1. Logic

2. Propositions A proposition is a statement which can be either true or false. A proposition is a statement which can be either true or false. Not all sentences are either true or false and therefore not all sentences are propositions. Not all sentences are either true or false and therefore not all sentences are propositions.

3. Are these sentences propositions? Hint: Would it make sense to say that these sentences are true or false? Hint: Would it make sense to say that these sentences are true or false? Elvis is alive! Elvis is alive! What are you doing? What are you doing? A square has four sides. A square has four sides. Good morning! Good morning! I promise that I will pay you back tomorrow. I promise that I will pay you back tomorrow.

4. If we can think of a way in which it might be possible to show that a statement is true, we can say that it is VERIFIABLE. If we can think of a way in which to show that a statement is false, we can say that it is FALSIFIABLE

5. Are these statements verifiable or falsifiable? All triangles have three sides. All triangles have three sides. All pigs have wings. All pigs have wings. Some pigs can fly. Some pigs can fly. No pigs can fly. No pigs can fly. My mother is very angry. My mother is very angry. Stealing is wicked. Stealing is wicked. I never tell the truth. I never tell the truth. This sentence is false. This sentence is false.

6. Paradoxes Were the last two particularly difficult? Were the last two particularly difficult? They are paradoxes. They are statements which, if true, lead to a contradiction. They are paradoxes. They are statements which, if true, lead to a contradiction. If “this sentence is false” is true, it’s false; if it’s false, it’s true. If “this sentence is false” is true, it’s false; if it’s false, it’s true. So is “this sentence is false” a meaningful proposition? What does this tell us about the nature of truth? So is “this sentence is false” a meaningful proposition? What does this tell us about the nature of truth?

7. Another Paradox The British philosopher A.J. Ayer argued that if a proposition is not verifiable, it is meaningless. The British philosopher A.J. Ayer argued that if a proposition is not verifiable, it is meaningless. However, can you verify this? However, can you verify this? If not, is it meaningless to say that a proposition which is not verifiable is meaningless? If not, is it meaningless to say that a proposition which is not verifiable is meaningless?

8. Necessary conditions A square must have four sides. A square must have four sides. A shape NEEDS to have four sides in order to be a square; it’s a NECESSARY condition. A shape NEEDS to have four sides in order to be a square; it’s a NECESSARY condition. A whale is a kind of mammal. A whale is a kind of mammal. Being a mammal is a NECESSARY condition of being a whale; no animal can be a whale unless it is a mammal. Being a mammal is a NECESSARY condition of being a whale; no animal can be a whale unless it is a mammal.

9. Necessary conditions What necessary conditions of being a Marymount student can you think of? What necessary conditions of being a Marymount student can you think of?

10. Sufficient conditions Anyone who has a son is a parent. Anyone who has a son is a parent. Having a son is a SUFFICIENT condition of being a parent but is not a NECESSARY condition. Why not? Having a son is a SUFFICIENT condition of being a parent but is not a NECESSARY condition. Why not? Any shape which has three sides is a triangle. Any shape which has three sides is a triangle. Is this a sufficient condition, a necessary condition, or both? Is this a sufficient condition, a necessary condition, or both?

11. Can you think of some sufficient conditions of being a Marymount student? Can you think of some sufficient conditions of being a Marymount student?

12. Four conditions Necessary but not sufficient Necessary but not sufficient Sufficient but not necessary Sufficient but not necessary Both necessary and sufficient Both necessary and sufficient Neither necessary nor sufficient Neither necessary nor sufficient

13. Sufficient? Necessary? Neither? Both? Being tall/ not being short Being tall/ not being short Being a Marymount student/ having rich parents Being a Marymount student/ having rich parents Being a regular pentagon/ having five sides Being a regular pentagon/ having five sides Being a circle/ having a circumference of 2πr Being a circle/ having a circumference of 2πr Being an aunt/ having a nephew Being an aunt/ having a nephew

14. Valid arguments: Being able to construct valid arguments is the most fundamental skill in philosophy. The groundwork in this field was done by Aristotle 2400 years ago. Being able to construct valid arguments is the most fundamental skill in philosophy. The groundwork in this field was done by Aristotle 2400 years ago. Valid arguments have premises and a conclusion. Valid arguments have premises and a conclusion. If the premises are true, then the conclusion must also be true. If the premises are true, then the conclusion must also be true. For example: For example: Premise 1: All cats are mammals. Premise 1: All cats are mammals. Premise 2: All mammals are animals. Premise 2: All mammals are animals. Conclusion: All cats are animals. Conclusion: All cats are animals.

15. Valid arguments An argument can still be valid even if its premises or its conclusion are false. An argument can still be valid even if its premises or its conclusion are false. All fish ride bicycles. All fish ride bicycles. Anything which can ride a bicycle is a teapot. Anything which can ride a bicycle is a teapot. Therefore, all fish are teapots. Therefore, all fish are teapots. Not a very convincing argument – but it IS a valid one! Not a very convincing argument – but it IS a valid one!

16. Valid arguments An argument may have true premises and a true conclusion but still be invalid. An argument may have true premises and a true conclusion but still be invalid. David Beckham is famous. David Beckham is famous. David Beckham is a football player. David Beckham is a football player. So David Beckham is a famous football player. So David Beckham is a famous football player. Why is this invalid? Why is this invalid?

17. Sound arguments If all the premises of an argument are TRUE If all the premises of an argument are TRUE And the argument is VALID And the argument is VALID Then the argument is SOUND. Then the argument is SOUND. Does this mean that its conclusion must be true? Does this mean that its conclusion must be true?

19. Patterns of valid arguments: Mind your Ps and Qs If P then Q If P then Q P Therefore Q Therefore Q Can you think of a SOUND argument following this pattern? Can you think of a SOUND argument following this pattern?

20. A common mistake If P then Q If P then Q Q Therefore P Therefore P All fish can swim. All fish can swim. Whales can swim. Whales can swim. Therefore whales are fish. Therefore whales are fish.

21. Another common mistake Some P are Q Some P are Q Some Q are R Some Q are R Therefore some P are R Therefore some P are R Sounds plausible enough? Sounds plausible enough? If so then if some girls are students… If so then if some girls are students… And some students are boys… And some students are boys… Then some girls are boys. Then some girls are boys.

22. Patterns of valid arguments If P then Q If P then Q Not Q Not Q Therefore not P Therefore not P If Peter loves Queenie then he will ask her to marry him. If Peter loves Queenie then he will ask her to marry him. Peter won’t ask Queenie to marry him. Peter won’t ask Queenie to marry him. Therefore Peter doesn’t love Queenie. Therefore Peter doesn’t love Queenie. Can you think of another example? Can you think of another example?

23. Another common mistake If P then Q Not P Therefore not Q If Gerald is a giraffe then he lives in Africa. Gerald is not a giraffe. Therefore Gerald does not live in Africa. Why isn’t this valid?

24. Chain arguments If P then Q If P then Q If Q then R If Q then R If R then S If R then S If S then T If S then T Therefore if P then T. Therefore if P then T.

25. A common mistake The slippery slope: The slippery slope: If P then probably Q If P then probably Q If Q then probably R If Q then probably R If R then there is a high chance of S If R then there is a high chance of S If S then maybe T If S then maybe T Therefore if P then T. Therefore if P then T. Can you think of an example of this kind of invalid argument? Can you think of an example of this kind of invalid argument?

26. Dilemma P or Q P or Q If P then R If P then R If Q then S If Q then S Therefore R or S Therefore R or S

27. If I do my English homework I won’t have time to do my maths and if I do my maths homework I won’t have time to do my English homework. If I don’t do my maths then Mrs Wong will kill me. If I don’t do my English then Mr Johncock will kill me. Either way, I’m dead! If I do my English homework I won’t have time to do my maths and if I do my maths homework I won’t have time to do my English homework. If I don’t do my maths then Mrs Wong will kill me. If I don’t do my English then Mr Johncock will kill me. Either way, I’m dead! Break this argument down into its premises and conclusions, and identify each premise and conclusion with a letter. Break this argument down into its premises and conclusions, and identify each premise and conclusion with a letter.

28. Another common mistake The false dilemma: The false dilemma: Either we close the tuckshop and ban fatty food from students’ lunchboxes or pretty soon everyone in the school will be morbidly obese. Either we close the tuckshop and ban fatty food from students’ lunchboxes or pretty soon everyone in the school will be morbidly obese. This may be the conclusion to a valid argument, but what would the premises of the argument be? This may be the conclusion to a valid argument, but what would the premises of the argument be? What hidden assumptions are implied? What hidden assumptions are implied?

29. Hidden assumptions Eating meat is not immoral because it is natural. Eating meat is not immoral because it is natural. This is NOT a valid argument. Why not? This is NOT a valid argument. Why not? What premise or premises would you need in order to construct a valid argument with this as its conclusion? What premise or premises would you need in order to construct a valid argument with this as its conclusion?

30. Equivocation A cat needs water in order to live. A cat needs water in order to live. Therefore my cat Tiddles needs water in order to live. Therefore my cat Tiddles needs water in order to live. A cat is sitting on the roof. A cat is sitting on the roof. Therefore my cat Tiddles is sitting on the roof. Therefore my cat Tiddles is sitting on the roof. Why is this argument invalid? Why is this argument invalid?

31. Equivocation Fido is my dog. Fido is my dog. Fido is a father. Fido is a father. Therefore Fido is my father. Therefore Fido is my father. An argument is only valid if the terms used in the premises and the conclusion have the same meaning! An argument is only valid if the terms used in the premises and the conclusion have the same meaning!

32. Is this a valid argument? My grandfather smoked 60 cigarettes a day and lived to the age of 96. My grandfather smoked 60 cigarettes a day and lived to the age of 96. Therefore, smoking can’t be as bad for you as people say it is. Therefore, smoking can’t be as bad for you as people say it is. Fallacy: insufficient sample Fallacy: insufficient sample

33. Is this a valid argument? Tom played video games for twelve hours a day before his exams and then he got straight A grades. Tom played video games for twelve hours a day before his exams and then he got straight A grades. Therefore, playing video games helped Tom perform well in his exams. Therefore, playing video games helped Tom perform well in his exams. A correlation does not prove that there is a causal relationship. A correlation does not prove that there is a causal relationship. Can you think of your own examples of this kind of fallacy? Can you think of your own examples of this kind of fallacy?

34. Deductive reasoning In a deductive argument, the premises are true by definition. This kind of argument is used in mathematics. In a deductive argument, the premises are true by definition. This kind of argument is used in mathematics.

35. Inductive reasoning This kind of reasoning is used in science and in everyday life. This kind of reasoning is used in science and in everyday life. We observe patterns in the world around us and base our assumptions about what will happen in the future on these patterns. We observe patterns in the world around us and base our assumptions about what will happen in the future on these patterns. Usually this works well, but all inductive arguments do involve a hidden assumption. Usually this works well, but all inductive arguments do involve a hidden assumption.

36. Are these valid arguments? No one has ever seen a green swan. No one has ever seen a green swan. Therefore green swans do not exist. Therefore green swans do not exist. The sun has risen every day for millions of years. The sun has risen every day for millions of years. Therefore the sun will rise tomorrow morning. Therefore the sun will rise tomorrow morning.

37. What about this? Turkey brain thinking: Turkey brain thinking: “Farmer Jones has fed us grain every morning of our lives.” “Farmer Jones has fed us grain every morning of our lives.” “Therefore, Farmer Jones will feed us grain again tomorrow morning.” “Therefore, Farmer Jones will feed us grain again tomorrow morning.” “Hurray for Christmas!” “Hurray for Christmas!” The turkey has used inductive reasoning, but the argument is invalid The turkey has used inductive reasoning, but the argument is invalid Is all inductive reasoning invalid since we only know what happened in the past and don’t know what will happen in the future? Is all inductive reasoning invalid since we only know what happened in the past and don’t know what will happen in the future?

38. And this? The Bible says that God exists. The Bible says that God exists. The Bible is always right because the Bible is the word of God. The Bible is always right because the Bible is the word of God. Therefore, God exists! Therefore, God exists! Fallacy: circular argument/ begging the question. Of course, the conclusion may be true, and the argument is formally valid but it is not sound. Why not?

39. Common Fallacies “Ad hominem” “Ad hominem” From Latin – to the person From Latin – to the person i.e. “It’s personal” i.e. “It’s personal” Barack Obama says that we should urgently deal with greenhouse gases. Barack Obama says that we should urgently deal with greenhouse gases. I admire/ despise Barack Obama I admire/ despise Barack Obama Therefore we should/ should not deal with greenhouse gases. Therefore we should/ should not deal with greenhouse gases. Of course, “to the person” arguments are often more subtle than this! Of course, “to the person” arguments are often more subtle than this!

40. Common Fallacies Appeal to ignorance. Appeal to ignorance. There is no evidence for P. There is no evidence for P. Therefore P is false. Therefore P is false. No extra-terrestrial life forms have ever made contact with planet earth. Therefore we can be confident that we are alone in the universe. No extra-terrestrial life forms have ever made contact with planet earth. Therefore we can be confident that we are alone in the universe.

41. Common fallacies Post hoc ergo propter hoc Post hoc ergo propter hoc Latin for “after this therefore because of this” Latin for “after this therefore because of this” Last week I got 100% in my dictation while wearing odd socks. I’m going to wear odd socks every time I have a dictation from now on. Last week I got 100% in my dictation while wearing odd socks. I’m going to wear odd socks every time I have a dictation from now on.

42. Common fallacies Straw man Straw man Misrepresenting/ exaggerating your opponent’s arguments so that you can defeat them more easily. Misrepresenting/ exaggerating your opponent’s arguments so that you can defeat them more easily. If we allow the tuck shop to sell unhealthy food we are in fact saying that it is OK for them to poison students. If we do that, we are ultimately accomplices to murder! If we allow the tuck shop to sell unhealthy food we are in fact saying that it is OK for them to poison students. If we do that, we are ultimately accomplices to murder!

43. How to prove an argument is unsound: The Socratic method. The Socratic method. I’ll assume that you are right. I’ll assume that you are right. I’ll see what conclusions we will have to accept based on this assumption. I’ll see what conclusions we will have to accept based on this assumption. If one of these conclusions involves something which is logically impossible e.g. if it contradicts itself, then I will have proven that you are wrong. If one of these conclusions involves something which is logically impossible e.g. if it contradicts itself, then I will have proven that you are wrong. In Maths they call this proof by contradiction. In Maths they call this proof by contradiction. In classical philosophy they call it ‘reductio ad absurdam’ (Reducing to silliness). In classical philosophy they call it ‘reductio ad absurdam’ (Reducing to silliness). No wonder they made Socrates drink poison! No wonder they made Socrates drink poison!

44. Dr Phantom claims that he has invented a chess machine which will always win, regardless of who it plays against and regardless of whether it plays black or white. Dr Phantom claims that he has invented a chess machine which will always win, regardless of who it plays against and regardless of whether it plays black or white. What question could you ask in order to prove that this is logically impossible? What question could you ask in order to prove that this is logically impossible?

45. Can you remember? Are these arguments valid or invalid? Are these arguments valid or invalid? If P then not Q If P then not Q Not P Not P Therefore Q Therefore Q Invalid! Invalid!

46. Can you remember? Is this valid? Is this valid? Some P are Q Some P are Q All Q are R All Q are R Therefore some P are R Therefore some P are R Valid! Valid!

47. Can you remember? Is this valid? Is this valid? If P then Q If P then Q Q Therefore P Therefore P Invalid! Invalid!

48. Can you remember Is this valid? Is this valid? Either P or Q Either P or Q If P then not R; if Q then S If P then not R; if Q then S R Therefore not P Therefore not P Therefore Q Therefore Q Therefore S Therefore S Valid! Valid!

49. Can you remember? Can you explain these fallacies and unsound arguments? Can you explain these fallacies and unsound arguments? Ad hominem (to the person) Ad hominem (to the person) False dilemma False dilemma Insufficient sample Insufficient sample Post hoc ergo propter hoc (after so because of) Post hoc ergo propter hoc (after so because of) Straw man Straw man Equivocation Equivocation Appeal to ignorance Appeal to ignorance Begging the question Begging the question