rose are red.	Some roses are red flowers.
All tigers are carnivorous.	All tigers are carnivorous animals.

b. nonstandard verbs – statements in ordinary usage often incorporate other forms of the verb to be. Such statements may be translated according to the following examples:

Some persons who go to college will become educated.	Some persons who go to college are persons who will be educated.
Some dogs would rather bark than bite.	Some dogs are animals that would rather bark than bite.

1. singular proposition – A singular proposition makes an assertion about a specific person, place, thing, or time. Singular propositions are typically translated into universals by means of a parameter, a phrase that when introduced into a statement affects the form but not the meaning. Some parameters that may be used to translate singular propositions are: persons identical to, place identical to, things identical to, times identical to.

Gloria Macapagal-Arroyo is the president of this country.	All persons identical to Gloria Macapagal-Arroyo are the president of this country.
There is a radio in the back bedroom.	All places identical to the back bedroom are places where there is a radio.

2. adverbs and pronouns – when a statement contains a spatial adverb such as where, wherever, anywhere, everywhere, or nowhere, or a temporal adverb such as when, whenever, anytime, always, or never, it may be translated in terms of places or times, respectively. a statement containing pronouns such as who, whoever, anyone, what, whatever, or anything may be translated in terms of persons or things, respectively.

He is always clean shaven.	All times are times he is clean shaven.
Whoever works hard will succeed.	All persons who work hard are persons who will succeed.

3. unexpressed quantifiers – many statements in ordinary usage have quantifiers that are implied but not expressed. In introducing the quantifiers one must be guided by the most probable meaning of the statement.

Emeralds are green gems.	All emeralds are green gems.
Children live next door.	Some children live next door.

4. nonstandard quantifiers – sometimes the quantity of the statement is indicated by a word or words other than the three quantifiers that are allowed.

A few soldiers are heroes.	Some soldiers are heroes.
Anyone who voted is a citizen.	All voters are citizens.

5. conditional statements – when the antecedent and consequent of a conditional statement talk about the same thing, the statement can usually be translated into categorical form.

If it is a mouse, then it is a mammal.	All mice are mammals.
If an animal has four legs, then it is not a bird.	No four-legged animals are birds.

In translating conditional statements it is sometimes useful to employ a rule called transposition. According to this rule, the antecedent and consequent of a conditional statement may switch places if both are negated. For example, the statement If something is not valuable, then it is not scarce is logically equivalent to If something is scarce, then it is valuable. This is then translated as All scarce things are valuable things.

The word unless means if…not. For example, the statement A car will not run unless there is gas in the tank means A car will not run if there is not gas in the tank which means If there is not gas in the tank, then a car will not run. by transposition, this means, If a car runs, then there is gas in the tank which is translated as All cars that run are cars with gas in the tank.

6. exclusive propositions – propositions that involve the words only, none but, none except, and no… except are exclusive propositions. Efforts to translate them into categorical propositions frequently lead to confusion of the subject term with the predicate term. Such confusion can be avoided if the statement is phrased as a conditional statement first, then as a categorical statement. For example, the statement Only executives can use the silver elevator is equivalent to If a person can use the silver elevator, he is an executive. The correct categorical proposition is All persons who can use the silver elevator are executives.

Only elected officials will attend the convention.

Only elected officials will attend the convention.

When only and none but occur in the middle of a statement, the statement must first be restructured so that the term preceded by only or none but occurs first. Then the statement can be translated as those above. For example, the statement Executives can use only the silver elevator is equivalent to Only the silver elevator can be used by executives. This, in turn, is equivalent to If an elevator can be used by executives, which is translated: All elevators that can be used by executives are elevators identical to the silver elevator.

He owns only the shirt on his back.

All things owned by him are things identical to the shirt on his back.

Statements beginning with the words the only are translated differently from those beginning with only. For example, the statement The only cars that are available are Chevrolets means that If a car is available, then it is a Chevrolet. This, in turn, is translated as All cars that are available are Chevrolets. In other words, the only, when it occurs at the beginning of a statement, can simply be replaced with all, and the order of the term is not reversed in the translation. When the only occurs in the middle of a statement, the statement must be restructured so that it occurs at the beginning. For example, Romances are the only books he sells is equivalent to The only books he sells are romances. This is then translated as All books that he sells are romances.

Accountants are the only ones who will be hired.

All those who will be hired are accountants.

7. exceptive propositions – propositions of the form All excepts S are P and All but S are P are exceptive propositions. They must be translated not as single categorical propositions but as pairs of conjoined categorical propositions. Statements that include the phrase none except, on the other hand, are exclusive and not exceptive propositions.

All except students are invited.

No students are invited persons + All non-students are invited persons.