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Reasoning Effectively

Reasoning Effectively. Six criteria for evaluating philosophical claims and theories:. Conceptual clarity = define your terms! Consistency = any contradictions? Logical inconsistency Self-referential inconsistency Rational coherence = how do the parts “hang together”?

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Reasoning Effectively

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  1. Reasoning Effectively

  2. Six criteria for evaluating philosophical claims and theories: • Conceptual clarity = define your terms! • Consistency = any contradictions? • Logical inconsistency • Self-referential inconsistency • Rational coherence = how do the parts “hang together”? • Comprehensiveness = does a philosophy account for a wide range of phenomena? • Compatibility = does a part of your philosophy fly in the face of well-established facts and theories? • Compelling = warranted?!

  3. Montreal is about 200 km from Ottawa, while Toronto is 400 km from Ottawa. Toronto is closer to Ottawa than Montreal. • Logical inconsistency

  4. There are no truths. • Self-referential inconsistency

  5. John is taller than Jake, and Jake is taller than Fred, while Fred is taller than John. • Logical inconsistency

  6. This sentence is not true. • Self-referential inconsistency

  7. A. It is always morally wrong to take the life of another human being. B. It is morally permissible to execute serious criminals. • Logical inconsistency

  8. The Goal of Philosophy • Excerpt from page 45

  9. Logic = • the study of methods for evaluating arguments and reasoning.

  10. Some Key Terms: • A set of statements in which one or more of the statements attempt to provide reasons or evidence for the truth of another statement = • ARGUMENT • A statement in an argument that serves to provide evidence for the truth of a claim = • PREMISE (OR REASON) • The statement in an argument that the premises are claimed to support or imply = • CONCLUSION

  11. List several premise indicators: • Since • Because • For/for one thing • For the reason that • Follows from • Inasmuch as • As shown by • Given that • Seeing that • Owing to • Seeing that • As/as indicated by • Assuming that • Considering that

  12. List several conclusion indicators: • Therefore • Hence • Thus/ergo • So • Follows that • Consequently • Which entails that • Accordingly • Which proves that • Which implies that • Necessarily • Must be the case that • Which means that • Demonstrates that • We can conclude that • As a result

  13. A ____ argument is one in which it is claimed that the conclusion necessarily follows from the premises. • Deductive

  14. An argument in which it is claimed that the premises make the conclusion highly probable: _____ • Inductive argument

  15. A form of reasoning that tries to show that a particular theory is superior to all its competitors and that it is therefore likely to be true: ___ • Abductive argument (inference to the best explanation)

  16. Deductive Arguments • First, is the argument valid or invalid? • The significance of validity… • If valid, is the argument sound?

  17. Example:1. If all events are caused, then we are not free. 2. All events are caused. Therefore: We are not free. • Valid? • Sound?

  18. Some key terms: • Two simpler statements that are connected with the words if and then = • CONDITIONAL STATEMENT • The first part of a conditional statement (the if clause) = • ANTECEDENT • The second part of a conditional statement ( the then clause) = • CONSEQUENT

  19. Example: • If I study for the Chapter 1 test on Monday, then I’ll earn a good grade.

  20. A conditional statement claims that the truth of the antecedent is a sufficientcondition for the truth of the consequent (page A2)

  21. More key terms: • Sufficient condition = statement A is a sufficient condition for statement B if the truth of A guarantees the truth of B • Example: Being pregnant (A) is a sufficient condition for being female (B). • Necessary condition: statement A is a necessary condition for statement B if the truth of B requiresthe truth of A • Example: Being a female (A) is a necessary condition for being pregnant (B). • [However, being a female is not a sufficient condition for being pregnant.]

  22. Sufficient Conditions (X guarantees Y) • Earning a total of 900 points (90%) in this Honors Philosophy class is a sufficient condition for earning a final grade of H-. If you have 900 points for the course, then it must follow that you will have a final grade of H-. [not necessary as 920 points would too] • Pouring a gallon of freezing water on my sleeping student is sufficient to wake him up. If I pour the gallon of freezing water on him then it’s guaranteed that he will wake up. [not necessary as a punch to the jaw would do it as well] • Rain pouring from the sky is a sufficient condition for the ground to be wet. [not necessary, as the sprinkler could be on]

  23. Necessary Conditions (If we don’t have X, we won’t have Y) • Having gasoline in my car (I have a gasoline engine) is a necessary condition for my car to start. Without gasoline (x) my car (y) will not start. Of course, having gasoline in the car does not guarantee that my car will start. There are many other conditions needed for my car to start. • Having oxygen in the earth’s atmosphere is a necessary condition for human life. Certainly, having oxygen will not guarantee human life. There are many other conditions needed for human life other than oxygen in the atmosphere. • Being 18 years of age is a necessary condition for being able to buy cigarettes legally in Ohio. Of course, being 18 does not guarantee that a person will buy cigarettes. There are many other conditions that lead to a person buying cigarettes than being 18 years of age.

  24. Is sunlight a necessary or sufficient condition for the roses to bloom? • Sunlight is a necessary condition for the roses to bloom, since without sunlight it would be impossible for the roses to bloom.  It is not a sufficient condition, though, because sunlight alone does not guarantee that the roses will bloom.

  25. Is earning a final grade of C a necessary or sufficient condition for passing the course? • Earning a final grade of C is a sufficient condition for passing this course because earning a C guarantees passing it.  It is not a necessary condition because there are other ways to pass the course other than earning final grade of C.

  26. Is being a male a necessary or sufficient condition for being a father? • Being a male is  a necessary condition for being a father since it is impossible to be a father without being a male.  Being a male is not a sufficient condition, however, since being a male does not guarantee that a male will be a father.

  27. Is having the flu virus a necessary or sufficient condition for being sick? • Having a flu virus is sufficient for being sick, but not necessary since there are other ways to be sick besides having a flu virus.

  28. Is being composed of H2O a necessary or sufficient condition for being water? • Both! Something must be H2O to be water, and if it is nothing but H2O that is sufficient to make it water.

  29. Well-Known Valid Deductive Argument Forms

  30. Modus Ponens (Affirming the Antecedent) • 1. If P, then Q. • 2. P. • 3. Therefore: Q. • 1. If Spot is a dog, then Spot is a mammal • 2. Spot is a dog. • 3. Therefore, Spot is a mammal.

  31. Philosophical Example of Modus Ponens • 1. If the universe shows evidence of design, then there is a God. • 2. The universe shows evidence of design. • 3. Therefore, there is a God.

  32. Modus Tollens (Denying the Consequent) • 1. If P, then Q. • 2. Not-Q. • 3. Therefore: not-P. • 1. If John is eligible for the award, then he is a junior. • 2. John is not a junior. • 3. Therefore, John is not eligible for the award.

  33. Philosophical Examples of Modus Tollens • 1. If we are morally responsible for our actions, then we have freedom of the will. • 2. We do not have freedom of the will. • 3. Therefore, we are not morally responsible for our actions. • 1. If God exists, there would be no unnecessary evil in the world. • 2. There is unnecessary evil in the world. • 3. Therefore, God does not exist.

  34. Fallacy • A fallacy is an argument form that is logically defective because the premises provide little or no support for the conclusion.

  35. Fallacy of Denying the Antecedent • 1. If P, then Q. • 2. Not-P. • 3. Therefore: not-Q. • 1. If Jones is a mother, then Jones is a parent. • 2. Jones is not a mother. • 3. Therefore, Jones is not a parent.

  36. Philosophical Example of the Fallacy of Denying the Antecedent • 1. If Thomas Aquinas’s arguments for God are valid, then there is a God. • 2. Thomas Aquinas’s arguments for God are not valid. • 3. Therefore, there is not a God.

  37. Fallacy of Affirming the Consequent • 1. If P, then Q. • 2. Q. • 3. Therefore: P. • 1. If George Washington was assassinated, then he is dead. • 2. George Washington is dead. • 3. Therefore, George Washington was assassinated.

  38. Philosophical Example of Affirming the Consequent • 1. If morality is completely subjective, then people will differ in their moral beliefs. • 2. People do differ in their moral beliefs. • 3. Therefore, morality is completely subjective. (There are no objective truths about what is morally right or wrong.)

  39. Another Example • 1. If medical science is completely subjective, then people will differ in their medical beliefs. • 2. People do differ in their medical beliefs. (Some people believe that sacrificing twin babies will cure the community of a plague; on the other hand, our society doesn’t believe this.) • 3. Therefore, medical science is completely subjective. (There are no objective truths about what will or won’t cure disease—a false conclusion.)

  40. Syllogism • A syllogism is a deductive argument with two premises and a conclusion.

  41. Hypothetical Syllogism • 1. If P, then Q. • 2. If Q, then R. • 3. Therefore: if P, then R. • 1. If I learn logic, then I will write better essays. • 2. If I write better essays, then I will get better grades. • 3. Therefore, if I learn logic, then I will get better grades.

  42. Philosophical Example of a Valid Hypothetical Syllogism • 1. If the methods of science give us only information about physical reality, then science cannot tell us whether a nonphysical reality exists. • 2. If science cannot tell us whether a nonphysical reality exists, then science cannot tell us whether we have a soul. • 3. Therefore, if the methods of science give us only information about physical reality, then science cannot tell us whether we have a soul.

  43. Disjunctive Statement • A disjunctive statement asserts that at least one of two alternatives is true. It typically is expressed as an either-or statement.

  44. Disjunctive Syllogism • 1. Either P or Q. • 2. Not-P. • 3. Therefore: Q. • 1. Either the bulb is burnt out or it is not receiving electricity. • 2. The bulb is not burnt out. • 3. Therefore, the bulb is not receiving electricity.

  45. Philosophical Example of a Disjunctive Syllogism • 1. Either the universe contains in itself a sufficient reason for its existence or it was caused to exist. • 2. The universe does not contain in itself a sufficient reason for its existence. • 3. Therefore, the universe was caused to exist.

  46. Fallacy of Affirming the Disjunct • 1. Either P or Q. • 2. P. • 3. Therefore: not-Q. • 1. Either the bulb is burnt out or it is not receiving electricity. • 2. The bulb is burnt out. • 3. Therefore, the bulb is receiving electricity.

  47. Philosophical Example of the Fallacy of Affirming the Disjunct • 1. Either reason is the source of moral principles or divine revelation is. • 2. Reason is the source of moral principles. • 3. Therefore, divine revelation is not the source of moral principles.

  48. Valid/Argument Form? • Either I left my wallet on my dresser or I must have lost it • The wallet is not on my dresser Therefore, I have lost it. Valid/Disjunctive syllogism

  49. Valid/Argument Form? • 1. If Queen Elizabeth is an American citizen, then she is a human being. • 2. Queen Elizabeth is not an American citizen. Therefore, Queen Elizabeth is not a human being. Invalid/Denying the Antecedent

  50. Valid/Argument Form? • If I have prepared thoroughly, I will do well. • I have prepared thoroughly. Therefore, I will do well. Valid/Modus Ponens (Affirming the Antecedent)

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