Critical_Thinkingproper_study notes.pptx

Critical Thinking proper study notes

1. Critical Thinking

2. PRESENTATION OUTLINE Course Technicalities Basic Concepts Language: Fallacies Categorical Propositions Categorical Syllogisms Deduction Induction

3. Preamble Critical Thinking studies a process which is indispensable to all educated persons--the process by which we develop and support our beliefs and evaluate the strength of arguments made by others in real-life situations.

4. It includes practice in inductive and deductive reasoning, presentation of arguments in oral and written form, and analysis of the use of language to influence thought . The course also applies the reasoning process to other fields such as business, science, law, social science, ethics, and the arts.

5. GOALS AND OBJECTIVES Successful completion of this course will enable you to : identify, evaluate, and construct inductive and deductive arguments in spoken and written forms; recognize common fallacies in everyday reasoning; distinguish the kinds and purposes of definitions; distinguish the functions of language and its capacity to express and influence meaning; and recognize and assess arguments in various forums of reasoning.

6. The goals of the course are to help you develop the habits of assessing and defending the reasonableness of your beliefs and values and those of others; appreciate the importance of looking at an issue from a variety of points of view and of recognizing the complexity that surrounds most controversial issues; and appreciate the value of critical thinking in both public and private decision-making.

7. After you have finished this course, you should be more: Self-aware , recognizing your own biases and influences; Inquisitive and curious , wanting to learn more about issues before passing judgment; Objective , basing your judgments on evidence and avoiding twisting evidence to fit your opinion; Open-minded , having the ability to say, "I don't know" or "I was wrong";

8. Sensitive to language , avoiding slanted language, recognizing ambiguous, vague, emotionally laden language, defining key terms; Imaginative , approaching topics and problems from various angles; Fair and intellectually honest , avoiding misrepresenting the ideas of others or misinterpreting data and research to fit your own purposes.

9. TEXTS AND MATERIALS   The required text for the course is How to argue: An Introduction to Critical Thinking by David J. Crossley and Petter A. Wilson since thinking critically depends largely on your being aware of your world, I recommend that you read a daily paper and familiarize yourself with some of the periodicals available in the library and with news sources available on the Internet.

10. METHODS, REQUIREMENTS AND GRADING   Because this course is intended to help you develop the skills necessary for making you an effective thinker, there will be very little lecturing. If you feel that the success of a course is measured by the amount of lecture notes a student can accumulate during a semester you will be very disappointed in this course. The course will consist almost entirely of discussion and practice.

11. Your participation --which means coming to class prepared, expressing and defending your ideas clearly and constructively, contributing relevant points of interest, making connections between course material and material from other classes and from the world outside CUNIMA, demonstrating enthusiasm, and completing in-class exercises.

12. Basically there will be two lecture hours per week and one tutorial hour per week.   Method of assessment will be as follows: 40% Continuous Assessment and 60% final examination.   ATTENDANCE   Attendance is mandatory in classes at CUNIMA.

13. Introduction: Basic Concepts In critical thinking we shall be using arguments An argument is simply putting together, in a reasonable order, facts and bits of evidence so we can reach a rational, logical conclusion .

14. Sometimes we use an argument to try to convince someone of something: e.g. “someone must have been in the house while we were away, the window was opened, there were footprints in the flower garden under the window, and the papers on my desk were messed up.” At other times you try to figure out what you should do in a given situation e.g. “ since I am going for a holiday to Italy in six months and will want to know some Italian, I had better enroll right away in that class of Italian” .

15. Sometimes there is emotion involved: “ you must be stupid to have talked to my wife” . At other times we make attempts at persuasion: “Smoke Tom Tom , the cigarette with less nicotine and tar and more flavor”.

16. WHY DO WE USE ARGUMENTS? There are four basic purposes you might have for an argument: Persuasion: Decision Explanation Prediction

17. Persuasion : often we feel we must persuade someone of our point of view or change someone’s mind. An example might be to have someone vote for one candidate rather than another in the upcoming election.

18. Decision : when it is time to vote, you have to consider the candidates carefully and look at all the reasons for voting for one candidate rather than the other. Only if you do this will you be voting responsibly. The evidence you collect and the conclusions will affect your vote.

19. Explanation: Why does a pot of water boil at less than 212⁰F at the top of a mountain? B ecause the atmospheric pressure affects the temperature at which liquids boil. Here we connect facts with natural laws. Some liquids will boil at 212⁰F at sea level; the water in our pot is a liquid; So this water will be affected in the same those liquids are – it will boil at 212⁰F at sea level.

20. Prediction. Explanation is connected with prediction in the sense that if you know what is generally true of a group or class of things, you know it will be true of all members of that group or class. E.g. if it is a chemical law that burning sodium in chlorine gas produces common salt (sodium chloride), then if you get some sodium tomorrow and burn it in chlorine gas, you will get common salt.

21. I Argument The subject matter of critical thinking

22. What is an argument? It is a group of statements, one or more of which (the premises) are claimed to provide support for, or reasons to believe, one of the others (conclusion). A term argument has a very specific meaning in critical thinking. It does not mean a mere verbal fight.

23. A group of statements : statement/proposition is sentence that is either TRUE or FALSE. The statements that make up an argument are divided into one or more premises and one and only conclusion. The conclusion is the statement that is claimed to follow from the premises e.g. All crimes are violation of the law Theft is a crime Therefore, theft is a violation of the law.

24. One of the most important tasks in the analysis of arguments is being able to distinguish premises from conclusion. Some of the conclusion indicators are: therefore, thus, consequently, we may infer, accordingly, we may conclude, it must be that, for this reason, so, entails that, hence, It follows that, implies that , as a result, then, points to, shows that,…….. Whenever a statement follows one of these indicators, it can usually be identified as the conclusion.

25. If an argument does not contain a conclusion indicator, it may contain a premise indicator. Some typical premise indicators are: Since, As indicated by, because, for, in that, may be inferred from, as given that, seeing that, for the reason that, inasmuch as, owing to…. e,.g . Expectant mothers should never use drugs, since the use of these drugs can jeopardize the development of the fetus.

26. Reasoning and Thinking Reasoning is that special type of thinking called inference in which conclusions are drawn from premises. All reasoning has been said to be thinking but not all thinking is reasoning.

27. Deductions and Inductions Arguments are traditionally divided into two groups: deduction and induction. A deductive argument is an argument in which the premises are claimed to support the conclusion in such as way that it is impossible for the premises to be true and conclusion false . In such argument the conclusion is claimed to follow necessarily from the premises.

28. Example 1: All Mammals are Animals A Cow is a Mammal Therefore a Cow is an Animal Example 2: All Masais are nomads Antony is a Masai Therefore Antony is a nomad. sometimes deduction is a mode of reasoning from the universal (general) to the particular .

29. An inductive argument is an argument in which the premises are claimed to provide probable support for the conclusion. In other words the conclusion of an inductive argument is a matter of probability but not certainty. The premises in an inductive argument do not give a conclusive support for the conclusion.

30. Example 1: All cows are mammals and have lungs All horses are mammals and have lungs All men are mammals and have lungs Therefore, probably all mammals have lungs. Example 2: Idi Amin was a dictator and was ruthless Adolf Hitler was dictator and was ruthless Peter is a dictator Therefore Peter is probably ruthless

31. 2 Words and Language

32. Using language We use language for communication however there are few general roles that language plays. We use language to describe the world,, events and ourselves. Such descriptions purport to offer information or facts. We explain the connections between facts and events. Sometimes we explain the meaning of a word.

33. We express feelings or emotions, either to communicate these to another person or to exhort that person to sympathise with us. We give orders, issue threats and use language in other similar ways in order to influence the actions of others. We use language usually in conjunction with particular actions or in special settings, to perform tasks. E.g , you say “I do” in a court of law as part of the action of swearing to tell the truth.

34. Communicating Have you ever thought how people communicate? On the surface it seems quite simple but it is not. We listen to someone talking, or we read a report or look at a work of art and we try to determine what it is we heard, read or saw. Very often what we perceive is not what was intended to be communicated*****

35. This unintentional alteration of language and meaning is a complex human phenomenon that psychologists, linguists and others have spent years analyzing. We tend not to read, listen, or look at everything that is directed towards us by the author, speaker or artist. This is because each of us uses what experts call Perceptual Selectivity . PS is a built-in screen that lets key words or pieces of information slip through while others are excluded, even ignored.

36. The careful author, the astute speaker, the clever artist have one thing in common: the ability to influence our thinking . In other words, he knows that some words will get through our selective screen and make an impression. What you must learn is the skill to choose words effectively and also to be alert so as to notice when others are trying to influence you e.g. advertisers. Psycholinguistics is the name given to the study of words and how they influence thinking.

37. meaning We communicate with words and since arguments involve statements that, in turn, are words in certain arrangement, we should first pay some attention to the meanings of words. There is a difficulty because it is not easy to determine the meaning, if any, of certain expression e.g. Fire! Understanding a word requires knowledge of the setting in which they are uttered and the tones in which they are spoken or written.

38. Some Pitfalls: Vagueness and Ambiguity Vagueness refers to a situation when the meaning of a word or phrase has no borderline cases such that it cannot be determined to which meaning it implies; love, rich, foolish etc Ambiguity refers to a situation where a word or a phrase has more than one possible clear meaning, but it is used in a context in which it is not clear which meaning is intended.

39. A word is ambiguous when it is used in such a way that is open to more than one possible interpretation e.g. bank, race, right etc Ambiguity often occurs because of poor grammatical structure or sloppiness in the use of pronouns or referring phrases e.g. The boys has taken the kittens over to their parents’ apartment. They were then treated to a bath .

40. DEFINITION A paramount aspect in Critical Thinking ( refer to the power-point presentation on Definition)

41. FALLACIES Do not let them fool you

42. 3. FALLACIES: Language is a powerful tool, but it can be misused. People will try to persuade you by means of all sorts of appeals – by playing on your sympathies, your like and dislikes, your fears or whatever. Now we shall point out some devises to watch for and avoid, either by not using them yourself or by not letting others use them on you.

43. The key point about these devices is that they are very frequently successful as persuasive measures. But they do not succeed by logically connecting facts and drawing reasonable conclusion from them; their effect depends on trickery, emotional appeals, or threats of one sort or another. Such tricks and illogical moves are called fallacies. In other words, a fallacy is a logical error in reasoning

44. A fallacy occurs when the premises of a given argument do not support the conclusion they are purported to support. In any argument there is a claim that the given premises, if granted, support its conclusion either necessarily, in the case of a deductive argument , or by some probability, in the case of an inductive argument . However, in most cases, upon closer examination and analysis of most arguments, it is found that the claim is not justifiable.

45. In such cases, the claim of the premises does not support the claim of the conclusion, or weakly support the conclusion. When such happens, it is said that the argument has committed a fallacy. A fallacy is therefore, a lack of coherence between the claim or the meaning of the premises taken together and conclusion of a given argument . The purpose of any argument is to assert or advance a justified position or view. And it is the premises that offer that justification. But an argument that commits a fallacy does not have its conclusion justified by its premises.

46. In such a case, one can comfortably accept the claims of the premises yet deny the claim of the conclusion without contradicting oneself since there is no necessary or strong probable relationship between the claims of the premises and the claim of the conclusion of the argument. An argument that commits a fallacy is sometimes referred to simply as a fallacy or a fallacious argument.

47. A fallacious argument should be avoided mainly because it fails in its purpose, which is, to advance a justified claim —a conclusion . Therefore, the truth of the conclusion of a fallacious argument is never justified or established.

48. KINDS OF FALLACIES There are two kinds of fallacies: - formal and informal fallacies. (1) FORMAL Fallacies Formal fallacies are reasoning that deviate from the established correct forms/structures of reasoning/ an argument. Any reasoning that does not conform to the established structure or form of correct reasoning definitely commits a formal fallacy. Therefore, to detect a formal fallacy simply requires an examination of any given argument against the many known correct forms.

49. INFORMAL FALLACIES (The reality of human life)

50. (2) INFORMAL Fallacies an informal fallacy emanates from inconsistent meanings within an argument . Therefore, to detect an informal fallacy requires an interpretation of an argument and understanding the meaning . Where the meaning of the premises collectively does not justify the conclusion then an informal fallacy is committed. So an informally fallacious argument may have a perfect form so long as the meaning of the premises, upon critical examination, does not support the claim of its conclusion.

51. It should also be noted that informal fallacies are too numerous to exhaust, besides, new ones continue to be identified or formulated. It is with this realization that this work only attempts to discuss some selected forms of informal fallacies. Further to note here is that even some of the selected forms are named differently by different authors.

52. Sub categories of INFORMAL Fallacies Informal fallacies are categorized into three groups, viz. fallacies of relevance , fallacies of presumption fallacies of ambiguity .

53. a. Fallacies of relevance The fallacies which are normally categorized as fallacies of relevance may perhaps be better referred to as fallacies of irrelevance since in them the conclusions are based on premises which are irrelevant to their claims. In such cases the given premises fail to justify or establish the claims or truth of the conclusions purportedly based on them.

54. Therefore in these fallacies of irrelevance there is an assumption that certain given premises or considerations are relevant to certain conclusions when in fact that is not the case. In these arguments, the given premises are irrelevant to the inferred conclusions. The following is a sample of Fallacies of Relevance/Irrelevance:

55. 1. Argument from Ignorance – (Argumentum ad Ignorantiam ) This fallacy occurs whenever a conclusion or a view is claimed to be true or correct simply because its contrary has not been proved. A conclusion of an argument is claimed to be true because the given premises have not proved it to be false, or it is claimed to be false because the premises have not proved it to be true. This is a fallacy because inability to prove a conclusion false is not a proof of its truth and vice versa.

56. In other words, ignorance of proof of a claim or an assertion is not a proof to the contrary. Example: From time immemorial, many philosophers especially logicians have been trying to disapprove of God's existence but to no avail. Therefore, it is obviously true that God exists. Or, on the contrary, look at the following argument: The non-existence of God can no longer be doubted given that the theologians have been trying for centuries to logically prove His existence but without any trace of success.

57. The failure of logicians to prove that God does not exist, in itself, is not a proof that God exist. Perhaps God does not exist and the logicians are only ignorant of how to prove that. "It is simply concluding something is true since you can't prove it is false or vice versa.e.g; Doctors can't explain how he recovered. It must have been through our prayers. I always leave my car unlocked, and nobody's ever broken in. It's fine to leave your car unlocked."

58. 2. Appeal to People ( Argumentum ad Populum ) Nearly everyone wants to be loved, admired, valued, recognized and accepted by others. The appeal to the people uses these desires to get the reader or listener to accept a conclusion In other words, they are used in such a way that manipulates the beliefs and emotions of a listener or reader so that he/she accepts the irrelevant conclusion.

59. Appeal to people may take different forms. a) Arousing a mob's mentality — this may happen by use of certain phrases or acts like patriotism, defender of workers, waving of flags and playing blaring(loud) music. These are likely to make the individuals in the audience want to share in the euphoria, camaraderie(friendship), and excitement; and in the process find themselves accepting a number of unjustified views, claim, or conclusions with ever increasing fervour(emotion) .

60. This kind of appeal to people is commonly used in public speech making and also in advertisements . It is sometimes called appeal to bandwagon fallacy e.g. Of course you want to buy a Toyota Corolla. Why 90 percent of Kenyan motorists drive it! In advertisement, appeal to people may also take the form of appeal to snobbery as the following example shows. Rolls Royce is not for everyone. If you qualify as one of the select few, this distinguished classic may be seen and driven at British Motor Car Ltd (By appointment only, please) Some examples of the bandwagon effect that commonly occur around us include buying a product because of its popularity or for the sake of gaining status in the society.For example,someone has just bought the latest mobile phone only to be considered a person without considering the needs and abilities to buy.

61. b) Appeal to vanity – this is another common appeal to people fallacy frequently used in advertisements. In this form, certain products or commodities, in their advertisements, are associated with certain celebrities or personages. This is intended to psychologically and emotionally make some people buy and use such products or commodities in the hope and with the desire that they too would become like those celebrities or personages and subsequently would be admirable.

62. For example, ponder upon the following and many other similar cases: The breakfast cereal or margarine "is associated with trim youthfulness, athletic prowess, and vibrant health; whisky is associated with luxury and achievement, and beer with high adventure; the automobile BMW to be sold is associated with romance, riches and sex... the men who use the advertised products are clear-eyed, broad-shouldered and distinguished; the women are slim, lovely, very well-dressed - or hardly dressed at all!

63. The acceptance of certain products or goods is not based on provable expected results, but only on the basis of the belief that those who use such products or goods would become like the characters associated with the advertisements of such products or goods.

64. 3. Fallacy of appeal to threats and intimidation /appeal to force ( Argumentum ad Baculum ) This fallacy seems to be based on the belief that “might make right”. It is also a kind of appeal to emotion fallacy It occurs when either physical or psychological threat, be it direct or indirect, is used against somebody in order to force or coerce one into agreeing to one’s conclusion, suggestion or view. In other words, if your opponent cannot see the wisdom of your point of view, then you force him into submission.

65. A Secretary to her employer: “ I deserve a raise in salary for the coming year. After all you know how friendly I am with your wife, and I am sure you would not want her find out what has been going on between you and that sexpot client of yours ” . In this fallacy one makes it clear to a real or possible opponent that if he/she does not agree to his/her position then certain harm or undesirable consequences will be meted out to him/her.

66. In the above example the employer may be forced to raise the salary of the secretary, not because it is deserved but to save his face. The premise of justification the secretary uses to justify her demand for a raise in the salary is a threat which should not be a consideration in a salary rise. The premise indeed does not justify the conclusion and is irrelevant to it.

67. 4. Fallacy of Appeal to Pity (playing on your feelings) This fallacy is committed when one evokes pity or emotion from listeners, reader or audience by appealing to his/her pitiable or miserable condition in order for the listener, reader or audience to accept his/her claim, conclusion or view. In this fallacy one appeals to mercy and altruism from the audience, listener or reader to have his or her conclusion accepted.

68. E.g. Student to lecturer: “ Sir, don’t fail me. You know I am a refugee in this country and I am putting up with a Christian community which is paying for my education and taking care of me. If I fail they will not keep me in the community. But I have nowhere to go; I cannot go back to my country since I do not know where any of my relatives live or even if they are alive” . One can see that the student’s condition evokes pity and mercy. But it has nothing to do with whether the student deserves so fail or pass. But the student uses that condition as proof that he deserves to pass his exams.

69. 5. Fallacy of appeal to authority ( Argumentum ad Verecundiam ) The fallacy is committed when appeal is made to an illegitimate or inappropriate authority in order to have a conclusion or view accepted. An appeal to such authority may be due to various reasons such us the cited authority , lack of relevant expertise , bias or prejudice , a motive to lie , or lack of ability to accurately perceive certain situations .

70. TV commercial in which famous people endorse certain products are often based on the same kind of fallacious reasoning. We should not be gullible enough to believe that just because some football star tells us he eats a certain cereal, it is the best cereal; or just because a beautiful actress says she uses a certain soap, it is the best soap. If truthful, such ads simply give you one person’s opinion; they do not provide a legitimate and authoritative testimonial for a product. Beware of appeals to authority.

71. 6. Fallacy of arguing against the person ( Argumentum ad Hominem ) Sometimes people get off the track and attack their opponent personally rather than focusing on their opponent’s position and beliefs. The fallacy of argument against the person occurs when someone who wishes to oppose a certain view attempts to discredit the person who holds the view rather than assessing the merits of the view itself.

72. Don’t waste your time studying the philosophy of Nietzsche. Not only was he an atheist, but he ended his days in an insane asylum. Pay no attention to that rabble-rouser can anything come from Nazareth. Of course John Paul II holds that birth control and abortion are morally wrong. He’s the pope any way.

73. B. Fallacies of Presumption In the fallacies of presumption, the premises presume the very conclusions they are supposed to prove or justify. In some cases, the arguments presume or conceal some premises.

74. 1. Fallacy of arguing in a circle/ Begging the Question ( Petittio principia ) Petittio principia literary means "postulation of the beginning". In this context to 'postulate' means to use as true a premise whose truth is contentious as basis for a conclusion. It is committed whenever the arguer creates the illusion that inadequate premises provide adequate support for the conclusion

75. … by leaving out a key premise, by restating the conclusion as a premise or by reasoning in a circle. In other words, the arguer “begs” (avoids or misses) the question at issue

76. Consider this example: Peter: The Bible is the word of God John: But that is only true if God exists. Peter: oh, I know God exists. John: How do you know? Peter: The Bible says so. John: But how can you trust the Bible? Peter: It’s the word of God! The observer is inclined to ask, “But how do you know X?” where X is the needed support.

77. Here the original question to be decided was whether the Bible is the word of God. But Peter assumes this both at the outset and later in the argument, thereby begging the question. The argument ends in the place where it began.

78. C. Fallacies of Ambiguity . The arguments in this category use either ambiguous terms or phrases (expressions) which then render them defective and hence fallacious. An ambiguity of a word or term is referred to as equivocation while an ambiguity of a phrase or a proposition is referred to as amphiboly.

79. When arguments use ambiguous words or phrases whose meanings shift and change, then the conclusions of such arguments cannot be logically correct.

80. 4. Validity, Truth, Soundness, Strength and Cogency

81. A deductive argument is either valid or invalid. A valid argument is an argument in which it is impossible for the conclusion to be false given that the premises are true; e.g. All donkeys are mammals All mammals have lungs Therefore, all donkeys have lungs

82. An argument can also have false propositions but can also be valid; e.g.; All spiders have six legs (false) All six legged creatures have wings (false) Therefore all spiders have wings (false)

83. Validity by itself will not establish the truth of the conclusion because if one or more of premises is not true, then even if the argument is valid, the conclusion will not have been established as true e.g. All men over 25 years of age are married John is over 25 years of age Therefore, John is married.

84. Invalid Deductive argument An invalid argument is one where the conclusion does not flow from the premises with logical necessity i.e. The meaning of the premises taken together does not entail the meaning expressed in the conclusion. In such a condition, one can accept the truth of the premises and still deny the truth of the conclusion at the same time without contradiction.

85. An invalid argument, therefore has a bad or incorrect structure such that the truth of its premises, if granted, does not justify the truth of the conclusion. Therefore it is a bad one e.g. All Africans are black All Malawians are black Therefore, all Malawians are Africans.

86. An invalid argument, therefore has a bad or incorrect structure such that the truth of its premises, if granted, does not justify the truth of the conclusion. Therefore it is a bad one e.g. All Africans are black All Malawians are black Therefore, all Malawians are Africans. All Kenyans are Africans All Ugandans are Africans Therefore, all Ugandans are Kenyans

87. Sound argument: Soundness or unsoundness applies only to deductive arguments and not to inductive arguments, A sound argument is deductive argument that is both valid and has all actually true premises. In such a case, the argument establishes the truth of its conclusion e.g. All human beings breathe, Mr. Chawanda is a human being. Therefore, Mr. Chawanda breathes.

88. Therefore, a sound argument is a deductive argument that is not defective either factually or logically. any sound argument must fulfill the following two conditions: It must be valid, and It must have all its premises being actually true.

89. Unsound Argument: It is a deductive argument that is either invalid or has at least a false premise. The argument may be valid, but if it has some false premises, it cannot justify or establish the truth of its conclusion e.g : All women are wise, (false) Sheila is a woman, Therefore, Sheila must be wise. The argument is valid but unsound because one of its premises(1) is false.

90. Another example: All catholic priests are unmarried, And all catholic nuns are unmarried, Therefore, all catholic nuns are catholic priest . This argument Is invalid. Despite the fact that both premises are actually true, its conclusion is actually false. It is not true that catholic nuns are catholic priests. The argument is unsound, not because it has any false premise, but because it is invalid.

91. Strength : It is normally used when referring to an inductive argument , and not to deductive one. Like validity and invalidity, strength is also a relational condition that holds between the proposition(premises and conclusion) of an inductive argument.

92. An inductive argument is said to be strong when it is such that if its premises are assumed or granted to be true, then its conclusion is most likely to be true. e.g.. There are 50 students in the CT class. 40 of them picked at random are found to be poor in CT. Therefore, probably all the 50 students in the class are poor in CT .

93. A weak inductive argument is such that if its premises are assumed true, then its conclusion has little or no probability of being true. E.g., There are 50 students in the CT class. 10 of them picked at random are found to be poor in CT. Therefore, probably all the 50 students are poor in CT . From the fact that 10 of the students picked at random are found to be poor in CT, it is least likely that all remaining 40 students are also poor in CT.

94. If the two ( strong and weak) kinds of inductive arguments are compared, then it is the case that in the strong inductive argument, the truth of the premises offers a greater probability of establishing the truth of its conclusion. But in the weak one, the truth of the premises offers little probability of establishing the truth of its conclusion. Therefore, on the basis of the truth of their premises, the conclusion is most likely to be true in a strong inductive argument, and least likely to be true in a weak one.

95. Truth : Some people view Critical Thinking as merely the study of arguments without or with less concern for actual truth of propositions constituting the arguments. Such view is misrepresentation of CT. The main aim of any reasoning is to establish the truth of the assertions made (given conclusions) on the basis of the truth of the given premises (evidence).

96. Cogent and Uncogent Arguments : Cogency or uncogency applies only to inductive arguments , and not to deductive arguments. A cogent argument is an inductive argument that is both strong and has all actually true premises. It has higher probability of establishing the truth of its conclusion e.g.

97. e.g. All the previous Vice-Chancellors of the Catholic University of Malawi have been men. Therefore, its next Vice-Chancellor will most likely be a man . An uncogent argument is an inductive argument that is either weak or has some actually false premises .

98. Unlike the validity and invalidity of deductive arguments, the strength and the weaknesses of inductive arguments admit degrees. To be considered strong, an inductive argument must have a conclusion that is more probable than unprobable . i.e. the likelihood that the conclusion is true must be more than 50% and as the probability increases, the argument becomes stronger.

99. e.g. a) This barrel contains 100 apples Three apples selected at random were found ripe Therefore, probably all 100 apples are ripe . b) This barrel contains 100 apples Eighty apples selected at random were found to be ripe Therefore, probably all 100 apples are ripe .

100. In conclusion we may say that a congent argument is an inductive argument that is STRONG and has ALL TRUE PREMISES . Otherwise uncogent argument is an inductive argument that is weak, has one or more false premises or both.

101. 5 Categorical Propositions

102. A proposition ( a statement, a claim) is a sentence that is either true or false. A proposition that relates two classes or categories is called a categorical proposition . The classes (categories) in question are denoted respectively by the subject term and the predicate term e.g. All human beings are animals

103. The proposition asserts that either ALL or PART of the class denoted by the subject term is excluded from or included in the class denoted by the predicate term. E.g. a) All prisoners are human beings b) Some convicted murderers get the death penalty.

104. There are four kinds of categorical propositions : Those that asserts that the whole subject class is included in the predicated class (All s are P). Those that assert that part of the subject class is included in the predicate class (Some S are P) Those that assert that the whole subject class is excluded from the predicate class (No S are P).

105. Those that assert that part of the subject class is excluded from the Predicate class (Some S are no P). Many categorical propositions are not in standard form because they do not begin with words: all, no or some e.g. Doing pastoral work is a taxing exercise. The words: All, No and some are called Quantifiers because they specify how much of the subject class is excluded or included from the predicate class.

106. The words “are ” and “are not” are called copula because they link (or couple) the subject term with the predicate term e.g. All students of ICI are persons holding ordinary level certificate from recognized schools .

107. The quantity of a categorical proposition is either universal or particular depending on whether the statement makes claim about “ every ” member or just “some ” members of the class denoted by the subject term. All S are P (universal) No S are P (Universal) Some S are P (Particular) Some S are not P (Particular)

108. The four categorical propositions are always referred to by the four vowels of Roman Alphabet: A,E,I,O. All S are P ( A ) No S are P ( E ) Some S are P ( I ) Some S are not P ( O )

109. The quality of the categorical proposition is either “affirmative” or “negative” depending on whether it affirms or denies a class membership. All S are P ( affirmative) No S are P (Negative) Some S are P (affirmative) Some S are not P (negative)

110. Categorical Syllogisms

111. Categorical Syllogisms A syllogism is a kind of deductive argument that has only three propositions. It has only two premises and a conclusion e.g. All Africans are black people (1 st premise ) All Malawians are Africans ( 2 nd premise) Therefore, all Malawians are black people. (conclusion)

112. A categorical syllogism is composed of categorical propositions. It must fulfill the following conditions: Be composed of exactly three categorical propositions Contains three terms . Each of the terms must appear twice in the argument, but Each term appears only once in one proposition. All Africans are black people All Malawians are Africans Therefore, all Malawians are black people

113. The three terms of a categorical syllogism are: Major term : this is the predicate term of the conclusion Minor term : this is the subject term of the conclusion Middle term : this appears in the two premises but does not appear in the conclusion All Africans are black people All Malawians are Africans Therefore all Malawians are black people .

114. Of the two premises of a categorical syllogism, one is a major premise and the other is a minor premise. The major premise is the one which contains the major term ( and of course the middle term as well). The minor premise is that one which contains the minor term (and the middle term as well) All Africans are black people (major premise) All Malawians are Africans (minor premise) Therefore all Malawians are black people.

115. A categorical syllogism is said to be in standard form when its propositions are in standard form i.e., they explicitly express the four components, Viz : quantifier , subject term , copular and predicate term And the propositions are arranged such that the major premise is stated first, followed by minor premise and finally the conclusion

116. DETERMINING THE VALIDITY OF CATEGORICAL SYLLOGISM BY USE OF VENN DIAGRAM TECHNIQUE

117. MOOD AND FIGURE After CS has been put into standard form its validity or invalidity may be determined through mere inspection of the form. The individual form of a syllogism consists of two factors – mood and figure . The mood of the CS is determined by the kind of propositions that make it up. E.g. if the major premise is A proposition, the minor premise an I proposition and the conclusion is also I proposition, the mood is AII

118. Examples: All M is P Some S is M :. Some S is P The mood is AII All M is P Some M is not S :. Some S is not P The mood is AOO All P is M No S is M :. No S is P The mood is AEE No P is M All M is S :. No S is P The mood is EAE

119. Figure The figure of a syllogism is determined solely by the position of the middle term. Four different arrangements are possible. If we let S represent the subject of the conclusion(minor term) , P the predicate of the conclusion (major term) and M the middle term, the four possible arrangements may be illustrated as follows:

120. 1 st figure M – P S – M S – P 3 rd Figure M – P M – S S – P 2 nd figure P – M S - M S – P 4 th Figure P – M M – S S – P

121. To describe a syllogism completely we must indicate both the mood and figure, always beginning with the former. E.g ; All renowned philosophers are university graduates. Some businessmen are university graduates. :. some businessmen are renowned philosophers. The form is AII-2

122. TESTING FOR VALIDITY: Table of valid argument forms There are 256 forms of syllogism that are theoretically possible. Only a few are valid. Actually only 15 are valid argument forms for categorical syllogisms. (See hand out) The table of valid argument forms provide yet another methods to test the validity of syllogisms.

123. The method is as follows: Restate the argument in schematic form Identify the mood and the figure of the argument Determine whether or not an argument of that mood and figure is listed in the table of valid argument; if not, the argument is invalid.

124. Table of Unconditionally Valid Forms Aristotelian and Boolean Standpoints Figure 1 Figure 2 Figure 3 Figure 4 AAA EAE IAI AEE EAE AEE AII IAI AII EIO OAO EIO EIO AOO EIO

125. Testing for Validity: Venn Diagrams Venn diagrams can also be used to test the validity of Standard Form Categorical syllogism. Three overlapping circles must be used The three circles represent respectively, the major term (P), the minor term (s) and the middle term(M). To diagram a syllogism, we diagram only the two premises.

126. Procedure of Venn diagramming and interpretation Only premises are to be represented on the Venn diagram. Always begin diagramming with universal premise. Universal premise is represented by shading while particular is represented by X .

127. Once the two premises have been diagrammed, then one needs only to check whether or not what the conclusion asserts has been expressed by the premises collectively (taken together). If it is the case then the syllogism is valid, but if not the syllogism is invalid.

128. Example All artists are individualists Some artists are Philosophers Therefore, some philosophers are individualists . We first determine the identity of S , P , M by examining the conclusion of the argument. In this argument, S = Philosophers, P =individualists and M = artists.

129. Next, we exhibit the form of the argument as follows: All M is P Some M is S :. Some S is P Now we are ready to diagram our two premises:

130. 6 INDUCTIVE REASONING

131. Inductive Reasoning Premises1 : The first Martian I saw was green and had three eyes. Premise 2 : The second Martian I saw was green and had three eyes. Premise 50 : The fiftieth Martian I saw was green and had three eyes . Conclusion : Therefore all Martians are green and have three eyes.

132. Inductive reasoning moves from specific individual facts to a general conclusion. In the above example, the speaker has taken individual facts, based on his own observation and worked to the general conclusion. In the example above, the speaker generalized on the basis of a number of particular examples encountered in his experience; hence her conclusion encompassed Martian not mentioned in the premises.

133. For this reason, inductive arguments cannot guarantee that their conclusions are absolutely true. E.g. it is always possible that the next Martian he meets will not be green. Induction in the classical sense of generalization from particular, specific examples is extremely useful provided we recognize its limitations. We often use inductive reasoning of this type to formulate hypotheses when searching for an explanation.

134. The majority of the general propositions expressing scientific laws and general truths about the world are inductive generalizations based on experience. This point deserves special attention. Inductive reasoning is crucial to our ability to think correctly about things and to argue logically, Inductive and deductive reasoning go together and sometimes deductive reasoning depends on inductive reasoning. E.g. you cannot draw deductive conclusions about whales and their properties if you have no information about whales.

135. DANGERS IN INDUCTIVE REASONING One must be aware of the pitfalls of induction. There are some general things to watch for in using and in analyzing inductive arguments. Never jump to a conclusion Evidence must be relevant .

136. Never jump to a conclusion: Although an inductive argument involves going beyond the premises in that an inductive argument offers a conclusion that exceeds the evidence offered in its premises one cannot reach a reasonable and acceptable inductive conclusion from just any set of premises. e.g. the vegetables are all terribly overcooked at Phiri’s Restaurant because the vegetables I had the first time I went to Phiri’s a couple of weeks ago was overcooked. And I have never gone back.

137. On the basis of one and only one experience, the speaker has claimed that all the vegetables at Phiri’s are always overcooked. The moral to be drawn is that one must have enough evidence to feel justified in drawing the conclusion. With inductive argument it is often a matter of judgment to decide when one has enough evidence. The error of jumping to a conclusion is sometimes called the “fallacy of hasty generalisation ”

138. Evidence must be relevant: Consider the following example: When we went to Phiri’s last night my vegetable was overcooked. And Peter was given a soiled napkin, and the lighting was harsh. Obviously they just don’t know how to cook food at Phiri’s . While this argument appears to provide several pieces of evidence for the conclusion that “they just do not know how to cook food at Phiri’s ,” it is based on the one overcooked vegetable.

139. The other issues –the soil napkin and the lightning – are not related to the cooking and therefore do not jump to the general conclusion that the food is poorly prepared. The key idea is that when either formulating or analysing an argument, you must stick to the point.

140. Statistical arguments Statistical arguments are inductive arguments by virtue of having conclusions that go beyond the evidence stated in the premises. Conclusion of statistical arguments are only probable. The advantage of such arguments is that they allow us to formulate a useful conclusion that has application beyond the range of items mentioned in the premises.

141. Suppose for example that we were grading the apples in a basket of apples. Our procedure would be to take a few samples from here and there in the basket. Imagine that 90% were found to be Grade A. We would then conclude that 90% of all the apples in the basket were Grade A. In other words, we would have moved from the evidence that 90% of the apples we observed in the sampling were Grade A to the general conclusion that 90% of all the apples in the basket were Grade A. This is obviously a useful method, because no one would want to have a look at every apple in a carload to decide whether they were Grade A.

142. However, one must be alert to the dangers of statistical arguments that employ insufficient statistics. Here is an example in which a conclusion is based on insufficient statistics : Our representative, in his speech to Parliament, reported that the people in his constituency were for capital punishment. He claimed he had talked to people at one of the local markets for half-hour on Monday morning.

143. Clearly, sampling a few people in one location in a short space of time is not very reliable in determining the opinions of the whole constituency. The inductive argument fails to be convincing because it employs insufficient evidence. As the example illustrates, you should watch for insufficient statistics when formulating and evaluating arguments.

144. Ways to evaluate Inductive Arguments In looking critically at an inductive argument, you should always ask three basic questions: Is the evidence sufficient ? Is the evidence biased or specially selected ? Is the evidence relevant ?

145. A great danger with both statistical and analogical arguments is that there may not be adequate or sufficient evidence. A statistical sampling may be too small to warrant conclusion. The similarities upon which someone bases an analogy may be too few.

146. ANALOGIES Another form of inductive argument is the analogy. Basically, an argument by analogy compares two or more things or classes of things and argues that because they are similar in certain respects, it is reasonable to conclude that they are similar in a further respect that we have not been able to observe directly.

147. Consider the case of an agricultural researcher testing new enriched feeds. One group of sheep is given normal feed while another is given an enriched diet. The researcher discovers that all the sheep given the enriched diet are more active, less disease-prone, and have thicker wool than the sheep that received ordinary feed. From this the researcher decides that all sheep of the farmers in the district would benefit similarly from enriched diet.

148. When the statements are expressed one by one, the argument involves the following steps: The enriched diet benefitted the sheep in the test group The farmers’ sheep are similar to the sheep in the test group. Therefore the farmers’ sheep will benefit from the enriched diet.

149. The enriched diet benefitted the sheep in the test group. The farmers’ sheep are similar to the sheep in the test group. Therefore the farmers’ sheep will benefit from the enriched diet. Premise 1 was something the researcher discovered by observation. Premise 2 is actually a summing up of a number of known facts about similarities in physiological structure, body chemistry and environment that exist between the researcher’s sheep and the farmers’ sheep.

150. Thus we have an analogy that involves a comparison of two different groups that have certain similarities. From a knowledge or observation of some similarities between the individuals of the two groups, we argue that they may be similar in other respects. In our example, the further suggested similarity has to do with the animals’ thriving on an enriched diet.

151. In summary we can say that an argument by analogy points out similarities between two things and then draws the conclusion – that is, argues – that they will be similar in further respect. E.g The red ball and the yellow ball are exactly alike in weight, texture and diameter; since the red ball can be made to bounce over the wall, therefore it should be possible to make the yellow ball bounce over the wall too.

152. We can express the structure of an argument by analogy more precisely in the following way; Thing X and Thing Y have property P. Thing X and Thing Y have property of Q Thing X and Thing Y have property of R Thing X and Thing Y have property of S Thing X had property of T Therefore Thing Y also (probably) had property of T

153. Here we have four premises – 1 through 4 – stating relevant similarities between the two items X and y. Premise 5 states that we have evidence that X has further property T. The proposition 6 concludes from theses premises that Thing Y will (probably) also have the further property T. We can see this structure in the case of the example of red and yellow balls just mentioned:

154. Let “R” stand for “red ball” and “Y” stand for “yellow ball”. We then have: R and Y both have the same weight. R and Y both have the same texture. R and y both have the same diameter. R will bounce over the wall The Y will (probably) bounce over the wall.

155. Legal Reasoning Many of the arguments used by lawyers to support a case trial are analogical arguments. The essential feature is its dependence on precedent (previously established decision). According to the requirement of precedent, similar cases must be decided similarly i.e. in arguing a case, a lawyer will often attempt to show that the case is analogous to some earlier case that was decided in a favourable way.

156. For example : suppose that you own a factory and one of your machines, a drill press, breaks down, causing the entire operation to come to a halt. Urgently you call a repair company and explain the whole situation. The company promises to have the drill press back in operation within two days. Unfortunately however, there are delays, and two weeks elapse before the drill press is repaired. In the mean time your company loses an additional K23,000,000.00 in profits. Because you relied on the companies assurance that the drill press would be fixed in two days, you demand that the repair company reimburse you for the additional lost profits. When the repair company refuses your demand, you file suit.

157. Applying this result to the drill press case, your lawyer will argue that because the repair company was informed that delays in repairing the drill press would result in lost profits, it should reimburse you for the losses incurred.

158. GENERALIZING Generalization is the process of moving from specific observation about some individuals within a group to general claims about the members of the group. Most frequently, generalizations are based on a series of observation or experiences. By recording a series of experiences or observations, researchers who conduct polls, survey and studies try to determine whether the majority of the population favours the capital punishment, whether mandatory seatbelt legislation really reduces injuries in traffic accidents by 40%, and so on.

159. Generalizations are, by definition, based on an incomplete survey of the evidence. In most cases this is because a complete survey is , for practical reasons, impossible. Consider the following example:

160. Suppose you operate a small business that assembles cell phones, and you have ordered a thousands microchips for them from a firm in Japan. The firm has agreed to produce them to your exact specification. Upon their arrival, you open one of the 10 boxes at random, pull out five of the 100 chips it contains, and examine each one carefully to ensure that it meets your requirements. You find that all five do. At random to open another box from the 10 and test five more chips, finding once again that they have been properly manufactured. You do the same with a third and a fourth box, with the same results. By this time you have carefully examined 20 of the 1,000 chips and are fully satisfied. Twenty out of 1,000 is a small ratio, but you conclude that “The computer chips meet our specifications”.

161. This is a good inference, even though the premises, consisting of limited observation, do not guarantee the truth of the conclusion if you examined all 1,000 of the chips sent and found each and every one to meet your specification. You could guarantee the truth of the conclusion if you examined all 1,000 of the chips sent and found each and every one meet your specifications. For practical reasons, we are rarely able to undertake such a complete review.

162. Sometimes the end result of such generalization is a universal claim . Universal claim has the form “ All Xs are Y . For the present example, the universal conclusion would read, “All the microchips are good.” Generalizations are also used to support general claims . A general claim has the form X s are , in general, Y, or X s are Y , or Each X is probably Y . In our case the conclusion would be; “The microchips meet our specification”.

163. General claims are not as strong as their universal counterparts. The statement “ The microchips meet our specification” is not as strong claim as “ All the microchips meet our specifications ”. The general claim implies that the microchips are, on the whole satisfactory. It leaves open the possibility that some chips may be defective. In contrast, the universal claim allows no exceptions. It is proved mistaken if we find one microchip that is defective.

164. In some cases , generalizations lead to neither universal nor general claims but to proportional claims . Suppose you open 10 boxes and at random select a dozen chips from each. You examine them all and conclude that the proportion of defective chips is probably 3 out of every 120, or that 2.5% of the chips fail to meet your specification. More generally, you conclude that the vast majority of the chips meet your specifications but that some proportion of them is defective. In both case, you are making a ‘proportional’ claim.

165. Representative Samples We have seen that generalization can lead to universal, general or proportional conclusions. In all three cases, the key to a good generalization is a ‘representative’ sampling of the members of the group in question. The sample that is examined in the course of a generalization is called a representative sample if it accurately represents the group (population) as whole.

166. In everyday life, we are inclined to make generalizations without a representation sample. Often this is because our generalization rely on ‘ anecdotal evidence ’, which consists of informal reports on incidents that have not been subjected to careful scrutiny. You should be cautious of such generalization which are often based on a few instances that may have been embellished and slanted according to the prejudices of those who utter them.

167. The ‘hasty generalizations' that frequently characterize ordinary reasoning have convinced some people that it is wrong to generalize. But bad generalization do not rule out the possibility of good generalization and we can use our critical faculties and common sense to decide whether a generalization is based on a representative sample. Two kinds of considerations must play a key role in this assessment: Sample Size and Sample Bias.

168. Sample Size : The first thing you must consider in determining the suitability of a sample is its size. Samples that are too small are unreliable and more likely to be affected by pure chance. E.g . I’ve a couple of Chinese students in my classes. They are both hardworking and get good grades. I suppose that all Chinese are like that.

169. E.g . I’ve a couple of Chinese students in my classes. They are both hardworking and get good grades. I suppose that all Chinese are like that. That’s generalizing from too small a sample. It’s a ‘hasty generalization’ using ‘anecdotal evidence’. In the cell phone example, a sample size of one or two or three chips chosen from one box is too vulnerable to the luck of the draw. As more and more chips are examined, the chances that your results are mere coincidence diminish.

170. Sample Bias : A representative sample must also avoid bias. A sample is biased if it is not representative of the population. Individuals tend to accept and repeat anecdotes that conform to their own perspective in the process of eliminating counter cases.

171. A common source of bias is a natural tendency to generalize from situations with which we are familiar without asking whether these situations are representative . e.g. when social workers generalize on the basis of their experience with single-parent families, they must keep in mind that they are working in specific geographic are with particular social, ethnic, economic and political characteristics. They must therefore ask themselves whether single mothers and fathers elsewhere share similar situation. Otherwise, their generalization cannot be extended beyond their sphere of experience .

172. Analogies and Generalizations Analogies are not generalization, but they require a generalization as a premise. The analysis of analogies usually ends in our trying to come up with a general claim that will make strong argument. Analogies lead to generalizations.

173. e.g . this car is like that one. They both had bad suspension. And here’s another one from the same manufacturer, which the owner says has bad suspension too. So if you buy one of these cars, it will have bad suspension, too. From two or three or seven examples, you figure that the next one will be same. That’s an analogy all right but the process is more one of generalization, for it is the unspoken general claim that needs to be proved: (Almost) all cars from this manufacturer have bad suspension.

174. Summary: We generalize all the time ; from a few instances (the sample) we conclude something about a bigger group (the population). Generalizations are arguments. They need two elements to be good: (a) the sample is representative and (b) the sample is big enough and unbiased.

175. Cause and Effect

176. Maria caused the accident Smoking causes cancer Gravity causes the moon to stay in orbit. These are causal claims . We make lots of them, though they may not always contain the word “cause” or “caused.” for example; Jogging keeps you healthy Taking an aspirin every other day cuts the risk of having a heart attack.

177. Causes and effects 1. What exactly is a cause? Consider what Dick said last night. ‘ Spot caused me to wake up ’ Spot is the thing that somehow caused Dick to wake up. But it’s not just that Spot existed. It’s what he was doing that caused Dick to wake up. ‘Spot’s barking caused Dick to wake up’. Spot barked (cause) Dick woke up(effect) caused

178. What is this relationship of being caused? it has to be a very strong relationship. Once Spot barked, it had to be true that Dick woke up. i.e. there is no way for “Spot barked” to have been true and “Dick woke up” to be false. It’s a relationship between the premises and the conclusion of a valid or strong argument.

179. The normal conditions; A lot has to be true for it to be (nearly) impossible for “Spot barked” to be true and “Dick woke up” to be false: Dick was sleeping soundly up to the time that Spot barked. Spot barked at 3 a.m. Dick doesn’t normally wake up at 3 a.m. Spot was close to where Dick was sleeping There was no other loud noise at the time….

180. we could go on forever. But as with arguments, we state what we think is important and leave out the obvious. If someone challenged us, we could ask “There was no earthquake at the time” – but we just assume things are the way they “normally” are. Normal Conditions: For a causal claim, the normal conditions are the obvious and plausible unstated claims that are needed to establish that the relationship between purported cause and purported effect is valid or strong.

181. The cause precedes the effect We wouldn’t accept that Spot’s barking caused Dick to wake up if Spot began barking only after Dick woke up. The cause has to precede the effect. That is, “Spot barked” became true before “Dick woke up” became true. For there to be cause and effect, the claim describing the cause has to become true before the claim describing the effect becomes true.

182. Gentlemen, that’s the end, alleluia

183. LOGIC

184. TESTING FOR VALIDITY Rules of Validity

185. The syllogism will be valid if and only it satisfies all of the following rules: RULE 1 A valid CS must have exactly three, and only three unequivocal terms. Each of the three terms of CS must be used in the same sense throughout in the argument. Fallacy committed: fallacy of four terms or fallacy of ambiguous middle . E.g. All plants are living things, all factories are plants. Therefore, all factories are living things.

186. Rule 2 A valid CS must have its middle term distributed in at least one of the premises. Fallacy committed : fallacy of undistributed middle. E.g. all Africans are human beings all Kenyans are human beings Therefore, all Kenyans are Africans.

187. Rule 3 In a valid CS no term should be distributed in the conclusion if it is not distributed in any of the premises. Fallacy committed: fallacy of illicit process . This fallacy can be either illicit process of the minor term or illicit process of the major term.

188. Example: Fallacy of illicit process of the minor term: No dogs are cats Some animals are cats Therefore, no animals are dogs. Fallacy of illicit process of the major term: All human beings are primates No monkeys are human beings Therefore, no monkeys are primates

189. Rule 4 A valid CS cannot have two negative premises. Fallacy: fallacy of exclusive premises It implies that there is no necessary relationship between the minor and the major terms. E.g : No cats are dogs No cows are dogs Therefore, some cows are cats.

190. Rule 5 A valid CS with a negative premise must have a negative conclusion. Any CS with at least one negative premise but does not have a negative conclusion is invalid and commits the fallacy of inferring an affirmative conclusion from negative premise . E.g : All crows are birds Some animals are not crows Therefore, some animals are birds.

191. Rule 6 A valid CS with a negative conclusion must have a negative premise. Fallacy : inferring a negative conclusion from affirmative premises . The conclusion of a valid CS with affirmative premises must also be affirmative. It cannot be negative. E.g.: All triangles are three-angled polygons All three-angled polygons are three-sided polygons. Therefore , some three-sided polygons are not triangles.

192. Rule 7 A valid CS cannot have two particular premises. If the two premises then the syllogism commits the fallacy of undistributed middle If both the premises are negative then it commits the fallacy of exclusive premises

193. Rule 8 A valid categorical syllogism with a particular premise must also have a particular conclusion. If it has to have a particular premise then it must be one. Fallacy of inferring a universal conclusion from a particular premise , e.g. All human beings are rational beings Some rational beings are spiritual beings Therefore, all spiritual are human beings.

194. The fallacies prohibited by these rules constitute a complete list of the formal fallacies that may invalidate categorical syllogism. a formal fallacy , as distinguished from an informal fallacy is a flaw in the form of a deductive argument such that the conclusion does not follow from the premises.