CATEGORICAL SYLLOGISM

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Based from the book : "Logic Made Simple for Filipinos" by Florentino Timbreza here is the summary made into powerpoint of Lesson 12: The Categorical Syllogism.
It Includes:
Introduction to categorical syllogism
General Axioms of the Syllogism
Eight Syllogistic Rules
Figures and Moods of the Categorical Syllogism

Examples in these slides are our own, there were no examples derived from the book.

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  • Judgement expresses –the mutual agreement or disagreement between 2 ideasthe mere analysis of the of the S and P or direct observation will not disclose their judgement.THEREFORE THE MIND IS IN STATE OF DOUBT WHENEVER IT CANNOT PERCEIVE THE AGREEMENT OR DISAGREEMENT OF THE 2 IDEASThe mind compares the two certain ideas with the third idea to which is familiar
  • IF THE TWO IDEAS AGREE WITH THE THIRDE IDEA – THEN THEY AGREE WITH EACH OTHER
  • IF ONE ONLY AGREES WITH THE THIRD AND THE OTHER DOES NOT THEN THEY DISAGREE AMONG THEMSELVESTHIS IS KNOWN FROM CHAPTER 3 LESSON 10 AS MEDIATE INFERENCE
  • THIS IS KNOWN FROM CHAPTER 3 LESSON 10MEDIATE INFERENCE –is one in which we derive conclusion from two or more premiseIt is the process of the mind in whereby we pass from one proposition to another with the aid of a third.The agreement between 2 uncertain ideas is known through the mediation of the 3rd idea with which both are compared
  • THEREFORE MEDIATE INFERENCE IS
  • THE DOUBTFUL IDEAS ARE THE DOG AND MORTAL THEN THEY ARE COMPARED TO THE SAME THIRD IDEA- ANIMAL THEREFORE THEY AGREE WITH EACH OTHER
  • THE VERBAL EXPRESSION OF AN IDEA IS THE TERM AND THAT OF JUDGEMENT IS A PROPOSITION.THE VERBAL EXPRESSION OF A MEDIATE INFERENCE IS ARGUMENTATION
  • IT IS ALSO The process of forming reasons, justifying beliefs, and drawing conclusions with the aim of influencing the thoughts and/or actions of othersARGUMENTATION TAKES THE FORM OF A SYLLOGISM
  • SYLLOGISM from the greekword  syllogismos  which means "conclusion," "inference“An argumentation in which, from two known propositions that contain a common idea, and one at least of which is universal, a third proposition, different from the two propositions, follow with necessity.
  • THERE ARE 2 TYPES OF SYLLOGISM CATEGORICAL AND HYPOTHETICAL
  • USUALLY THE MAJOR PREMISE COMES FIRST FOLLOWED BY THE MINOR PREMISE THEN FINALLY THE CONCLUSION BUT IT IS ONLY FOR CLARITY AND UNIFORMITY
  • MAJOR PREMISE:Is the one wherein the major term (P) is compared to the middle term (M)Usually contains more Universal class; is a general statementnot challenged and assumed to be trueMINOR PREMISE:is the one wherein the minor term (S) is compared to the middle term (M)IT CONTAINS less universal class
  • conclusion is a third statement, based on a combination of the major and minor premise.
  • MIDDLE TERM:Is term of comparison between the minor term and the major term in the premisesIt appears twice in the premise but NEVER in the conclusion
  • the middle term is fish in which the major term and minor term is compared. major term is sea creatures which stands for the universal class and the predicated of the conclusion minor term is shark which stands for the lesser class and the subject of the conclusion
  • THE RULE STATES THAT; An affirmative major premise and an affirmative minor premise should produce an affirmative conclusionThe major term (P) and minor term (S) of both affirmative premises are identical or agrees with the middle term.
  • the conclusion cannot legitimately make any statement of agreement or disagreement existing between the major and minor term if the middle term fails in its function as a term of comparison.
  • A violation of this rule leads to the fallacy of 2 negative premises
  • IF ONE PREMISE Is PARTICULAR Only a portion of either the minor term (S) or major term (P) referents share something in common with the middle term.
  • a violation of this rule leads to the FALLACY OF ILICIT MINOR
  • if one of the premises is negative, then neither agrees with the middle term therefore they don’t agree with each other
  • if both premises are particular there are 3 possibilitiesa violation of of this rule will give rise to the fallacy of 2 particulars
  • the subject of both premises are particular and the predicates will be particular because both premise are affirmative and affirmative premises always have a particular predicate.according to the six rule no conclusion can be drawn from 2 negative premises. a violation will leads to the fallacy of double negatives
  • THEREFORE IN MAKING SYLLOGISMS ONE PREMISE MUST BE UNIVERSAL
  • The problem here is that the middle term (that connects the first two statements) is assumed to refer to the same thing -- typically all of the members in its category
  • CATEGORICAL SYLLOGISM

    1. 1. CATEGORICALSYLLOGISM
    2. 2. INTRODUCTION the mere analysis of the of the S and P or direct observation will not disclose their judgment. The mind compares the two certain ideas with the third idea to which is familiar
    3. 3. INTRODUCTION IDEA 1 IDEA 2 IDEA 3  
    4. 4. INTRODUCTION IDEA 1 IDEA 2 IDEA 3  OR 
    5. 5. INTRODUCTION • MEDIATE INFERENCE – we derive conclusion from two or more premise • MEDIATION of the THIRD IDEA
    6. 6. MEDIATE INFERENCE a process of the mind in which from the agreement or disagreement of 2 ideas with a third idea we infer their agreement or disagreement with each other
    7. 7. EXAMPLE All animal is mortal. But every dog is an animal. Therefore, every dog is mortal.
    8. 8. THE SYLLOGISM IDEA : TERM JUDGEMENT : PROPOSITION MEDIATE INFERENCE : ARGUMENTATION
    9. 9. THE SYLLOGISM• ARGUMENTATION – a discourse which logically deduces one proposition from the others
    10. 10. SYLLOGISM An argumentation in which, from two known propositions that contain a common idea, and one at least of which is universal, a third proposition, different from the two propositions, follow with necessity. (Timbreza, 1992)
    11. 11. SYLLOGISM is a kind of logical argument in which one proposition (the conclusion) is inferred from two or more others (the premises) of a certain form. (Merriam-Webster Dictionary)
    12. 12. CATEGORICAL SYLLOGISM is a piece of deductive, mediate inference which consists of three categorical propositions, the first two which are premises and the third is the conclusion It contains exactly three terms, each of which occurs in exactly two of the constituent propositions.
    13. 13. EXAMPLE All fish swim. (Major Premise) Every shark is a fish. (Minor Premise) Therefore every shark swim. (Conclusion)
    14. 14. STRUCTURES OF A CATEGORICAL SYLLOGISM Three Propositions: Three terms: 1. Major Premise 1. Major term (P) 2. Minor Premise 2. Minor term (S) 3. Conclusion 3. Middle term (M)
    15. 15. THREE PROPOSITIONSMAJOR PREMISE: MINOR PREMISE: is the one wherein the is the one wherein the minor major term (P) is compared term (S) is compared to the to the middle term (M) middle term (M) less universal class universal class not challenged and assumed to be true
    16. 16. THREE PROPOSITIONSCONCLUSION: is the new truth arrived at , the result of reasoning, wherein the agreement or disagreement between the minor term (S) and the major term (P) is enunciated or expressed.
    17. 17. THREE TERMSMAJOR TERM (P): MINOR TERM (S):• compared to the • compared to the middle term in a major middle term in a minor premise premise• more universal class • less universal class• predicate of the conclusion • subject of the conclusion
    18. 18. THREE TERMSMIDDLE TERM: term of comparison appears twice in the premise but NEVER in the conclusion
    19. 19. EXAMPLE All fish (M) are sea creatues (P) (Major Premise) Every shark (S) s a fish (M) (Minor Premise) Therefore every shark (S) are sea creatures (P) (Conclusion)
    20. 20. EXERCISE _________ All mammals (_) have lungs (_). _________ All whales (_) have lungs (_). _________ Therefore, all whales (_) are mammals(_).
    21. 21. EXERCISE A land and water dwellers are called amphibians. All salamanders are land and water dwellers. All salamanders are amphibians.
    22. 22. TO SUMMARIZE All M is P – Major premise All is S is M – Minor premise Therefore, all S is P - Conclusion
    23. 23. General Axioms (Principles) of the Syllogism Prepared by: Agnes Baculi, Rn Geinah R. Quiñones, RN
    24. 24. 1. Principle of Reciprocal Identity If two terms agree (or are identical) with a third term, then they are identical with each other. M is P. M agrees with P. S is M. S agrees with M. ∴ S is P. ∴ S agrees with P.
    25. 25. Example: A dog is an animal. A hound is a dog. ∴ a hound is an animal.
    26. 26. 2. Principle of Reciprocal Non-Identity If two terms, one of which is identical with a third, but the other of which is not, then they are not identical with each other. P is M. P agrees with M. S is not M. S does not agree with M. ∴ S is not P. ∴ S does not agree with P.
    27. 27. Example: Nuclear-powered submarines are not commercial vessels. All nuclear-powered submarines are warships. ∴ warships are not commercial vessels.
    28. 28. 3. Dictum de Omni (The Law of All) What is affirmed of a logical class may also be affirmed of its logical member. P M S
    29. 29. Formula: 1. P is affirmed of M. But M is affirmed of S. Hence, P may also be affirmed of S. 2. Circle M is inside circle P. But circle S in inside circle M. Therefore, circle S is inside circle P.
    30. 30. Formula: 3. M is part of P. But S is a part of M. Therefore, S is also a part of P. 4. Circle P contains circle M. But circle M contains circle S. Therefore, circle P also contains circle S.
    31. 31. Example:All terriers are mammals.Terriers are dogs.Therefore, all dogs are mammals. Mammals Dogs Terrier
    32. 32. 4. Dictum de Nullo (The Law of None) What is denied of a logical class is also denied of its logical member. What is denied universally of a term is also denied of each of all referents of that term.
    33. 33. Example:Graduate students are voters.No person under eighteen years of age is a voter.Therefore, graduate students are not under eighteen years of age. Voters Under eighteen Graduate years of students age
    34. 34. Eight General Syllogistic Rules1. There must be only three terms in the syllogism.2. Neither the major nor the minor term may be distributed in the conclusion, if it is undistributed in the premises.3. The middle term must not appear in the conclusion.4. The middle term must be distributed at least once in the premises.
    35. 35. Eight General Syllogistic Rules5. Only an affirmative conclusion can be drawn from two affirmative premises.6. No conclusion can be drawn from two negative premises.7. If one premise is particular, the conclusion must also be particular; if one premise is negative, the conclusion must be negative.8. No conclusion can be drawn from two particular premises.
    36. 36. Rule 1: There must be only three terms in the syllogism. -Minor Term (S) -Major Term (P) -Middle Term (M)
    37. 37. Fallacy of Four Terms occurs when a syllogism has four (ormore) terms rather than the requisitethree. All M is P. All S is R. ∴ all S is P.
    38. 38. Example:All academicians are egotists.Susan is someone who works in a university.Therefore, Susan is an egotist.
    39. 39. Fallacy of Ambiguous MiddleSound travels very fast.His knowledge of law is sound.Therefore, his knowledge of law travels very fast.
    40. 40. Rule 2: Neither the major nor the minorterm may be distributed in the conclusion, if it is undistributed in the premises.a) Major term must not become universal in the conclusion if it is only particular in the major premise.b) Minor term must not become universal in the conclusion if it is only particular in the minor premise.
    41. 41. Fallacy of Illicit Processa) Fallacy of Illicit Majorb) Fallacy of Illicit Minor
    42. 42. Fallacy of Illicit MajorCommitted if and only if the majorterm (P) becomes universal in theconclusion while it is only particular inthe major premise.
    43. 43. Example:All Texans are Americans.No Californians are Texans.Therefore, no Californians are Americans.
    44. 44. Mu PpA- All Texans are Americans. Su MuE- No Californians are Texans. Su PuE- Therefore, no Californians are Americans.
    45. 45. Fallacy of Illicit MinorMinor term becomes universal inthe conclusion while it is onlyparticular (undistributed) in theminor premise.
    46. 46. Example:All animal rights activists are vegans.All animal rights activists are humans.Therefore, all humans are vegans.
    47. 47. Mu PpA- All animal rights activists are vegans. Mu SpA- All animal rights activists are humans. Su PuA- Therefore, all humans are vegans.
    48. 48. Rule 3: The middle term must not appear in the conclusion.All tables have four legsAll dogs have four legsTherefore all dogs and tables have four legs.
    49. 49. Rule 4: The middle term must be distributed at least once in the premises.Middle term must be used as least once asuniversal in any of the premises.It must be shown in the premises that atleast all members or referents of themiddle term are identical or not identicalwith all the members or referents of eitherthe minor or the major term.
    50. 50. Example:Contradictories are opposites.Black and white are opposites.∴ black and white are contradictories.
    51. 51. Pu MpContradictories are opposites. Su MpBlack and white are opposites. Su Pp∴ black and white are contradictories.
    52. 52. Fallacy of Undistributed Middle Arises when the middle term is not used at least once as universal in the premises.
    53. 53. RULES ON PREMISES5. Only an affirmative conclusion can be drawn from affirmative premises• The major term (P) and minor term (S) of both affirmative premises agree with the middle term.• Hence, the conclusion must express agreement between the major term (P) and minor term (S).
    54. 54. EXAMPLEEvery carnivore is a meat-eater. (affirmative) A lion is a carnivore. (affirmative)Therefore, a Lion is a meat-eater. (affirmative)
    55. 55. RULES ON PREMISES6. No conclusion can be drawn from two negative premises• If both the premises are negative, major term (P) and the minor term (S) disagree with the middle term, then the middle term cannot establish any relation between the major term (P) and the minor term (S)
    56. 56. FALLACY OF TWO NEGATIVES No vegetables are fruits. (negative) All tomatoes are not vegetables. (negative) Therefore, all tomatoes are not fruits. (negative)
    57. 57. RULES ON PREMISES7. If one premise is particular, the conclusion must be particular; if the one premise is negative the conclusion must be negative.• Only a portion of either the minor term (S) or major term (P) referents share something in common with the middle term.
    58. 58. FALLACY OF ILLICIT MINOR All Spartans are Greek. Some warriors are Spartans. (particular) Therefore, all warriors are Greek.
    59. 59. EXAMPLE All Spartans are Greek. Some warriors are Spartans. Therefore, some warriors are Greek.
    60. 60. RULES ON PREMISES if one of the premises is negative, then neither agrees with the middle term therefore they don’t agree with each other negative propostion: S is not P
    61. 61. EXAMPLE No cube is round. (negative) A box is a cube. Therefore a box is not round. (negative)
    62. 62. RULES ON PREMISES8. No conclusion can be drawn from two particular premises.• THREE POSSIBILITIES: a) either both are affirmative b) both are negative c) one is affirmative and the other is negative
    63. 63. THREE POSSIBILITIESa) either both are affirmative • if both premises are particular affirmative then all four terms will be particular.b) if both premises are particular negative no conclusion can be made.
    64. 64. THREE POSSIBILITIES c) if either of the particular premises is negative then the syllogism will contain either a fallacy of illicit major or undistributed middle
    65. 65. FALLACY OF ILLICIT MAJOR Some priests are Dominicans. Some teachers are not priests. Therefore, some teachers are not Dominicans.
    66. 66. FALLACY OF UNDISTRIBUTEDMIDDLE Some elephants are big. Some boys are big. Therefore some boys are elephants.
    67. 67. Figures and Moods of the Categorical Syllogism
    68. 68. FigureProper arrangement (position) of themiddle term (M) with respect to themajor term (P) and the minor term (S)in the premises.
    69. 69. 4 Syllogistic Figures 1st M-p p-M M-p p-MPremise 2nd s-M s-M M-s M-sPremise Figure 1 2 3 4
    70. 70. Figure 1: The middle term is the subject of the major premise and the predicate of the minor premise Some people are difficult to get along with.M-p All Americans are people.s-M Therefore, some Americans are difficult to getS-P along with.
    71. 71. Figure 2: The middle term is the predicate of both premises.p-M Registered students are members of this class.s-M John is a member of this class.S-P Therefore, John is a registered student.
    72. 72. MoodProper arrangement of the premisesaccording to quantity and quality. AAAA EEEE IIII OOOO AEIO AEIO AEIO AEIO
    73. 73. Valid Moods of the Four Figures Figure 1 AAA , EAE, AII, EIO Figure 2 EAE, AEE, EIO, AOO Figure 3 AAI, EAO, IAI, AII, OAO, EIO Figure 4 AAI, AEE, IAI, EAO, EIO
    74. 74. Example:A- All textbooks are books intended for careful study.I- Some reference books are intended for careful study.I- Therefore, some reference books are textbooks.
    75. 75. Example:A- All criminal actions are wicked deeds.A- All prosecutions for murder are criminal actions.A- Therefore, all prosecutions for murder are wicked deeds.

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