CHAPTER 6. INFERENCE

6. INFERENCE
a) Kinds of inference- Immediate and Mediate.
b) Opposition of proposition- Types of opposition- inference by opposition of propositions- opposition of Singular propositions.

AN INFERENCE is a mental process by which we pass from one or more statements to another that is logically related to the former.

a) Kinds of inference –

Inferences are classified on the basis of their scope into Deductive and Inductive. Deductive Inference have a conclusion that stays within the scope of premises. Inductive Inferences are the ones that go beyond the scope of the premises.

The Deductive Inferences are of two types, Mediate and Immediate.

Inductive Inferences are of two types, perfect induction and imperfect induction.

Immediate & Mediate

We are studying the Immediate and mediate inferences here.

Based on the number of their premise, inferences are basically classified into two types, immediate and mediate:

Immediate Inference consists in passing directly from a single premise to a conclusion. It is reasoning, without the intermediary of a middle term or second proposition, from one proposition to another which necessarily follows from it.

Ex: No Dalmatians are cats. Therefore, no cats are Dalmatians.

All squares are polygons. Therefore, some polygons are squares.

Mediate Inference consists in deriving a conclusion from two or more logically interrelated premises. Involving an advance in knowledge, it is reasoning that involves the intermediary of a middle term or second proposition which warrants the drawing of a new truth.

Ex: All true Christians are theists.

Paul is a true Christian.

Therefore, Paul is a theist.

Let us see the various types of inferences and their sub classes:

The following outline serves as a guide in understanding the different types of inference according to various classifications.

I. Induction

A. Perfect Induction

B. Imperfect Induction

II. Deduction

A. Immediate Inference

1. Oppositional Inference

a. Contrary Opposition

b. Contradictory Opposition

c. Subaltern Opposition

d. Subcontrary Opposition

2. Eduction

a. Obversion

b. Conversion

c. Contraposition

d. Inversion

3. Possibility and Actuality

B. Mediate Inference

1. Categorical Syllogism

2. Hypothetical Syllogism

a. Conditional Syllogism

b. Disjunctive Syllogism

c. Conjunctive Syllogism

3. Special Types of Syllogism

a. Enthymeme

b. Epichireme

c. Polysyllogism

d. Sorites

e. Dilemma

b) Opposition of proposition –

Opposition of propositions is the traditional way to classify general propositions into four types on the basis of their quality and quantity. We have already discussed this in details in earlier chapters.

Types of opposition –

The opposition relation is of three types.

And we have the oppositions on the basis of

quality = Contrary [ A-E] & sub-contrary [I-O], or

quantity = sub-altern [A-I, E-O] or

both = contradictory [A X O, E X I]

Inference by opposition of proposition –

Opposite or Opposed Propositions Are propositions that cannot be simultaneously true or that cannot be simultaneously false, or that cannot be either simultaneously true or simultaneously false.

This impossibility of being simultaneously true, or false, or either true or false is the essential note of logical opposition.

Propositions are opposed if they have the same subject and predicate but differ from one another in quality or quantity, or both in quality and quantity.

When we draw the opposite of any type as a conclusion on the basis of a proposition that is known, we have an inference by opposition of proposition.

The truth functional relationship between oppositions can help us know how this relation can be effective.

Let us see the table of truth and falsity of opposition relations:

Original || Result → V	A	E	I	O
A	T / F	F / T	T / ?	F / T
E	F / ?	T / F	F / T	T / ?
I	? / F	? / T	T / F	? / T
O	F / T	? / F	? / T	T / F

Using the above table, we can infer the valid conclusions for the inferences based on the opposition relations of propositions.

Opposition of singular propositions

Singular proposition is the proposition having a singular term as its subject. In the four fold classification, this is treated as a universal proposition.

But the only difference is that unlike the general propiositions, the singular propositions do not have subalterns and contradictories. They have only contraries.

So, when we have an opposition relation of an affirmative singular proposition, taken as A, we get an E proposition. But we do not have any other variations in it.

Similarly, when we have an opposition relation of a negative singular proposition, taken as E, we get an A proposition. But we do not have any other variations in it.

This is known as opposition of singular propositions.