PLEASE STANDBY, WE WILL START IN A FEW MINUTES. CATEGORICAL SYLLOGISM TOPIC OUTLINE: I. Definition of terms II. Categorical Syllogism in Standard Form III. Structure of a Categorical Syllogism IV. Moods and Figures of C.S. V. Rules of a Categorical Syllogism VI. Fallacies of Categorical Syllogism SYLLOGISM a deductive argument composed of exactly two premises and one conclusion CATEGORICAL TERM - designates a class of things - basic unit of meaning or content in the deductive system - usually expressed grammatically as a noun or noun phrase CATEGORICAL PROPOSITION a statement about the relationship between categories. It states whether one category or categorical term is fully contained with another, is partially contained within another, or is completely separate. Contains the following elements: a. Quantity - may refer to all, some, or no members of a category Universal prepositions: refers to "all", "none" Particular prepositions: refers to "some" b. Quality - affirmative ( represented by A and I; Affirmo) or negative (represented by E and O; nEgO) c. noun or noun phrase - the class or category is expressed by a noun or noun phrase Noun: genera, species, time, fruits, date, etc. Noun phrase: involves modifier and noun (ex. a vicious lion, a friendly dog) d. Copula - conjugation of the verb "to be" ( "is" or "are" ) - can be negated or not Example: Some politicians are not corrupt Some politicians are corrupt A categorical proposition affirms or denies that at least one, or all members of the subject category are members of the predicate category. CATEGORICAL SYLLOGISM a kind of mediate deductive argument which is composed of three categorical propositions (2 premises + a conclusion) with exactly three categorical terms, each of which appears in exactly two of the three propositions Examples of Categorical Syllogism: All toads are reptiles No cows are toads No cows are reptiles All parrots are birds All birds are animals All parrots are animals STRUCTURE OF A CATEGORICAL SYLLOGISM: 1.MAJOR PREMISE 2.MINOR PREMISE 3.CONCLUSION The premise that contains the major term The premise that contains the minor term The agreement or disagreement b/w P and S is expressed or enunciated. Major Premise Conclusion All mammals are animals All cats are mammals All cats are animals Minor Premise STRUCTURE OF A CATEGORICAL SYLLOGISM: 4.MAJOR TERM (P) 5. MINOR TERM (S) 6. MIDDLE TERM (M) The predicate term of the conclusion The subject term of the conclusion The term repeated in the premises but not in the conclusion All mammals are animals All cats are mammals All cats are animals minor term (S) major term (P) middle term (M) CATEGORICAL SYLLOGISM IN STANDARD FORM MAJOR PREMISES + MINOR PREMISES + CONCLUSION Examples: All fish can swim. A guppy is a fish. Therefore, a guppy can swim. No geese are felines. Some birds are geese. Therefore, some birds are not felines. Activity 1: Identify the terms and premises in the syllogism. All fish can swim. A guppy is a fish. A guppy can swim. All fish can swim. Major Premise A guppy is a fish. Minor Premise A guppy can swim. Major term: swim Minor term: guppy Middle term: fish Activity 2: WHICH CATEGORICAL SYLLOGISM IS IN STANDARD FORM? All birds are animals All parrots are birds All parrots are animals No cows are toads All toads are reptiles No cows are reptiles All birds are animals All parrots are birds All parrots are animals No cows are toads All toads are reptiles No cows are reptiles The argument is in standard form categorical syllogism. The argument is NOT in a standard-form categorical syllogism. - the premises are not in the right order MOODS AND FIGURES OF SYLLOGISM To know if the syllogisms are valid or invalid, we must determine the following: MOOD a series of three letters corresponding to the type of proposition the premises (major and minor), and the conclusion are (A,E,I or O) FIGURE a number that corresponds to the placement of the two middle terms MOODS In logic, it is the classification of categorical syllogisms according to the quantity (universal or particular) and quality (affirmative or negative) of their constituent propositions. Forms of Propositions A (Universal Affirmative) All S are P E (Universal Negative) No S are P I (Particular Affirmative) Some S are P O (Particular Negative) Some S are not P EXAMPLE: All soldiers are patriots. (A) No traitors are patriots. (E) Therefore no traitors are soldiers (E). The syllogical form based on the mood is AEE. Activity 3: Identify the mood of this syllogism. All ducks are birds. All griffins are ducks. Some griffins are birds. All ducks are birds -A All griffins are ducks - A Some griffins are birds - I The syllogical form based on the mood is AAI. FIGURES In logic, it is the classification of categorical syllogisms according to the arrangement of the middle term, namely, the term (subject or predicate of a proposition) that occurs in both premises but not in the conclusion. FORMS OF FIGURES: FORMS OF FIGURES: EXAMPLE: All soldiers are patriots. No traitors are patriots. Therefore no traitors are soldiers The syllogical form shown is 2nd figure. (AEE-2) Activity 4: Identify the figure of this syllogism. All cats are felines No dogs are cats No dogs are felines All cats are felines No dogs are cats No dogs are felines -A -E -E The syllogical form shown is 1st figure (AEE-1) RULES OF CATEGORICAL SYLLOGISM RULE 1 A valid categorical syllogism only has three terms: major, minor and middle term. RULE 2 Each term must occur in two prepositions of the argument. RULE 3 A major or minor term may not be universal in the conclusion, unless they are universal in the premises. P1: All politicians are sociable people P2: All councilors are politicians C: All councilors are sociable people Major term: sociable people Minor term: councilors Middle term: politicians RULE 4 The middle term must be distributed in at least one premise. RULE 5 If both the premises are affirmative, then the conclusion must also be affirmative. RULE 6 If one premise is affirmative and the other is negative, the conclusion must be negative. Example: All politicians are sociable people All councilors are politicians All councilors are sociable people Example: All risk-takers are gamblers. (A) Some Filipinos are gamblers. (I) Some Filipinos are risk-takers. (I) Example: No computer is useless. (E) All ATM are computers. (A) No ATM is useless. (E) RULE 7 A categorical syllogism cannot have two negative premises. RULE 8 At least one premise must be universal. Example: No country is leaderless. (E) No ocean is a country. (E) No ocean is leaderless. (E) Example: Some kids are athletic. (I) Some Filipinos are kids. (I) Some Filipinos are athletic.(I) RULE 9 If a premise is particular, the conclusion must also be particular. RULE 10 The actual existence of a subject may not be asserted in the conclusion, unless it has been asserted in the premises. Example: All eagles are winged-beings. (A) Some creatures are eagles. (I) Some creatures are winged-beings. (I) Example: This wood floats That wood floats All wood floats FALLACIES IN STANDARD -FORM CATEGORICAL SYLLOGISM SYLLOGISTIC FALLACY A "fallacy" is the name for a mistake in logic. Syllogistic fallacies happen when logical fallacies occur in the syllogisms of deductive reasoning. This occurs with a reference to something general, and then makes a conclusion about something more specific. Examples of Categorical Syllogism: All sharks are fish All salmon are fish Therefore all salmon are sharks. The two generalities in the first two statements are true, but they do not validate the conclusion being drawn. 6 FALLACIES OF CATEGORICAL SYLLOGISM Fallacy of Four Terms Fallacy of Undistributed Middle Term Fallacy of Illicit Major and Minor Fallacy of Exclusive Premises Fallacy of Drawing an Affirmative Conclusion from a Negative Premise Existential Fallacy Fallacy of Four Terms The fallacy of four terms is the formal fallacy that occurs when a syllogism has four (or more) terms rather than the requisite three. This form of argument is thus invalid. Fallacy of Undistributed Middle Term The fallacy of the undistributed middle is a formal fallacy that is committed when the middle term in a categorical syllogism is not distributed in either the minor premise or the major premise. It is thus a syllogistic fallacy. Distribution: If a categorical proposition asserts something definite about every member of a class, then the term designating that class is said to be distributed. Categorical Propositions A - All S are P E - No S are P Categorical Propositions: A: S is distributed to P E: Both terms are distributed I: Both terms are not distributed O: P is distributed to S I - Some S are P O - Some S are not P EXAMPLES ALL S ARE M ALL M ARE P ALL S ARE P SOME S ARE M SOME M ARE P SOME S ARE P Fallacy of Illicit Major and Minor Illicit major is a formal fallacy committed in a categorical syllogism that is invalid because its major term is undistributed in the major premise but distributed in the conclusion. Illicit minor is a formal fallacy committed in a categorical syllogism that is invalid because its minor term is undistributed in the minor premise but distributed in the conclusion. EXAMPLES Illicit Major Illicit Minor ALL HOTDOGS ARE FAST FOOD. ALL CATHOLICS ARE CHRISTIAN. NO HAMBURGERS ARE HOTDOGS. ALL CHRISTIANS ARE JESUS LOVERS. THEREFORE, NO HAMBURGERS ARE FAST FOOD. THEREFORE, ALL JESUS LOVERS ARE CATHOLIC. Fallacy of Exclusive Premises The fallacy of exclusive premises is a syllogistic fallacy committed in a categorical syllogism that is invalid because both of its premises are negative EXAMPLES No kangaroos are MMA fighters. Some MMA fighters are not Mormons. Therefore, some Mormons are not kangaroos. No animals are insects. No insects are dogs. Therefore, no dogs are animals. No animals are insects. Some insects are not dogs. Therefore, some dogs are not animals. Fallacy of Drawing an Affirmative Conclusion from a Negative Premise Affirmative conclusion from a negative premise is a formal fallacy that is committed when a categorical syllogism has a positive conclusion and one or two negative premises. EXAMPLES No people under the age of 66 are senior citizens. No senior citizens are children. Therefore, all people under the age of 66 are children. No donkeys are fish. Some asses are donkeys. Therefore, some asses are fish. Existential Fallacy A formal logical fallacy, which is committed when a categorical syllogism employs two universal premises (“all”) to arrive at a particular (“some”) conclusion. EXAMPLES All babysitters have pimples. All babysitter club members are babysitters. Therefore, some babysitter club members have pimples. All forest creatures live in the woods. All leprechauns are forest creatures. Therefore, some leprechauns live in the woods. ACTIVITY: Determine if the following categorical syllogisms are valid or not. Some parrots are not pests. All parrots are pets. Therefore, no pets are pests. AAA - 2 Some parrots are not pests. All parrots are pets. Therefore, no pets are pests. ANSWER: INVALID All S are M All P are M All S are P ANSWER: INVALID THANK YOU FOR LISTENING! Prepared by: Keth Arvin B. Burac Sophia Loren V. Dagñalan Precious M. Mella