[Free]Moods & Figure – categorical propositions [Syllogisms] Logical Reasoning UGC NET Paper-1 Study Notes & MCQ Download PDF for Free

Before Understand Moods & Figure We Have to Understand first What is Categorical Syllogisms & The Structure of Syllogism

A categorical syllogism is an argument consisting of exactly three categorical propositions (two premises and a conclusion) in which there appear a total of exactly three categorical terms, each of which is used exactly twice.

As explained above, a syllogism is made up of 3 propositions, with 2 being premises and 1 as the conclusion. Of the two premises, one will be the minor premise, whereas the other will be a major premise.

In order to differentiate a minor premise from a major premise, we shall first take a look at the conclusion. It has been defined in the last section that a conclusion, being a proposition, will have a subject and a predicate. Although we have already defined a Subject and Predicate, we must also be aware that the Subject and Predicate are also known as terms

there will always be 2 terms in a Categorical Proposition (Subject and Predicate). Therefore, the conclusion of a syllogism will have a Subject and a Predicate as well. Here are two rules to take note of:

1. The Subject of a conclusion will be the Minor Term of the syllogism.
2. The Predicate of a conclusion will be the Major Term of the syllogism.

A syllogism is made up of 2 premises and 1 conclusion. So how do we differentiate between one premise from the other? Simple, take a look at that following two rules:

3. The Premise in which the Minor Term appears will be called the Minor Premise.
4. The Premise in which the Major Term appears will be called the Major Premise.

Let us the following syllogism as an example:

Socrates is a man.

All men are mortal.

Socrates is mortal.

The conclusion of this syllogism is “Socrates is mortal”.
The subject here is “Socrates”, which is also the minor term. “Socrates” appeared within the premise “Socrates is a man” making it the minor premise in this syllogism.
Socrates is a man. ← Minor premiseAll men are mortal.Socrates is mortal.

The predicate of the conclusion will be “mortal”, thus the second proposition, “All men are mortal”, will be the major premise.
Socrates is a man.All men are mortal. ← Major premiseSocrates is mortal.

The middle term will appear in both the minor and major premises, but not in the conclusion. Therefore, the middle term in this syllogism will be “man/men”.
Socrates is a man.All men are mortal.Socrates is mortal.

To summarize:

What is Mood & Figure ?

Mood and Figure
The mood of a categorical syllogism in standard form is a string
of three letters indicating, respectively, the forms of the major
premise, minor premise, and conclusion of the syllogism. Thus,
the mood of the syllogism in Example Given Below is EAE.
Note, however, that syllogisms can have the same mood but still
differ in logical form.

Example 1

1. No birds are mammals.
2. All dogs are mammals.
3. Therefore, no dogs are birds.
   Definition: The major premise of a categorical syllogism (in standard form) is the premise containing the major term.
   Definition: The minor premise of a categorical syllogism (in standard form) is the premise containing the minor term.
   Comment: It follows that, in a standard form categorical syllogism, the first
   premise is the major premise and the second premise is the minor premise

Consider the following example:
Example 2

• No mammals are birds.
• All mammals are animals.
• Therefore, no animals are birds.
• 
  Example 3 also has the form EAE. But, unlike Example 2, it is
  invalid. What’s the difference?
  The syllogisms in Examples 1 and 2 have the following forms, respectively:
  No P are M. No M are P.
  All S are M. All M are S.
  No S are P. No S are P.
  
• These two syllogisms differ in figure.
  
  The figure of a categorical syllogism is determined by the position
  of the middle term. There are four possible figures:
  First Figure
• Second Figure
• Third Figure
• Fourth figure
• M-P P-M M-P P-M
• S-M S-M M-S M-S
  S-P S-P S-P S-P
• 
  The syllogism in Example 1 exhibits second figure. The one in
  Example 2 exhibits third figure.
• 
  Now for the central fact about syllogistic validity:
  The form of a categorical syllogism is completely determined
  by its mood and figure.
• 
  Aristotle worked out exhaustively which combinations of mood and
  figurec result in valid forms and which result in invalid forms. Thus,
  the form of Example 2 (“EAE-2”) is valid; that of Example 3 (“EAE3”) is invalid.
  There are 256 combinations of mood and figure (64 (4 × 4 × 4)
  moods × 4 figures). Only fifteen are valid.
  
  The valid syllogistic forms
  First figure: AAA, EAE, AII, EIO
  Second figure: EAE, AEE, EIO, AOO
  
• Third figure: IAI, AII, OAO, EIO
  Fourth figure: AEE, IAI, EIO
• 
  In working out the valid forms, Aristotle made an assumption that
  is rejected by most modern logicians, namely, that all terms deno
  nonempty classes. On this assumption, nine more forms turn out
  valid in addition to the fifteen above.
  Forms valid in Aristotelian logic only
  First figure: AAI, EAO
  Second figure: AEO, EAO
  Third figure: AAI, EAO
  Fourth figure: AEO, EAO, AAI

Types of Proposition

All forms of Propositions can exist in one of 4 different types. These 4 types are denoted by the code letters A,E,I,O. These code letters are derived from the 2 Latin vowels affirmo and nego.

Type A proposition

Type A – Universal Affirmative proposition
All of the subject will be distributed in the class defined by the predicate.

Example:
All birds have wingsType E proposition

Type E – Universal Negative proposition
None of the subject will be distributed in the class defined by the predicate.

Example:
No birds have gillsType I and O proposition

Type I – Particular Affirmative proposition
Some of the subject will be distributed in the class defined by the predicate.

Example:
Some birds can fly

Type O – Particular Negative proposition
Some of the subject will not be distributed in the class defined by the predicate.

Example:
Some birds cannot fly

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