Logic

1. Logic The foundation of philosophy

2. What is Logic? • Logic is the study of reasoning well. • Reasoning is not the same as offering reasons. • Reasons are supporting statements to a premise. They answer the question “Why” or “Why do you say that”? • Reasoning is an act of the mind. It is stacking up supportable statements (premises) which lead to a conclusion or claim. • To reach a good or reasonable conclusion, the premises must be stacked up in a reasonable (rational) manner. • IMPORTANT: Logic describes what the mind does and how the mind puts things together.

3. Reasoning well • Everyone reasons. • Logic or reason is not based on culture or “smarts.” • Education can train the ability to reason; but all humans have the capacity to reason • Exception: If one is irrational purposefully or due to a mental deficiency brought on by stress, chemicals or disability. • Logic is innate. • Everyone reasons the same way. • Logic is the same for everyone regardless of race, age, culture, century, etc. (In fact, animals reason just as humans do, but to a limited extent.) • Example: 2 true statements always lead to a true conclusion • Example: Everyone agrees that 2 + 2 = 4.

4. Reasoning well • Logic is an absolute law which describes how people reason. • But logical reasoning is not an absolute law which governs the universe. • Just because something is logically impossible doesn’t mean it’s impossible. • Example: miracles; Euclidean geometry (logical, but not the only kind of geometry); light as wave andparticle • Example: Using mathematical logic alone, can you ever reach the door?

5. Reasoning well • Logic is not a set of rules which govern human behavior. • Behavior has to do with ethicsand is not necessarily logical. • Behavior is influenced by variables. Decisions may seem illogical because there are two logical variables which are conflicting. • Example: John must speak to whoever is in charge to get approval for a project. The person in charge is Steve. Therefore John should speak to Steve. (Logical) However, Steve has promised never to approve any of John’s work. Therefore, John would be foolish to speak to Steve. (Logical) So John speaks to Mary, who presents John’s idea to Steve without John’s name, and gets the approval John needs.

6. Reasoning well • Good reasoning requires these elements: • Clear Terms • one word • reveals essence • answers the question “what a thing is” • can be concrete (ball) or conceptual or universal/idea (sphere) • True Premises • complete sentence • reveals existence • answers the question “whether it is” or “what are we saying” • must have at least two which lead to a conclusion • Valid Logic • the “movement” of the argument • conclusion which necessarily (must) follow from the premises

7. Arguments • Good logic leads to a good argument. • We use the word argue in at least 3 different ways: • To describe a heated discussion (oral disagreement; altercation; verbal opposition) • I argued with my mother about using the car. • Often includes “the automatic gainsaying of what the other person says” (i.e,. contradiction). • Most common but also poorest (imprecise) use of the word “argue” and it gives a true argument a bad name.

8. Arguments • To describe a debate between two or more persons • The politicians argued about a policy • Might include reasons, but commonly the purpose is not to persuade or convince, but merely to present the viewpoints/opinion so that others may decide which is best • Not arguing but Too often, that's what passes for a true argument.

9. arguments • To describe a series of statements which lead to the truth. • A process of reasoning; a series of reasons leading to a conclusion. • Derivative meanings • A speech or composition intended to persuade or convince using supported reasons • A theme or thesis or summary of a paper or speech which then presents the reasons • “Here is my argument…”

10. ARguments • Two types of arguments • Inductive: From particular premises to general conclusion; leads to probabilities; based on trends and past experience • Example 1 • The cookie jar has cookies in it. • You have a cookie. • ∴ You must have taken a cookie from the cookie jar. • Example 2 • Since 1995, baseball teams that won 95 games went to the playoffs. • The Tigers won 95 games this year. • ∴ The Tigers will go to the playoffs.

11. Arguments • Deductive: From general premises to specific conclusion; leads to certain truth • Deductive arguments lead to truth only when good logic is employed. • The reasons (premises) are presented with clear, unambiguous (precise) terms (not “thing” or “like”) • The reasons (premises) are true or supportable statements (not questions or guesses/hopes) • The reasons (premises) build on each other in an orderly pattern (valid logic). • These are the three basic parts of all logic: clear terms, true premises, valid logic (reasoning). They lead to a conclusion.

12. Arguments • Two ways to build a deductive argument. • Begin at the end, and then build your case (What are you trying to prove or argue?) • OR Start with a series of premises and see where they lead you. (Socratic Method) • Socrates’ goal was to argue himself from the known to the truth.

13. Syllogism • Most deductive arguments are syllogisms, which consist of premises which lead to a conclusion. • Commonly, a major premise is followed by a minor premise • There may be unspoken premises (inferences) • There may be many premises • Support for each premise is not part of the outline

14. Syllogisms • Example 1: • MrGawel is human. • Humans die. • ∴ MrGawel will die. • Example 2: • Rome is the capital of Italy. • I went to Rome. • ∴ I went to Italy. • Example 3: • Either the meeting is at school or at home. • The meeting is not at home. • ∴ the meeting is at school.

15. Syllogisms • Example 4: • All water boils at 100 C at sea level. • The liquid in the test tube at the beach is water. • The beach is at sea level. • I have built a fire on the beach. • ∴ When the water boils I know that the temperature of the water has reached 100 C.

16. Syllogisms • Example 5: • Premise: Every event has a cause • Premise: The universe has a beginning • Premise: All beginnings involve an event • Inference: This implies that the beginning of the universe involved an event • Inference: Therefore the beginning of the universe had a cause • Conclusion: The universe had a cause • The proposition in line 4 is inferred from lines 2 and 3. Line 1 is then used, with the proposition derived in line 4, to infer a new proposition in line 5. The result of the inference in line 5 is then re-stated (in slightly simplified form) as the conclusion.

17. Syllogism • Example 6 (thought experiment) • A car is not a boat. • Some boats are water bicycles. • No boat is a water bicycle. • False: contradicts second premise • Some water bicycles are not cars. • No boat is a car. • False: repeats first premise • Some cars are not water bicycles. • False: moves the qualifier “some” from boats to cars

18. Assignment • Watch the Argument Clinic (my website) • Answer these questions • What is an argument? • What was wrong with the argument? • Where does the argument go right? • Answers • An argument is a connected series of statements intended to establish a proposition. • A wrong argument is simply “gainsaying” or contradictions; terms not clear; invalid logic • If you want me to go on arguing, you'll have to pay for another five minutes; Aha. If I didn't pay, why are you arguing? I Got you!

19. Good Arguments • Key Question: How does one establish a good argument which does not fail? • How does one establish clear, unambiguous terms? • Must define terms, often with support • How does one establish true premises? • Must support statements (unless they are generally, commonly, universally true) • Key: If you or your peers or your audience did not know it before you started researching, then it is not common, general, universal. • How does one establish valid logic? • Most important question; and where most arguments fail. • Simple rule of thumb: connect the terms and/or premises

20. Good Arguments • A bad argument fails (is false, fallacious) because one or more of the three basics parts are incorrect. (Terms not clear; premises not true; logic not valid) • Example 1: • Shaylais a woman. • All men are mortal. • ∴Maynor is immortal. • Problem: terms not clear • Example 2: • A sacrament gives God’s grace using a visible non-human element. • Reconciliation has no visible non-human element. • ∴ Reconciliation is not a sacrament. • Problem: false major premise

21. Good Arguments • Example 3: • Ostriches are birds. • All birds can fly. • ∴ Ostriches can fly. • Problem: false minor premise • Example 4: • Hitler was crazy. • Hitler ruled Germany. • ∴ The U.S. had to fight in WWII. • Problem: logic not valid

22. Valid Logic • What is Valid Logic? • The conclusion must necessarily follow from the premises. • Valid logic means that true premises will always lead to a true conclusion. • Valid logic means that false premises will always lead to an uncertain conclusion. • Example 1 • I am a cat. (false premise) • All cats are gods. (false premise) • ∴I am a god. (valid logic; false conclusion) • Example 2 • Moscow is the capital of the US. (false premise) • I went to Moscow. • ∴I went to the US. (false or uncertain conclusion)

23. Valid Logic • Valid logic also means that one or more false premises can lead to a true conclusion. • Example • All fish live in the ocean. • Sea otters are fish. (false premise) • ∴Sea otters live in the ocean. (valid logic) • Valid Logic means that true premises will lead to a true conclusion • And that true premises will never lead to a false conclusion

24. Valid Logic • . • Valid Logic follows common sense. • If an argument is logically valid, but does not seem to follow common sense (or the argument is not true), then usually one or more of the premises are false or the “common sense” is not actually common sense. • NB: Don’t confuse common sense with conventional wisdom. Conventional wisdom is what most people think is good, right, valid. Common sense is common to rational people of all places and times; it is where logic always leads.

25. Valid Logic • Invalid Logic leads to a conclusion that is always false. • This may be due to missing premises, unclear terms, or poor logic. The latter is often the easiest to spot since the augment simply doesn’t make sense. The first two, however, are more challenging. • Example 1: • If Johnny eats candy every day, he is placing himself at risk for diabetes. • Johnny does not eat candy every day. • ∴ Johnny is not placing himself at risk for diabetes. • Problem: Premises are too broad, require further support. Candy is assumed to be the sole contributor to diabetes. “Every day” is too narrow. Diabetes may be hereditary.

26. Valid Logic • Example 2: • Brandon loves his mother. • Brandon loves his grandmother. • ∴ Brandon loves his niece. • Problem: No internal connection between premises and conclusion. • Example 3: • Tomatoes are a fruit. • Vegetables are located in the vegetable aisle. • ∴ Tomatoes should be displayed next to apples. • Problem: Missing premises.