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Tag: UGC NET Paper 1 Logical Reasoning Study Material

  • UGC NET Paper 1 – UNIT 6 — LOGICAL REASONING

    (For NTA UGC NET Paper I: Teaching & Research Aptitude)

    🎯 1. Purpose of this Unit

    Logical reasoning checks your ability to analyse arguments, evaluate evidence, and draw valid conclusions.
    In NET Paper 1, questions test:

    • The structure of reasoning (statements, premises, conclusions)

    • Valid vs invalid arguments

    • Categorical logic (propositions, syllogisms, square of opposition)

    • Inductive vs deductive logic

    • Venn-diagram validity tests

    • Indian logic (pramāṇas and hetvābhāsas)

    🧠 2. Understanding Arguments

    2.1 Structure of an Argument

    An argument is a group of statements where one (the conclusion) is claimed to follow from the others (the premises).

    Example
    Premise 1: All students are learners.
    Premise 2: Ravi is a student.
    ∴ Conclusion: Ravi is a learner.

    Term Meaning
    Premise Evidence / reason offered
    Conclusion Claim drawn from premises
    Indicator words Therefore, Hence, Thus → conclusion; Since, Because → premise

    ⚙️ 3. Argument Forms

    3.1 Deductive Reasoning

    • Moves from general to specific truth.

    • If premises true → conclusion must be true.

    • Validity matters, not factual truth.

    Form:
    All A are B. All B are C. ∴ All A are C.
    ✅ Valid Syllogism

    3.2 Inductive Reasoning

    • From particular to general.

    • Conclusion probable, not certain.
      Example: Observed 100 swans white ⇒ “All swans are white.”

    3.3 Abductive Reasoning

    • Inference to best explanation.
      Example: Wet road ⇒ Probably rained.

    🔢 4. Categorical Propositions

    A categorical proposition relates two categories (subject & predicate).

    Type Form Example Quantity Quality
    A All S are P All dogs are animals Universal Affirmative
    E No S are P No dogs are cats Universal Negative
    I Some S are P Some students are athletes Particular Affirmative
    O Some S are not P Some students are not athletes Particular Negative

    🧩 5. Classical Square of Opposition

    A (All S are P) ──contradictory── O (Some S are not P)
    │ \‾‾‾‾‾‾‾‾‾‾‾/ │
    │ contrary │
    │ │
    E (No S are P) ──contradictory── I (Some S are P)
    Relation Meaning
    Contradictory Opposite truth values (A ↔ O, E ↔ I)
    Contrary Both cannot be true (A & E)
    Sub-contrary Both cannot be false (I & O)
    Sub-alternation Truth flows downward (A → I; E → O)

    ⚖️ 6. Mood and Figure of Syllogism

    6.1 Mood

    Type sequence of propositions (A/E/I/O) for major, minor, conclusion.
    Example AAA (Barbara), EAE (Celarent).

    6.2 Figure

    Determined by position of the middle term (M).

    Figure Form Example
    1st M–P / S–M ⇒ S–P All men are mortal; Socrates is man ⇒ Socrates mortal.
    2nd P–M / S–M ⇒ S–P No reptile is warm-blooded; All snakes are reptiles ⇒ No snake is warm-blooded.

    🧮 7. Fallacies (Errors in Reasoning)

    7.1 Formal Fallacies (logical structure)

    • Affirming the consequent: p→q, q ⇒ p ❌

    • Denying the antecedent: p→q, ¬p ⇒ ¬q ❌

    7.2 Informal Fallacies (content errors)

    • Ad hominem: attacking person not argument.

    • Straw man: misrepresenting opponent’s claim.

    • False cause (post hoc): assuming A→B because A came first.

    • Circular reasoning: premise repeats conclusion.

    • Appeal to authority: treating authority as proof.

    💬 8. Language: Connotation and Denotation

    Term Meaning Example
    Denotation Literal dictionary meaning “Rose” = flower species
    Connotation Emotional or associated meaning “Rose” = love, beauty

    🔄 9. Analogies

    • Show relation similarity between two pairs.
      Example: Finger : Hand :: Toe : Foot
      Test → Find the same logical relationship (type, function, degree).

    🔷 10. Venn Diagrams & Testing Validity

    • Circles represent sets of objects.

    • Use to verify syllogistic arguments.

    Example:
    All A are B, All B are C ⇒ All A are C ✅
    Draw A inside B, B inside C.

    Common patterns:

    • Overlapping circles → “some”

    • Separate circles → “none”

    • Nested circles → “all”

    🪶 11. Indian Logic (Ānvīkṣikī Tradition)

    11.1 Pramāṇa — Means of Valid Knowledge

    1. Pratyakṣa (Perception): Direct sense experience.

    2. Anumāna (Inference): Reasoning from sign to proposition.

    3. Upamāna (Comparison): Knowledge through similarity.

    4. Śabda (Verbal Testimony): Trustworthy authority or scripture.

    5. Arthāpatti (Postulation / Implication): Presumption to explain facts.

    6. Anupalabdhi (Non-apprehension): Knowledge of absence.

    11.2 Structure of Anumāna (Inference)

    Traditional five steps (Nyāya syllogism):

    1. Pratijñā (Statement): Hill has fire.

    2. Hetu (Reason): Because it has smoke.

    3. Udāharaṇa (Example): Where there is smoke, there is fire (kitchen).

    4. Upanaya (Application): Like that, this hill has smoke.

    5. Nigamana (Conclusion): Therefore hill has fire.

    11.3 Vyāpti (Invariable Relation)

    • Universal relation between hetu (reason) and sādhya (conclusion).

    • Example: Smoke → Fire (always co-exist).

    11.4 Hetvābhāsas (Fallacies of Inference)

    Type Nature Example
    Asiddha Unproven reason Sky lotus fragrant (but no lotus exists).
    Viruddha Contradictory reason Fire is cold because it is fire.
    Satpratipakṣa Counter-reason Hill has no fire because there is water.
    Bādhita Opposed by perception Fire is cool (conflicts with experience).
    Anaikāntika Inconclusive / non-exclusive Crow visible ⇒ daytime (not always).

    🧭 12. Evaluating Deductive vs Inductive Reasoning

    Feature Deductive Inductive
    Direction General → Specific Specific → General
    Strength Certainty (if valid) Probability only
    Basis Logic of form Observation & pattern
    Example All humans mortal → Socrates mortal 100 crows seen black → All crows black

    🔍 13. Common Question Types in NET

    1. Identify valid/invalid argument.

    2. Determine type of proposition (A/E/I/O).

    3. Find contradictory statement.

    4. Use Venn diagram for syllogism.

    5. Spot logical fallacy.

    6. Apply Indian logic (pramāṇa, hetvābhāsa).

    7. Match deductive/inductive features.

    8. Solve analogy pattern reasoning.

    🧩 14. Shortcut Revision Map

    Concept Key Clue
    Argument = Premises + Conclusion Test validity via form
    A/E/I/O forms All/No/Some/Some not
    Square of Opposition A↔O contradictory
    Valid form p→q; p ⇒ q ✔️
    Fallacy Form invalid or premise irrelevant
    Venn diagram All = subset, Some = overlap, None = disjoint
    Indian Logic 6 Pramāṇas, 5 steps of Anumāna, 5 Hetvābhāsas

    🧠 15. Preparation Strategy

    Step Action
    1 Memorize A/E/I/O propositions & square.
    2 Practise truth-tables & syllogisms.
    3 Draw Venn diagrams for common patterns.
    4 Review Indian logic terms daily (Pratyakṣa → Anumāna → Hetvābhāsa).
    5 Attempt mock MCQs — mix concept + diagram + terminology.

    ✅ 16. Quick Summary

    • Argument = Premise → Conclusion.

    • Deductive = certainty; Inductive = probability.

    • Categorical logic: A, E, I, O + Square of Opposition.

    • Fallacies: Formal & Informal.

    • Language: Connotation/Denotation influence meaning.

    • Venn Diagrams: visual validity tests.

    • Indian Logic: 6 Pramāṇas, Anumāna structure, Hetvābhāsa types.