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UGC NET PAPER 1 · UNIT 06 · MODULE 1: WESTERN LOGIC: ARGUMENTS AND CATEGORICAL REASONING · TOPIC 3

The Categorical Syllogism

Structure of the syllogism, mood and figure, the valid moods and their mnemonic names, and the syllogism rules with the fallacy each one prevents.

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  1. 3.1StructureA categorical syllogism is a mediate inference with three categorical propositions (major premise, minor premise, conclusion) and exactly three terms , each appearing twice.
    • mediate inference
    • three categorical propositions
    • exactly three terms
    • Major term (P)
    • Minor term (S)
  2. 3.2Mood and figureMood is determined by the types (A, E, I, O) of the three propositions in order (major premise, minor premise, conclusion).
    • Mood
    • 64 possible moods
    • Figure
    • position of the middle term
    • four figures
  3. 3.3Valid moods and mnemonic names (memory heavy)Covers Figure 1, Figure 2, Figure 3, Figure 4.
    • Camenes, Dimaris, Fresison
    • Mnemonic reading
    • initial consonant
    • Figure-wise features
    • Figure 1
  4. 3.4The rules of the syllogism and their fallacies# Rule Fallacy if violated 1 Exactly three terms Four terms ( quaternio terminorum ); equivocation of the middle term is a common cause 2 The middle term must be distributed…
    • Undistributed middle
    • Illicit major
    • Illicit minor
    • Worked example
    • Camestres

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3.1Structure#

In brief

A categorical syllogism is a mediate inference with three categorical propositions (major premise, minor premise, conclusion) and exactly three terms , each appearing twice.

  • mediate inference
  • three categorical propositions
  • exactly three terms
  • Major term (P)
  • Minor term (S)
  • Middle term (M)
  • Major premise
  • Minor premise

A categorical syllogism is a mediate inference with three categorical propositions (major premise, minor premise, conclusion) and exactly three terms, each appearing twice.

  • Major term (P): predicate of the conclusion.

  • Minor term (S): subject of the conclusion.

  • Middle term (M): appears in both premises, never in the conclusion.

  • Major premise: the premise containing the major term.

  • Minor premise: the premise containing the minor term.

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3.2Mood and figure#

In brief

Mood is determined by the types (A, E, I, O) of the three propositions in order (major premise, minor premise, conclusion).

  • Mood
  • 64 possible moods
  • Figure
  • position of the middle term
  • four figures
  • 256 possible syllogistic forms
  • 24 are valid
  • 15 are unconditionally valid

Mood is determined by the types (A, E, I, O) of the three propositions in order (major premise, minor premise, conclusion). Since each of three propositions can be one of four forms, there are 4 × 4 × 4 = 64 possible moods.

Figure is determined by the position of the middle term in the premises. There are four figures:

Figure Major premise Minor premise Middle term position
1 M – P S – M Subject of major, predicate of minor
2 P – M S – M Predicate of both
3 M – P M – S Subject of both
4 P – M M – S Predicate of major, subject of minor

With 64 moods and 4 figures there are 256 possible syllogistic forms. Of these, 24 are valid on the Aristotelian view. On the Boolean view only 15 are unconditionally valid (the other 9 depend on existential import).

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3.3Valid moods and mnemonic names (memory heavy)#

In brief

Covers Figure 1, Figure 2, Figure 3, Figure 4.

  • Camenes, Dimaris, Fresison
  • Mnemonic reading
  • initial consonant
  • Figure-wise features
  • Figure 1
  • Figure 2
  • always negative
  • Figure 3
Figure Valid moods (unconditional) Mood letters
1 Barbara, Celarent, Darii, Ferio AAA, EAE, AII, EIO
2 Cesare, Camestres, Festino, Baroko EAE, AEE, EIO, AOO
3 Disamis, Datisi, Bocardo, Ferison IAI, AII, OAO, EIO
4 Camenes, Dimaris, Fresison AEE, IAI, EIO

Conditional (Aristotelian only, existential import needed): Barbari (AAI-1), Celaront (EAO-1), Cesaro (EAO-2), Camestrop (AEO-2), Darapti (AAI-3), Felapton (EAO-3), Bramantip (AAI-4), Camenop (AEO-4), Fesapo (EAO-4).

Mnemonic reading: the three vowels of each name give the mood. The initial consonant (B, C, D, F) shows the first-figure mood to which it is reduced. Letters inside the name tell the method of reduction: s (simple conversion), p (conversion by limitation), m (mutare, transpose the premises), c (reductio ad absurdum).

Figure-wise features:

  • Figure 1: minor premise must be affirmative; major premise must be universal. It gives conclusions of all four kinds (A, E, I, O) and is called the perfect figure; the only one whose conclusion can be A.

  • Figure 2: one premise must be negative; major premise must be universal; conclusion is always negative (E or O).

  • Figure 3: minor premise must be affirmative; conclusion is always particular (I or O).

  • Figure 4: the Galenic figure (named after Galen, though added later); if the major premise is affirmative then the major must be universal... (rarely asked in detail).

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3.4The rules of the syllogism and their fallacies#

In brief

# Rule Fallacy if violated 1 Exactly three terms Four terms ( quaternio terminorum ); equivocation of the middle term is a common cause 2 The middle term must be distributed…

  • Undistributed middle
  • Illicit major
  • Illicit minor
  • Worked example
  • Camestres
# Rule Fallacy if violated
1 Exactly three terms Four terms (quaternio terminorum); equivocation of the middle term is a common cause
2 The middle term must be distributed at least once Undistributed middle
3 A term distributed in the conclusion must be distributed in its premise Illicit major (major term) or Illicit minor (minor term)
4 No conclusion follows from two negative premises Exclusive premises
5 If one premise is negative, the conclusion must be negative (and vice versa) Affirmative conclusion from a negative premise
6 No conclusion follows from two particular premises (Two particular premises)
7 If one premise is particular, the conclusion must be particular Existential or similar error
8 From two affirmative premises, the conclusion must be affirmative (Corollary of rule 5)

Quick test procedure for a syllogism: (1) put it in standard form and name S, P, M; (2) identify the mood and figure; (3) check each rule above in order; (4) the first rule broken names the fallacy.

Worked example. All dogs are mammals; no fish are mammals; therefore no fish are dogs. Terms: M = mammals, P = dogs, S = fish. Mood EAE? Arranging: major premise "All dogs are mammals" (A), minor premise "No fish are mammals" (E), conclusion "No fish are dogs" (E). Figure 2 (middle term is predicate of both). Mood AEE-2 is Camestres, which is valid.

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