Logic: Understanding Validity and Soundness in Arguments

1. Logic Arguments must be consistent and not contradict one another. You cannot make logical sense and be inconsistent

2. Logic - The study of the methods and principals of correct reasoning we must learn to distinguish valid from invalid reasoning • Valid reasoning – the conclusion follows from the evidence by logical necessity.

3. Law of Contradiction • Also called Principle of Consistency • Nothing can be said both to be and not to be

4. Law of Contradiction • For Example, we cannot say: • “The sky is blue, but the sky is not blue.” • To be inconsistent is to speak nonsense.

5. In a good deductive argument, the premises entail the conclusion. That is, if the premises are all true, then the conclusion has to be true. • In a good inductive argument, the premises probabilize the conclusion. That is, if the premises are all true, then the conclusion probably is true

6. Validity and soundness (of deductive arguments) • An argument is valid if its form or logical structure guarantees that if the premises are all true then the conclusion is also true. • An argument is sound if both (1) it is valid in form, and (2) all of its premises are in fact true.

7. Validity • An argument form is valid if there is no substitution instance which renders the premises true and the conclusion false. • An argument is valid if its form is valid. • An argument is sound if 1. it is valid, and 2. all its premises are true.

8. Valid and Invalid Arguments: • We have a way of deciding how strong an argument is: i.e. whether or not we are warranted in making the inference from the premises to the conclusion and accepting the conclusion as true. We say that a Valid, or strong argument is one which, if the premises are true, then so is the conclusion. • If the premises of a deductive argument can be true and the conclusion false at the same time, we call it an invalid, or weak argument. Our goal is to make valid - strong arguments.

9. In a valid deductive argument, the conclusion has to be true if the premises are true. (a) All men are mortal (b) Socrates is a man __________________ (c) Therefore, Socrates is mortal

10. Valid but not sound • If the South won the Civil War, then the slaves were freed • The South won the Civil War __________________________________ (c) Therefore, the slaves were freed. This argument is Valid because is (a) and (b) were true, then (c) would also have to be true. This argument is unsound because the premises (a) and (b) are both false.

11. If it is raining, then the sky is cloudy • The sky is cloudy. ________________________ (c) Therefore, is it raining. This arguments is invalid, because if its premises were both true, its conclusion would not necessarily be true.

12. How can you find out if a categorical syllogism is valid? One method, follow these steps. • Find the form of the syllogism by replacing its terms with letters (2) See if you can find an example of another syllogism that has the same form but in which the conclusion in false even though the premises are true. (3) If it is not possible, then a syllogism with that form must be valid.

13. Let’s see how this method works: All unmarried mothers are on welfare Some people on welfare are cheats • _____________________________ Therefore, some unmarried mothers are cheats • This syllogism has the form All U are W. Some W are C ____________________ Therefore, some U are C

14. Consider this argument which has the same form: All men are human. Some humans are women. __________________________ Therefore, some men are women. • This argument has the same form, the premises are true, but the conclusion false. Therefore, it is invalid.

15. Invalid argument All unmarried mothers are on welfare Some people on welfare are cheats • _____________________________ Therefore, some unmarried mothers are cheats

16. Another Example • All cows are mammals • All cows have horns ___________________ Therefore, some mammals have horns This argument has the following form: All C are M All C have H _______________ Therefore, some M are H This syllogism is valid and any syllogism with the same form is valid.

17. Four Rules to determine Validity in categorical syllogisms • The middle term ( the term that is present in both premises but absent from the conclusion) must refer to all members of the class in at least one premise. • If either term in the conclusion refers to all members of the class, it must also refer to all members of the class in the premises. • Both premises must not be negative. • If one of the premises is negative, then the conclusion must be negative

18. Example which breaks rule 1 • Some X are Y • Some X are Z ____________________ Therefore, some Y are Z.

19. Example which breaks rule 1 Some mammals are apes Some mammals are whales _______________________ Therefore, some apes are whales

20. Hypothetical Syllogisms Valid Forms If P, then Q. If P, then Q. P. Not Q. __________ __________ Therefore, Q. Therefore, not P.

21. Hypothetical Syllogisms • If it is raining, then the ground is wet. • It’s raining. _______________ (c) Therefore, the ground is wet. If P, then Q P. ------------------ Therefore Q.

22. Hypothetical Syllogisms • If it’s raining, then the ground is wet. • The ground is not wet ________________________ (c) Therefore, it’s not raining.

23. What about this one? • If interest rates rise, then the price of stocks will decline. • Interest rates are not rising ________________________ (c) Therefore, the price of stocks will not decline.

24. Invalid forms of hypothetical Syllogisms If P, then Q. If P, then Q Not P Q. __________ ___________ Therefore, not Q. Therefore, P.

25. Disjunctive Syllogisms There are 4 forms of disjunctive syllogisms. Two are valid and two are invalid. VALID Either P or Q. P or Q. Not P. Not Q. ____________ _________ Therefore, Q. Therefore, P.

26. Disjunctive Syllogisms Either it is raining or the sprinklers are on. It is not raining. __________________ Therefore, the sprinklers must be on. Either I will study or watch tv I am not watching tv ___________________ Therefore I will study.

27. Disjunctive Syllogisms Two invalid forms: Either P or Q. Either P or Q. P. Q. ____________ _____________ Therefore, not Q. Therefore, not P. These forms are invalid because Disjunctive Syllogisms leave open the possibility that both disjuncts are true. Consequently, even though one is true, the other also might be true.

28. FALLACIES • Fallacy – a piece of reasoning in which the conclusion does not logically follow the evidence given as support, an argument that tries to persuade psychologically but not logically; a false notion.

29. FALLACIES • Logic also discusses the incorrect ways of reasoning. A set of statements that appears to be an argument but is not is a fallacy. There are formal fallacies, which break specific rules of logic, and there are informal fallacies which usually are phrased to appear as an argument but the statements purporting to be premises to do not support the conclusion.

30. Informal Logical Fallacies • The Fallacy of Begging the Question • Involves assuming the point that needs to be proven. • One ends up arguing in a vicious circle. • Phil: Did you here that Charlie talks to angels? • Dave: No Kidding! How do you know that he’s telling the truth. • Phil: Come on! A guy who talks to angels wouldn’t lie! • The problem is that the only evidence Phil offers to prove his assertions is his original statement about Charlie talking to angels.

31. The Fallacy of Ignoring the Question • Consists in proving something other than the point to be established. Consists in evading the original issue. • Reporter: Minister, do you agree that your sale of the 407 to a private company failed to protect consumers? • Minister: The opposition is merely trying to score political points by bringing up this issue. Our government has been very fiscally responsible in all actions.

32. The Fallacy of False Cause • In assuming that when one event precedes another, it is the cause of the succeeding event. • “Since 1840 every president elected in a “zero” year has either died in office of natural causes or been assassinated. Obviously, if you want to live through your term in office, don’t run in a “zero” year.

33. The Fallacy of accident • Consists in treating what is accidental to a subject as something essential to that subject. • “Now that Charlie has gone bald, he’s no longer the man that I knew and loved! Its over!” • Charlie’s hair is accidental to who he is as a person, meaning it is not essential to who he is.

34. The Fallacy of Part and Whole • Attributing to a whole what belongs only to its parts. (The fallacy of generalization). • All who wear turbans and have beards are terrorists. • All teens who hand in late assignments have really bad grades. • Or the fallacy occurs when a person attributes to the part what belongs only to the whole. • Since America is a prosperous nation, all of its citizens must be well off.

35. The Fallacy of Misplaced Authority • It consists in concluding that something is true because somebody of authority said it. Yet the kind of authority he or she has and the issue at hand are simply incongruent. • “Mr. Dr., assured me that Fords are the best cars. Therefore, I’m going to buy a Ford/ After all he is a doctor.

36. The Fallacy of Ad Hominem • Directed to the individual. • This involves the criticism of some person’s position or belief by criticizing the person rather than the position itself. • “Look at the way he stutters when he talks. He must not know what he’s talking about, so I’m not going to vote for him.”

37. The Fallacy of the Double Standard • Applying one standard for one group of individuals and another standard for an opposing group or individual. • Tina and Tom both have untucked shirts • Tina gets 3 days suspension. Tom gets 5.

38. Appeal to the People • Occurs when a speaker attempts to get some group to agree to a particular position by appealing solely to their bigotry, biases, prejudices or in some cases merely to their desire to hear what they already believe. • Hitler says Jews are lower than rats and they’re the scum of the earth and they’re taking German jobs, etc… • Plays on the fears of the people.

39. The Fallacy of False Analogy • Occurs when a person argues a position merely by drawing an analogy without justifying the use of the analogy. • Going to church is like belonging to a team. If you want to play in the big game you have to go to practice. • Analogies only illustrate a point, they do not prove a point.

40. The Fallacy of Appeal to Ignorance • Occurs whenever someone argues that a statement is false because it has not been proven true or it is true because it has not been proven false. • Elephants have red eyes so that they can hide in cherry trees. Have you ever seen an elephant in a cherry tree? That proves my point!

41. The Fallacy of Equivocation • Occurs when a word or expression is used with more than one meaning in an argument. • The conservative candidate supports sex before marriage. That’s not a conservative position.

42. Sophistry • An instance of ignoring the question. • A flawed but deceptive method of argument used commonly by early philosophers.