Valid vs. Sound

1. Valid vs. Sound

2. Valid vs. Sound • I. Truth, Validity, and Soundness: probably the three most important concepts of the course. • A. First, let us briefly characterize these concepts. • 1. truth: a property of statements, i.e., that they are the case. • 2. validity: a property of arguments, i.e., that they have a good structure. • (The premises and conclusion are so related that it is absolutely impossible for the premises to be true unless the conclusion is true also.)

3. Valid vs. Sound • 3. soundness: a property of both arguments and the statements in them, i.e., the argument is valid and all the statement are true. • Sound Argument: (1) valid, (2) true premises (obviously the conclusion is true as well by the definition of validity).

4. B. The fact that a deductive argument is valid cannot, in itself, assure us that any of the statements in the argument are true; this fact only tells us that the conclusion must be true if the premises are true.

5. 1. Let's look at the variety of valid arguments that can be given as sorted by the truth of premises and conclusion: If it were possible to have true premises and a false conclusion, logic would be useless to prove anything.

6. 2. Let's look at the variety of invalid arguments that can be given as sorted by the truth of premises and conclusion: That is, all possibilities can be represented.

7. II. One way to summarize these concepts is to represent the logical territory in a "tree-diagram."

8. III. Consider these examples A. Tell whether the following statements are true or false. • 1. A sound argument is a deductive argument which is valid and has true premises. • 2. It is impossible for a deductive argument to be both valid and unsound. • 3. If a deductive argument is valid, it cannot be unsound. • 4. If the premises of a deductive argument are true, then the argument must be sound. • 5. If the conclusion of a deductive argument is true, then the argument might be sound or it might be unsound. • 6. If the premises of a deductive argument are true, then the conclusion must be true. • 7. If a deductive argument is valid, then its conclusion might be true or it might be false. • 8. A sound argument is a deductive argument that has valid premises. • 9. If a valid argument has a false conclusion, then it must have at least one false premise. • 10. If a deductive argument is valid and at least one of its premises is false, then its conclusion is also false.

9. 1. A sound argument is a deductive argument which is valid and has true premises. • TRUE • 2. It is impossible for a deductive argument to be both valid and unsound. • FALSE • 3. If a deductive argument is valid, it cannot be unsound. • FALSE • 4. If the premises of a deductive argument are true, then the argument must be sound. • FALSE • 5. If the conclusion of a deductive argument is true, then the argument might be sound or it might be unsound. • TRUE • 6. If the premises of a deductive argument are true, then the conclusion must be true. • FALSE • 7. If a deductive argument is valid, then its conclusion might be true or it might be false. • TRUE • 8. A sound argument is a deductive argument that has valid premises. • FALSE • 9. If a valid argument has a false conclusion, then it must have at least one false premise. • TRUE • 10. If a deductive argument is valid and at least one of its premises is false, then its conclusion is also false. • FALSE

10. Invalid & Unsound • Invalid and unsound: at least one premise is false, and conclusion does not follow from the premises. Example: • All GPS satellites are positioned underwater. • Everything positioned underwater becomes wet. • therefore, GPS satellites are dry. • Invalid: premises may be true but conclusion does not follow from them. Example: • Mangosteen is a fruit. • Mangosteen is purple. • Therefore, all fruit is purple.

11. Valid vs Sound • Valid but unsound: conclusion follows from the premises but at least one of the premises is false. Example: • All art movements started in India. • Bauhaus was an art movement. • Therefore, Bauhaus started in India. • Sound: all premises are true and conclusion follows from the premises. Example: • Investment strategies may be profitable. • "Dogs of the Dow" is an investment strategy. • therefore, the "Dogs of the Dow" strategy may be profitable.

12. Homework- Logical Arguments • After reading “Logical Fallacies,” attempt to create 1 sound argument, 1 valid (but not sound) argument and 2 common examples of arguments for Correlation equals Causation and ad hominem.

13. Logical Fallacy • In philosophy, the term logical fallacy properly refers to a formal fallacy: a flaw in the structure of a deductiveargument which renders the argument invalid. • However, the same terms are used in informal discourse to mean an argument which is problematic for any reason. Logical form alone can guarantee that given true premises, a true conclusion must follow.

14. Material fallacies • The taxonomy of material fallacies is based on that of Aristotle's logical works Organon (Sophisticielenchi). This taxonomy is as follows:

15. Fallacy of accident or sweeping generalization • Fallacy of accident or sweeping generalization: a generalization that disregards exceptions. • Example • Argument: Cutting people is a crime. Surgeons cut people, therefore, surgeons are criminals. • Problem: Cutting people is not a crime in certain situations. • Argument: It is illegal for a stranger to enter someone's home uninvited. Firefighters enter people's homes uninvited, therefore firefighters are breaking the law. • Problem: The exception does not break nor define the rule; a dictosimpliciter ad dictum secundum quid (where an accountable exception is ignored).

16. Converse fallacy of accident or hasty generalization • Converse fallacy of accident or hasty generalization: argues from a special case to a general rule. • Example • Argument: Every person I've met has ten fingers, therefore, all people have ten fingers. • Problem: Those who have been met are not a representative subset of the entire set. • Also called reverse accident, destroying the exception, a dictosecundum quid ad dictum simpliciter

17. Irrelevant conclusion • Irrelevant conclusion: diverts attention away from a fact in dispute rather than addressing it directly. • Example • Argument: Oliver believes that humans can fly, therefore humans can fly. • Problem: Oliver can be wrong. Just because he believes in something does not make it true unless he is an expert. (In particular this is an appeal to authority.) • Also called IgnoratioElenchi, a "red herring"

18. Affirming the consequent/Denying the antecedent • Affirming the consequent and Denying the antecedent: gives a conclusion from premises that do not support that conclusion. • Affirming the consequent Example: • Argument: If people have the flu, they cough. Torres is coughing. Therefore, Torres has the flu. • Problem: Other things, such as asthma, can cause someone to cough. The argument treats having the flu as a necessary condition of coughing; in fact, having the flu is a sufficient condition of coughing, but it is not necessary to have the flu for one to cough. • Argument: If it rains, the ground gets wet. The ground is wet, therefore it rained. • Problem: There are other ways by which the ground could get wet (e.g. someone spilled water). • Denying the antecedent Example • Argument: If it is raining outside, it must be cloudy. It is not raining outside. Therefore, it is not cloudy. • Problem: Rain is a sufficient condition of cloudiness, but cloudy conditions do not necessarily imply rain.

19. Fallacy of false cause • Fallacy of false cause or non sequitur: incorrectly assumes one thing is the cause of another. Non Sequitur is Latin for "It does not follow." • Example • Argument: I hear the rain falling outside my window; therefore, the sun is not shining. • Problem: The conclusion is false because the sun can shine while it is raining. • Special cases • post hoc ergo propter hoc: believing that succession implies a causal relation. • Example

20. Fallacy of false cause • Argument: It rained just before the car broke down. The rain caused the car to break down. • Problem: There may be no connection between the two events. Two events co-occurring is not an indication of causation. • cum hoc ergo propter hoc: believing that correlation implies a causal relation. • Example • Argument: More cows die in the summer months. More ice cream is consumed in summer months. Therefore, the consumption of ice cream in the summer months is killing cows. • Problem: No premise suggests the ice cream consumption is causing the deaths. The deaths and consumption could be unrelated, or something else could be causing both, such as summer heat. • Also called causation versus correlation.

21. Fallacy of many questions • Fallacy of many questions or loaded question: groups more than one question in the form of a single question. • Example • Argument: Have you stopped beating your wife? • Problem: Either a yes or no answer is an admission of guilt to beating your wife. (See also Mu.) • Also called PluriumInterrogationum and other terms

22. Straw man • Straw man: A straw man argument is an informal fallacy based on misrepresenting an opponent's position so as to more easily refute it.[2] • Examples • Person A: Sunny days are good. • Person B: If all days were sunny, we'd never have rain, and without rain, we'd have famine and death. Therefore, you are wrong. • Problem: B has misrepresented A's claim by falsely suggesting that A claimed that only sunny days are good, and then B refuted the misrepresented version of the claim, rather than refuting A's original assertion.

23. No true Scotsman • No true Scotsman: When faced with a counterexample to a universal claim, rather than denying the counterexample or rejecting the original universal claim, this fallacy modifies the subject of the assertion to exclude the specific case or others like it by rhetoric, without reference to any specific objective rule. • Example • Person A: All Scotsmen enjoy haggis. • Person B: My uncle is a Scotsman, and he doesn't like haggis! • Person A: Well, all true Scotsmen like haggis.

24. Proof by verbosity • Proof by verbosity, sometimes colloquially referred to as argumentum verbosum - a rhetorical technique that tries to persuade by overwhelming those considering an argument with such a volume of material that the argument sounds plausible, superficially appears to be well-researched, and it is so laborious to untangle and check supporting facts that the argument might be allowed to slide by unchallenged.

25. Which fallacy is most commonly used? -WIT • How do you see it in life? -WIT

26. Read 5 Logical Fallacies that make you wrong more than you think. • Which two most describe you? Is there one that does not describe you. Be sure to share and explain your answer to a partner. -WIT

27. Read 5 Logical Fallacies that make you wrong more than you think. • What is the concern for society if “We’re programmed to win?” • How does our brain not understanding probability, effect our ability to argue? • What does “Everyone’s out to get us” mean? • Why do we have a double standard when it comes to other people? • Why don’t facts change our mind and what is its effect on us as a society?

28. Read Propositions (Pro/Con) • What type of logical Fallacies did you find? (What made some arguments better than others?) • Why is knowing how to recognize “good” vs. “bad” arguments important? -WIT