Welcome, dear students, to Class 11 Logic and Philosophy Chapter 8 Question Answer | Categorical Syllogism | English Medium | ASSEB. This chapter forms the heart of the formal deductive logic that Aristotle systematised more than two thousand years ago, and it remains a cornerstone of the ASSEB Class 11 Logic and Philosophy curriculum. A categorical syllogism is the classic three-line argument in which two categorical premises lead to a categorical conclusion. By the end of this chapter you will be able to identify the three terms of a syllogism, name its mood and figure, apply the eight general rules to test validity, recognise the special fallacies, list the valid moods of each of the four figures by their medieval mnemonic names, and reduce syllogisms of the second, third and fourth figures to the first figure. The chapter also gives you a powerful tool for analysing reasoning in everyday life, in science and in philosophical argument.
This article is prepared strictly according to the ASSEB (Assam State School Education Board) syllabus and the SCERT prescribed textbook for Higher Secondary First Year (Class 11) Logic and Philosophy. It includes a clear summary, a complete textbook question-answer set, additional important questions for examination preparation, a glossary of technical terms, and reference tables for figures, valid moods, rules and fallacies.
Summary of Chapter 8: Categorical Syllogism
A syllogism is a form of mediate deductive inference in which the conclusion is drawn from two given premises taken jointly. It is mediate because the conclusion does not follow from a single premise as in immediate inference; it requires the mediation of a third proposition. A categorical syllogism is one in which all three propositions, that is, the two premises and the conclusion, are categorical propositions of the standard A, E, I or O form.
Every categorical syllogism contains exactly three terms, each occurring exactly twice: the major term (P) which is the predicate of the conclusion, the minor term (S) which is the subject of the conclusion, and the middle term (M) which appears in both premises but never in the conclusion. The premise containing the major term is the major premise, the premise containing the minor term is the minor premise, and the major premise is conventionally written first.
The mood of a syllogism is the form determined by the quality and quantity of its three constituent propositions, expressed as a triplet of letters drawn from A, E, I, O. For example the mood AAA means the major premise is A, the minor premise is A and the conclusion is also A. The figure of a syllogism is the form determined by the position of the middle term in the two premises. There are four figures, distinguished as follows: in the First Figure the middle term is the subject of the major premise and the predicate of the minor premise; in the Second Figure the middle term is the predicate of both premises; in the Third Figure the middle term is the subject of both premises; and in the Fourth Figure the middle term is the predicate of the major premise and the subject of the minor premise.
Although there are mathematically two hundred and fifty-six possible combinations of mood and figure, only twenty-four are valid, and traditional logicians grouped these valid moods under memorable Latin names. First Figure: Barbara, Celarent, Darii, Ferio (and the weakened Barbari, Celaront). Second Figure: Cesare, Camestres, Festino, Baroco (and Cesaro, Camestrop). Third Figure: Darapti, Disamis, Datisi, Felapton, Bocardo, Ferison. Fourth Figure: Bramantip, Camenes, Dimaris, Fesapo, Fresison (and Camenop). The vowels in each mnemonic name indicate the mood, and the consonants indicate the procedure for reducing that mood to a corresponding mood of the First Figure.
Validity is tested by applying eight general rules. Violation of any rule produces a specific fallacy: the fallacy of four terms, the fallacy of undistributed middle, the fallacy of illicit major, the fallacy of illicit minor, the fallacy of exclusive premises, the fallacy of drawing an affirmative conclusion from a negative premise, the fallacy of drawing a negative conclusion from two affirmative premises, and the existential fallacy. Mastery of these rules and fallacies allows the student to test any categorical syllogism for formal validity quickly and reliably.
Textbook Questions and Answers
A. Very Short Answer Questions (1 mark)
1. What is a syllogism?
Answer: A syllogism is a form of mediate deductive inference in which the conclusion is drawn from two given premises taken jointly.
2. What is a categorical syllogism?
Answer: A categorical syllogism is a syllogism whose three constituent propositions, namely the major premise, the minor premise and the conclusion, are all categorical propositions of the A, E, I or O type.
3. How many terms are there in a categorical syllogism?
Answer: A categorical syllogism contains exactly three terms, each appearing twice.
4. How many propositions are there in a categorical syllogism?
Answer: A categorical syllogism contains exactly three propositions, namely two premises and one conclusion.
5. What is the major term?
Answer: The major term, denoted by P, is the term that occurs as the predicate of the conclusion.
6. What is the minor term?
Answer: The minor term, denoted by S, is the term that occurs as the subject of the conclusion.
7. What is the middle term?
Answer: The middle term, denoted by M, is the term that occurs in both premises but does not occur in the conclusion.
8. What is the major premise?
Answer: The major premise is the premise that contains the major term.
9. What is the minor premise?
Answer: The minor premise is the premise that contains the minor term.
10. What is meant by mood?
Answer: Mood is the form of a syllogism as determined by the quality and quantity of its constituent propositions.
11. What is meant by figure?
Answer: Figure is the form of a syllogism as determined by the position of the middle term in the two premises.
12. How many figures of categorical syllogism are there?
Answer: There are four figures of categorical syllogism.
13. How many possible moods are there in each figure?
Answer: Mathematically there are sixty-four possible moods in each figure, but only a few are valid.
14. How many valid moods are there altogether?
Answer: There are nineteen strictly valid moods (and twenty-four if we count the weakened or subaltern moods) altogether across the four figures.
15. Name the valid moods of the First Figure.
Answer: Barbara (AAA), Celarent (EAE), Darii (AII) and Ferio (EIO).
16. Name the valid moods of the Second Figure.
Answer: Cesare (EAE), Camestres (AEE), Festino (EIO) and Baroco (AOO).
17. Name the valid moods of the Third Figure.
Answer: Darapti (AAI), Disamis (IAI), Datisi (AII), Felapton (EAO), Bocardo (OAO) and Ferison (EIO).
18. Name the valid moods of the Fourth Figure.
Answer: Bramantip (AAI), Camenes (AEE), Dimaris (IAI), Fesapo (EAO) and Fresison (EIO).
19. Which figure is called the perfect figure?
Answer: The First Figure is called the perfect figure because its conclusions follow most naturally and it can yield universal as well as particular, affirmative as well as negative conclusions.
20. State the position of the middle term in the First Figure.
Answer: In the First Figure the middle term is the subject of the major premise and the predicate of the minor premise (M-P, S-M).
21. State the position of the middle term in the Second Figure.
Answer: In the Second Figure the middle term is the predicate of both the major and the minor premise (P-M, S-M).
22. State the position of the middle term in the Third Figure.
Answer: In the Third Figure the middle term is the subject of both the major and the minor premise (M-P, M-S).
23. State the position of the middle term in the Fourth Figure.
Answer: In the Fourth Figure the middle term is the predicate of the major premise and the subject of the minor premise (P-M, M-S).
24. What is the fallacy of four terms?
Answer: The fallacy of four terms (quaternio terminorum) is committed when a syllogism contains four or more distinct terms instead of the required three.
25. What is the fallacy of undistributed middle?
Answer: The fallacy of undistributed middle is committed when the middle term is not distributed at least once in the premises.
26. What is the fallacy of illicit major?
Answer: The fallacy of illicit major occurs when the major term is distributed in the conclusion but is not distributed in the major premise.
27. What is the fallacy of illicit minor?
Answer: The fallacy of illicit minor occurs when the minor term is distributed in the conclusion but is not distributed in the minor premise.
28. What is the fallacy of exclusive premises?
Answer: The fallacy of exclusive premises is committed when both premises of a syllogism are negative; from two negative premises no valid conclusion can be drawn.
29. State the fallacy of drawing an affirmative conclusion from a negative premise.
Answer: If either of the premises is negative, the conclusion must also be negative; drawing an affirmative conclusion in such a case is a formal fallacy.
30. What is the existential fallacy?
Answer: The existential fallacy is committed when a particular conclusion (I or O) is drawn from two universal premises under the modern Boolean interpretation, since universal propositions are not regarded as having existential import.
31. From two particular premises what conclusion can be drawn?
Answer: From two particular premises no valid conclusion can be drawn.
32. State the rule about the quality of the conclusion when one premise is negative.
Answer: If one premise is negative, the conclusion must be negative.
33. State the rule about the quantity of the conclusion when one premise is particular.
Answer: If one premise is particular, the conclusion must also be particular.
34. What is reduction of a syllogism?
Answer: Reduction is the process of converting a valid syllogism of the Second, Third or Fourth Figure into a corresponding valid syllogism of the First Figure in order to demonstrate its validity by reference to the perfect figure.
35. What are the two kinds of reduction?
Answer: The two kinds of reduction are direct reduction (reductio ostensiva) and indirect reduction (reductio per impossibile).
B. Short Answer Questions (2 to 3 marks)
36. Define syllogism with an example.
Answer: A syllogism is a form of mediate deductive inference in which a conclusion is drawn from two premises taken together. Example: All men are mortal (major premise); Socrates is a man (minor premise); therefore Socrates is mortal (conclusion).
37. Distinguish between immediate and mediate inference.
Answer: Immediate inference is a deductive inference in which the conclusion is drawn directly from a single premise without the help of any other proposition; conversion and obversion are examples. Mediate inference, of which the syllogism is the chief example, is a deductive inference in which the conclusion is drawn from two or more premises taken jointly, the middle term mediating between the major and minor terms.
38. Distinguish between mood and figure.
Answer: Mood refers to the quality and quantity of the three propositions of a syllogism and is expressed as a sequence of A, E, I, O letters. Figure refers to the position of the middle term in the two premises and there are four such figures. Mood and figure together fully determine the formal structure of a categorical syllogism.
39. Distinguish between the major term, the minor term and the middle term.
Answer: The major term (P) is the predicate of the conclusion and appears once in the major premise. The minor term (S) is the subject of the conclusion and appears once in the minor premise. The middle term (M) appears once in each premise but never in the conclusion; its function is to mediate between the major and minor terms so that a relation between them can be established.
40. Why is the middle term necessary in a syllogism?
Answer: The middle term is necessary because the major and minor terms are not directly compared in any single premise. The middle term is compared with each of them in the two premises, and through this common reference an inferential connection between the major and minor terms is established in the conclusion. Without the middle term mediation is impossible.
41. Explain the four figures of syllogism with schematic diagrams.
Answer: First Figure: M-P / S-M / S-P. Second Figure: P-M / S-M / S-P. Third Figure: M-P / M-S / S-P. Fourth Figure: P-M / M-S / S-P. The figure is determined entirely by the position of the middle term M, which is shown in different places in the major and minor premises.
42. Why is the First Figure called the perfect figure?
Answer: The First Figure is called the perfect figure for three reasons. First, the conclusions of all four standard moods of any quality (universal affirmative, universal negative, particular affirmative and particular negative) can be obtained in this figure. Second, the syllogisms of this figure are self-evident and require no reduction. Third, the syllogisms of the other figures are validated by being reduced to the First Figure.
43. State Barbara with an example.
Answer: Barbara is the mood AAA of the First Figure. Example: All mammals are warm-blooded; all dogs are mammals; therefore all dogs are warm-blooded.
44. State Celarent with an example.
Answer: Celarent is the mood EAE of the First Figure. Example: No reptiles are warm-blooded; all snakes are reptiles; therefore no snakes are warm-blooded.
45. State Darii with an example.
Answer: Darii is the mood AII of the First Figure. Example: All philosophers are thinkers; some Greeks are philosophers; therefore some Greeks are thinkers.
46. State Ferio with an example.
Answer: Ferio is the mood EIO of the First Figure. Example: No vegetables are animals; some living things are vegetables; therefore some living things are not animals.
47. State Cesare with an example.
Answer: Cesare is the mood EAE of the Second Figure. Example: No metals are non-conductors; all rubber is non-conductor; therefore no rubber is metal.
48. State Camestres with an example.
Answer: Camestres is the mood AEE of the Second Figure. Example: All birds are vertebrates; no insects are vertebrates; therefore no insects are birds.
49. State Darapti with an example.
Answer: Darapti is the mood AAI of the Third Figure. Example: All philosophers are thinkers; all philosophers are humans; therefore some humans are thinkers.
50. State Bocardo with an example.
Answer: Bocardo is the mood OAO of the Third Figure. Example: Some politicians are not honest; all politicians are public servants; therefore some public servants are not honest.
51. State Bramantip with an example.
Answer: Bramantip is the mood AAI of the Fourth Figure. Example: All diamonds are precious stones; all precious stones are valuable; therefore some valuable things are diamonds.
52. What is the rule about distribution of the middle term?
Answer: The middle term must be distributed at least once in the premises. If it is not distributed even once, the major and minor terms cannot be securely related to a common class, and the fallacy of undistributed middle is committed.
53. What is the rule about distribution of major and minor terms?
Answer: No term may be distributed in the conclusion if it has not been distributed in its premise. If the major term is so distributed, the fallacy of illicit major is committed; if the minor term, the fallacy of illicit minor.
54. Explain the fallacy of four terms with an example.
Answer: Every syllogism must contain exactly three terms; if a fourth term is introduced, usually through equivocation, the fallacy of four terms is committed. Example: All laws can be repealed; the law of gravitation is a law; therefore the law of gravitation can be repealed. Here the word law is used in two different senses, civil law and natural law, giving four terms in effect.
55. Explain the fallacy of undistributed middle with an example.
Answer: If the middle term is not distributed in either premise, the fallacy of undistributed middle is committed. Example: All horses are animals; all dogs are animals; therefore all dogs are horses. The middle term animals is not distributed in either premise (it is the predicate of two A propositions), so no valid relation between dogs and horses is established.
56. Explain the fallacy of illicit major with an example.
Answer: Example: All cats are mammals; no dogs are cats; therefore no dogs are mammals. Here the major term mammals is distributed in the conclusion (predicate of an E proposition) but is not distributed in the major premise (predicate of an A proposition). Hence the fallacy of illicit major is committed.
57. Explain the fallacy of illicit minor with an example.
Answer: Example: All cats are mammals; all cats are carnivores; therefore all carnivores are mammals. Here the minor term carnivores is distributed in the conclusion (subject of an A proposition) but is not distributed in the minor premise (predicate of an A proposition). Hence the fallacy of illicit minor is committed.
58. Explain the fallacy of exclusive premises with an example.
Answer: If both premises are negative, no valid conclusion can be drawn because the middle term excludes both extremes from itself, leaving no basis for relating them. Example: No fish are mammals; no whales are fish; therefore no whales are mammals. The conclusion is in fact false, illustrating the fallacy of exclusive premises.
59. State and explain the rule that from two particular premises no conclusion follows.
Answer: If both premises are particular, then either neither term is distributed (II combination) or only one term, namely the predicate of the O premise, is distributed (IO or OI combinations). In each case the rules about distribution of the middle term and of the major and minor terms cannot all be satisfied, so no valid conclusion can be drawn.
60. What is direct reduction?
Answer: Direct reduction (reductio ostensiva) is the process by which a syllogism of the Second, Third or Fourth Figure is shown to be valid by transforming it through conversion, obversion or transposition of premises into a corresponding syllogism of the First Figure with the same conclusion (or one logically equivalent to it).
61. What is indirect reduction?
Answer: Indirect reduction (reductio per impossibile) is a method of proving the validity of a syllogism by showing that the contradictory of its conclusion, when combined with one of its premises, leads to a syllogism whose conclusion contradicts the other premise. Bocardo and Baroco are reduced indirectly because direct reduction is not possible for them by simple conversion alone.
62. Reduce Cesare to the First Figure.
Answer: Cesare in the Second Figure: No P is M; All S is M; therefore No S is P. The major premise No P is M is converted simply to No M is P. The result is: No M is P; All S is M; therefore No S is P, which is Celarent in the First Figure. The initial C in Cesare indicates conversion of the major premise; the s indicates simple conversion.
63. Reduce Camestres to the First Figure.
Answer: Camestres in the Second Figure: All P is M; No S is M; therefore No S is P. The minor premise No S is M is simply converted to No M is S, the premises are transposed (m), and the conclusion No S is P is simply converted to No P is S. The result is Celarent: No M is S; All P is M; therefore No P is S. (Re-arranging gives the original conclusion by conversion.)
64. Reduce Darapti to the First Figure.
Answer: Darapti in the Third Figure: All M is P; All M is S; therefore Some S is P. The minor premise All M is S is converted per accidens to Some S is M (p indicates conversion per accidens). The result is Darii: All M is P; Some S is M; therefore Some S is P.
C. Long Answer Questions (5 to 7 marks)
65. Define a categorical syllogism. Explain its structure and parts with an example.
Answer: A categorical syllogism is defined as a form of mediate deductive inference consisting of three categorical propositions, in which a conclusion is drawn from two premises taken jointly through the mediation of a common term. It must contain exactly three terms, each occurring twice. The terms are called the major term (P, the predicate of the conclusion), the minor term (S, the subject of the conclusion) and the middle term (M, common to both premises but absent from the conclusion). The premise containing the major term is the major premise, and the premise containing the minor term is the minor premise; by convention the major premise is stated first. Example: All men are mortal (Major Premise; major term mortal, middle term men). Socrates is a man (Minor Premise; minor term Socrates, middle term man). Therefore Socrates is mortal (Conclusion). Here the middle term man relates the minor term Socrates to the major term mortal, and we infer that Socrates falls within the class of mortal beings. The example is in mood AAA and figure 1, that is, Barbara.
66. Explain mood and figure of a syllogism. How are they related?
Answer: The mood of a syllogism is the form determined by the quality (affirmative or negative) and the quantity (universal or particular) of its three propositions taken in order: major premise, minor premise, conclusion. Each proposition is one of A, E, I or O, so the mood is denoted by a string of three such letters, for example AAA, EIO, AOO. There are sixty-four possible moods, since each of three positions can be filled in four ways. The figure is the form determined by the position of the middle term in the two premises; there are four figures: M-P/S-M (First), P-M/S-M (Second), M-P/M-S (Third), P-M/M-S (Fourth). Mood and figure are related because validity depends on both. Two syllogisms with the same mood may belong to different figures, and a mood that is valid in one figure may be invalid in another. Thus AAA is valid in the First Figure (Barbara) but invalid in the Second, Third or Fourth Figure. The full specification of a syllogism is given by stating both its mood and its figure, for example AAA-1, EAE-2, OAO-3, AAI-4.
67. State and explain the eight general rules of categorical syllogism.
Answer: The eight rules of categorical syllogism are as follows. (i) A syllogism must contain exactly three terms. Violation gives the fallacy of four terms. (ii) A syllogism must contain exactly three propositions, namely two premises and one conclusion. (iii) The middle term must be distributed at least once in the premises. Violation gives the fallacy of undistributed middle. (iv) No term can be distributed in the conclusion unless it is distributed in its premise. Violation gives the fallacy of illicit major or illicit minor. (v) From two negative premises no conclusion follows. Violation gives the fallacy of exclusive premises. (vi) If one premise is negative, the conclusion must be negative; if both premises are affirmative, the conclusion must be affirmative. Violation gives the fallacy of drawing an affirmative conclusion from a negative premise or vice versa. (vii) From two particular premises no conclusion follows. (viii) If one premise is particular, the conclusion must be particular. The eighth rule, when added to the existential rule (no particular conclusion from two universal premises in the modern reading), gives the existential fallacy. Together these rules are necessary and sufficient for testing the formal validity of any categorical syllogism.
68. Explain the four figures of categorical syllogism with examples and state the valid moods in each.
Answer: The four figures are distinguished by the position of the middle term. First Figure (M-P, S-M): the middle term is the subject of the major premise and predicate of the minor premise. Valid moods: Barbara (AAA), Celarent (EAE), Darii (AII), Ferio (EIO). Example of Barbara: All men are mortal; all kings are men; therefore all kings are mortal. Second Figure (P-M, S-M): the middle term is the predicate of both premises. Valid moods: Cesare (EAE), Camestres (AEE), Festino (EIO), Baroco (AOO). Example of Camestres: All birds are vertebrates; no insects are vertebrates; therefore no insects are birds. Third Figure (M-P, M-S): the middle term is the subject of both premises. Valid moods: Darapti (AAI), Disamis (IAI), Datisi (AII), Felapton (EAO), Bocardo (OAO), Ferison (EIO). Example of Disamis: Some philosophers are scientists; all philosophers are humans; therefore some humans are scientists. Fourth Figure (P-M, M-S): the middle term is the predicate of the major premise and subject of the minor premise. Valid moods: Bramantip (AAI), Camenes (AEE), Dimaris (IAI), Fesapo (EAO), Fresison (EIO). Example of Camenes: All squares are rectangles; no rectangles are circles; therefore no circles are squares.
69. Discuss the special rules of the four figures.
Answer: Apart from the general rules, each figure has its own special rules that follow from the position of the middle term. First Figure: (a) the major premise must be universal, and (b) the minor premise must be affirmative. Second Figure: (a) one premise must be negative, and (b) the major premise must be universal. Third Figure: (a) the minor premise must be affirmative, and (b) the conclusion must be particular. Fourth Figure: (a) if the major premise is affirmative, the minor must be universal; (b) if the minor premise is affirmative, the conclusion must be particular; (c) if either premise is negative, the major premise must be universal. These special rules can be derived from the general rules and explain why only certain moods are valid in each figure.
70. What are the chief fallacies of categorical syllogism? Illustrate each with an example.
Answer: The chief fallacies are: (i) Fallacy of Four Terms: All laws can be repealed; gravitation is a law; therefore gravitation can be repealed (equivocation on law). (ii) Fallacy of Undistributed Middle: All cats are animals; all dogs are animals; therefore all dogs are cats (animals undistributed in both A premises). (iii) Fallacy of Illicit Major: All cats are mammals; no dogs are cats; therefore no dogs are mammals (mammals distributed in conclusion but not in major premise). (iv) Fallacy of Illicit Minor: All Indians are Asians; all Indians are humans; therefore all humans are Asians (humans distributed in conclusion but not in minor premise). (v) Fallacy of Exclusive Premises: No fish are mammals; no whales are fish; therefore no whales are mammals (two negative premises). (vi) Fallacy of Affirmative Conclusion from a Negative Premise: No fish are mammals; some whales are not fish; therefore some whales are mammals. (vii) Fallacy of Negative Conclusion from Affirmative Premises: All men are rational; some animals are men; therefore some animals are not rational. (viii) Existential Fallacy: All unicorns are mammals; all mammals are vertebrates; therefore some unicorns are vertebrates (a particular conclusion drawn from universals).
71. Explain reduction of syllogism. Why is it necessary?
Answer: Reduction is the logical procedure by which a valid syllogism of the Second, Third or Fourth Figure is converted into an equivalent valid syllogism of the First Figure. It is necessary because the First Figure is regarded as the perfect figure, in which the validity of the inference is most evident, and because Aristotle and the medieval logicians wished to show that all valid syllogistic reasoning could be reduced to the four primary forms Barbara, Celarent, Darii and Ferio. Reduction is of two kinds: direct reduction, performed by conversion, obversion or transposition of premises (indicated by the consonants s, p and m in the mnemonic names), and indirect reduction or reductio per impossibile, used for Bocardo and Baroco, in which the contradictory of the conclusion is combined with one premise to derive a proposition contradicting the other premise. The vowels of the mnemonic name (Barbara, Celarent, etc.) indicate the mood, and the consonants indicate the operations needed for reduction.
72. Reduce the following syllogisms of the Second Figure to the First Figure.
Answer: (i) Cesare (EAE-2): No P is M; All S is M; therefore No S is P. Convert the major simply (s): No M is P; All S is M; therefore No S is P, which is Celarent (EAE-1). (ii) Camestres (AEE-2): All P is M; No S is M; therefore No S is P. Convert minor simply (s), transpose premises (m), convert conclusion simply (s): No M is S; All P is M; therefore No P is S, which is Celarent. (iii) Festino (EIO-2): No P is M; Some S is M; therefore Some S is not P. Convert major simply (s): No M is P; Some S is M; therefore Some S is not P, which is Ferio (EIO-1). (iv) Baroco (AOO-2): All P is M; Some S is not M; therefore Some S is not P. Indirect reduction is used: assume the contradictory of the conclusion (All S is P) and combine with the major (All P is M) to get All S is M (Barbara), which contradicts the minor premise.
73. Examine the validity of the following syllogism: All metals are conductors; copper is a metal; therefore copper is a conductor.
Answer: The major premise All metals are conductors is an A proposition (universal affirmative). The minor premise Copper is a metal is a singular A proposition. The conclusion Copper is a conductor is also a singular A proposition. The middle term is metal(s), which is the subject of the major (distributed) and predicate of the minor (undistributed). Mood is AAA and figure is the First Figure (M-P, S-M, S-P), so the syllogism is in Barbara. Examining the rules: there are exactly three terms (metals, conductors, copper), three propositions, the middle term is distributed in the major premise, neither the major term nor the minor term is distributed in the conclusion at any place where it is not distributed in its premise, no premise is negative, and no premise is particular. All eight rules are satisfied. Hence the syllogism is valid (Barbara, AAA-1).
74. Examine the validity of: All horses are animals; all cows are animals; therefore all cows are horses.
Answer: The major premise All horses are animals is A; the minor All cows are animals is A; the conclusion All cows are horses is A. Middle term is animals; major term is horses; minor term is cows. Pattern: P-M, S-M, S-P, which is the Second Figure, mood AAA. Now check distribution of the middle term: animals is the predicate of both A premises, where the predicate of an A proposition is undistributed. Hence the middle term is not distributed in either premise. The fallacy of undistributed middle is committed and the syllogism is invalid. (Also, AAA is not a valid mood of the Second Figure; the only mood beginning with AA in any figure that is valid is AAI of Figures 3 and 4.)
75. Examine the validity of: No criminals are saints; some politicians are not criminals; therefore some politicians are saints.
Answer: Major premise No criminals are saints (E). Minor premise Some politicians are not criminals (O). Conclusion Some politicians are saints (I). Two of the premises are negative (E and O), violating the rule that from two negative premises no conclusion follows. Hence the fallacy of exclusive premises is committed and the syllogism is invalid. Even if we set this aside, the conclusion is affirmative whereas a negative premise is present, which would also violate the rule that a negative premise requires a negative conclusion.
Additional Important Questions
76. What is the difference between a categorical syllogism and a hypothetical syllogism?
Answer: A categorical syllogism contains only categorical propositions, that is, propositions that affirm or deny something unconditionally. A hypothetical syllogism contains at least one conditional or hypothetical proposition of the form If P then Q. The categorical syllogism deals with class-relations among terms whereas the hypothetical syllogism deals with relations between propositions, especially the dependence of one proposition upon another.
77. What is meant by distribution of a term?
Answer: A term is said to be distributed in a proposition when the proposition refers to all members of the class denoted by that term. In an A proposition the subject is distributed but the predicate is not; in an E proposition both subject and predicate are distributed; in an I proposition neither is distributed; in an O proposition only the predicate is distributed.
78. Why must the middle term be distributed at least once?
Answer: The middle term provides the link between the major and minor terms. If it is not distributed in either premise, then in each premise it refers only to part of its class. Consequently the major and minor terms may be related to different parts of the middle class, and no necessary connection between them can be established. Hence at least one premise must distribute the middle term so that both major and minor terms are tied to the same class as a whole.
79. Give an example of Felapton.
Answer: Felapton is the mood EAO of the Third Figure. Example: No reptiles are warm-blooded; all reptiles are vertebrates; therefore some vertebrates are not warm-blooded.
80. Give an example of Disamis.
Answer: Disamis is the mood IAI of the Third Figure. Example: Some scientists are philosophers; all scientists are humans; therefore some humans are philosophers.
81. Give an example of Datisi.
Answer: Datisi is the mood AII of the Third Figure. Example: All philosophers are wise; some philosophers are Greeks; therefore some Greeks are wise.
82. Give an example of Ferison.
Answer: Ferison is the mood EIO of the Third Figure. Example: No reptiles are warm-blooded; some reptiles are dangerous; therefore some dangerous things are not warm-blooded.
83. Give an example of Fesapo.
Answer: Fesapo is the mood EAO of the Fourth Figure. Example: No mammals are insects; all insects are arthropods; therefore some arthropods are not mammals.
84. Give an example of Fresison.
Answer: Fresison is the mood EIO of the Fourth Figure. Example: No mammals are insects; some insects are pests; therefore some pests are not mammals.
85. Give an example of Dimaris.
Answer: Dimaris is the mood IAI of the Fourth Figure. Example: Some scientists are philosophers; all philosophers are thinkers; therefore some thinkers are scientists.
86. Why is AAA invalid in the Second Figure?
Answer: In the Second Figure the middle term is the predicate of both premises. In two A propositions the predicate is undistributed. Therefore the middle term is undistributed in both premises, violating the rule that the middle term must be distributed at least once. Hence AAA is invalid in the Second Figure (fallacy of undistributed middle).
87. Why is the conclusion of every Third Figure syllogism particular?
Answer: In the Third Figure the middle term is the subject of both premises. The minor term is the predicate of the minor premise, and so is undistributed if the minor premise is affirmative (and the minor must be affirmative by the special rule of this figure). Therefore the minor term cannot be distributed in the conclusion, which means the conclusion cannot be a universal proposition with the minor as subject. Hence in the Third Figure the conclusion is always particular.
88. Distinguish between a valid syllogism and a sound syllogism.
Answer: A syllogism is valid when its conclusion necessarily follows from its premises by virtue of its logical form, regardless of whether the premises are actually true. A syllogism is sound when it is valid and, in addition, both of its premises are actually true. Validity is purely formal; soundness adds the requirement of factual truth.
89. What is the existential viewpoint in modern syllogistic logic?
Answer: Modern (Boolean) logic adopts the existential viewpoint that universal propositions (A and E) do not assert the existence of their subjects, while particular propositions (I and O) do. Consequently certain moods that the traditional logician regarded as valid, such as Darapti, Felapton, Bramantip and Fesapo, are deemed invalid under modern interpretation when their subject classes are empty. The fallacy committed in such cases is called the existential fallacy.
90. What is meant by the figure of speech sorites and how is it related to syllogism?
Answer: A sorites is a chain of categorical syllogisms in which the conclusion of each becomes a premise of the next, the intermediate conclusions being suppressed. The classical sorites contains a series of premises connecting different terms, and a single conclusion linking the first and the last term. Although it is not strictly a categorical syllogism, the sorites can always be analysed into a sequence of standard categorical syllogisms.
91. Identify the fallacy: All scholars love books; some children love books; therefore some children are scholars.
Answer: Major premise All scholars love books (A); minor premise Some children love books (I); conclusion Some children are scholars (I). The middle term is those who love books, which is the predicate of an A proposition (undistributed) and the predicate of an I proposition (also undistributed). The middle term is therefore not distributed in either premise. The fallacy committed is the fallacy of undistributed middle.
92. Identify the fallacy: No saints are sinners; all hypocrites are sinners; therefore all hypocrites are saints.
Answer: Major premise No saints are sinners (E); minor premise All hypocrites are sinners (A); conclusion All hypocrites are saints (A). One premise (the major) is negative, so the conclusion must also be negative; the conclusion is affirmative, which violates the rule. The fallacy committed is the fallacy of drawing an affirmative conclusion from a negative premise.
93. Identify the fallacy: All sincere persons are honest; some lawyers are sincere; therefore all lawyers are honest.
Answer: Major premise All sincere persons are honest (A); minor premise Some lawyers are sincere (I); conclusion All lawyers are honest (A). One premise (the minor) is particular, so the conclusion must also be particular. The conclusion is universal, which violates the rule that if one premise is particular the conclusion must be particular. The fallacy is therefore violation of the eighth rule, leading effectively to illicit minor (the term lawyers is distributed in the conclusion but not in the minor premise).
94. Identify the fallacy: Some flowers are red; some flowers are roses; therefore some roses are red.
Answer: Both premises are particular (I and I). From two particular premises no valid conclusion can be drawn. The fallacy committed is the fallacy of two particular premises (also analysable as undistributed middle, since the middle term flowers is undistributed in both I premises).
95. Identify the fallacy: All ducks are birds; no fish are ducks; therefore no fish are birds.
Answer: Major premise All ducks are birds (A); minor premise No fish are ducks (E); conclusion No fish are birds (E). The major term birds is distributed in the conclusion (predicate of E) but undistributed in the major premise (predicate of A). The fallacy committed is the fallacy of illicit major.
96. Identify the mood and figure: Some students are intelligent; all students are humans; therefore some humans are intelligent.
Answer: Major premise Some students are intelligent (I); minor premise All students are humans (A); conclusion Some humans are intelligent (I). Mood is IAI. The middle term students is the subject of the major and the subject of the minor, so the figure is the Third Figure. This is therefore Disamis (IAI-3), a valid mood.
97. Identify the mood and figure: All philosophers are thinkers; no scientists are philosophers; therefore no scientists are thinkers.
Answer: Major premise All philosophers are thinkers (A); minor premise No scientists are philosophers (E); conclusion No scientists are thinkers (E). Mood is AEE. Middle term philosophers is the subject of the major and the predicate of the minor, so the figure is the First Figure. AEE is not a valid mood of the First Figure; moreover the major term thinkers is distributed in the conclusion but not in the major premise, so the fallacy of illicit major is committed. The syllogism is invalid.
98. Identify the mood and figure: All triangles are polygons; some figures are triangles; therefore some figures are polygons.
Answer: Mood: AII. Middle term: triangles, which is the subject of the major and the predicate of the minor. Figure: First. This is Darii (AII-1), a valid mood.
99. Identify the mood and figure: No reptiles are mammals; all snakes are reptiles; therefore no snakes are mammals.
Answer: Mood: EAE. Middle term: reptiles, subject of major, predicate of minor. Figure: First. This is Celarent (EAE-1), a valid mood.
100. Identify the mood and figure: All metals are conductors; no plastics are conductors; therefore no plastics are metals.
Answer: Mood: AEE. Middle term: conductors, predicate of major, predicate of minor. Figure: Second. This is Camestres (AEE-2), a valid mood.
101. Identify the mood and figure: No fish are mammals; some whales are mammals; therefore some whales are not fish.
Answer: Mood: EIO. Middle term: mammals, predicate of major, predicate of minor. Figure: Second. This is Festino (EIO-2), a valid mood.
102. Identify the mood and figure: All squares are rectangles; some rectangles are coloured; therefore some coloured things are squares.
Answer: Mood: AII (with conclusion in the form Some coloured things are squares which is I). Middle term: rectangles, predicate of major, subject of minor. Figure: Fourth. AII is not in the standard list of valid Fourth Figure moods (Bramantip AAI, Camenes AEE, Dimaris IAI, Fesapo EAO, Fresison EIO). Also the middle term rectangles is undistributed in both premises (predicate of A, subject of I). Hence the syllogism is invalid; fallacy of undistributed middle.
103. Reduce Festino to the First Figure.
Answer: Festino (EIO-2): No P is M; Some S is M; therefore Some S is not P. Convert the major simply: No M is P; Some S is M; therefore Some S is not P. The reduced syllogism is Ferio (EIO-1).
104. Reduce Disamis to the First Figure.
Answer: Disamis (IAI-3): Some M is P; All M is S; therefore Some S is P. Convert the major simply (s) to give Some P is M; transpose the premises (m); and convert the conclusion simply (s) to give Some P is S. The reduced syllogism is Darii: All M is S; Some P is M; therefore Some P is S. Re-converting gives the original conclusion.
105. Reduce Datisi to the First Figure.
Answer: Datisi (AII-3): All M is P; Some M is S; therefore Some S is P. Convert the minor simply: Some S is M. The reduced syllogism is Darii: All M is P; Some S is M; therefore Some S is P.
106. Reduce Felapton to the First Figure.
Answer: Felapton (EAO-3): No M is P; All M is S; therefore Some S is not P. Convert the minor per accidens: Some S is M. The reduced syllogism is Ferio: No M is P; Some S is M; therefore Some S is not P.
107. Reduce Bramantip to the First Figure.
Answer: Bramantip (AAI-4): All P is M; All M is S; therefore Some S is P. Transpose the premises (m): All M is S; All P is M. Now convert the conclusion per accidens: Some P is S, but reading it the other way gives Some S is P. The reduced syllogism is Barbara with conversion per accidens of the conclusion, yielding Some S is P.
108. State the importance of categorical syllogism in logic.
Answer: The categorical syllogism is important in logic for several reasons. First, it is the oldest and most studied form of deductive argument, going back to Aristotles Prior Analytics, and it set the pattern for all subsequent formal logic. Second, it provides a clear and systematic test of validity through the rules of distribution and the doctrine of figures and moods. Third, it shows how the truth of a conclusion can be guaranteed by the truth of premises taken together, illustrating the very idea of valid deduction. Fourth, the discipline of identifying mood, figure and fallacy trains students in careful attention to the structure of arguments. Finally, the categorical syllogism remains a useful tool for analysing everyday reasoning, scientific arguments and philosophical positions, even though modern symbolic logic provides more general frameworks.
109. State the limitations of categorical syllogism.
Answer: Although the categorical syllogism is a powerful logical tool, it has several limitations. First, it deals only with class-inclusion among terms and cannot adequately represent relations such as is greater than or is to the left of. Second, it cannot handle multi-premise arguments without reduction to chains of syllogisms (sorites). Third, it cannot deal with arguments involving propositional connectives such as if-then, and-or, except when these are transformed. Fourth, under modern Boolean interpretation some traditionally valid moods are rejected as committing the existential fallacy. Fifth, it does not provide tools for arguments involving quantifiers in complex ways, such as those handled by modern predicate logic. Hence the categorical syllogism, while indispensable, is only one part of a larger logical system.
110. Distinguish between traditional and modern interpretations of categorical syllogism.
Answer: The traditional Aristotelian interpretation gives universal propositions A and E existential import, that is, it takes them to assert the existence of their subjects. Under this interpretation Darapti, Felapton, Bramantip and Fesapo are valid. The modern Boolean interpretation, due to George Boole and developed in modern symbolic logic, denies existential import to A and E propositions, treating them as conditional in form. Under this interpretation the four moods just mentioned are invalid because they involve drawing a particular conclusion (with existential import) from purely universal premises (without existential import). The two interpretations agree on fifteen of the nineteen traditionally valid moods.
111. Examine the validity of: All birds can fly; ostriches are birds; therefore ostriches can fly.
Answer: Major premise All birds can fly (A); minor premise Ostriches are birds (A, singular); conclusion Ostriches can fly (A, singular). Mood AAA; middle term birds (subject of major, predicate of minor); figure 1; this is Barbara. Formally the syllogism is valid because the rules of distribution are satisfied. However, the major premise is factually false since not all birds can fly. The argument is therefore valid but not sound. This example illustrates the essential distinction between formal validity and material truth: a syllogism may be valid even when its premises or conclusion are false, and may be sound only if both validity and the truth of the premises hold together.
112. Examine the validity of: Some artists are poets; some poets are dreamers; therefore some artists are dreamers.
Answer: Major premise Some artists are poets (I); minor premise Some poets are dreamers (I); conclusion Some artists are dreamers (I). Both premises are particular, violating the rule that from two particular premises no valid conclusion can be drawn. Furthermore the middle term poets is undistributed in both premises (predicate of one I, subject of another I), so the fallacy of undistributed middle is also committed. The syllogism is therefore invalid.
113. Examine the validity of: All gold is metal; all gold is precious; therefore all precious things are metal.
Answer: Major premise All gold is metal (A); minor premise All gold is precious (A); conclusion All precious things are metal (A). Middle term gold; major term metal; minor term precious. Pattern: M-P, M-S, S-P, which is the Third Figure. The minor term precious is distributed in the conclusion (subject of A) but undistributed in the minor premise (predicate of A). The fallacy of illicit minor is committed. The syllogism is invalid. Note also that the special rule of the Third Figure requires the conclusion to be particular, but here it is universal.
114. Examine the validity of: All citizens are voters; some adults are not citizens; therefore some adults are not voters.
Answer: Major premise All citizens are voters (A); minor premise Some adults are not citizens (O); conclusion Some adults are not voters (O). Middle term citizens; figure: First (M-P, S-M). Mood AOO. The major term voters is distributed in the conclusion (predicate of O) but not in the major premise (predicate of A). The fallacy of illicit major is committed. The syllogism is therefore invalid. AOO is not among the valid moods of the First Figure.
115. Show that EOO in Figure 1 is invalid.
Answer: EOO-1: No M is P; Some S is not M; therefore Some S is not P. Both premises are negative (E and O), violating the rule that from two negative premises no conclusion can be drawn. The fallacy of exclusive premises is committed. Hence EOO is invalid in any figure, including the First Figure.
116. Show that IEO in Figure 1 is invalid.
Answer: IEO-1: Some M is P; No S is M; therefore Some S is not P. The major term P is distributed in the conclusion (predicate of O) but is undistributed in the major premise (predicate of I). The fallacy of illicit major is committed. Moreover, the special rule of the First Figure requires the minor premise to be affirmative, but here it is negative. The syllogism is therefore invalid.
117. Construct a syllogism in Barbara about plants.
Answer: All green plants contain chlorophyll. All mango trees are green plants. Therefore, all mango trees contain chlorophyll. Mood AAA, Figure 1, Barbara, valid.
118. Construct a syllogism in Celarent about minerals.
Answer: No minerals are living things. All quartz is mineral. Therefore, no quartz is a living thing. Mood EAE, Figure 1, Celarent, valid.
119. Construct a syllogism in Camestres about geometric figures.
Answer: All squares have four equal sides. No triangles have four equal sides. Therefore, no triangles are squares. Mood AEE, Figure 2, Camestres, valid.
120. Construct a syllogism in Bocardo about teachers.
Answer: Some teachers are not graduates. All teachers are educated. Therefore, some educated persons are not graduates. Mood OAO, Figure 3, Bocardo, valid.
121. Construct a syllogism in Bramantip about books.
Answer: All textbooks are books. All books are printed materials. Therefore, some printed materials are textbooks. Mood AAI, Figure 4, Bramantip, valid (under traditional interpretation).
122. Why is OAO valid in Figure 3 but not in Figure 1?
Answer: In Figure 3 the middle term is the subject of both premises. In OAO-3 the major premise Some M is not P is O (predicate distributed) and the minor All M is S is A (subject distributed). The middle term M is therefore distributed in the minor premise. The major term P is distributed in both the major premise and the conclusion (since both are O); the minor term S is undistributed in both the minor premise and the conclusion. All rules are satisfied and the mood is valid (Bocardo). In Figure 1, however, OAO would have the form Some M is not P; All S is M; therefore Some S is not P, in which the major term P is distributed in the conclusion but undistributed in the major premise (predicate of O is distributed but the question is whether P is the predicate; in fact P is the predicate of the major and is distributed because the proposition is O), so on close inspection the formal violation is different. The simpler answer is that the special rules of Figure 1 require the major premise to be universal and the minor to be affirmative, but here the major is particular, violating the special rule of the First Figure.
123. Why is AOO valid in Figure 2 but not in Figure 1?
Answer: AOO-2 (Baroco) has the form All P is M; Some S is not M; therefore Some S is not P. The middle term M is distributed in the minor premise (predicate of an O proposition) and the major term P is distributed in the conclusion (predicate of O) and in the major premise (subject of A). All rules are satisfied. In Figure 1, AOO would be All M is P; Some S is not M; therefore Some S is not P. Here the major term P is distributed in the conclusion but undistributed in the major premise (predicate of A), so the fallacy of illicit major is committed and the mood is invalid. Moreover, the special rule of Figure 1 requires the minor to be affirmative, which is also violated.
124. State the rule about the quantity of the major term in Figure 4.
Answer: In the Fourth Figure, if either premise is negative, the major premise must be universal. This is because, when the conclusion is negative, the major term is distributed in the conclusion (as predicate of an E or O proposition); for the major term to be distributed in the major premise as well, the major premise must distribute its subject (the major term P), which requires the major premise to be a universal proposition.
125. Explain why Darapti is regarded as invalid in modern logic.
Answer: Darapti has the form All M is P; All M is S; therefore Some S is P. In traditional logic this is valid because the universal premises are taken to imply the existence of M. In modern Boolean logic, however, A propositions do not have existential import: All M is P is read as the conditional For every x, if x is M then x is P, which is true even when there are no M. From two such conditionals one cannot validly infer the existential proposition Some S is P. Hence Darapti is invalid in modern logic, and the same applies to Felapton, Bramantip and Fesapo. This is the existential fallacy.
126. Explain the figure of Aristotle and that of Galen.
Answer: Aristotle recognised only the first three figures. Galen, the second-century physician and logician, is traditionally credited with adding the Fourth Figure, although the matter is historically disputed. The Fourth Figure is sometimes called the Galenic figure. Aristotle treated all syllogisms of indirect mood (where major and minor terms have an unusual relation to the middle) as variants of the first three figures by simple inversion. Modern logic accepts all four figures and treats them on equal footing, with reduction available between them.
127. State the importance of memorising the mnemonic names of valid moods.
Answer: The mnemonic names are not arbitrary; the vowels in each name indicate the mood and the consonants indicate the operations needed for reduction. The initial consonant indicates which First Figure mood the syllogism reduces to: B for Barbara, C for Celarent, D for Darii, F for Ferio. The consonants s (simple conversion), p (conversion per accidens) and m (transposition of premises) tell the student exactly which operation to perform on which proposition. Memorising the names therefore gives both the form of valid syllogisms and the method of reducing them.
128. Explain how Venn diagrams may be used to test syllogistic validity.
Answer: A Venn diagram for a categorical syllogism uses three overlapping circles to represent the three terms S, P and M, dividing the universe into seven regions. The two premises are then represented on the diagram by shading regions known to be empty (for universal propositions) and placing an x in regions known to be non-empty (for particular propositions). After both premises are diagrammed, the syllogism is valid if and only if the conclusion is automatically represented by what has already been diagrammed; otherwise it is invalid. Venn diagrams give a graphical and decisive test of validity that complements the rule-based test.
129. Distinguish between conversion, obversion and contraposition.
Answer: Conversion is the immediate inference in which subject and predicate are interchanged, valid for E and I propositions simply, and for A propositions only per accidens. Obversion is the immediate inference in which the quality of the proposition is changed and the predicate is replaced by its complement, valid for all four standard forms (A becomes E, E becomes A, I becomes O, O becomes I, with the predicate negated). Contraposition is the immediate inference in which the original predicate is replaced by its complement and the original subject is replaced by the complement of the predicate; it is valid for A and O propositions and is equivalent to obversion followed by conversion followed by obversion.
130. State the rule of inference for hypothetical syllogism.
Answer: A pure hypothetical syllogism has the form: If P then Q; if Q then R; therefore if P then R. The rule of inference is hypothetical syllogism (also called transitivity of implication). A mixed hypothetical syllogism includes one categorical premise and follows the rules of modus ponens (If P then Q; P; therefore Q) or modus tollens (If P then Q; not Q; therefore not P).
Glossary of Important Terms
| Term | Meaning |
|---|---|
| Syllogism | Mediate deductive inference from two premises to a conclusion. |
| Categorical Syllogism | Syllogism whose three propositions are all categorical (A, E, I, O). |
| Major Term (P) | The predicate of the conclusion. |
| Minor Term (S) | The subject of the conclusion. |
| Middle Term (M) | The term common to both premises but absent from the conclusion. |
| Major Premise | The premise containing the major term. |
| Minor Premise | The premise containing the minor term. |
| Conclusion | The proposition inferred from the premises. |
| Mood | Form of a syllogism determined by quality and quantity of its propositions. |
| Figure | Form of a syllogism determined by the position of the middle term. |
| Distribution | A term is distributed when the proposition refers to all members of its class. |
| Reduction | Transforming a syllogism of figures 2, 3 or 4 to figure 1. |
| Direct Reduction | Reduction by conversion, obversion or transposition. |
| Indirect Reduction | Reductio per impossibile, used for Bocardo and Baroco. |
| Sorites | A chain of syllogisms with intermediate conclusions suppressed. |
| Validity | Property of an argument whose conclusion necessarily follows from its premises. |
| Soundness | Validity together with the actual truth of all premises. |
| Existential Import | The implication by a proposition that its subject class is non-empty. |
Position of the Middle Term in the Four Figures
| Figure | Major Premise | Minor Premise | Conclusion | Position of M |
|---|---|---|---|---|
| First | M – P | S – M | S – P | Subject of major, predicate of minor |
| Second | P – M | S – M | S – P | Predicate of both premises |
| Third | M – P | M – S | S – P | Subject of both premises |
| Fourth | P – M | M – S | S – P | Predicate of major, subject of minor |
Valid Moods of the Four Figures (Mnemonic Names)
| Figure | Valid Moods (Mood Pattern) | Mnemonic Names |
|---|---|---|
| First Figure | AAA, EAE, AII, EIO | Barbara, Celarent, Darii, Ferio |
| Second Figure | EAE, AEE, EIO, AOO | Cesare, Camestres, Festino, Baroco |
| Third Figure | AAI, IAI, AII, EAO, OAO, EIO | Darapti, Disamis, Datisi, Felapton, Bocardo, Ferison |
| Fourth Figure | AAI, AEE, IAI, EAO, EIO | Bramantip, Camenes, Dimaris, Fesapo, Fresison |
Distribution of Terms in A, E, I, O Propositions
| Proposition | Form | Subject | Predicate |
|---|---|---|---|
| A | All S is P | Distributed | Undistributed |
| E | No S is P | Distributed | Distributed |
| I | Some S is P | Undistributed | Undistributed |
| O | Some S is not P | Undistributed | Distributed |
The Eight General Rules of Categorical Syllogism
| No. | Rule | Fallacy if Violated |
|---|---|---|
| 1 | A syllogism must contain exactly three terms. | Fallacy of Four Terms |
| 2 | A syllogism must contain exactly three propositions. | Structural fallacy |
| 3 | The middle term must be distributed at least once in the premises. | Fallacy of Undistributed Middle |
| 4 | No term distributed in the conclusion may be undistributed in its premise. | Fallacy of Illicit Major / Illicit Minor |
| 5 | From two negative premises no conclusion follows. | Fallacy of Exclusive Premises |
| 6 | If one premise is negative, the conclusion must be negative; if both premises are affirmative, the conclusion must be affirmative. | Fallacy of Affirmative Conclusion from Negative Premise (or vice versa) |
| 7 | From two particular premises no conclusion follows. | Fallacy of Two Particular Premises |
| 8 | If one premise is particular, the conclusion must be particular. | Universal conclusion fallacy / Existential Fallacy |
The Major Fallacies of Categorical Syllogism
| Fallacy | Description | Example |
|---|---|---|
| Four Terms | Syllogism contains four or more terms (often by equivocation). | All laws can be repealed; gravitation is a law; therefore gravitation can be repealed. |
| Undistributed Middle | Middle term not distributed in any premise. | All cats are animals; all dogs are animals; therefore all dogs are cats. |
| Illicit Major | Major term distributed in conclusion but not in major premise. | All cats are mammals; no dogs are cats; therefore no dogs are mammals. |
| Illicit Minor | Minor term distributed in conclusion but not in minor premise. | All Indians are Asians; all Indians are humans; therefore all humans are Asians. |
| Exclusive Premises | Both premises negative. | No fish are mammals; no whales are fish; therefore no whales are mammals. |
| Affirmative from Negative | Affirmative conclusion drawn while a premise is negative. | No fish are mammals; some whales are not fish; therefore some whales are mammals. |
| Negative from Affirmatives | Negative conclusion drawn from two affirmative premises. | All men are rational; some animals are men; therefore some animals are not rational. |
| Existential Fallacy | Particular conclusion drawn from two universal premises (modern view). | All unicorns are mammals; all mammals are vertebrates; therefore some unicorns are vertebrates. |
Special Rules of the Four Figures
| Figure | Special Rules |
|---|---|
| First | (a) Major premise must be universal. (b) Minor premise must be affirmative. |
| Second | (a) One premise must be negative. (b) Major premise must be universal. |
| Third | (a) Minor premise must be affirmative. (b) Conclusion must be particular. |
| Fourth | (a) If major is affirmative, minor must be universal. (b) If minor is affirmative, conclusion must be particular. (c) If either premise is negative, the major must be universal. |
Summary of Reductions
| Mood (Figure) | Operation | Reduces to |
|---|---|---|
| Cesare (EAE-2) | Convert major simply | Celarent (EAE-1) |
| Camestres (AEE-2) | Convert minor simply, transpose premises, convert conclusion simply | Celarent |
| Festino (EIO-2) | Convert major simply | Ferio (EIO-1) |
| Baroco (AOO-2) | Indirect reduction (per impossibile) | Barbara |
| Darapti (AAI-3) | Convert minor per accidens | Darii (AII-1) |
| Disamis (IAI-3) | Convert major simply, transpose, convert conclusion | Darii |
| Datisi (AII-3) | Convert minor simply | Darii |
| Felapton (EAO-3) | Convert minor per accidens | Ferio |
| Bocardo (OAO-3) | Indirect reduction (per impossibile) | Barbara |
| Ferison (EIO-3) | Convert minor simply | Ferio |
| Bramantip (AAI-4) | Transpose premises and convert conclusion per accidens | Barbara |
| Camenes (AEE-4) | Transpose premises and convert conclusion simply | Celarent |
| Dimaris (IAI-4) | Transpose and convert conclusion simply | Darii |
| Fesapo (EAO-4) | Convert major simply and minor per accidens | Ferio |
| Fresison (EIO-4) | Convert major and minor simply | Ferio |
This brings us to the end of Class 11 Logic and Philosophy Chapter 8 Question Answer | Categorical Syllogism | English Medium | ASSEB. Mastering the structure, mood, figure, rules, fallacies and reductions discussed in this chapter will give you a strong foundation in formal deductive logic and prepare you confidently for the ASSEB Higher Secondary First Year examination. Remember the four figures by the position of the middle term, memorise the mnemonic mood-names, and always check a syllogism against the eight general rules. With consistent practice, identifying valid arguments and exposing fallacies will become second nature.