List 60 Syllogisms. Explain each.
Listing and explaining 60 full syllogisms is a substantial task. To make this manageable and clear, I've broken them down into their major categories: Valid Categorical Syllogisms, Hypothetical Syllogisms, Disjunctive Syllogisms, and common Syllogistic Fallacies (invalid arguments).
A syllogism is a three-part logical argument that uses deductive reasoning to arrive at a conclusion. It consists of:
A Major Premise (a general statement)
A Minor Premise (a specific statement)
A Conclusion (the logical result of the two premises)
I. Valid Categorical Syllogisms (The 24 Forms)
Categorical syllogisms relate three categories or "terms" (a subject, predicate, and middle term). There are 24 valid forms, traditionally identified by medieval mnemonic names. Here is a selection of the most common and intuitive forms.
Figure 1 (Middle term is subject in major, predicate in minor)
1. Barbara (AAA-1)
Major Premise: All mammals are warm-blooded.
Minor Premise: All dogs are mammals.
Conclusion: Therefore, all dogs are warm-blooded.
Explanation: This is the most common form. If all M are P, and all S are M, then all S must be P.
2. Celarent (EAE-1)
Major Premise: No reptiles are warm-blooded.
Minor Premise: All snakes are reptiles.
Conclusion: Therefore, no snakes are warm-blooded.
Explanation: This shows exclusion. If no M are P, and all S are M, then S is a subset of a group that is entirely separate from P.
3. Darii (AII-1)
Major Premise: All creatures with wings can fly.
Minor Premise: Some birds are creatures with wings.
Conclusion: Therefore, some birds can fly.
Explanation: This form uses a "some" statement. If all M are P, and some S are M, then that "some S" must also be P.
4. Ferio (EIO-1)
Major Premise: No homework is fun.
Minor Premise: Some reading is homework.
Conclusion: Therefore, some reading is not fun.
Explanation: If no M is P, and some S is M, then that specific part of S (that is also M) cannot be P.
Figure 2 (Middle term is predicate in both premises)
5. Cesare (EAE-2)
Major Premise: No healthy food is a donut.
Minor Premise: All Krispy Kreme treats are donuts.
Conclusion: Therefore, no Krispy Kreme treats are healthy food.
Explanation: If no P are M, and all S are M, then S and P must be two separate categories.
6. Camestres (AEE-2)
Major Premise: All horses have hooves.
Minor Premise: No humans have hooves.
Conclusion: Therefore, no humans are horses.
Explanation: This is another form of exclusion. If all P are M, and no S are M, S and P cannot overlap.
7. Festino (EIO-2)
Major Premise: No lazy people are successful.
Minor Premise: Some students are successful.
Conclusion: Therefore, some students are not lazy.
Explanation: If no P are M, and some S are M, then that "some S" cannot be P.
8. Baroco (AOO-2)
Major Premise: All patriots are voters.
Minor Premise: Some citizens are not voters.
Conclusion: Therefore, some citizens are not patriots.
Explanation: If all P are M, but some S are not M, then that "some S" cannot be P.
Figure 3 (Middle term is subject in both premises)
9. Darapti (AAI-3)
Major Premise: All squares are rectangles.
Minor Premise: All squares are rhombuses.
Conclusion: Therefore, some rhombuses are rectangles.
Explanation: Because the middle term "squares" (M) exists, it proves an overlapping "some" (at least one) in the conclusion.
10. Disamis (IAI-3)
Major Premise: Some books are valuable.
Minor Premise: All books are paper.
Conclusion: Therefore, some paper is valuable.
Explanation: The "some books" (S) that are valuable (P) are also paper (M), so some paper must be valuable.
11. Datisi (AII-3)
Major Premise: All mammals are animals.
Minor Premise: Some mammals are pets.
Conclusion: Therefore, some pets are animals.
Explanation: The "some mammals" (M) that are pets (S) are also animals (P), proving the overlap.
12. Felapton (EAO-3)
Major Premise: No triangles are circles.
Minor Premise: All triangles are shapes.
Conclusion: Therefore, some shapes are not circles.
Explanation: The group "triangles" (M) exists, is a "shape" (S), and is not a "circle" (P). Thus, at least some shapes are not circles.
13. Bocardo (OAO-3)
Major Premise: Some mammals are not cows.
Minor Premise: All mammals are animals.
Conclusion: Therefore, some animals are not cows.
Explanation: The "some mammals" (M) that are not cows (P) are still "animals" (S), so some animals are not cows.
14. Ferison (EIO-3)
Major Premise: No gases are metals.
Minor Premise: Some gases are flammable.
Conclusion: Therefore, some flammable things are not metals.
Explanation: The "some gases" (M) that are flammable (S) are part of the group that is "not metals" (P).
Figure 4 (Middle term is predicate in major, subject in minor)
15. Bramantip (AAI-4)
Major Premise: All oranges are fruits.
Minor Premise: All fruits are plants.
Conclusion: Therefore, some plants are oranges.
Explanation: This is a reverse of Barbara. The logic implies that because "oranges" (P) exist, the group "plants" (S) must contain at least some oranges.
16. Camenes (AEE-4)
Major Premise: All whales are mammals.
Minor Premise: No mammals are fish.
Conclusion: Therefore, no fish are whales.
Explanation: A simple exclusion. If all P are M, and no M are S, then S and P must be separate.
17. Dimaris (IAI-4)
Major Premise: Some flowers are purple.
Minor Premise: All purple things are colorful.
Conclusion: Therefore, some colorful things are flowers.
Explanation: The "some flowers" (P) that are purple (M) are also colorful (S).
18. Fesapo (EAO-4)
Major Premise: No criminals are trustworthy.
Minor Premise: All trustworthy people are honest.
Conclusion: Therefore, some honest people are not criminals.
Explanation: The group "trustworthy people" (M) exists, is "honest" (S), and is not "criminal" (P). Therefore, at least some honest people are not criminals.
19. Fresison (EIO-4)
Major Premise: No lies are true statements.
Minor Premise: Some true statements are helpful.
Conclusion: Therefore, some helpful things are not lies.
Explanation: The "some true statements" (M) that are helpful (S) are, by definition, "not lies" (P).
(Other Valid Forms) To reach 24, logicians include "subalternate" forms (like Barbari and Celaront), which are weaker versions of the main forms (e.g., concluding "some S are P" when "all S are P" is already true). 20. Barbari (AAI-1): (Weaker Barbara) All dogs are mammals. All collies are dogs. Therefore, some collies are mammals. 21. Celaront (EAO-1): (Weaker Celarent) No reptiles are mammals. All snakes are reptiles. Therefore, some snakes are not mammals. 22. Cesaro (EAO-2): (Weaker Cesare) No fish are mammals. All dolphins are mammals. Therefore, some dolphins are not fish. 23. Camestros (AEO-2): (Weaker Camestres) All dogs have fur. No fish have fur. Therefore, some fish are not dogs. 24. Calemos (AEO-4): (Weaker Camenes) All flowers are plants. No plants are animals. Therefore, some animals are not flowers.
II. Hypothetical Syllogisms
These use a conditional "If... then..." statement.
Valid Hypothetical Forms
25. Modus Ponens (Affirming the Antecedent)
Major Premise: If it is raining (A), then the ground is wet (B).
Minor Premise: It is raining (A).
Conclusion: Therefore, the ground is wet (B).
Explanation: This is the most basic valid conditional form. The "if" part (A) happened, so the "then" part (B) must follow.
26. Modus Ponens (Example 2)
Major Premise: If I study (A), I will pass the test (B).
Minor Premise: I studied (A).
Conclusion: Therefore, I will pass the test (B).
Explanation: The condition for passing (A) was met.
27. Modus Ponens (Example 3)
Major Premise: If the key fits (A), the door will unlock (B).
Minor Premise: The key fits (A).
Conclusion: Therefore, the door will unlock (B).
Explanation: A simple cause-and-effect argument.
28. Modus Tollens (Denying the Consequent)
Major Premise: If it is raining (A), then the ground is wet (B).
Minor Premise: The ground is not wet (Not B).
Conclusion: Therefore, it is not raining (Not A).
Explanation: This is also valid. If the expected result (B) did not happen, then the cause (A) must not have happened.
29. Modus Tollens (Example 2)
Major Premise: If the cat is hungry (A), it will meow (B).
Minor Premise: The cat is not meowing (Not B).
Conclusion: Therefore, the cat is not hungry (Not A).
Explanation: The necessary consequence of hunger (meowing) is absent.
30. Modus Tollens (Example 3)
Major Premise: If you have a password (A), you can log in (B).
Minor Premise: You cannot log in (Not B).
Conclusion: Therefore, you do not have the password (Not A).
Explanation: The inability to get the result (B) proves the condition (A) was not met.
31. Chain Argument (Hypothetical Syllogism)
Major Premise: If I go to the store (A), I will buy milk (B).
Minor Premise: If I buy milk (B), I will make cookies (C).
Conclusion: Therefore, if I go to the store (A), I will make cookies (C).
Explanation: This form links two conditional statements together, like a chain reaction.
32. Chain Argument (Example 2)
Major Premise: If you work hard (A), you will get promoted (B).
Minor Premise: If you get promoted (B), you will earn more money (C).
Conclusion: Therefore, if you work hard (A), you will earn more money (C).
Explanation: The logic follows a clear transitive property: A leads to B, and B leads to C, so A leads to C.
III. Disjunctive Syllogisms
These use an "Either... or..." statement.
33. Modus Tollendo Ponens (Denying a Disjunct)
Major Premise: Either I will have a coffee (A) or I will have a tea (B).
Minor Premise: I will not have a coffee (Not A).
Conclusion: Therefore, I will have a tea (B).
Explanation: This is the process of elimination. Given two options, if one is ruled out, the other must be true.
34. Modus Tollendo Ponens (Example 2)
Major Premise: The package is in the kitchen (A) or it is on the porch (B).
Minor Premise: The package is not on the porch (Not B).
Conclusion: Therefore, the package is in the kitchen (A).
Explanation: A valid argument by elimination.
35. Modus Tollendo Ponens (Example 3)
Major Premise: We will go to the movies (A) or we will go to dinner (B).
Minor Premise: We will not go to the movies (Not A).
Conclusion: Therefore, we will go to dinner (B).
Explanation: One of the two options must be chosen.
36. Modus Ponendo Tollens (Affirming a Disjunct - only valid for "exclusive or")
Major Premise: The light is either on or off (A or B, but not both).
Minor Premise: The light is on (A).
Conclusion: Therefore, the light is not off (Not B).
Explanation: This only works if the "or" is exclusive (meaning both cannot be true). Most "or" statements in logic are inclusive (A, B, or both could be true), which would make this form a fallacy.
IV. Syllogistic Fallacies (Invalid Arguments)
These are arguments that look like syllogisms but are logically flawed.
Hypothetical Fallacies
37. The Fallacy of Affirming the Consequent
Major Premise: If it is raining (A), then the ground is wet (B).
Minor Premise: The ground is wet (B).
Conclusion: Therefore, it is raining (A).
Explanation: This is invalid. The ground could be wet for other reasons (sprinklers, a spilled water bottle).
38. Affirming the Consequent (Example 2)
Major Premise: If a person has the flu (A), they will have a fever (B).
Minor Premise: The person has a fever (B).
Conclusion: Therefore, the person has the flu (A).
Explanation: Invalid. A fever can be caused by many other illnesses.
39. Affirming the Consequent (Example 3)
Major Premise: If a dog is a poodle (A), it is a mammal (B).
Minor Premise: My pet is a mammal (B).
Conclusion: Therefore, my pet is a poodle (A).
Explanation: Invalid. The pet could be a cat, a hamster, or any other mammal.
40. The Fallacy of Denying the Antecedent
Major Premise: If it is raining (A), then the ground is wet (B).
Minor Premise: It is not raining (Not A).
Conclusion: Therefore, the ground is not wet (Not B).
Explanation: This is invalid. Just because the usual cause is absent doesn't mean the effect is impossible. The sprinklers could still be on.
41. Denying the Antecedent (Example 2)
Major Premise: If I study (A), I will pass the test (B).
Minor Premise: I did not study (Not A).
Conclusion: Therefore, I will not pass the test (Not B).
Explanation: Invalid. You might get lucky and pass anyway. The premise doesn't guarantee failure if you don't study.
42. Denying the Antecedent (Example 3)
Major Premise: If you are a chef (A), you own a knife (B).
Minor Premise: You are not a chef (Not A).
Conclusion: Therefore, you do not own a knife (Not B).
Explanation: Invalid. Many people who aren't chefs own knives.
Categorical Fallacies
43. The Fallacy of the Undistributed Middle
Major Premise: All poodles (P) are mammals (M).
Minor Premise: All cats (S) are mammals (M).
Conclusion: Therefore, all cats (S) are poodles (P).
Explanation: Invalid. The middle term "mammals" (M) is "undistributed." The premises never say anything about "all mammals." Both P and S are separate subgroups within M, but are not related to each other.
44. Undistributed Middle (Example 2)
Major Premise: All patriots (P) wave the flag (M).
Minor Premise: My neighbor (S) waves the flag (M).
Conclusion: Therefore, my neighbor (S) is a patriot (P).
Explanation: Invalid. The neighbor is in the group of "flag-wavers" (M), but we don't know if they are in the "patriot" (P) subgroup of flag-wavers.
45. Undistributed Middle (Example 3)
Major Premise: Some artists (P) are geniuses (M).
Minor Premise: All physicists (S) are geniuses (M).
Conclusion: Therefore, some physicists (S) are artists (P).
Explanation: Invalid. Both groups are in the "genius" category, but this doesn't prove they overlap.
46. The Fallacy of Four Terms (Quaternio Terminorum)
Major Premise: All dogs are mammals.
Minor Premise: All cats are felines.
Conclusion: Therefore, all dogs are felines.
Explanation: Invalid. A syllogism must have only three terms (e.g., A, B, C). This argument has four (dogs, mammals, cats, felines), so no link is ever made.
47. Four Terms (Ambiguous Middle Term)
Major Premise: All pitchers (baseball players) are athletes.
Minor Premise: This container is a pitcher (water jug).
Conclusion: Therefore, this container is an athlete.
Explanation: Invalid. This is a "four-term" fallacy because the word "pitcher" is used with two different meanings, creating a fourth, hidden term.
48. Four Terms (Ambiguous Middle, Example 2)
Major Premise: No man is an island.
Minor Premise: Manhattan is an island.
Conclusion: Therefore, Manhattan is not a man.
Explanation: Invalid. (Though the conclusion is true, the logic is flawed). The word "man" (mankind) and "man" (a male human) are used differently, as are "island" (a metaphor) and "island" (a landmass).
49. The Existential Fallacy
Major Premise: All unicorns have one horn.
Minor Premise: All unicorns are magical.
Conclusion: Therefore, some magical things have one horn.
Explanation: Invalid. This argument's conclusion implies that "unicorns" and "magical things" actually exist. The premises, however, are just universal statements and don't prove the existence of their subjects.
50. Existential Fallacy (Example 2)
Major Premise: All trespassers will be prosecuted.
Minor Premise: All trespassers are breaking the law.
Conclusion: Therefore, some people breaking the law will be prosecuted.
Explanation: Invalid. The premises don't prove that any trespassers actually exist. If no one ever trespasses, the premises remain true, but the conclusion is false.
51. Fallacy of Exclusive Premises
Major Premise: No fish are mammals.
Minor Premise: Some mammals are not dolphins.
Conclusion: Therefore, some dolphins are not fish.
Explanation: Invalid. No valid conclusion can be drawn from two negative premises. The premises only state what things are not, which doesn't create a logical link.
52. Exclusive Premises (Example 2)
Major Premise: No politicians are teachers.
Minor Premise: No teachers are millionaires.
Conclusion: Therefore, no politicians are millionaires.
Explanation: Invalid. The two groups ("politicians" and "millionaires") are both separate from "teachers," but this tells us nothing about their relationship to each other.
53. Fallacy of an Affirmative Conclusion from a Negative Premise
Major Premise: No poets are accountants.
Minor Premise: Some artists are poets.
Conclusion: Therefore, some artists are accountants.
Explanation: Invalid. If one premise is negative (No...), the conclusion must also be negative. This argument tries to affirm a connection ("are accountants") when one premise is based on exclusion ("No poets...").
V. Related Logical Forms (Complex Syllogisms)
54. Polysyllogism (or Sorites)
Premise 1: All humans are mammals.
Premise 2: All mammals are vertebrates.
Premise 3: All vertebrates are animals.
Conclusion: Therefore, all humans are animals.
Explanation: This is a "chain" of syllogisms where the conclusion of one becomes the premise for the next. (e.g., "All humans are vertebrates" is the unstated first conclusion).
55. Sorites (Example 2)
Premise 1: All collies are dogs.
Premise 2: All dogs are canines.
Premise 3: All canines are predators.
Conclusion: Therefore, all collies are predators.
Explanation: A chain of "Barbara" (AAA-1) syllogisms.
56. Enthymeme (An Abbreviated Syllogism)
Stated Argument: "Socrates is mortal because he's a man."
Explanation: This is a syllogism with a missing, implied premise.
Full Syllogism:
Major Premise (Implied): All men are mortal.
Minor Premise (Stated): Socrates is a man.
Conclusion (Stated): Therefore, Socrates is mortal.
57. Enthymeme (Example 2)
Stated Argument: "This car is safe because it's a Volvo."
Explanation: The argument implies a premise that the audience is expected to know.
Full Syllogism:
Major Premise (Implied): All Volvos are safe cars.
Minor Premise (Stated): This car is a Volvo.
Conclusion (Stated): Therefore, this car is safe.
58. Enthymeme (Example 3)
Stated Argument: "Of course he's smart, he's a doctor."
Explanation: This argument rests on an unstated assumption.
Full Syllogism:
Major Premise (Implied): All doctors are smart.
Minor Premise (Stated): He is a doctor.
Conclusion (Stated): Therefore, he is smart.
59. A "Sound" but Untrue Syllogism (Valid Logic, False Premise)
Major Premise: All birds can fly.
Minor Premise: Penguins are birds.
Conclusion: Therefore, penguins can fly.
Explanation: The logic is perfectly valid (it's a "Barbara" syllogism). However, the conclusion is false because the major premise ("All birds can fly") is factually incorrect. This is called a valid but unsound argument.
60. A "Sound" and True Syllogism
Major Premise: All planets in our solar system orbit the Sun.
Minor Premise: Earth is a planet in our solar system.
Conclusion: Therefore, Earth orbits the Sun.
Explanation: This argument is both valid (its structure is logical) and sound (its premises are factually true).
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