CATEGORICAL CATEGORICAL PROPOSITIONS and classesPROPOSITIONS and classes

The Aristotelian study of deduction focused on arguments containing propositions of a special kind called “Categorical Propositions” because they are about categories or classes.

No professionals are vegetarians.

All lawyers are professionals.____________

Therefore no lawyers are vegetarians.

FOUR DIFFERENT FORMS OF CATEGORICAL PROPOSITIONS:

1. All lawyers are liars.

2. No lawyers are liars.

3. Some lawyers are liars.

4. Some lawyers are not liars.

1.UNIVERSAL AFFIRMATIVE PROPOSITION1.UNIVERSAL AFFIRMATIVE PROPOSITION

“All lawyers are liars.”

- It is about two classes, the class of all lawyers and the class of all liars, saying that the first class is included or contained in the second.

- It says that every member of the first class is also a member of the second class.

All S is P.

2. UNIVERSAL NEGATIVE PROPOSITION2. UNIVERSAL NEGATIVE PROPOSITION

“No lawyers are liars.”

- It denies of lawyers universally that they are liars. Concerned with two classes that says that the first class is wholly excluded from the second, which is to say that there is no member of the first class that is also a member of the second.

No S is P.

3. PARTICULAR AFFIRMATIVE PROPOSITION3. PARTICULAR AFFIRMATIVE PROPOSITION

“Some lawyers are liars.” - It affirms that some members of the class of all

lawyers are also members of the class of all liars. But it does not affirm this of lawyers universally but some particular lawyers or lawyers are said to be liars.

- At least one member of the class designated by the subject term S is also a member of the class designated by the predicate term P.

Some S is P.

4. PARTICULAR NEGATIVE 4. PARTICULAR NEGATIVE PROPOSITIONPROPOSITION “Some lawyers are not liars.” - It does not refer to politicians universally but

only to some member or members of that class which is particular.

- It does not affirm that the particular members of the first class referred to are included in the second class; this is precisely what is denied.

- At least one member of the class designated by the subject term S is excluded from the whole of the class designated by the predicate term P.

Some S is not P.

Universal Affirmative - called A propositions

Universal Negative - called E propositions

Particular Affirmative - called I propositions

Particular Negative - called O propositions

QUALITY, QUANTITY QUALITY, QUANTITY AND DISTRIBUTIONAND DISTRIBUTION

QUALITYQUALITY

Every standard-form categorical proposition is said to have quality, either affirmative or negative.

A. AFFIRMATIVE - If the proposition affirms some class

inclusion, whether complete or partial its quality is affirmative.

- Both universal propositions and particular affirmative propositions are affirmative in quality and their letter names, A and I respectively comes from the:

Latin Word: “ AffIrmo” meaning “ I Affirm.”

B. NEGATIVE

- If the proposition denies class inclusion, whether complete or partial, its quality is negative.

- - Both universal negative propositions and particular negative propositions are negative in quality, and their letter names, E and O, respectively, are thought to come from the:

- Latin word: “nEgO,” meaning “ I deny.”

QUANTITYQUANTITY

UNIVERSAL QUANTITY -If the proposition refers to all members of the

class designated by its subject term. Thus the A and E propositions are universal in

quantity.PARTICULAR QUANTITY - If the proposition refers only to some

members of the class designated by its subject term.

Thus the I and O propositions are particular in quantity.

“All” & “No” - indicate the proposition is Universal

“Some” - indicates that the quantity is particular

GENERAL SCHEMA OF STANDARD-FORM GENERAL SCHEMA OF STANDARD-FORM CATEGORICAL PROPOSITIONSCATEGORICAL PROPOSITIONS

Between the subject and predicate terms of every standard-form categorical propositions occurs some form of the verb “to be” (accompanied by the word “not” in the case of the O proposition).

This verb serves to connect the subject and predicate terms and is called “COPULA”.

Some Roman emperors were monsters.All squares are rectangles.Some soldiers will not be heroes.

Schema:

Quantifier (subject term) copula (predicate term)