Eduction

A. Inference

1. Broad Meaning: any process by which the mind proceeds from one or more propositions seen to be implied in the former.

2. Strict Meaning: the operation by which the mind gets new knowledge by drawing out the implications of what it already knows.

3. Any series of propositions so arranged that the consequent flows from the antecedent.

B. Antecedent

The antecedent is the part of the inference from which the conclusion is drawn or deducted. The antecedent may also be referred to as the premises.

C. Consequent

The consequent is the part of the inference, which signifies the conclusion or the new knowledge, derived from the antecedent. The consequent may also be referred to as the conclusion.

D. Sequence

The sequence is the necessary connection between the antecedent and the consequent.

E. Argument

An argument is “any group of propositions of which one claimed to follow from others, which are regarded as providing support or grounds for the truth of that one.” the group of propositions becomes an argument if it follows a logical structure. It must have a conclusion and a premise or premises.

So, for an inference to be valid there must be a logical sequence, a necessary connection must exist.

Analyze the examples that fallow.

(premise) Roses are red.

(premise) violet are blue.

(conclusion) therefore, I am cute.

This inference is invalid because there is no sequence. There is no reason how the consequent “I am cute” can be inferred from the antecedent.

Some  Examples.

- It is daytime.

therefore, the sun is shining brightly.

Some men are rapists.

- The Pope is a man.

so, the Pope is a rapist.

There is no sequence in this inference; hence, it is also invalid. Being a man does not necessarily mean being a rapist.

- All students are learners.

Lasallians are students.

Therefore, Lasallians are learners.

Immediate and Mediate Inference

Inference involves drawing out a conclusion from the antecedent or the premises. In drawing out the conclusion, two other types of inference, aside from deduction and deduction may be considered: 

The differences between these two types of inference are summarized in the table below.

A. In immediate inference, the conclusion is drawn from only one proposition. In mediate inference, the conclusion passes from two propositions. Study the examples that follow.

B. A medium is an intermediary proposition. It stands between the first proposition of the antecedent and the conclusion. Only mediate inference has a medium because its conclusion passes from two propositions.

Material Eduction

is a type of immediate inference, which emphasizes validity, based on the meaning or thought content suggested by the entirety of the inference.

if the meaning or thought-content suggested by the inference is true, then the inference is said to be materially valid.

Eduction by Added Determinant

the formulation of a new proposition in which the subject and predicate of the original proposition are limited by the addition of a modifier which has exactly the same meaning in relation to both of them.

Original Proposition: Frogs are animals.

New Proposition: Ergo, noisy frogs are noisy animals.  Materially valid

A juggler is a circus performer.

Ergo, a skillful juggler is a skillful circus performer.

A thesaurus is a treasury of words;

ergo, a thick thesaurus is a thick treasury of words.

A soprano is a woman;

ergo, a flat soprano is a flat woman.

A singer is a person;

ergo, a bad singer is a bad person.

Eduction by Complex Conception

is the formulation of a new proposition whose subject consists of term modified by the subject of the original proposition and whose predicate consists of the very same term modified by the predicate of the original proposition. The term that is added is a term that signifies quantitative relations.

A sports complex is a venue for athletic competition; ergo, the owner of a sports complex is an owner of a venue for athletic competition.

A cult is a system of religious belief; therefore, the leader of a cult is the leader of a system of religious belief.

* The newly added term is “leader” once added to the original proposition, it is immediately qualified as :the leader of a cult” and “the leader of a system of religious belief”. The S and P  are in no way affected by the new term added.

Anger is an emotion; therefore,

the expression of anger is the expression of an emotion.

Dogs are animals; therefore, half of the dogs in the world are half of the animals in the world.

Eduction by Omitted Determinant

is the formulation of a new proposition in which the modifier of the original predicate is omitted. A materially valid eduction by omitted determinant retains the truth of the propositions despite the removal of the original modifier of the predicate.

Tanaka is a strong man; ergo,

 Tanaka is a man.

Platinum is a precious kind of metal;

therefore, platinum is a kind of metal.

Some lay people are religious leaders; hence, some lay people are leaders.

Several women are caring mothers; thus, several women are mothers.

A bighorn sheep is not a rational animal; therefore, a bighorn sheep is not an animal.

That he has a million dollar check is a pretended fact; therefore, it is a fact.

New Topic

Eduction is the process of formulating a new proposition by the interchange of subject and predicate of an original proposition and/or by the use or removal of negatives.”

Starting with this module, the student will be introduced to formal rules that govern logical thinking. The different types of immediate inference will first be enumerated to give the student an overview of the upcoming discussions. However, this module will specifically cover the first type of immediate inference only. 

After giving a general definition of eduction, the first type of formal eduction (conversion) will be explained in detail. The emphasis will be more on the formal rules governing conversion. The other types of eduction will be discussed in the latter modules.

Recommended Preparation

Mastery of the following:

1. Quantity of proposition: singular, particular and universal.

2. Quality of propositions: affirmative and negative.

3. Symbols of propositions: A, E, I, O

4. Quantity of predicate; singular, particular and universal.

Conversion

Conversion is “the process of formulating a new proposition by interchanging the subject and predicate of an original proposition but leaving its quality unchanged.”  The original proposition (or the premise) in the process of conversion is called the convertend while the new proposition (or the conclusion) is called the converse.

A. The formal rules governing conversion

1. Interchange the subject and the predicate of the convertend.

2. Retain the quality of the convertend.

3. Do not extend any term

Remember:

1. The A proposition is validly converted via partial conversion (A-I). It is validly converted via simple conversion (A to A) under exceptional circumstances only. 

2. The E Proposition may be validly converted via simple conversion (E to E) or via partial conversion ( E to O).

3. The I proposition can only validly converted via simple conversion (I to I).

4. the O proposition cannot be validly converted.