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**UGC NET Exam Study Notes on â€śStructure of Categorical propositionsâ€ť and â€śMood and Figureâ€ť**

Topics Based on UGC NET Syllabus** of Logical Reasoning**

**Understanding the structure of arguments: argument forms, the structure of categorical propositions, Mood and Figure, Formal and Informal fallacies, Uses of language, Connotations, and denotations of terms, and Classical square of opposition.****( This is a Big Section, Categorical Propositions & Mood and Figure Part is covered in this article,Other topics covered as well)****Evaluating and distinguishing deductive and inductive reasoning.****Analogies.****Venn diagram: Simple and multiple uses for establishing the validity ofÂ arguments.****Indian Logic: Means of knowledge.****Pramanas: Pratyaksha (Perception), Anumana (Inference), Upamana(Comparison), Shabda (Verbal testimony), Arthapatti (Implication) andÂ Anupalabddhi (Non-apprehension).****Structure and kinds of Anumana (inference), Vyapti (invariable relation), Hetvabhasas (fallacies of inference).**

#### What are the Categorical Propositions?

A â€ś**Subject**â€ť of a sentence is the thing that has some property or class is being attributed to, the **â€śPredicateâ€ť **is the property or class that is being attributed to the subject, and the â€ś**Copula**â€ť is the word that links the two together.

For Example â€“ All dogs are mammals

Here, â€śdogsâ€ť is the subject, â€śmammalsâ€ť is the predicate, and â€śareâ€ť is the copula. This particular statement about bunnies has a certain form, the form of a categorical proposition.

So in simple words, â€śA proposition that relates two classes or categoriesâ€ť is known as a **Categorical Proposition**.

If you look at the above example in addition to subject, predicate and coupla it also has â€ś**quantifiers**â€ť that tells you HOW MANY of the subjects are being referred into the statement.

**Categorical propositions tell us one of four things:**(1) ALL members of the subject class are included in the predicate class.

(2) NONE of the members of the subject class are included in the predicate class.

(3) SOME of the members of the subject class are included in the predicate class.

(4) SOME of the members of the subject class are NOT included in the predicate class.

**Here are some examples of each of these 4 kinds of the categorical proposition:**(1) All dogs are mammals.

(2) No dogs are reptiles.

(3) Some dogs are cute.

(4) Some dogs are not potty-trained.

**Here is the FORM of each of these 4 kinds of categorical proposition:**(1) All S are P.

(2) No S are P.

(3) Some S are P.

(4) Some S are not P

**Now, letâ€™s go over some definitional terms: Categorical statements each have a quantity and a quality.**

Quantity: Refers to HOW MUCH of the subject class is included in the predicate class.

*Quantity is either:*

(a) Universal â€“ Tells us something about how ALL of the subjects are related to the predicate.

(b) Particular â€“ Tells us how SOME of the subjects are related to the predicate.

Quality: Refers to whether the proposition is AFFIRMING something or DENYING something of a subject.

*Quality is either:*

(a) Affirmative â€“ Members of the subject ARE included in the predicate.

(b) Negative â€“ Members of the subject are NOT included in the predicate.

*For instance, of the 4 kinds of the categorical proposition we discussed above:*

Proposition | Quantity | Quality | Letter |

All S are P. | universal | affirmative | A |

No S are P. | universal | negative | E |

Some S are P. | particular | affirmative | I |

Some S are not P. | particular | negative | O |

Those letters are A, E, I, and O.

Now, you must be wondering what are these â€śA, E, I, Oâ€ť, Letâ€™s understand with more examples.

**A is universal positive.**- All apples are good.
- All milk is white .

**EÂ Is universal negative.**- No bread is butter.
- No egg is white.

**I is particular positive**- Some apples are good.

- Some bread is butter.

- Some eggs are white.

**O is particular negative**- No apple are good.
- No bread is butter.
- NO eggs are white.

**Categorical Syllogisms**

**Syllogism**: An argument consisting of three statements: TWO premises and ONE conclusion.

**Categorical syllogism:** A syllogism consisting of three categorical propositions, and containing THREE DISTINCT TERMS, each of which appears in exactly two of the three propositions.

So, what are these 3 terms mentioned? Consider the following syllogism:

- All
**mammals**are**creatures that have hair**. - All
are*dogs***mammals**. - Therefore, all
**dogs**are**creatures that have hair**.

There are THREE different terms in this argument (besides the quantifiers and the copulas). The three different terms are called the â€ś**major term**â€ť, the â€ś**minor term**â€ť, and the â€ś**middle term**.â€ť

Notice that the conclusion only contains TWO of the three terms but one of the terms is

found only on the premises.

Here are some definitions:

Major Term: The predicate term of the conclusion (above, â€ścreatures that have hairâ€ť)

Minor Term: The subject term of the conclusion (above, â€śdogsâ€ť)

Middle Term: The term that does NOT appear in the conclusion (above, â€śmammalsâ€ť)

*Finally, note that premise 1 contains the major term, while premise 2 contains the minor term. Premise 1 is therefore called the major premise, while premise 2 is called the minor premise. The standard form demands that the major premise (i.e., the one containing the major term) ALWAYS be listed first.*

Easy to grasp right? We will cover a very simple trick to remember these â€śthere termsâ€ť and this question is the favourite of a UGC NET examiner from the last few years.

**Warning!**Â Tricks to remember â€śMAJORâ€ť, â€śMINORâ€ť andÂ â€śMIDDLEâ€ť terms.Â Letâ€™s take another example.

- Statement 1 â€“ All A are B .
- Statement 2 â€“ All B are C .
- Conclusion â€“ All A are C .

Here â€“Â

- Statement first is also known as premises 1 and Statement second is also known as premises 2.
- In the above statement â€śBâ€ť is the
**middle term**which is also known as**cancelling term**and in Indian logic known as â€ś**Hetu**â€ť. - In the above statement â€śAâ€ť is minor term and â€śCâ€ť is major term.

Now, how to find out which one is major term, minor term and middle term?

**MAJOR TERM â€“** Â Â the term in a syllogism that is the predicate of the conclusion is known as major term .

*You should always check â€śconclusionâ€ť for major term. For example is above statement, the conclusion is All A are C . *So, the last term in the conclusion that is C is your major term.Â

**Example 1**â€“ If the conclusion is â€ś All parrots are greenâ€ť

So, in the above statement â€śgreenâ€ť is major term.

**Example 2**â€“ No apple is good .

So, in the above statement â€śgoodâ€ť is your major term .

**Tip**â€“ second word of your conclusion is always your **major** term.

**MINOR TERM- **the term in a syllogism that is the subject of the conclusion is known as Minor term. It is also known as subject.

You always should look into conclusion to find out Minor term. Remember- major term was the last term of conclusion but Minor term is the first term in the conclusion .

This Minor term is known as **â€śpakshaâ€ť .**

Remember it as â€“ it is in the increasing order that is it goes from small to big. In the above given statement our conclusion isÂ â€ś**All A are Câ€ťÂ **so, in this statement â€śaâ€ť is minor term because A is the first term in the conclusion. Â

For more clarity have a look on the given examples :

1^{st} example â€“ Â No blackboard is green

- Minor term â€“Â blackboard
- Major term â€“ green

2^{nd} example â€“ some bread is butter

- Minor term- bread
- Major term â€“ butter

**MIDDLE TERM-** In syllogism, a middle term is a term that appears in both premises but not in the conclusion of a categorical syllogism. This is also known as cancelling term and Indian logic this is known as â€śHetuâ€ť or â€śReasonâ€ť.

To find out which one is middle term, you always should look into premises. Middle term never appears in the conclusion.

The term which is present in both premises- premises 1 and premises 2 is called middle term.

The mutual term present in both statements are called middle term.

Example 1

- Statement1 â€“ some breads are milk .
- Statement2- some milk is butter .

Conclusion â€“ some butter are Â bread .

In this given statement â€ś milkâ€ť is the mutual word available in both statements.Â So, milk is our middle term . Observe carefully â€ś Milk is not present in conclusionâ€ť.

Â

## Mood and Figure

Now that we know the correct FORM of categorical syllogisms, we can learn some tools that will help us to determine when such syllogisms are valid or invalid.

All categorical syllogisms have what is called a â€śmoodâ€ť and a â€śfigure.â€ť

*What are mood and Figures?*

**Mood**: The mood of a categorical syllogism is a series of three letters corresponding to the type of proposition the major premise, the minor premise, and the conclusion is (A, E, I, or O).

Mediaeval logicians invented a simple method of labelling the various forms in which a categorical syllogism may occur by simply stating its mood and figure.

**Mood **â€“Â It usually depends upon the type of propositions (A, E, I, O).

**Figure** â€“ It depends on the arrangement of the middle term in the proposition.

The figure of the syllogism is based on the arrangement of Subject and predicate and middle term or the common term.

The different types of figures in syllogism are:

First figure |
Second figure |
Third figure |
Fourth figure |

M-P | P-M | M-P | P-M |

S-M | S-M | M-S | M-P |

S-P | S-P | S-P | S-P |

Tips to remember this above table-

- In first figure â€“ M makes a sort of vertical right hand like this â€ś \â€ť.
- In second figure- M makes a straight hand in right direction like this â€ś|â€ť in right hand side.
- In Third figure- M makes a right hand is left direction like this â€ś|â€ť in left hand side.
- In Fourth figure- M makes a sort of vertical left hand like this â€ś/â€ť .

There is 256 combination of the different forms of mood and figure. Out of these 256 combinations, only 15 were found to be valid by Aristotle. There are 9 conditionally valid argument forms for categorical syllogisms in addition to the 15 unconditionally valid argument forms: The valid combinations are given below in the table.

Â

Unconditionally Valid Forms: There are 15 combinations of mood and figure that are valid from the Boolean standpoint (we call these â€śunconditionally validâ€ť argument forms).

The below chart depicts ALL of 15 the unconditionally valid argument forms

First figure | AAA,EAE,AII,EIO |

Second figure | EAE,AEE,EIO,AOO |

Third figure | IAI, AII, OAO, EIO |

Fourth figure | AEE,IAI,EIO |

Recall this argument from earlier:

- All mammals are creatures that have hair.
- All dogs are mammals.
- Therefore, all dogs are creatures that have hair.

*Its mood is â€śAAAâ€ť since all three propositions are â€śAâ€ť propositions (i.e., they are all of the forms â€śAll S are Pâ€ť). Its figure is â€śfigure 1â€ť*

**Points to keep in mind( only for the first figure)**

- If both the premises are positive (A or I), then the conclusion will also be positive (A Or I)
- If one of the premises is negative (E or O), then the conclusion will also be negative (E or O).
- If one of the premises is particular (I or O), then the conclusion will also be particular (I or O)
- If one of the premises is particular negative (O) , then the conclusion will aslo be particular negative .
- If one of the premises is particular and the second one is negative, then also the conclusion will be particular negative (0).

**Some of the mood and figure** **examples**

**Examples of the First figure **

**AAA**

- Major premises : All B are C.
- Minor premises : All A are B.
- Conclusion :Â All A are C.

**EAE**

- Major premises : No B are C.
- Minor premises : All A are B.
- Conclusion : No A are C.

**AII**

- Major premises : All B are C.
- Minor premises : Some A are B.
- Conclusion : Some A are C.

**EIO**

- Major premises : No B are C.
- Minor premises : some A are B.
- Conclusion : some A are not C.

*Special cases*

**AAI**

- Major premises :All B are C.
- Minor premises : All A are B.
- Conclusion : Some A are not C.

**EAO**

- Major premises : No B are C.
- Minor premises : All A are B.
- Conclusion : Some A are not C.

**Examples of the second figure**

**EAE**

- Major premises : No C are B.
- IMinor premises : All A are B
- Conclusion : No A are C.

**AEE**

- Major premises : All C are B
- Minor premises : No A are B.
- Conclusion :No A are C.

**EIO**

- Major premises: No C are B.
- Minor premises : Some A are B
- Conclusion : Some A are not C.

**AOO**

- Major premises : All C are B .
- Minor premises : Some A are not B.
- Conclusion : Some A are not C.

**Special cases**

**AEO**

- Major premises : All C are B.
- Minor premises : No A are B.
- Conclusion : Some A are not C

**EAO**

- Major premises : No C are B.
- Minor premises : All A Are B.
- Conclusion : Some A are not C.

**Examples of the Third figure**

**IAI**

- Major premises : Some B are C.
- Minor premises : All B are A.
- Conclusion : Some A are C.

**A**II

- Major premises: All A are C.
- Minor premises :Some B are A.
- Conclusion: Some A are C.

**OAO**

- Major premises : Some B are not C.
- Minor premises: All B are A.
- Conclusion: Some A are not C.

**EIO**

- Major premises : No B are C.
- Minor premises : some B are A.
- Conclusion : some A are not C

**Special cases**

**AAI**

- Major premises : All A are C.
- Minor premises :All B are A.
- Conclusion : Some A are C.

**EAO**

- Major premises :No B are C.
- Minor premises :All B are A.
- Conclusion : some A are not C.

**Examples of the Fourth figure**

**AEE**

- Major premises : All C are B.
- Minor premises : No B are A.
- Conclusion : No A are C

**IAI**

- Major premises : Some C are B.
- Minor premises : All B are A .
- Conclusion : Some A are C .

**EIO**

- Major premises : No C are B .
- Minor premises : Some B are A.
- Conclusion : Some A are not C.

**Special cases**

**AEO**

- Major premises :All C are B.
- Minor premises :No B are A.
- Conclusion : Some A are not C.

**EAO**

- Major premises : No C are B
- Minor premises :All B are A.
- Conclusion : Some A are not C.

**AAI**

- Major premises : All C are B.
- Minor premises : All B are A.
- Conclusion :Some A are C.

**Solved MCQ Based on Mood and Figure**

**Identify the mood and figure of the following syllogism:**

**Question 1 â€“ **Â

- some B are A
- All B are C
- Some A areÂ C

**Options **:

- IAI â€“ 3 [Answer]
- IAI â€“ 2
- IAI â€“ 1
- IAI â€“ 4

**Question 2 â€“ **

- No A are B
- ALL c are B
- NO A are C

**Options **:

- EAE -3
- EAE â€“ 2 [Answer]
- EAE â€“ 1
- EAE â€“ 4

**Question- 3 **

- All C are A
- Some B are A
- Some C are A

**Options **:

- First [Answer]
- Second
- Third
- Fourth

#### References â€“

*Study Notes from â€“ https://rintintin.colorado.edu/~vancecd/phil1440/notes.html*

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