Categorical Syllogism

Categorical Syllogism एक deductive argument है जिसमें तीन categorical propositions (two premises + one conclusion) होते हैं, और three terms होते हैं, जिनमें से प्रत्येक exactly two propositions में आता है।

Example:

• Premise 1 (Major): All humans are mortal. (All M are P)
• Premise 2 (Minor): Socrates is a human. (All S are M)
• Conclusion: Therefore, Socrates is mortal. (All S are P)

• Major Term (P) — प्रमुख पद: वह term जो conclusion का predicate है। (Mortal in the example)
• Minor Term (S) — गौण पद: वह term जो conclusion का subject है। (Socrates in the example)
• Middle Term (M) — मध्य पद: वह term जो both premises में आता है, लेकिन conclusion में नहीं आता। (Humans in the example)

Identification:

• Major Premise: वह premise जिसमें Major Term (P) होता है
• Minor Premise: वह premise जिसमें Minor Term (S) होता है
• Middle Term (M): दोनों premises में आता है, conclusion में नहीं

Example:

• Major Premise: All humans (M) are mortal (P)
• Minor Premise: Socrates (S) is a human (M)
• Conclusion: Socrates (S) is mortal (P)

Mood syllogism में three propositions (two premises + one conclusion) के types (A, E, I, O) का sequence है।

Example:

• All M are P = A
• All S are M = A
• All S are P = A
• Mood = AAA

Another Example:

• All M are P = A
• Some S are M = I
• Some S are P = I
• Mood = AII

Total Possibilities: 4×4×4 = 64 possible moods (but only some are valid).

Figure syllogism में middle term (M) की position को दर्शाता है — M किस term के साथ और कहाँ आता है।

Four Figures:

• Figure 1: M — P (Major), S — M (Minor) → M is subject of major and predicate of minor
• Figure 2: P — M (Major), S — M (Minor) → M is predicate of both
• Figure 3: M — P (Major), M — S (Minor) → M is subject of both
• Figure 4: P — M (Major), M — S (Minor) → M is predicate of major and subject of minor

Visual Representation:

• Figure 1: M — P / S — M → ∴ S — P
• Figure 2: P — M / S — M → ∴ S — P
• Figure 3: M — P / M — S → ∴ S — P
• Figure 4: P — M / M — S → ∴ S — P

A syllogism is in standard form when:

• Premises are in proper order (Major premise first, then Minor premise)
• Conclusion is stated last
• Propositions are in standard categorical form (A, E, I, O)

Standard Form Structure:

• Major Premise: contains Major Term (P) and Middle Term (M)
• Minor Premise: contains Minor Term (S) and Middle Term (M)
• Conclusion: contains Minor Term (S) and Major Term (P)

Example:

• Major Premise: All M are P
• Minor Premise: All S are M
• Conclusion: All S are P
• Mood and Figure: AAA-1

A syllogism is valid only if it follows all these rules:

• Rule 1 (Distribution of Middle Term): The middle term must be distributed at least once. (M must be distributed in at least one premise)
• Rule 2 (Distribution of Terms in Conclusion): If a term is distributed in the conclusion, it must be distributed in the premise. (No term can be distributed in conclusion if not distributed in premise)
• Rule 3 (Quality of Premises): Two negative premises are not allowed. (At least one premise must be affirmative)
• Rule 4 (Quality of Conclusion): If either premise is negative, the conclusion must be negative. If both premises are affirmative, conclusion must be affirmative.
• Rule 5 (Existential Import): If both premises are universal, the conclusion cannot be particular (unless existential import is assumed).
• Rule 6 (From Two Particulars): Two particular premises are not allowed.
• Rule 7 (Particular Premise with Negative): If one premise is particular and the other is negative, the conclusion cannot be universal.

Steps to Test Validity:

• Step 1: Identify the Major, Minor, and Middle Terms
• Step 2: Identify the Mood (A, E, I, O sequence)
• Step 3: Identify the Figure (position of Middle Term)
• Step 4: Check all 7 rules — if any rule is violated, the syllogism is invalid
• Step 5: If all rules are satisfied, the syllogism is valid

Valid Mood-Figure Combinations (Traditional):

• Figure 1: AAA, EAE, AII, EIO, (AAI), (EAO)
• Figure 2: EAE, AEE, EIO, AOO, (EAO), (AEO)
• Figure 3: AII, EIO, IAI, OAO, (AAI), (EAO)
• Figure 4: AEE, IAI, EIO, (AAI), (EAO), (AEO)

Note: Moods in parentheses require existential import (valid only if the subject class exists).

Existential Fallacy तब होता है जब एक valid syllogism में universal premises से particular conclusion निकाला जाता है, बिना यह माने कि subject class का existence confirmed है।

Example (Invalid in Boolean):

• Major Premise: All M are P (A)
• Minor Premise: All M are S (A)
• Conclusion: Some S are P (I)
• Mood: AAI (Figure 3)
• In Traditional logic, this is valid (assuming M exists).
• In Boolean logic, this is invalid because the conclusion has existential import but premises do not.

Key Point:

• Universal propositions (A and E) do not assert existence in Boolean interpretation.
• Particular propositions (I and O) do assert existence.
• So, from universal premises, we cannot derive a particular conclusion in Boolean logic without a separate existence assumption.

• Categorical Syllogism: 3 propositions, 3 terms, each term used twice
• Major Term (P): Conclusion predicate
• Minor Term (S): Conclusion subject
• Middle Term (M): Appears in both premises, not in conclusion
• Mood: Sequence of A, E, I, O in (Major, Minor, Conclusion)
• Figure: Position of Middle Term (1-4)
• Standard Form: Major Premise → Minor Premise → Conclusion
• Rules: 7 rules to test validity
• Existential Fallacy: Universal premises → Particular conclusion without existence assumption

• Trap 1: Major Term = Predicate of conclusion → ✅ True
• Trap 2: Minor Term = Subject of conclusion → ✅ True
• Trap 3: Middle Term = appears in conclusion → ❌ Middle term does NOT appear in conclusion.
• Trap 4: Two negative premises are allowed → ❌ Two negative premises are NOT allowed.
• Trap 5: If conclusion is negative, both premises must be negative → ❌ At least one premise must be negative, but not necessarily both.
• Trap 6: Existential fallacy = always invalid → ❌ In Traditional logic it's valid; in Boolean logic it's invalid.
• Trap 7: Mood = Figure → ❌ Mood and Figure are different concepts.

In the syllogism "All cats are animals. All animals are living things. Therefore, all cats are living things." Identify the Middle Term.

• A. Cats
• B. Animals
• C. Living things
• D. None of these

Explanation: Middle term appears in both premises but not in conclusion — "animals" is the middle term.

What is the mood of: "All M are P. All S are M. Therefore, All S are P."

• A. AAA
• B. AAE
• C. EAE
• D. AAI

Explanation: All three propositions are A (Universal Affirmative) → Mood = AAA.

In the syllogism "All M are P. All S are M. Therefore, All S are P." what is the figure?

• A. Figure 1
• B. Figure 2
• C. Figure 3
• D. Figure 4

Explanation: M is subject of major (M—P) and predicate of minor (S—M) → Figure 1.

Which rule is violated by: "All M are P. Some S are not M. Therefore, Some S are not P."

• A. Middle term not distributed
• B. Two negative premises
• C. Illicit major
• D. Illicit minor

Explanation: M appears as subject in "All M are P" (distributed) but in "Some S are not M" (predicate — not distributed). M is not distributed in either premise → Rule 1 violated.

Which syllogism commits the existential fallacy in Boolean interpretation?

• A. AAA-1
• B. AAI-3
• C. EAE-1
• D. AEE-2

Explanation: AAI-3 has universal premises (A and A) and a particular conclusion (I) → existential fallacy in Boolean logic.

Which of the following is a valid mood in Figure 1?

• A. AII
• B. EIO
• C. AAA
• D. All of the above

Explanation: AAA-1, AII-1, and EIO-1 are all valid moods in Figure 1.

Terms:

• Major Term (P): Conclusion Predicate
• Minor Term (S): Conclusion Subject
• Middle Term (M): In both premises, NOT in conclusion

Mood & Figure:

• Mood: A, E, I, O sequence (Major, Minor, Conclusion)
• Figure: Position of Middle Term (1-4)

7 Rules:

• 1. M distributed at least once
• 2. If term distributed in conclusion → distributed in premise
• 3. No two negative premises
• 4. Negative premise → Negative conclusion; Affirmative premises → Affirmative conclusion
• 5. Universal premises → No particular conclusion (without existential import)
• 6. No two particular premises
• 7. Particular + Negative → No universal conclusion

Existential Fallacy:

• Universal premises → Particular conclusion (invalid in Boolean, valid in Traditional if existence assumed)

Exam Formula:

UGC NET में Categorical Syllogism के questions terms identification, mood-figure, rules, और existential fallacy पर based होते हैं।