Introduction to logic
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The document is an introduction to logic, covering concepts such as deductive and inductive reasoning, syllogisms, and logical validity. It explains the differences between various forms of reasoning, provides examples of categorical syllogisms, and outlines rules for syllogistic reasoning. The document also discusses conditional syllogisms and their validity based on affirming or denying antecedents and consequents.
Introduction to logic
- 1. Introduction to Logic IB Theory of Knowledge Mrs. Loffredi
- 2. Why do we need logic? • http://penguingeek.files.w ordpress.com/2007/08/hu mor-penguin- logic.jpg?w=432&h=436
- 3. What is the difference between deductive and inductive reasoning? DEDUCTIVE REASONING INDUCTIVE REASONING ● Stated as facts or general premises or principles ● Conclusion is specific. It is reached directly by applying logical rules to the premises. ● If the premises are true, the conclusion must be true. ● More difficult to use. One needs facts which are definitely true ● Based on observations of specific cases ● Conclusion is more general than the information the premises provide. ● If the premises are true, the conclusion is probably true. ● Used often in everyday life. Evidence is used instead of proved facts. Watch the following video that briefly explains the difference between deductive and inductive reasoning: Deductive vs. Inductive Arguments
- 4. Logic - Basic Terms Important Concepts you must know
- 5. Logic: the study of how to reason well. Validity: Valid thinking is thinking in conformity with the rules. If the premises are true and the reasoning is valid, then the conclusion will be necessarily true.
- 6. Non-sequitur: (it does not follow). This means that the proposed conclusion cannot be deduced with certitude from the given premises. For example: If Jews and Palestinians were of the same religion, there wouldn’t be conflict in the Middle East. Therefore, it is religion that is the source of the conflict.
- 7. The categorical proposition: A complete sentence, with one subject and one predicate, that is either true or false. For example: All babies are cute.
- 8. The Subject: that about which something is said. All giraffes are animals. (giraffes = subject) The Predicate: that which is said about something. All giraffes are animals. (animals = predicate) The copula: connects together or separates the S and the P. All giraffes are animals. (is/is not)
- 16. The parts of a CATEGORICAL Syllogism: Watch this video on Logical Syllogisms a. The two premises. All A is B (first premise also known as major premise) Some B is C (second premise aka minor premise) Therefore, Some C is A b. The Conclusion. In the above syllogism, Therefore, Some C is A
- 17. Major, Minor, & Middle Terms The major term: this term is always the P (predicate) of the conclusion. In the example directly above, A is the major term. The minor term: this term is always the S (subject) of the conclusion. In the example directly above, C is the minor term. The middle term: this term is never in the conclusion but appears twice in the premises. (The function of the middle term is to connect together or keep apart the S and P in the conclusion).
- 18. Example: • All Italians eat spaghetti. • Giovanni Rossi eats spaghetti. • Therefore, Giovanni Rossi is an Italian. MAJOR TERM MINOR TERM MIDDLE TERM
- 19. What is Distribution? This is a very important term in logic. A distributed term covers 100% of the things referred to by the term. An undistributed term covers less than 100% of the things referred to by the term (few, many, almost all). For instance, All men are mortal. In this statement, "men" is distributed; for it covers 100% of the things referred by the term "men". In Some men are Italian, "men" is undistributed; for the term covers less than 100% of the things referred to by the term "men".
- 21. Note the following (bold and underline = distributed): A = All S is P I = Some S is P E = No S is P O = Some S is not P
- 23. Rules for Categorical Syllogisms 1. From two negative premises, no conclusion can be drawn. 2. If a premise is particular, the conclusion must be particular. 3. In a valid categorical syllogism, the middle term must be distributed at least once. 4. In a valid categorical syllogism, any term which is distributed in the conclusion must also be distributed in the premises. 5. A syllogism must have three and only three terms. 6. If a premise is particular, the conclusion must be particular.
- 24. Violations of the Syllogism Rules
- 25. Some Italians are from Calabria. All Italians love spaghetti Therefore, all those from Calabria love spaghetti.
- 26. No dogs are cows No cows are pigs Therefore, no dogs are pigs.
- 27. All Germans love beer All Irishmen love beer Therefore, all Irishmen are Germans.
- 28. All principals know about administrative problems. No secretary is a principal. Therefore, no secretary knows about administrative problems.
- 29. All Canadians like hockey. All Italians like soccer. Therefore, some Canadians like soccer.
- 30. Some men are American. All Americans love apple pie. Therefore, all men love apple pie.
- 31. Steps to proving Categorical Syllogisms valid
- 32. Let’s start with our Categorical Syllogism All Italians eat spaghetti. Giovanni Rossi eats spaghetti. Therefore, Giovanni Rossi is an Italian.
- 33. Step 1: Circle the Middle Term All Italians eat spaghetti. Giovanni Rossi eats spaghetti. Therefore, Giovanni Rossi is an Italian.
- 34. Step 2: Determine what type of statement is the first premise All Italians eat spaghetti. Giovanni Rossi eats spaghetti. Therefore, Giovanni Rossi is an Italian. “A” STATEMENT
- 35. Step 3: Determine what type of statement is the second premise All Italians eat spaghetti. Giovanni Rossi eats spaghetti. Therefore, Giovanni Rossi is an Italian. “A” STATEMENT
- 36. Step 4: Determine what type of statement is the conclusion All Italians eat spaghetti. Giovanni Rossi eats spaghetti. Therefore, Giovanni Rossi is an Italian.“A” STATEMENT
- 37. Step 5: Identify the Distributed Terms All Italians eat spaghetti. Giovanni Rossi eats spaghetti. Therefore, Giovanni Rossi is an Italian. IS THIS SYLLOGISM VALID? NO!!
- 38. Let’s practice some more No Martians have red noses. Rudolph has a red nose. Therefore Rudolph is not a Martian.
- 39. Let’s practice some more All bull-fighters are brave people. Some brave people are compassionate. Therefore, all bull-fighters are compassionate.
- 40. Let’s practice some more Some monks are Tibetans. All Tibetans are good at yoga. Therefore, some monks are good at yoga.
- 41. The Conditional Syllogism: a.k.a. The Hypothetical Syllogism “If I had a millions dollars, then I’d buy you a house” The Barenaked Ladies
- 42. The Conditional Syllogism Sometimes an argument can take a conditional or hypothetical form. For example, consider the following: Look, I know criminals. If John is innocent, he’ll be willing to testify. But John refuses to testify. It follows that he’s guilty. These arguments are not always valid. In fact, many are invalid, like the argument above.
- 43. Conditional SyllogismForm The conditional syllogism takes the following form: If p, then q p q
- 44. Valid or Invalid? For example, consider whether this conclusion follows from the given premises: If Johnnie eats cake every day, then he is placing himself at risk for diabetes. Johnnie eats cake every day. Therefore, Johnnie is placing himself at risk for diabetes.
- 45. Valid or Invalid? If Johnnie eats cake every day, then he is placing himself at risk for diabetes. Johnnie does not eat cake every day. Therefore, Johnnie is not placing himself at risk for diabetes. Invalid: He might drink pop every day.
- 46. Valid or Invalid? If Johnnie eats cake every day, then he is placing himself at risk for diabetes. Johnnie is placing himself at risk for diabetes. Therefore, Johnnie is eating cake every day. Invalid: He might be drinking pop every day, or eating chocolate bars, etc.
- 47. Valid or Invalid? If Johnnie eats cake every day, then he is placing himself at risk for diabetes. Johnnie is not placing himself at risk for diabetes. Therefore, Johnnie is not eating cake every day.
- 48. The major premise in this kind of syllogism is a conditional proposition: "If Johnnie eats cake every day, then he is placing himself at risk for diabetes". There are two parts to the conditional proposition. Notice that one clause begins with "if", another with "then". The "if" clause is called the antecedent, the "then" clause is called the consequent.
- 49. If Johnnie eats cake every day, then he is placing himself at risk for diabetes. Johnnie eats cake every day. Affirming the Antecedent Therefore, Johnnie is placing himself at risk for diabetes. This is called: Affirming the Antecedent
- 50. If Johnnie eats cake every day, then he is placing himself at risk for diabetes. Johnnie does not eat cake every day. Denying the Antecedent Therefore, Johnnie is not placing himself at risk for diabetes. This is called: Denying the Antecedent
- 51. If Johnnie eats cake every day, then he is placing himself at risk for diabetes. Johnnie is placing himself at risk for diabetes. Affirming the Consequent Therefore, Johnnie is eating cake every day. This is called: Affirming the Consequent
- 52. If Johnnie eats cake every day, then he is placing himself at risk for diabetes. Johnnie is not placing himself at risk for diabetes. Denying the Consequent Therefore, Johnnie is not eating cake every day. This is called: Denying the Consequent
- 53. Which forms are valid? Which are invalid? Affirming the Antecedent Denying the Antecedent Affirming the Consequent Denying the Consequent
- 54. Hypothetical Syllogisms • affirming the antecedent – If A then B – A – Therefore B • affirming the consequent – If A then B – B – Therefore A • denying the antecedent – If A then B – Not A – Therefore not B • denying the consequent – If A then B – Not B – Therefore not A
- 55. Affirming the Antecedent: A A = Alcoholics Anonymous Denying the Consequent: D C = Washington D.C AA is a good program, and Washington is a great place to visit.
- 56. Affirming the Consequent: A C = Acne Denying the Antecedent: D A = Dumb A** No one wants acne, and no one wants to be a dumb a**