kinds of reasoning

8/9/2019 Kinds of Reasoning

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KINDS OF REASONING


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Deductive Reasoning

Deductive reasoning is one of the two basic forms of

valid reasoning.

It works from the more general to the more specific.

Reasons based on laws and rules.

Example:

All men are mortal.

Socrates is a man.

(Therefore,) Socrates is a mortal.

One of the most common and useful forms of deductive

reasoning is the syllogism.


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Inductive Reasoning

It is essentially the opposite of deductive reasoning.

It works from the particular to general.

Reasons based on observation.

Strong Induction

All observed crows are black.

Therefore, all crows are black.

A strong induction is thus an argument in which the truth of the

premises would make the truth of the conclusion probable, but

not necessary.


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Inductive Reasoning

Weak Induction

I always hang pictures on nails.

therefore, all pictures hang from nails.

The link between the premise and the inductive conclusion is weak.


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CATEGORI

CAL SYLLOGISM


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Categorical Syllogism

Syllogism is derived from the Greek word which

means conclusion, or inference.

Categorical syllogism is a deductive argument

consisting of three categorical propositions that

together contain exactly three terms, each of which

occurs in exactly two of the constituent propositions.


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BASIC STRUCTURE

A categorical syllogism consists of three parts:

Major premise

- contains the major term. (predicate of the

conclusion)

Minor premise

- contains the minor term. (subject of theconclusion)

Conclusion


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Example:

Major premise: All humans are mortal.

Minor premise: Some animals are human.Conclusion: Some animals are mortal.


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Formal Aspects of Categorical Syllogism

There are two formal aspects of syllogisms

necessary to the determination of validity.

MOOD FIGURE


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Moods of Categorical Syllogism

Moods are defined as the arrangement of the

premises according to quantity (universal or

particular) and quality (affirmative or negative).

It is determined by the logical forms of the

constituent propositions.

Example:

No mammals have gills.

All horses are mammals.

So, no horses have gills.

Mood EAE

-E

-A

-E


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Figures of Categorical Syllogism

The position of the middle term in the premises is called

the figure of the syllogism. Because there are two

premises, and two possible positions in each premise,

there are four figure.

Figure 1 Figure 2 Figure 3 Figure 4

Major premise: M-P P-M M-P P-M

Minor premise: S-M S-M M-S M-S


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Figure 1

MP All animals (M) are a nuisance (P).

SM All dogs (S) are animals (M).

SP Therefore, All dogs (S) are a nuisance (P).

The middle term is the subject of the major premise and the predicate

of the minor premise.

RULES FOR FIGURE 1:

1. The minor premise must be affirmative.

2. The major premise must be universal.


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Figure 2

PM No statesman (P) are good politicians (M).

SM Some journalists (S) are good politicians (M).

SP Therefore, some journalists (S) are not

statesman (P).

The middle term is the predicate of both premises.

RULES FOR FIGURE 2:

1. One premise must be negative.

2. The major premise must be universal.


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Figure 3

MP All writers (M) are intelligent (P).

MS Some writers (M) are American citizens (S).

SP Therefore, Some American citizens (S) are

intelligent (P).

The middle term is the subject of both premises.

RULES FOR FIGURE 3:

1. The minor premise must be affirmative.

2. The conclusion must be particular.


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Figure 4

PM All Americans (P) are happy people (M).

MS All happy people (M) are fun-loving (S).

SP Therefore, Some fun-loving people (S) areAmericans (P).

The middle term is the predicate of the major premise and thesubject of the minor premise.

RULES FOR FIGURE 4:

1. If the major premise is affirmative, the minor premise must beuniversal.

2. If the minor premise is affirmative, the conclusion must beparticular.

3. If one premise is negative, the major premise must be universal.


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Syllogistic Forms

Figure 1 Figure 2 Figure 3 Figure 4

Barbara Cesare Darapti Bramantip

Celarent Camestres Disamis Camenes

Darii Festino Datisi Dimaris

Ferio Baroco Felapton Fesapo

Bocardo Fresison

Ferison

The letters A, E, I, and O have been used since the

medieval schools to form mnemonic names for the

forms.


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Syllogistic Forms

Barbara

All animals are mortal.

All men are animals.

All men are mortal.

Celarent

No reptiles have fur.

All snakes are reptiles.

No snakes have fur.


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Syllogistic Forms

Darii

All kittens are playful.

Some pets are kittens.

Some pets are playful.

Ferio

No homework is fun.

Some reading is homework.

Some reading is not fun.


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Syllogistic Forms

Cesare

No healthy food is fattening.

All cakes are fattening.

No cakes are healthy.

Camestres

All horses have hooves.

No humans have hooves.

No humans are horses.


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Syllogistic Forms

Festino

No lazy people pass exams.

Some students pass exams.

Some students are not lazy.

Baroco

All informative things are useful.

Some websites are not useful.

Some websites are not informative.


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Syllogistic Forms

Darapti

All fruit is nutritious.

All fruit is tasty.

Some tasty things are nutritious.

Disamis

Some mugs are beautiful.

All mugs are useful.

Some useful things are beautiful.


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Syllogistic Forms

Datisi

All the industrious boys in this school have red hair.

Some of the industrious boys in this school are boarders.

Some boarders in this school have red hair.

Felapton

No jug in this cupboard is new.

All jugs in this cupboard are cracked.

Some of the cracked items in this cupboard are not new.


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Syllogistic Forms

Bocardo

Some cats have no tails.

All cats are mammals.

Some mammals have no tails.

Ferison

No tree is edible.

Some trees are green.

Some green things are not edible.


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Syllogistic Forms

Bramantip

All apples in my garden are wholesome.

All wholesome fruit is ripe.

Some ripe fruit are apples in my garden.

Camenes

All colored flowers are scented flowers.

No scented flowers are grown indoors.

No flowers grown indoors are colored flowers.


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Syllogistic Forms

Dimaris

Some small birds live on honey.

All birds that live on honey are colorful birds.

Some colorful birds are small birds.

Fesapo

No humans are perfect creatures.

All perfect creatures are mythical creatures.

Some mythical creatures are not human.


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Syllogistic Forms

Fresison

No competent people are people who always make

mistakes.

Some people who always make mistakes are people

who work here.

Some people who work here are not competent people.


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RULES FOR VALIDCATEGORICAL

SYLLOGISM


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Rules for Valid Categorical Syllogism

RULE 1:

The middle term must always be taken in the same

sense.

Fallacy: Fallacy of equivocation

Example:

Head is the upper division of the human body.

But, a leader is a head;Therefore, a leader is the upper division of the human

body.


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RULE 2:

In a valid categorical syllogism if a term is

distributed in the conclusion, then it must be

distributed in the premise.

Fallacy: IlicitMajor; IlicitMinor

Example:

All horses are animals.Some dogs are not horses.

Some dogs are not animals.


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RULE 3:

The middle term should not occur in the conclusion.

Fallacy:M

is

placed

midd

le

Example:

Today is Friday;

Today is fine;Today is a fine Friday.


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RULE 4:

The middle term must be distributed at least once.

Fallacy: Undistributedmiddle

Example:

All sharks are fish

All salmon are fishAll salmon are sharks


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RULE 5:

Two affirmative premises cannot give a negative

conclusion.

Fallacy: Negative conclusion drawn from affirmative premises

Example:

All stones are hard;Some diamonds are stones;

Some diamonds are not hard.


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RULE 6:

Two negative premises, nothing follows.

Fallacy: Negative premises

Example:

A chair is not a table;

But, a table is not a pen;A pen is not a chair.


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RULE 7:

If both premises are universal, the conclusion cannot

be particular.

Fallacy: Existential fallacy

Example:

All mammals are animals

All tigers are mammals

Some tigers are animals


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Rules of Valid Categorical Syllogism

RULE 8:

The conclusion follows the weaker premise.

Fallacy: Universal conclusion drawn from a particular

premise/ affirmative conclusion drawn from a negative

premise

Example:

All mongoloids are mentally-retarded;

But, some mongoloids are special children;

All special children are mentally-retarded.

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