Immediate Inference - Eduction

is a type of immediate inference in which we deduce the truth of other propositions with a different structure from a given proposition.

Rule:  Particular terms cannot be turned into universal. What is true to some may not be true to all.

For example:

                All men are mortals.

From this proposition, I can deduce an apparently equivalent proposition: Some mortals are men, but NOT all mortal are men.

Remember that we do not give additional knowledge when we deduce propositions from a given proposition when we use eduction. In fact, all other new propositions deduced from a given proposition are not something new. In meaning, they are the same with the original proposition.

Kinds of Eduction:

1.       Conversion – it is done by simply interchanging the subject and the predicate. We call the original proposition convertend, and the new proposition converse.

Examples:

Convertend                                                                        Converse

All men are mortals.                                                       Some mortals are men.

Some politicians are liars.                                             Some liars are not politicians.

No stones are flowers                                                   No flowers are stones.

Some animals are not mammals.                              no converse

2.       Obversion – it is done by changing the quality of the proposition (from affirmative to negative, from negative to affirmative) and replacing the predicate with its contradictory. We call the original proposition obvertend, and the new proposition obverse.

Examples:

Obvertend                                                                          Obverse

All men are mortals.                                                       No men are non-mortals.

Some politicians are liars.                                             Some politicians are not non-liars.

No stones are flowers.                                                  All stones are non-flowers.

Some animals are not mammals.                              Some animals are non-mammals.

3.       Contraposition 1 – It is done by doing obversion, and then conversion. We call the original proposition contraposend  and the new proposition contraposit 1.

Examples:

Contraposend                                                                   Contraposit 1

All men are mortals.                                                       No non-men are mortals.

Some politicians are liars.                                             no contraposend 1

No stones are flowers.                                                  Some non-flowers are stones.

Some animals are not mammals.                              Some non-mammals are animals.

4.       Contraposition 2 – it is done by doing obversion, then conversion, then obversion again. We call the original proposition contraposend and the new proposition contraposit 2.

Examples:

Contraposend                                                                   Contraposit 2

All men are mortals.                                                       All non-men are non-mortals.

Some politicians are liars.                                             no contraposend 2

No stones are flowers.                                                  Some non-flowers are not non-stones.

Some animals are not mammals.                              Some non-mammals are not non-animals.

Immediate Inference - Oppositional Inference

A.      Oppositional Inference – it is a type of immediate inference in which we deduce the truth value of another proposition (can be A, E, I, O) from a given truth value of a proposition of the same structure.

Example:

                                “All men are mortals” is true.

                                Therefore, “No men are mortals” is _______.

                                The answer is false.

Types of Oppositional Inference:

1.       Contrary – it is the opposition between A and E propositions.

                        Rule: If one is true, the other is false. If one is false, the other is unknown.

Example:

        If one is true:

                        (A) All men are mortals. – True                  (E) No men are angels. – True

                        (E) No men are mortals. – False                 (A) All men are angels. – False

        If one is false:

                        (A) All men are angels. – False                   (E) No men are mortals. – False

                        (E) No men are angels. – Unknown         (A) All men are angels. – Unknown

Explanation: If one is false, we cannot immediately infer that the other is true because it might be the case that if one is false the other might also be false. Hence, the better answer is unknown.

2.       Sub-contrary – it is the opposition between I and O propositions.

                        Rule: If one is true, the other is Unknown. If one is false, the other is true.

Example:

        If one is true:

                        (I) Some animals are mammals. – True                  

                        (O) Some animals are not mammals. – Unknown

                        (O) Some animals are not mammals. – True

                        (I) Some animals are mammals. – Unknown

Explanation: If one is true, we cannot immediately infer that the other is false since it is possible that the other could also be true; hence, Unknown.

        If one is true:

                        (I) Some animals are flowers. – False                     

                        (O) Some animals are not flowers. – True

                        (O) Some mammals are not animals. – False

                        (I) Some mammals are animals. – True

3.       Sub-altern – it is the opposition between A & I propositions and E & O propositions.

Rule:      If the universal proposition is true, the particular proposition is true. If the universal proposition is false, the particular proposition is Unknown.

                If the particular proposition is false, the universal proposition is false. If the particular proposition is true, the universal proposition is Unknown.

Example:

        If the universal is true:

                        (A) All men are mortals. – True                  (E) No men are angels. – True

                        (I) Some men are mortals. – True             (O) Some men are not angels. – True

If the universal is false:

                (A) All men are angels. – False                   (E) No men are mortals. – False

                (I) Some men are angels – Unknown      (O) Some men are not mortals. Unknown

Explanation: If the universal is false, we cannot immediately infer that the particular is also false since it is possible that the particular can be true.

If the particular is true:

                (I) Some animals are mammals. – True

                (A) All animals are mammals. – Unknown

                (O) Some animals are not mammals. – True

                (E) No animals are not mammals. – Unknown

Explanation: If the particular is false, it is possible that the universal can be true or can be false; hence, Unknown.

If the particular is false:

                (I) Some animals are mammals. – False

                (A) All animals are mammals. – False

                (O) Some animals are not mammals. – False

                (E) No animals are not mammals. – False

4.       Contradictory – the opposition between A & O propositions and E & I propositions.

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

Examples:

 (A) All men are mortals. – True | False

(O) Some men are not mortals. – False | True

(O) Some men are not mortals. – False | True

(A) All men are mortals. – True | False

(E) No men are angels. – True | False

(I) Some men are angels. – False | True

(I) Some men are angels. – False | True

(E) No men are angels. – True | False

INFERENCE

Inference – it is a process by which the mind proceeds from one proposition to another proposition seen to be implied in the former. It is the fundamental element in an argument. Without inference, there can never be an argument.

Example:

                Givens                                                                                                  Therefore:

The cloud is dark.                                                             It will rain.

All people have dignity.                                                 That poor man has dignity.

“All people are mortals” is true.                                 “Some people are not mortals” is false.

Some politicians are corrupt.                                      Some corrupt people are politicians.

Two Kinds of Inference

1.       Mediate Inference – an inference which requires a mediating proposition.

Example:

(a)    All people are mortals.

(b)   Socrates is a person.

(c)    Therefore, Socrates is mortal.

It is a mediate inference because we cannot arrive from (a) to (c) without going through (b).

Other example:

(a)    Some students are rich.

(b)   She is a student.

(c)    Therefore, she might be rich.

2.       Immediate Inference – a kind of inference which does not require a mediating proposition.

Example:

(a)    No people are immortals.

(b)   Therefore, all people are mortals.

(a)    All objects occupy space and have mass.

(b)   Therefore, there are no objects that do not occupy space and have no mass.

There is no need for a mediating proposition here. You proceed from (a) to (b) without going through any proposition.

Caution: There are inferences which seem to be an immediate inference but will be found to be mediate inferences upon careful analysis.

Example:

(a)    The cloud is dark.

(b)   Therefore, it will rain.

It seems that there is no need for us to go through a mediating proposition to arrive at proposition (b). However, if we analyze it carefully we will discover that proposition (a) is not enough in order for us to arrive at proposition (b). This entails that there is a hidden proposition which mediates (a) and (b). That mediating proposition is: “Whenever the cloud is dark, it will rain.”

Other examples:

(a)    Today is February 14.

(b)   Therefore, it is Valentine’s Day.

(a)    Students must be diligent in their students.

(b)   Therefore, you must be diligent.