QUANTITY OR EXTENSION OF THE PREDICATE

Rule 1: The predicate of an affirmative proposition is generally particular.

Exceptions are predicates that are: 1) singulars, 2) essential definitions, and 3) essential properties. These are universal or in full extension

Rule 2: The predicate of a negative proposition is always universal or in full extension.

IMMEDIATE INFERENCE

An immediate inference is a process of reasoning which consists in passing directly from one proposition, without the aid of a second proposition or a third term, called medium, to a new proposition but not to a new truth.

Two main types: Logical Opposition and Eduction

Logical Opposition is a repugnance or relation existing between a pair of proposition which have the same subject and predicate but they differ in quality, quantity or both in quantity and quality.

Eduction is the formulation of a new proposition, either by interchanging the subject and predicate and/or by the use or omission of negatives.It is also known as equivalence or equipollence. It is the method of rephrasing the truth or falsity expressed in a given proposition.

LOGICAL OPPOSITION OF CATEGORICAL PROPOSITIONS

CONTRARIES – relationship between A and E propositionsSUBCONTRARIES – relationship between I and O propositionsCONTRADICTORIES – A and O, E and ISUBALTERNS – A and I, E and O

Rules for Contradictories

If one is true, the other is false.If one is false, the other is true

Rules for Contraries

If one is true the other is false.If one is false, the other is doubtful.

Rules for Subcontraries

If one is false, the other is true.If one is true, the other is doubtful

Rules for Subalterns

If the universal is true, the particular is true. If the universal is false, the particular is doubtful.If the particular is true, the universal is doubtful. If the particular is false, the universal is false.

Types of Eduction

CONVERSION - the process of reformulating the truth of a proposition by interchanging the subject and predicate of a given proposition without changing its quality.

The original proposition is called “convertend.”The new proposition is called “converse.”

Rules: 1. Interchange subject and predicate 2. The convertend or original form must be in its logical form.3. Retain the quality of the proposition4. Do not over-extend the term.

Ex. Some seminarians are prayerful – Some prayerful people are seminarians. No atheist is a believer of God – No believer of God is an atheist All beautiful girls are attractive – Some attractive (people) are beautiful girls.

OBVERSION - The method of rephrasing the truth of a given proposition by changing the quality of the copula.

Obvertend – the original propositionObverse – the new proposition

Rules/Procedure:

1. Change the quality of the copula.2. Change the quality of the predicate term.3. Retain the quantity.

Examples

All human beings are rational – No human being is non-rational (irrational).No criminal is moral – All criminals are non-moral (immoral).Some leaders are responsible – Some leaders are not non-responsible (irresponsible).Some lawmakers are not ethical – Some lawmakers are non-ethical (unethical).

CONTRAPOSITION - The method of rephrasing the truth of a given proposition by combining the processes of obversion and conversion.

Partial Contraposition – applicable to A, E, and O propositions.

Rules:

1. Obvert the contraponend (original proposition)2. Convert the Obverse

Examples:

All Christians are believers of Christ – No non-believer of Christ is a Christian

Step 1 – No Christian is a non-believer of Christ.Step 2 – No non-believer of Christ is a Christian

No seminarian is stupid – Some non-stupid people are seminarians.Some laws are not beneficial to citizens – Some (things) non-beneficial to citizens are laws.

Complete Contraposition – applicable to A, E, and O propositions

Rules/Procedures:

1. Obvert.2. Convert the Obverse3. Obvert the converse.

Examples:

All squares are equal in sides – All non-equal in sides are non-squares.

Step 1 Obvert – No square is non-equal in sides.Step 2 Convert – No non-equal in sides is a square.Step 3 Obvert – All non-equal in sides are non-squares.No goat is a cow – Some non-cows are not non-goats.Some lawyers are not honest – Some non-honest (people) are not non-lawyers.

INVERSION – It consists in helping us to be alert to the quantity and quality of the subject and to the quality of the copula.

Simple Inversion (A and E propositions)

Rules:

1. Change the subject of the invertend to its contradiction e.g., honest = non-honest.

2. Change the quantity of the invertend3. Change the quality of the copula4. Retain the original predicate

Examples:

All communists are revolutionary. – Some non-communists are not revolutionary.No criminal is law-abiding. – Some non-criminals are law-abiding.

Complete Inversion

Rules/Procedures:

1. Change the subject to its contradiction2. Change the quantity3. Retain the quality4. Change the predicate to its contradiction

Examples:

All communists are revolutionary – Some non-communists are non-revolutionary.No criminal is law-abiding – Some non-criminals are not non-abiding of the law.No cheater is honest – Some non-cheaters are not non-honest (dishonest).