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UGC NET PAPER 1 · UNIT 06 · MODULE 2: WESTERN LOGIC: ARGUMENT FORMS, FALLACIES AND LANGUAGE · TOPIC 4

Other Forms of Argument

Conditional and disjunctive arguments, dilemma, sorites and enthymeme, the three laws of thought, and the truth tables for basic connectives.

  • 6 sub-topics
  • 3 min read
  • Topic 4 of 19

What this topic covers

6 sub-topics, in the order to study them. Tap one to jump to it.

  1. 4.1Hypothetical (conditional) propositions and syllogismsA hypothetical proposition has the form "If P then Q".
    • antecedent
    • consequent
    • only
    • Modus ponens
    • Modus tollens
  2. 4.2Disjunctive syllogism"Either P or Q; not P; therefore Q." Valid.
  3. 4.3DilemmaA dilemma combines a hypothetical and a disjunctive argument.
    • minor premise is a disjunction
    • Constructive dilemma
    • Destructive dilemma
    • Three ways to meet a dilemma
    • Escape between the horns
  4. 4.4Sorites and enthymemeCovers Sorites, Enthymeme, Epicheirema.
    • Sorites
    • Enthymeme
    • Epicheirema
  5. 4.5The Laws of ThoughtLaw Statement Symbolic Identity Whatever is, is; A is A A is A Non-contradiction Nothing can both be and not be at the same time and in the same respect not (A and not-A)…
    • Law of Sufficient Reason
  6. 4.6Basic truth-functional logicCovers Tautology, Contradiction (self-contradiction), Contingent statement, De Morgan's laws.
    • Tautology
    • Contingent statement
    • De Morgan's laws

Revision mode hides the full explanations and keeps each section's key terms, lists and tables. Use it from your second read onward.

4.1Hypothetical (conditional) propositions and syllogisms#

In brief

A hypothetical proposition has the form "If P then Q".

  • antecedent
  • consequent
  • only
  • Modus ponens
  • Modus tollens
  • Fallacy
  • Pure hypothetical syllogism

A hypothetical proposition has the form "If P then Q". P is the antecedent, Q is the consequent. It is false only when the antecedent is true and the consequent false.

Form Pattern Status
Modus ponens (affirming the antecedent) If P then Q; P; therefore Q Valid
Modus tollens (denying the consequent) If P then Q; not Q; therefore not P Valid
Affirming the consequent If P then Q; Q; therefore P Fallacy
Denying the antecedent If P then Q; not P; therefore not Q Fallacy
Pure hypothetical syllogism If P then Q; if Q then R; therefore if P then R Valid

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4.2Disjunctive syllogism#

In brief

"Either P or Q; not P; therefore Q." Valid.

"Either P or Q; not P; therefore Q." Valid. If the disjunction is inclusive, affirming one disjunct does not allow denying the other ("Either P or Q; P; therefore not Q" is a fallacy for inclusive disjunction but valid for exclusive disjunction).

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4.3Dilemma#

In brief

A dilemma combines a hypothetical and a disjunctive argument.

  • minor premise is a disjunction
  • Constructive dilemma
  • Destructive dilemma
  • Three ways to meet a dilemma
  • Escape between the horns
  • Grasp (take) it by the horns
  • Rebut it

A dilemma combines a hypothetical and a disjunctive argument. The major premise contains two conditionals (hypotheticals); the minor premise is a disjunction.

  • Constructive dilemma: (P→Q) and (R→S); P or R; therefore Q or S.

  • Destructive dilemma: (P→Q) and (R→S); not-Q or not-S; therefore not-P or not-R.

Three ways to meet a dilemma:

  1. Escape between the horns: reject the disjunctive premise by showing that other alternatives exist.

  2. Grasp (take) it by the horns: deny the truth of one of the conditional propositions.

  3. Rebut it: construct a counter-dilemma that proves the opposite conclusion.

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4.4Sorites and enthymeme#

In brief

Covers Sorites, Enthymeme, Epicheirema.

  • Sorites
  • Enthymeme
  • Epicheirema

  • Sorites: a chain of syllogisms in which the conclusion of each becomes a premise of the next, and all intermediate conclusions are left unstated. Only the final conclusion is given.

  • Enthymeme: a syllogism in which one premise or the conclusion is suppressed (understood but unstated). It is the form in which most everyday arguments occur.

  • Epicheirema: a syllogism in which one or both premises are supported by a reason.

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4.5The Laws of Thought#

In brief

Law Statement Symbolic Identity Whatever is, is; A is A A is A Non-contradiction Nothing can both be and not be at the same time and in the same respect not (A and not-A)…

  • Law of Sufficient Reason
Law Statement Symbolic
Identity Whatever is, is; A is A A is A
Non-contradiction Nothing can both be and not be at the same time and in the same respect not (A and not-A)
Excluded middle Everything either is or is not; there is no third possibility A or not-A

A fourth, the Law of Sufficient Reason, was added by Leibniz. A statement "P and not-P" violates non-contradiction; "A is B or not B, and a middle option exists" violates excluded middle.

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4.6Basic truth-functional logic#

In brief

Covers Tautology, Contradiction (self-contradiction), Contingent statement, De Morgan's laws.

  • Tautology
  • Contingent statement
  • De Morgan's laws
Connective Symbol True when
Negation ~P P is false
Conjunction P ∧ Q Both true
Disjunction (inclusive) P ∨ Q At least one true (false only if both false)
Conditional P → Q False only when P true and Q false
Biconditional P ↔ Q Both have the same truth value

  • Tautology: true under every assignment of truth values (e.g., P ∨ ~P).

  • Contradiction (self-contradiction): false under every assignment (e.g., P ∧ ~P).

  • Contingent statement: true under some and false under others.

  • De Morgan's laws: ~(P ∧ Q) ≡ ~P ∨ ~Q, and ~(P ∨ Q) ≡ ~P ∧ ~Q.

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Test yourself on Other Forms of Argument

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↑ Module 2: Western Logic: Argument Forms, Fallacies and Language · All 19 topics in Logical Reasoning · Unit overview and sample MCQs

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