“Introduction to Logic”

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## “Introduction to Logic”

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1. “Introduction to Logic” Ateneo de Manila High School English IV Mr. Galinato

2. OBJECTIVES At the end of the lesson, the students should be able to… • Define LOGIC • Define an ARGUMENT • Define a PROPOSITION • Define and identify PREMISE(S) and CONCLUSION(S) in an argument • Identify INDICATORS for arguments, premises, and conclusions

3. OBJECTIVES At the end of the lesson, the students should be able to… • Determine and differentiate GOOD from BAD arguments • Determine and differentiate DEDUCTIVE from INDUCTIVE reasoning in arguments • Determine whether a proposition is TRUE or FALSE • Determine and differentiate a VALID argument from a SOUND argument

4. What is Logic? • Logic differs from other academic disciplines in that it studies the forms of thought, whereas the other disciplines study their own fields of study. • Examples: • Sociology studies human society. • Economics studies the economic relations in society.

5. What is Logic? • Logic studies the question how to distinguish between good and bad arguments. • Thus, LOGIC is a “normative” discipline (as opposed to a “descriptive / empirical” discipline) – it tries to separate the “GOOD” from the “BAD.” • In Logic, we are concerned with the following: What is there in a good argument that makes it good? In other words, what makes it so compelling and forceful that it is not possible not to believe it?

6. What is an Argument? • We have seen that Logic studies how good arguments differ from bad ones. But then, what is an Argument? • In order to answer this, let us look at some examples: • Suppose someone says to you: “The weather today is terrible.” He is stating a fact.

7. What is an Argument? • But if he says to you: “Classes should be suspended because of the terrible weather,” what is he trying to do? • He is trying to persuade you to believe what he wants you to believe. • This is the essence of an ARGUMENT. • Argumentsare sets of sentences designed to persuadethe listener or the reader to believe their conclusions.

8. What is an Argument? • Thus, to simply say that the weather is terrible is not an argument. When you say this to your friend, you are not trying to change his or her mind. • But if you say, “Classes should be suspended because of the terrible weather,” you are ARGUING. You are not merely stating a fact.

9. What is an Argument? • Identify whether the following are arguments or not: • The blackboard is made of wood. • All blackboards are actually green. • Everyone in this class is male. • Everyone in this class should do well in English. • Our country has a democratic type of government. • Democracy may not be best for the Philippines.

10. Form of Argument • Arguments are composed of PROPOSITIONS. • Propositions are statements that are either TRUE or FALSE. • Examples: • The earth is flat. • Vampires exist. • All Ateneo High School students are male. • Kobe Bryant is currently the best basketball player in the NBA.

11. Form of Argument • Arguments have two (2) parts: • One part states what the listener should believe – the point of the argument. We call this the CONCLUSIONof the argument. • The other part concerns the reasons supporting why the conclusion should be accepted. We call this the PREMISE of the argument.

12. Form of Argument • Thus, in the argument: “Classes should be suspended because of the terrible weather,” the CONCLUSION is “Classes should be suspended,” and the PREMISE is “the terrible weather.”

13. Form of Argument • Another example: • Suppose someone says: “All Ateneo High School students are male. Girlie is a student from the Ateneo High School. Therefore, Girlie is male.” • This is also an argument. • What is the CONCLUSIONof the argument? • What are the PREMISESof the argument?

14. Indicators

15. Good & Bad Arguments • Let’s look at this argument again: • All Ateneo High School students are male. • Girlie is a student from the Ateneo High School. • Therefore, Girlie is male. • Question: If the premises are true, can the conclusion be anything but true?

16. Good & Bad Arguments • Let’s look at another argument: • Josef is an Ateneo High School student. • Some students from the Ateneo High School love math. • Hence, Josef loves math. • The premises are all true, but are you compelled to accept that Josef MUST love math because of what the premises say?

17. Good & Bad Arguments • Now we say that Logic seeks to establish the criteria for good arguments. In other words, Logic tries to distinguish between “good” and “bad” arguments. • A GOOD argument is one whose premise establishes its conclusion. • On the other hand, a BAD argument weakly establishes its conclusion or not at all. • We are compelled to accept the conclusions of good arguments, but we are not compelled to accept the conclusions of bad ones.

18. Deductive & Inductive Arguments • Look at this argument: • All Ateneo High School students have to study English. • Therefore, fourth-year Ateneo High School students have to study English. • Apart from the question whether this argument is good or bad, there is another aspect of this argument. • It is a DEDUCTIVEone.

19. Deductive & Inductive Arguments • Another example: • One-third of the students in this room love math. • Consequently, one-third of the students in the Ateneo High School love math. • This is a totally different kind of argument from what we have been working on. • This is an INDUCTIVE argument.

20. Deductive & Inductive Arguments • In a DEDUCTIVEargument, the content of the conclusion lies entirely within the domain or the content of the premises. • Going back to the example: • All Ateneo High School students have to study English. • Therefore, fourth-year Ateneo High School students have to study English.

21. Deductive & Inductive Arguments • In an INDUCTIVEargument, the content of the conclusion lies at least partially outside the content of the premises. • Going back to the example: • One-third of the students in this room love math. • Consequently, one-third of the students in the Ateneo High School love math.

22. Deductive & Inductive Arguments INDUCTIVE DEDUCTIVE Premise(s) Premise(s) Conclusion Conclusion

23. Deductive & Inductive Arguments • With INDUCTIVE reasoning, we add one piece of information to another until we have enough evidence to draw a conclusion. • With DEDUCTIVE reasoning, we use earlier conclusions, reached inductively by ourselves or others, to answer new questions about material.

24. Deductive & Inductive Arguments • Here is another example: • All the mangoes I have tasted in the basket are sweet. • One may infer that all the mangoes in the basket are sweet. • Which is the premise of the argument? • Which is the conclusion? • Is it Deductive or Inductive?

25. Deductive & Inductive Arguments • Yet another example: • If it rains, the road will be wet. • It is not raining right now. • It follows that the road is dry. • Which is the conclusion of the argument? • Which are the premises? • Is it Deductive or Inductive? • Is it a good or a bad argument? Why?

26. Validity, Truth, & Soundness • Look at this argument: • All human beings have four eyes. • Cyclops is a human being. • It follows that Cyclops has four eyes. • Question: If we accept the premises as true, then are we compelled to accept the conclusion? • If the answer is yes, then we have to accept that this argument is valid.

27. Validity, Truth, & Soundness • Thus, a VALID argument is one whose premises, if taken as true, are able to establish their conclusion. • The premises do not have to be really true. The point is that, if they were true, then the conclusion would also be true. • However in Logic, we do not want our system to simply distinguish valid from invalid arguments. We want the system to give us a TRUE conclusion, which merely valid arguments cannot guarantee.

28. Validity, Truth, & Soundness • So we introduce another criteria: An argument is SOUND if and only if it is valid and contains all true premises. • Look at the following argument: • Kim is an Ateneo High School student. • All Ateneo High School students are female. • One can conclude that Kim is female. • Which are the premises of the argument? • Which is the conclusion? • Is this a valid argument or an invalid one? Why? • Is it a sound argument? Why?

29. Validity, Truth, & Soundness • Look at the following argument: • All 4E, 4H, and 4L students belong to the Ateneo High School. • Gabs is from 4E. • It follows that Gabs is a student from the Ateneo High School. • Which is the conclusion of the argument? • Which are the premises? • Is this a valid argument or an invalid one? Why? • Is it a sound argument? Why?

30. SUMMARY • LOGIC studies the forms of thought. It is not an empirical study. • Logic studies criteria for distinguishing GOOD from BAD arguments. • Good arguments are those whose PREMISES establish their CONCLUSION.

31. SUMMARY • INDUCTIVE arguments are those the content of whose conclusion exceeds that of the premises. Vice versa for DEDUCTIVE arguments. • An argument is VALID if there is no possibility for the conclusion to be false if the premises are true. • An argument is SOUND if it is both valid and contains all true premises.

32. “Exercises on Logic”

33. Exercises on Logic • What is LOGIC? • What is an ARGUMENT? • What is a PROPOSITION? • What is the difference between a GOODargument and a BAD one?

34. Exercises on Logic • When do we say that an argument is VALID or INVALID? • Is there such a thing as a TRUEorFALSEargument? How about a VALID or INVALIDproposition? • When is a proposition TRUE? • What are the conditions of a SOUND argument?

35. Exercises on Logic Look at the following argument: • I think we can assume that all male teachers from the English Department are handsome since Mr. G., who is from the English Department, is such a very good-looking teacher. • Identify the premise(s). • Identify the conclusion. • Is the argument deductive or inductive? • If it is deductive, turn it into an inductive argument, and vice versa.

36. Exercises on Logic Look at the following argument: • All two-legged creatures are humans. • Chickens are two-legged creatures. • Consequently, chickens are humans. • Is the argument valid or invalid? • Are the propositions true or false? • Is the argument sound?

37. “Points for Reflection”

38. Points for Reflection “We may not be aware of it but we are surrounded by ARGUMENTS. We are bombarded with statements from media and other people, trying to PERSUADE us into believing what they want us to believe. The challenge is for us to be sensitive to these PROPOSITIONS and identify which are TRUE or FALSE. We must be vigilant; we must constantly watch out for arguments which may be VALID but actually hold false PREMISES. We must be extra cautious in simply taking in any information. We must constantly practice the value of learning to think for ourselves.”

39. “Homework”

40. Homework • Review the concepts of logical reasoning as discussed in class • LOGIC • ARGUMENT • PROPOSITIONS • PREMISE / CONCLUSION • GOOD / BAD argument

41. Homework • Review the concepts of logical reasoning as discussed in class • DEDUCTIVE / INDUCTIVE reasoning • VALID / INVALID argument • TRUE / FALSE proposition • SOUND argument

42. Homework • Try to jumble and mix up these concepts. For example: • Can an INVALID argument contain TRUE propositions? • Is a GOOD argument necessarily a VALID one? • Etc.

43. Homework • Read “Induction and Deduction,” pp. 303-309, AIE. Pay special attention to SYLLOGISMS. • Read “The Importance of Not Being Smith” by Bob Bagnall, pp. 310-311, AIE.

44. “Thank you and goodbye class!”